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MICROWAVE STUDIES OF ELECTRON PARAMAGNETIC RESONANCE IN DILUTED MAGNETIC SEMICONDUCTORS (MERCURY-MANGANESE - SELENIDE, CADMIUM, TELLURIDE, ZINC)

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8324013
K re m e r, Russell Eugene
MICROWAVE STUDIES O F ELECTRON PARAMAGNETIC RESONANCE IN
DILUTED MAGNETIC SEMICONDUCTORS
Ph.D.
P u rd u e University
University
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1983
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MICROWAVE STUDIES OF ELECTRON PARAMAGNETIC RESONANCE
IN DILUTED MAGNETIC SEMICONDUCTORS
A Thesis Submitted to the Faculty
of
Purdue U n iv e rs ity
(
^
Russell Eugene Kremer
In P a rtia l F u lfillm e n t o f the
Requirements fo r the Degree
of
Doctor o f Philosophy
May 1983
(
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G ra d . School
Form N o . 9
Revised
3 2
^
P U R D U E
7
U N IV E R S IT Y
G r a d u a te S chool
T h i s is to c e r t i f y th a t th e th e s is p r e p a r e d
B y ____________ Russell Eugene Kremer_______________________________________________
E n title d
Microwave Studies of Electron Paramagnetic Resonance i n Diluted
_________________ Magnetic Semiconductors__________________________________________
C o m p lie s
w ith
th e
U n iv e r s ity
s ta n d a r d s o f th e G r a d u a te
r e g u la tio n s
School
w ith
and
re s p e c t
th a t
to
it
m e e ts th e a c c e p te d
o r ig in a lity
an d
q u a lity
F o r th e d e g r e e of:
Doctor of Philsophy
S ig n e d by th e fin a l e x a m in in g c o m m itte e :
ch a i rm a n
< k ~ J i ^
A p p r o v e d b y th e h e a d o f s c h o o l.
^
rtm e n t:
.
19 & 3
T o th e l i b r a r i a n :
is.
T h i s th e s is (T s not^to b e r e g a r d e d as c o n fid e n tia l
P r o f e s s o r in c h a r g e o f t h e m e s is
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ACKNOWLEDGEMENTS
/
The author would lik e to express h is deep g ra titu d e to Professor
J.
K. Furdyna f o r i n i t i a l l y suggesting the to p ic o f th is th e s is , and
then p ro v id in g countless suggestions and g e ntle proddings as to the way
to proceed to o b ta in the best re s u lts .
He is also g ra te fu l to
Professors W. G ir ia t and R. R. Galazka fo r p ro vid in g some o f the
samples used in the experiments.
Special thanks are due to Dr. Jean S a n s o n e tti, Mr. Dave
K irch h o fe r, Dr. M elvin M oriw aki, Mr. N itin Samarth, Dr. Malgorzata
(
Dobrowolska and Dr. Andrzej Witowski fo r many hours o f in te re s tin g
and f r u i t f u l d iscu ssio n s, some o f which d e a lt w ith physics and a few
of
which may even have impinged s lig h t ly on the to p ic o f th is th e s is .
In
a d d itio n , the te c h n ic a l e xp e rtis e o f Mr. Bob Mugge is
g r a te fu lly
acknowledged.
The constant support and encouragement o f the a u th o r's fa m ily
and frie n d s is very deeply appreciated.
F in a lly , the fin a n c ia l support o f the National Science Founda­
tio n through the NSF-MRL program a t Purdue is acknowledged.
(
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iii
TABLE OF CONTENTS
Page
LIST OF TABLES.....................................................................................................
v
LIST OF FIGURES................................................................................................
vi
ABSTRACT..................................................................................................................... x i i i
{
CHAPTER I
- INTRODUCTION............................................................................
1
CHAPTER I I
- THEORETICAL PRELIMINARIES ................................................
4
Wave Propagation in DMS................................................................
Bloch Model fo r the Dynamic Magnetic S u s c e p tib ility . . .
Fine and H yperfine S tru c tu re in the EPRSpectrum....................
M icroscopic Model fo r " * - * ................................................................
M icroscopic Form o f xo....................................................................
5
7
9
13
16
CHAPTER I I I - MATERIALS AND EQUIPMENT....................................................
20
A.
B.
C.
D.
E.
A.
B.
C.
M a t e r ia ls .............................................................................................
1. C rystal P ro p e rtie s ......................................................................
2. Band S tru c tu re .............................................................................
3. Magnetic P ro p ertie s .................................................................
4. Exchange In te r a c tio n ..................................................................
C rystal Growth.....................................................................................
Experimental Apparatus....................................................................
CHAPTER IV
A.
B.
20
22
25
28
32
33
39
- ZERO-GAP AND NARROW-GAP DMS............................................
43
H elicon Propagation in a Paramagnetic Medium..........................
Experimental R e s u lts ........................................................................
1. EPR and Dynamic Magnetic S u s c e p tib ility ............................
a. Low Mn2 C oncentrations (x < 0 . 0 0 5 ) ..........................
b. Interm ediate Mn2 Concentrations
(0.005 < x < 0 .1 0 )............................................................
2. EPR L in e w id th ..............................................................................
45
47
49
49
(
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63
72
iv
(
CHAPTER V - WIDE-GAP MATERIALS ...............................................................
A.
79
Theory...................................................................................................
1. M odified Bloch Model o f Dynamic Magnetic
S u s c e p t ib ilit y ............................................................................
2. Faraday R otation and E l l i p t i c i t y ........................................
Experimental R e s u lts .......................................................................
1. C d i-xMnxTe: The "Bloch Model" Region .............................
2. C di-xMnx Te: The "M odified-B loch Model" Region. . . .
3. Cdi_xMnx Te: Unexplained E ffe c ts .........................................
4. Other Wide-Gap DMS (x ~ 0 . 1 ) ................................................
80
84
91
91
98
112
120
CHAPTER VI - MISCELLANEOUS TOPICS CONCERNINGEPR IN DMS .................
129
B.
A.
B.
C.
D.
E.
F.
80
Fine and H yperfine S tru c tu re in CdMnTe...................................
"P h o to c o n d u c tiv ity " in Zero-Gap DMS .......................................
Heating E ffe c ts in CdMnSe ...........................................................
H ysteresis E ffe c ts in CdMnTe.......................................................
EPR in ZnCoS.......................................................................................
Study o f PbMnTe...............................................................................
129
131
139
142
146
147
LIST OF REFERENCES...........................................................................................
152
APPENDICES
{
A nalysis o f the Faraday E ffe c t D a t a .......................................
An H is to r ic a l Note on the EPR FaradayE ff e c t .........................
158
174
VITA.........................................................................................................................
177
A.
B.
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V
LIST OF TABLES
Table
Page
3 .1.
C rystal p ro p e rtie s o f I I - V I and Mn-VI compounds .................
23
3 .2.
Io n ic r a d ii o f ca tio ns in DMS.....................................................
24
3 .3.
Temperature o f the m elt used to grow s in g le -c ry s ta l DMS .
24
4 .1 .
E le c tr ic a l p ro p e rtie s o f the Hgi_xMnxSe samples used in
th is in v e s tig a tio n ............................................................................
50
Parameters used to c o m p u te r-fit the Faraday ro ta tio n and
e l l i p t i c i t y data fo r the 30% CdMnTe sample............................
103
P ro p e rtie s o f the wide-gap DMS used in th is in v e s tig a tio n
124
5.1.
5.2.
(.
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vi
i
LIST OF FIGURES
Figure
2 .1.
2.2.
2 .3.
(
3.1.
3 .2.
3.3.
3.4 .
Page
Fine s tru c tu re s p lit t in g o f the Mn2+ 3d5 le v e l in
a magnetic f i e ld . The s ix le v e ls lead to fiv e lin e s
in the EPR spectrum.........................................................................
11
Amplitude o f the fin e s tru c tu re s p lit t in g as a
fu n c tio n o f the angle from the [100] d ir e c tio n .
The dc magnetic f i e ld is in the [110] p la n e .........................
12
Energy le v e ls o f the Mn2+ ion in a magnetic f i e ld
showing fin e and h yp erfin e s p li t t in g . T ra n s itio n s
corresponding to aMj = 1, Ami = 0 are shown.
T ra n s itio n s from Mj = - 3/2 -<->■ - 1/2 and
1/2 -*-*■ 3/2 are om itted fo r c l a r i t y ........................................
14
The II-V I-M n fa m ily o f DMS. The m is c ib ilit y and
c ry s ta l s tru c tu re o f the various compounds are
shown....................................................................................................
21
L a ttic e constant as a fu n c tio n o f manganese concen­
tr a tio n fo r Cdi_xMnx Te and Zn]_xMnx Te. E x tra p o la tio n
to x = 1.0 in d ic a te s a f i c t i t i o u s zinc blende form
o f MnTe w ith a la t t i c e constant o f 6.34 A............................
26
Band gap energy o f Cdi_xMnx Te as determined by the
e x c ito n energy ................................................................................
27
Band gap o f Hgi_xMnx Te as a fu n c tio n o f com position.
The sem im etal-to-sem iconductor tr a n s itio n occurs when
the r 6 and r 8 bands become degenerate a t about
x = 0.07. The s p in - o r b it s p lit t in g is given by A,
c .b . re fe rs to the conduction band and l . h . and h .h .
denote the l ig h t hole and heavy hole bands,re s p e c tiv e ly
29
3.5.
Magnetic phase diagram fo r CdMnTe.............................................
31
3.6.
Exciton Faraday ro ta tio n in CdMnTe a t 77 K fo r
several d if fe r e n t compositions ................................................
34
(
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v ii
Figure
3.7.
3 .8.
4 .1.
4 .2 .
4 .3 .
4 .4.
i(
4 .5 .
4 .6 .
4.7.
4 .8 .
4 .9 .
(
Page
O u tlin e o f the procedure used to grow ZnMnTe and
CdMnSe c ry s ta ls . BN denotes boron n it r id e . The
e n tire assembly is placed in s id e a Bridgman furnace. . .
37
Diagram o f the microwave spectrom eter used in the
experim ents........................................................................................
41
Rayleigh in te rfe ro g ra m fo r HgMnSe a t 4.2 K.
x = 3 • 10"lf. The fo u r traces were taken w ith
the phase o f the reference arm s e t a t 0 °, 90°, 180°
and 270°. The dotted lin e corresponds to the
in te rfe ro g ra m envelope ................................................................
48
Rayleigh in te rfe ro g ra m fo r HgMnSe w ith x = 3 • 10-1+
a t 2.5 K showing hyp erfin e s tru c tu re in the EPR
s p e c tru m ............................................................................................
51
EPR spectrum o f undoped HgMnTe showing an incom pletely
resolved m ixture o f fin e and h yp erfin e s tru c tu re . . . .
Real p a rt o f the dynamic magnetic s u s c e p tib ility fo r
HgMnSe w ith x = 3 • 10-Lt a t several temperatures.
The curves have been displaced v e r t ic a lly fo r c l a r i t y .
53
.
55
Imaginary p a rt o f the dynamic magnetic s u s c e p tib ility
fo r HgMnSe w ith x = 3 • 10_l+ a t several temperatures . .
56
Temperature dependence o f the inverse s t a t ic suscept­
i b i l i t y f o r several lo w -co n cen tra tio n samples. The
s tr a ig h t lin e s in d ic a te C u rie -lik e b e h a vio r.........................
59
Imaginary s u s c e p tib ility f o r samples w ith x = 3 • 10_1+
a t 2.5 K and x = 5 • 10"5 a t 1.3 K showing th a t x is
d ir e c t ly p ro p o rtio n a l to x in th is co n cen tra tio n range .
60
Rayleigh interferogram s fo r a sample w ith x = 3 • 10-1+
on two consecutive days showing the enhancement o f EPR
due to an increase in the e le c tro n co n ce n tra tio n . The
two interferogram s were taken on the same sample a t
the same tem perature. The increased e le c tro n concen­
tr a tio n is evidenced by the decreased h e lico n period
in 4.8 b ............................................................................................
62
Rayleigh in te rfe ro g ra m fo r a HgMnSe sample w ith
x = 0.02 a t 75 K ............................................................................
64
4.10. Real p a rt o f the dynamic magnetic s u s c e p tib ility fo r
a 2% HgMnSe sample. The p o in ts are measured data and
the lin e s are the best f i t s obtained by f i t t i n g the ........
real and im aginary p a rts sim u lta n e o u sly................................
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
vi i i
^
Figure
4.11.
Page
Imaginary p a rt o f the dynamic magnetic s u s c e p tib ility
f o r a 2% HgMnSe sample. The p o in ts are data and the
lin e s are computer f i t s ................................................................
66
Inverse s t a t ic s u s c e p t ib ility as a fu n c tio n o f tempera­
tu re f o r a 5% HgMnSe sample. The lin e is a guide fo r
the e y e s ............................................................................................
68
Rayleigh in te rfe ro g ra m fo r a 2% HgMnSe sample a t 1.3 K.
The a b sorp tive tra ce (phase = 0 °) is com pletely e x tin ­
guished by EPR .................................................................................
70
Imaginary s u s c e p t ib ility f o r samples w ith x = 0.02 and
0.05 a t 4.2 K showing th a t x is in v e rs e ly p ro p o rtio n a l
to x in th is r a n g e ........................................................................
71
Rayleigh in te rfe ro g ra m traces f o r a 9% HgMnSe sample a t
4 K, 8 K and 40 K. The arrow marks the EPR p o s itio n . •
73
Imaginary p a rt o f the s u s c e p t ib ility fo r samples o f
HgMnSe w ith x = 0.02 a t 75 K and x = 3 • 10"^ a t 2.5 K.
The v e r tic a l scale is a r b it r a r y , showing th a t the lin e w id th ( f u l l w idth a t h a lf max) a t high temperatures can
a c tu a lly be less than the sum o f the s ix h yp e rfin e peaks
76
4.17. Linew idth ( f u l l w id th a t h a lf max) fo r a 5% HgMnSe
sample
as a fu n c tio n o f te m p e ra tu re ....................
77
4.18. Linew idth a t 4.2 K f o r Hgi_xMnx Se as a fu n c tio n o f
manganese co n ce n tra tio n x ............................................................
78
4.12.
4.13.
4.14.
4.15.
4.16.
{_
5 .1 .
5 .2.
5 .3.
5 .4.
5.5.
(
Linew idth ( f u l l w id th a t h a lf max) o f Cd]__xMnxTe as a
fu n c tio n o f temperature f o r several compositions . . . .
81
Comparison o f the re a l and im aginary p a rts o f the
dynamic magnetic s u s c e p t ib ility as p re dicte d by the
Bloch and m odified-B loch th e o r ie s ............................................
86
I llu s t r a t io n o f Faraday ro ta tio n and e l l i p t i c i t y .
The
magnetic f i e ld is a p plied p a r a lle l to the wave v e c to r. .
88
Linear p o la riz a tio n data f o r 10% CdMnTe a t 4.2 K.
y is
the angle between the in c id e n t p o la riz a tio n and the
d e te c to r/a n a ly z e r.............................................................................
93
Faraday r o ta tio n fo r a 10% CdMnTe sample a t several
tem peratures. P oints are measured data. Lines are the
best f i t s obtained by computer f i t t i n g the ro ta tio n and
e l l i p t i c i t y sim ultaneously ..........................................................
94
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ix
Figure
5 .6.
5 .7.
5.8.
5 .9.
5.10.
5.11.
5.12.
5.13.
5.14.
5.15.
5.16.
Page
Faraday e l l i p t i c i t y fo r the 10% CdMnTe sample a t
several tem peratures. P oints are data and lin e s are
computer f i t s ....................................................................................
95
Inverse re la x a tio n time f o r the 10% CdMnTe sample as a
fu n c tio n o f tem perature. The p o in ts correspond to
re la x a tio n times obtained as f i t t i n g parameters and the
lin e is a guide f o r the e y e s ......................................................
96
Inverse s t a t ic s u s c e p t ib ility fo r the 10% CdMnTe sample
as a fu n c tio n o f tem perature. The p o in ts were obtained
as f i t t i n g parameters. E x tra p o la tio n from the high
temperature p o in ts y ie ld s aWeiss constant o f ew = -21 K
97
Faraday e l l i p t i c i t y data fo r a 22.5% CdMnTe sample a t
7 K. The e l l i p t i c i t y is obtained from the d iffe re n c e
between the two t r a c e s ................................................................
99
Faraday ro ta tio n data f o r the 22.5% CdMnTe sample a t
7 K. The r o ta tio n is obtained from the d iffe re n c e
between the two t r a c e s ................................................................
100
Faraday ro ta tio n f o r a 30% CdMnTe sample a t several
tem peratures. The p o in ts are the measured ro ta tio n s
and the lin e s are the best f i t to the data. The f i t t i n g
parameters are lis t e d in Table 5 . 1 ........................................
102
The temperature a t which the lo w - fie ld Faraday ro ta tio n
becomes zero as a fu n c tio n o f manganese concentration
in CdMnTe. This c o n d itio n (oiT = 1) corresponds to a
re la x a tio n time o f T = 4.5 * 10"12 s. The magnetic
phase diagram o f CdMnTe (see Figure 3.5) is superimposed
104
Lines o f constant re la x a tio n time as determined by
computer f i t t i n g the Faraday ro ta tio n data. The
magnetic phase diagram o f CdMnTe is superimposed . . . .
105
Inverse re la x a tio n time as a fu n c tio n o f temperature
fo r several CdMnTe samples. The re la x a tio n times were
obtained by computer f i t t i n g the Faraday r o ta tio n data
.
106
Faraday e l l i p t i c i t y fo r the 30% CdMnTe sample a t several
tem peratures. The p o in ts are the measured e l l i p t i c i t i e s
and the lin e s are the b e st f i t s to the data. The
f i t t i n g parameters are lis t e d in Table 5.1 ........................
108
The Landd g -fa c to r as a fu n c tio n o f temperature fo r
several CdMnTe samples. The g -fa c to rs were obtained
by computer f i t t i n g the Faraday r o ta tio n data. . . . . .
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure
5.17.
5.18.
5.19.
5.20.
5.21.
5.22.
5.23.
5.24.
5.25.
5.26.
5.27.
6.1.
Page
Inverse s t a t ic s u s c e p tib ility as a fu n c tio n o f temper­
ature fo r the 30% CdMnTe sample. The p o in ts were
obtained by computer f i t t i n g our Faraday r o ta tio n data.
The s o lid lin e is the conventional s u s c e p t ib ility
measurement made byGalazka e t al_...............................................
Ill
Faraday r o ta tio n data f o r a 45% CdMnTe sample a t several
tem peratures. The ro ta tio n is obtained from the d i f f e r ­
ence between the two l i n e s ..........................................................
113
Faraday e l l i p t i c i t y fo r a 50% CdMnTe sample a t two
temperatures ....................................................................................
115
Faraday ro ta tio n data fo r a 44% CdMnTe sample a t 4.2 K.
The ro ta tio n is obtained from the d iffe re n c e between
the t r a c e s ........................................................................................
116
Faraday e l l i p t i c i t y data fo r a 44% CdMnTe sample a t
4.2 K. The e l l i p t i c i t y is obtained from the d iffe re n c e
between the t r a c e s ........................................................................
117
Progression o f Faraday ro ta tio n behavior as illu s t r a t e d
by co o lin g a 45% CdMnTe sample. The p o in ts are the
measured ro ta tio n s and the lin e s are sim ply included
fo r c l a r i t y ........................................................................................
119
Progression o f Faraday ro ta tio n behavior as illu s t r a t e d
by incre a sing the manganese co n cen tra tio n in the CdMnTe
samples, a ll o f which are measured a t 4.2 K. The lin e s
are included f o r c l a r i t y ............................................................
121
Progression o f the Faraday e l l i p t i c i t y behavior as
illu s t r a t e d by decreasing the temperature o f a 17.5%
CdMnTe sample. The lin e s are guides fo r the eyes. . . .
122
Faraday ro ta tio n a t 4.2 K fo r the wide-gap DMS w ith
x = 0 .1 . The lin e s correspond to the best f i t s to the
data w ith the r o ta tio n and e l l i p t i c i t y data being f i t
sim ultaneously ................................................................................
125
Faraday e l l i p t i c i t y a t 4.2 K fo r the wide-gap DMS w ith
x = 0 .1. The lin e s are the best f i t s to the d a ta . . . .
126
Linew idth ( f u l l w idth a t h a lf max) f o r the wide-gap DMS
w ith x = 0.1 as a fu n c tio n o f tem perature. The lin e s
are guides fo r the eyes................................................................
128
Microwave transm ission EPR spectrum fo r a Cd]_xMnxTe
s in g le -c ry s ta l slab w ith x = 3 • 10-l+ a t 4.2 K ................
130
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xi
Figure
6 .2.
6 .3 .
6.4.
6 .5.
6 .6 .
6.7.
6.8.
6 .9.
6.10.
6.11.
6.12.
Page
Microwave transm ission EPR spectrum f o r a powdered
sample o f Cd;]_xMnx Te w ith x = 3 • 10_tf a t 4.2 K. Only
the h yp erfin e s tru c tu re is present ..........................................
132
P h o to co n d u ctivity signal (voltage across the sample)
fo r a 2.5% HgMnTe sample doped w ith indium a t 4.2 K as
a fu n c tio n o f magnetic f i e ld . Data is shown fo r several
d if fe r e n t amounts o f in c id e n t power. The sharp change
in r e s is t iv i t y a t 1.25 Tis dueto EPR .......................................
134
P h o to co n d u ctivity as observed by W it t lin e t al_. f o r a
1.8% HgMnTe sample a t 4.2 K as a fu n c tio n o f magnetic
f i e ld . The sharp change in r e s is t iv i t y a t 4.3 T is due
to ......... EP R .........................................................................................
136
P h o to co n d u ctivity sig n a l fo r a 3% HgMnSe sample a t 4.2 K
as a fu n c tio n o f magnetic f i e l d ................................................
137
P h o to co n d u ctivity peak number from Figure 6.5 (peak a t
h ig h e st f i e l d is number 1) p lo tte d versus 1/B. The
abrupt change in slope may in d ic a te the onset o f spin
s p l i t t i n g ............................................................................................
138
Transmission spectra fo r a 10% CdMnSe sample a t 4 .2 K
showing the e ffe c t o f d if fe r e n t amounts o f in c id e n t
power. Each tra c e has fo u r times more in c id e n t power
than the one above i t ....................................................................
140
Faraday ro ta tio n data fo r a 25% CdMnTe sample a t 1.3 K.
The ro ta tio n is obtained from the d iffe re n c e between the
tra c e s . The s o lid lin e s in d ic a te increasing magnetic
f ie ld s and the dotted lin e s correspond to decreasing
f i e l d s ................................................................................................
144
I llu s t r a t io n o f the " tr a in in g " e ffe c t o f repeated sweeps
in the same f i e l d d ir e c t io n ........................................................
145
D ire c t transm ission data fo r a sample o f Z n ^ C o ^ w ith
x = 1 • 10"3 a t 4.2 K. The sharp resonance occurred a t
1.12 T fo r our frequency o f 35 G H z........................................
148
Faraday ro ta tio n data f o r the ZnCoS sample a t 4.2 K
showing the extreme sharpness o f the resonance and the
small a d d itio n a l s tru c tu re o f the spectrum ........................
149
Microwave r e fle c tio n signal fo r a 4% sample o f PbMnTe
a t 4 .2 K. The resonance occurs in the p o la riz a tio n
opposite o f the one th a t sustains helicon waves................
151
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xi i
r
Appendi x
Figure
A .I.
A .2.
A .3.
A .4.
Page
Geometry o f the p o la riz a tio n apparatus. 0 is the
angle between the in c id e n t p o la riz a tio n and the
o rie n ta tio n o f the c ir c u la r p o la riz e r, y is the
angle between th is o rie n ta tio n and th a t o f the
d e te c to r............................................................................................
159
Linear p o la riz a tio n data (e = 0°) w ith d if fe r e n t
values fo r the angle between the in c id e n t p o la riz a ­
tio n and the d e te c to r ( y = 0 ° ,4 5 ° ,9 0 ° ,1 3 5 ° ) ....................
164
I llu s t r a t io n o f how the Faraday ro ta tio n was e xtra cte d
from the data. The in c id e n t p o la riz a tio n was lin e a r
and values o f x and y were m easured....................................
167
I llu s t r a t io n o f how the Faraday e l l i p t i c i t y was
e x tra c te d from the data. The in c id e n t p o la riz a tio n
was e l l i p t i c a l and values o f x and y were measured. . .
170
(
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ABSTRACT
Kremer, Russell Eugene. Ph.D., Purdue U n iv e rs ity , May 1983. Microwave
Studies o f E lectron Paramagnetic Resonance in D ilu te d Magnetic Semicon­
d uctors. Major P rofessor: J. K. Furdyna.
E lectron paramagnetic resonance (EPR) stu d ies can give valuable
in fo rm a tio n on the dynamic magnetic p ro p e rtie s o f s o lid s .
We have used
EPR as a to o l to in v e s tig a te the fa m ily o f m a te ria ls known as d ilu te d
magnetic semiconductors (DMS).
Our method o f observing EPR is based on
microwave transm ission and is thus s e n s itiv e to both d isp e rsion e ffe c ts
associated w ith the real p a rt o f the magnetic s u s c e p tib ility and
(
ab sorp tio n e ffe c ts due to the im aginary p a rt.
We have used helicons ( c ir c u la r ly p o la riz e d microwaves which
tra v e l through a medium w ith r e la t iv e ly l i t t l e
a tte n u a tio n ) to e x c ite
EPR in conducting (zero-gap and narrow-gap) Hg^_xMnxSe fo r values o f x
up to 0 .1 .
We have e sta b lish e d th a t the h e lic o n technique becomes
im p ra c tic a l fo r x > 0 .1 0 in narrow-gap DMS.
Cadmium- and zinc-based DMS are
tra n sp a re n t to microwaves. We
measured EPR in these wide-gap m a te ria ls by observing
tio n and e l l i p t i c i t y associated w ith the resonance.
Cd.
X* X
the Faradayro ta ­
We studied
Mn Te over the e n tire range o f p o ssib le manganese concentrations
X
(x < 0 .7 ).
For x < 0.15, the observed
p lained using the standard Bloch model
s u s c e p t ib ility .
Faraday e ffe c t could be ex­
o f the dynamic magnetic
Above x = 0 .1 5 , however, the in c re a s in g ly la rg e EPR
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x iv
lin e w id th s prevented the Bloch model from adequately e x p la in in g the
data.
M o d ific a tio n o f the model to a llo w fo r very s h o rt re la x a tio n
tim es, which lead to broad lin e s , allowed us to f i t the data in th is
range.
At the h ighest concentrations a new type o f behavior emerged
a t low tem peratures.
Sm all, sharp features appeared in the Faraday
e ffe c t spectra th a t even the m odified form o f the Bloch model fa ile d
to e x p la in .
We also studied o th e r wide-gap DMS:
CdMnSe, CdMnS,
ZnMnTe, ZnMnSe and ZnMnS, a ll co n ta in in g about 10% manganese.
Although
the re s u lts we observed were q u a lita tiv e ly the same, several trends
became e v id e n t.
The stre n g th o f the absorption and d isp e rsion due to
EPR were s tro n g e s t in cadmium-based DMS.
Also the e ffe c ts were
s tro n g e s t fo r s u lfid e s , follow ed by selenides and then te llu r id e s .
F in a lly , th is th e sis re p orts on several b r ie f experiments which
gave in fo rm a tio n on EPR in DMS.
We discuss fin e and hyp erfin e s tru c tu re
in the EPR spectra o f very d ilu te DMS, microwave heating e ffe c ts ,
magnetic h y s te re s is , microwave "p h o to c o n d u c tiv ity ," and EPR in DMS
o th e r than II-V I-M n compounds.
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1
(
CHAPTER I - INTRODUCTION
D ilu te d magnetic semiconductors (DMS) are formed by randomly
2+
s u b s titu tin g magnetic io n s, u s u a lly Mn
a I I - V I compound semiconductor [1 -4 ].
p o s s ib le , Hg.
1“ X
Mn Te and Cd,
1"X
a
, on the ca tio n s u b la ttic e in
Of the various combinations
Mn Te are the best known.
X
The presence
o f the lo c a liz e d magnetic ions leads to very in te re s tin g physical
p ro p e rtie s , p a r tic u la r ly in the presence o f an external magnetic f ie ld
[3 ,4 ].
This th e s is re p o rts on e le c tro n paramagnetic resonance (EPR)
(
stu d ie s in DMS using the method o f microwave helicon transm ission in
the narrow-gap m a te ria ls and th a t o f Faraday ro ta tio n and e l l i p t i c i t y
fo r the wide-gap compounds.
The study o f EPR gives in fo rm a tio n on the
dynamic magnetic s u s c e p tib ility o f DMS.
From the dynamic s u s c e p tib il­
i t y we can e x tra c t values o f the s t a t ic s u s c e p t ib ility xQ and the
s p in -s p in re la x a tio n time
both o f which are im portant in under­
standing the magnetic behavior in these compounds.
We present a b r ie f in tro d u c tio n to the problem o f electromag­
n e tic wave propagation in DMS in Chapter I I .
The Bloch model o f the
dynamic magnetic s u s c e p tib ility is discussed along w ith a d e s c rip tio n
o f the fin e and hyp erfin e in te ra c tio n s .
In a d d itio n we develop
m icroscopic models fo r the d ie le c t r ic te n so r
s u s c e p t ib ility xQ.
and the s ta tic
Chapter I I I contains a d e s c rip tio n o f DMS and
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2
discusses some o f t h e ir unique p ro p e rtie s in c lu d in g the c ry s ta l
s tru c tu re , band s tru c tu re and p ro p e rtie s a ris in g from the exchange
in te ra c tio n between the band e le c tro n s and the lo c a liz e d magnetic
d ip o le moments o f the manganese io n s .
We also give a b r ie f d e s c rip ­
tio n o f the spectrom eter used in the experiments.
The work done on narrow-gap DMS, Hg,
1“ X
described in Chapter IV.
Mn Se in p a r tic u la r , is
X
Using the method o f microwave helicon
transm ission [5 ,6 ] we have studied EPR fo r very low co n centrations o f
manganese where the resonance is s p l i t in to s ix lin e s by the hyp erfin e
in te r a c tio n .
For the higher values o f x , where the resonance co n sists
o f a s in g le lin e , we have studied the behavior o f EPR as a fu n c tio n o f
manganese content and tem perature.
In Chapter V we discuss the wide-gap DMS.
Rather than describe
the e n tire m a trix o f p o ssib le m a te ria ls and p o ssible manganese
co n ce n tra tio n s, we present our re s u lts in a "row and column" approach.
We show re s u lts fo r one m a te ria l, Cd,
I "
Mn Te, fo r a ll values o f x and
a
A
then take one com position, x = 0 .1 , and describe our re s u lts fo r a ll
the wide-gap DMS w ith th a t com position.
For manganese concentrations
g re a te r than about 15%, the Bloch model fo r the s u s c e p tib ility must
be m odified to account fo r the extrem ely wide resonance lin e s caused
by very s h o rt re la x a tio n tim es.
We have studied the dynamic magnetic
s u s c e p tib ility associated w ith EPR a t these higher concentrations by
using a microwave "m agnetooptical" approach in v o lv in g Faraday ro ta tio n
and e l l i p t i c i t y .
This new technique allow s us to study the dynamic
s u s c e p tib ility even under co n d itio n s when EPR is too broad to be
detected by conventional EPR apparatus [7 ].
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3
Chapter VI contains the re s u lts o f a number o f lim ite d
experim ents, which, w h ile n o t an in te g ra l p a rt o f the th e s is , did
in vo lve the study o f EPR in d ilu te d magnetic semiconductors.
The
chapter includes sections d e ta ilin g the fin e and h y p e rfin e EPR
s tru c tu re observed in lo w -co n ce n tra tio n CdMnTe, microwave "photo­
c o n d u c tiv ity " in mercury-based DMS, anomalous microwave heating
observed in CdMnSe, and h y s te re s is e ffe c ts observed in the microwave
transm ission data f o r CdMnTe in the spin glass phase, as w ell as EPR
measurements on DMS m a te ria ls o th e r than I I - V I : Mn-VI compounds
( e .g ., PbMnTe, ZnCoS).
A ll o f the experiments described in th is
chapter are p re lim in a ry in n a tu re , b u t they may serve as p o in ts o f
departure fo r fu tu re stu d ie s o f DMS.
F in a lly , the Appendix presents a mathematical a n a ly s is o f the
Faraday ro ta tio n and e l l i p t i c i t y and in p a r tic u la r , the method by
which the e ffe c ts were measured.
We also b r ie f ly discuss the h is to ry
o f the technique o f studying EPR by measuring the Faraday ro ta tio n and
e llip tic it y .
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CHAPTER I I - THEORETICAL PRELIMINARIES
Before we discuss microwave EPR in d ilu te d magnetic semicon­
d u cto rs, we must f i r s t present the th e o re tic a l underpinnings o f the
problem.
D ilu te d magnetic semiconductors are m a te ria ls th a t are
rendered both e le c t r ic a lly and m a g ne tica lly a n is o tro p ic ( i . e . ,
g y ro tro p ic ) by the a p p lic a tio n o f a dc magnetic f i e ld .
We w il l
th e re fo re begin by d e s c rib in g fo rm a lly ( i . e . , m a croscopically) wave
propagation in a medium where both the p e r m it t iv it y and p e rm e a b ility
are g y ro tro p ic tensors.
We w i l l then form ulate a model fo r the
dynamic magnetic s u s c e p t ib ility in terms o f the Bloch th e o ry which
describes EPR using a tw o -le v e l spin system.
Since in very d ilu te
DMS the s u s c e p t ib ility contains e x p li c i t c o n trib u tio n s due to fin e
and hyp erfin e in te r a c tio n s , the s u s c e p tib ility model w i l l then be
extended to inclu d e these e ffe c ts .
F in a lly we w il l present m icro­
scopic models fo r the d ie le c t r ic constant and the dc magnetic
s u s c e p t ib ility in these m a te ria ls .
A d d itio n a l th e o re tic a l discussions
p e rta in in g to c e rta in s p e c ific s itu a tio n s in zero-gap DMS (Chapter IV)
o r wide-gap DMS (Chapter V) w i l l be presented in the ap pro p ria te
chapters.
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5
A.
Wave Propagation in DMS
D ilu te d magnetic semiconductors are examples o f g y ro tro p ic
media, where the a p p lic a tio n o f a magnetic f ie ld renders the m a te ria l
e le c t r ic a lly and m a g n e tica lly a n is o tro p ic .
In such media the
e le c tr ic a l c o n d u c tiv ity and the magnetic s u s c e p tib ility become tensors
having the well-known g y ro tro p ic form
Axx
Axy
0
-Axy
Axx
0
( 2 . 1)
A
zz
0
when the a p plied f i e ld is in the z - d ir e c ti on.
1
coordinate frame
A.
*
1
/S
A.
By using a ro ta tin g
A-
— ( x + iy ) , — ( x - iy ) , z
/2
ft
tensors such as Equation
(2 .1 ) may be dia g o n alize d:
fA,
0
0
0
A_
0
0
0
A
zz
(2 .2 )
where
A±
=
Axx * 1 Axy
(2-3)
The c o n s titu tiv e re la tio n s fo r the medium are given by
ft
=
eQ
,
t
=
y0 V * ^ •
(2 .4 )
Here k and n are the r e la tiv e d ie le c t r ic and r e la tiv e p e rm e a b ility
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6
te n so rs, re s p e c tiv e ly , given by
i
K "
1
CT ’
o
(2 ' 5)
and
<—y
n
where
te n so r,
=
■<—■>•
,_
I + x ,
«
(2 .6 )
= e^/e0 is the l a t t i c e d ie le c tr ic c o n s t a n t , T is the u n it
is the c o n d u c tiv ity tensor a n d Y is the dynamic magnetic
s u s c e p t ib ility te n so r.
In considering wave propagation in such media, we w il l assume
plane wave s o lu tio n s o f the form exp[i(Tc-r-cut)] where t is the wave
ve cto r and u is the microwave angular frequency.
From the c o n s titu tiv e
re la tio n s and M axwell's equations we can w rite the wave equation as
[5 ,8 ]
2
T x fn
^ •(£ * £ )]
=
K*]t .
(2 .7 )
c
In the Faraday geometry
k || B || z ) , in which a ll o f our experiments
w il l be c a rrie d o u t, Equation (2 .7 ) can be solved to give a p a r tic u ­
l a r l y sim ple d isp e rsio n r e la tio n [8 ],
k±
=
c /K±n± »
( 2,S )
where the (+) and ( - ) s u b s c rip ts re fe r to two opposite c ir c u la r
p o la riz a tio n s in the x-y plane.
For an in c id e n t e le c t r ic f i e ld o f
am plitude EQ, then, the e le c t r ic and magnetic f i e ld vectors are given
by
E±
H±
=
, . i ( k +z-u>t)
EQ(x ± iy )e
-
=
_____
+ i / ( e0/v>0 ) ( K+/ ri± )
(2 .9 )
- - i ( k z -u t)
EQ(x ± iy )e
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7
(
The propagation constants k+ are complex and may be d iv id e d in to
t h e ir re a l and im aginary p a rts ,
k+
=
( 2 . 10)
«+ + i B+ ,
where a and e are the phase and a tte n u a tio n c o e ffic ie n ts , re s p e c tiv e ly .
From Equation (2 .8 ) we have
l\ <+\ |n+ |+ ( K ; n ; - K > " ) ]^ ,
ft
( 2 . 11)
0)
[ | k+ I |n+ |-(ic |n |-K " n ")]^
,
ft c
where the s in g le and double primes in d ic a te the real and im aginary
p a rts , re s p e c tiv e ly .
B.
(
Bloch Model f o r the Dynamic Magnetic S u s c e p tib ility
The response o f the lo c a liz e d magnetic moments to the c ir c u la r ly
p o la riz e d EM wave enters through the dynamic magnetic s u s c e p t ib ility ,
x+.
Using the Bloch model (see, e .g ., [ 9 ] ) , we can fo rm ulate an
expression f o r x-
With the ap plied magnetic f i e l d in the z - d ir e c tio n ,
we can w r ite the equation o f motion o f the m agnetization o f the system
as [9]
dj
dt
-
y (ftxit) -
[V M
ol
l Tl
'f ^ x + M y y '
A
L
“
J
[ T2
^
( 2 . 12 )
J
The f i r s t term on the r ig h t o f Equation (2 .1 2 ) describes the motion o f
the m agnetization in the lo s s le s s case.
Losses, e n te rin g through re la x a tio n processes, are described by
(
the remaining two terms on the r ig h t side o f Equation (2 .1 2 ).
The basic
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8
^
assumption o f Equation (2.12) made by Bloch is th a t the two re la x a tio n
terms in v o lv e two d is t in c t processes, ch a racterize d by two d if fe r e n t
re la x a tio n tim es.
The second term on the r ig h t hand side o f
Equation (2.12) in d ic a te s th a t the instantaneous z-component o f the
m agnetization relaxes to the value o f the e q u ilib riu m ( i . e . , dc)
A
A
m agnetization Mqz .
This process invo lve s a change in the z-component
o f ft, i . e . , a change in the energy, given by ft*ft , and thus involves
in te r a c tio n w ith the l a t t i c e .
The re la x a tio n time T^ associated w ith
th is term is th e re fo re c a lle d the " s p in - la t tic e " re la x a tio n tim e.
The la s t term on the r ig h t o f Equation (2.12) in d ic a te s th a t the
m agnetization term in the x-y plane has no "memory," i . e . , th a t upon
c o llis io n , the x- and y-components re la x independently back to zero
(since the e q u ilib riu m value o f ft in th is plane is z e ro ).
(
V-
Changes in
M o r M in v o lv e no changes in the energy o f the spin system and thus
x
y
the re la x a tio n time c h a ra c te riz in g th is process, Tg, is d if fe r e n t from
T j.
T2 is u s u a lly re fe rre d to as the "s p in -s p in " re la x a tio n tim e.
The Bloch equation o f motion fo r the m agnetization (Equation
(2 .1 2 )) and i t s s o lu tio n s are w ell known.
They lead to the fo llo w in g
form o f the dynamic magnetic s u s c e p t ib ility [1 0 ]:
,,
,
X+( “ )
1
- X q I» o <“ ; “ o >T 2
“
? 2
1 +
2
+ “ l Tl T2
’
(2.13)
_
±xo V 2
? ?
o
>
1 + (w+o>0 ) T2 + “iTiT2
where x0 is the dc o r s t a t ic magnetic s u s c e p t ib ility , w is the
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9
C
microwave angular frequency, uQ = geB/2m is the Larmor precession
frequency and
= geBr ^/2m where B ^ is the microwave magnetic f i e ld .
The (+) and ( - ) s u b s c rip ts r e fe r to the two c ir c u la r p o la riz a tio n s in
the x-y plane.
Note th a t the resonance in x occurs fo r the (+)
p o la riz a tio n which, as w il l be discussed in Chapter IV, is the same
one in which helicons propagate through the m a te ria l.
Unless the r f
2
fie ld s are extrem ely la rg e , the term W]Tj T2 1"n the denominator o f x+
is very s m a ll.
(
C.
For the normal case, then, Equation (2.13) reduces to
x+(w;
-
-X0»0 (»™ 0 )T2
o-o
1 + ( cj+o)0 ) T2
X »
=
± ---- ° ° 2 2 2
1 + (w+u)o ) T2
•
(2-14)
Fine and H.yperfine S tru c tu re in the EPR Spectrum
The model o f the dynamic magnetic s u s c e p tib ility presented above
corresponds
very
to a sim ple tw o -le ve l spin system. This simple
form
is
useful f o r the understanding o f EPR dynamics, but becomes
inadequate f o r discussing the EPR in te r a c tio n in samples th a t are
m a g ne tica lly very d ilu t e .
We must then also inclu d e the h yperfine
2+
e le c tro n s o f the Mn
ion and i t s
5
nuclear spin and the fin e in te r a c tio n between the 3d e le c tro n s and
in te r a c tio n between the o u te r 3d
5
the c ry s ta l f i e l d o f the host la t t ic e .
The o u te r e le c tro n c o n fig u ra tio n o f a manganese atom co n sists
o
o f 3d ,4s . When doubly io n ize d the two s -e le c tro n s become d e lo c a l­
c
ized in the valence band, lea vin g only the f iv e 3d e le ctro n s bound to
C
the io n .
Since a d -s h e ll may contain up to ten e le c tro n s , Hund's ru le s
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^
in d ic a te th a t the low est energy c o n fig u ra tio n f o r the h a lf - f u ll Mn2+
3d s h e ll co n sists o f a ll fiv e e le ctro n s unpaired [1 1 ].
The fiv e
e le ctro n s then c o n trib u te a net spin o f 5/2 to the io n ic magnetic
moment.
This leads to s ix possible spin o rie n ta tio n s fo r the io n :
Mj = + 5 /2 , + 3 /2 , _+ 1 /2 , w ith the energy le v e ls being degenerate in
zero magnetic f i e ld .
The a p p lic a tio n o f a magnetic f i e ld s p lit s the
system in to s ix e q u a lly spaced le v e ls .
le v e ls
Since tr a n s itio n s between the
are governed by the s e le c tio n ru le aMj = +1, a ll possible
tr a n s itio n s correspond to the same energy.
I f we now place the manganese ion in to a cubic l a t t i c e , the
c ry s ta l f i e l d breaks the z e r o -fie ld degeneracy.
The s in g le s ix - fo ld
degenerate le v e l s p lit s in to a quadruplet s ta te a t +a and a doublet
s ta te a t -2a where a is the fin e s tru c tu re s p li t t in g constant.
(
The
a p p lic a tio n o f a magnetic f i e ld w il l again s p l i t the le v e ls fu r th e r
in to a to ta l o f s ix le v e ls , removing a ll degeneracy, as shown in
Figure
2 .1 .
As b e fo re, the allowed tr a n s itio n s correspond to aMj = +1.
However, since the le v e ls are now no longer e q u a lly spaced, each
p o ssib le tr a n s itio n ( - 5/2 «->• - 3 /2 , - 3/2 «-»• - 1 /2 , . . . 3 / 2 -«-»■ 5/2)
corresponds to a s lig h t ly d if fe r e n t energy and the EPR spectrum exhib­
i t s fin e s tru c tu re c o n s is tin g o f fiv e lin e s , as shown in Figure 2.1.
Since the fin e s tru c tu re in te r a c tio n is due to the c ry s ta l
f i e l d , the amount o f s p lit t in g in the spectrum is s tro n g ly dependent
on the o rie n ta tio n o f the applied magnetic f i e l d w ith respect to the
c ry s ta l axes.
As shown in Figure 2 .2 , the am plitude o f the s p lit t in g
is la rg e s t when the applied f i e ld is in the [110] plane along the [100]
a xis and vanishes a t about 30° from the [100] a xis (see, e .g ., [1 2 ]) .
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11
Mi = 5/2
(.
3/2
1/2
1/2
-
-3 /2
-5 /2
Figure 2.1.
Fine s tru c tu re s p li t t in g o f the Mn2+ 3d5 le v e l in a
S 9I1cJdC f i e l d - The s ix le v e ls lead to f iv e lin e s in
the EPR spectrum.
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12
O
z
II-
[m ]
[n o ]
iLl
a:
3
IO
D
ac
O)
Id
z
iL.
Figure 2 .2 .
Amplitude o f the fin e s tru c tu re s p lit t in g as a fu n c tio n o f
the angle from the [100] d ir e c tio n . The dc magnetic f ie ld
is in the [110] plane.
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13
The hyp erfin e in te r a c tio n a rise s from the coupling between the
spin o f the 3d
e le c tro n s and the nuclear s p in , which in the case o f
the manganese ion has the value m^ = 5 /2 .
This in te ra c tio n s p lit s
each fin e
corresponding
s tru c tu re le v e l in to s ix le v e ls
p o ssib le values o f the nuclear
to the s ix
sp in (nij = + 5 /2 , + 3 /2 , + 1 /2 ).
a d d itio n a l s p lit t in g is shown in Figure 2 .3 .
This
T ra n s itio n s between these
le v e ls are governed by the h yp e rfin e s e le c tio n ru le s which re q u ire
Am = 0.
With each o f the fiv e fin e s tru c tu re lin e s being h y p e rfin e -
s p l i t in to s ix lin e s , the to ta l EPR spectrum co n sists o f a maximum o f
30 lin e s .
Although we do not have an a n a ly tic expression fo r x in c lu d in g
the c o n trib u tio n s o f the fin e and h y p e rfin e s p li t t in g , we can use a
phenomenological p ic tu re where
X =
w ith each
I Xi -
(2.15)
in d iv id u a l x.,- having the Bloch form o f Equation (2.14) but
w ith a s lig h t ly d if fe r e n t Larmor frequency coQ, such th a t
=
aE..
,
(2.16)
where AE.. is the energy difference for a particular transition allowed
by the selection rules described above.
D.
>
M icroscopic Model fo r k
The m icroscopic form o f the d ie le c t r ic tensor w il l be im portant
in our a n alysis o f h e lic o n -e x c ite d EPR, i . e . , when h ig h ly mobile fre e
c a r rie r s are present.
To develop th is model we must f i r s t consider
< 1>
the c o n d u c tiv ity tensor a.
We w i l l r e s t r i c t ourselves to the c la s s ic a l
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14
I
itij
= 5/2
3/2
1/2
-
-3 /2
- 5/2
3/2
1/2
-2a
-
1/2
r3/2
-5 /2
-3 /2
-
-5/2
Figure 2 .3.
1/2
1/2
3/2
5/2
Energy le v e ls o f the Mn2+ ion in a magnetic f ie ld showing
fin e and h y p e rfin e s p lit t in g . T ra n s itio n s , corresponding
to a M j = 1, Ami = 0 are shown. T ra n s itio n s from
Mj = - 3/2 ++ - 1/2 and 1/2 -*->■ 3/2 are om itted fo r c l a r i t y .
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15
(
o n e -c a rrie r Drude model in which the c a rrie rs are assumed to be non­
in te r a c tin g , so th a t t h e ir motion is in response o n ly to the external
f ie ld s .
The equation o f motion can be w ritte n
m * f?
=
q tr f + q M
- 2 / ,
(2.17)
★
where the e ffe c tiv e mass m and the re la x a tio n time t r e f le c t the
in flu e n c e o f the l a t t i c e , q and v are the charge and d r i f t v e lo c ity o f
the c a r r ie r s , re s p e c tiv e ly ,
t = £Q
is the microwave e le c t r ic f i e ld and
^ is the to ta l magnetic f i e l d .
We now assume th a t the dc
magnetic f i e l d is much la rg e r than the r f f i e ld so th a t t % §Q.
assuming a tim e dependence o f the form e
_ ■?(|)+
Then,
->*
, and re p la c in g v w ith the
c u rre n t d e n s ity J = nqv, where n is the c a r r ie r c o n c e n tra tio n ,
Equation (2.17) becomes
if-y
-ium J
=
?- >
•k-y
-y -y
m
nq Er f + qJ*B0 - ^
,1
/
.
v
(2.18)
< ■>
.
W ritin g Equation (2 .1 8 ) in the form o f Ohm’ s law , J = cr • £ , the
elements o f the tensor can be obtained [51:
_
„_2
nq x
( l-ian:)±co t
______ ' c
m*
(l-i(D T )2+(a)cT) 2
9
±
(2.19)
a
zz
=
.ng_L
*
m
I ___
1 - icot
’
•k
where we have introduced the c y c lo tro n frequency, toc a qBQ/m .
Note
th a t the sign o f u)c is determined by the sign o f the c a r r ie r .
Once we have obtained the elements o f the c o n d u c tiv ity te n so r,
we can o b ta in the d ie le c t r ic tensor from Equation (2 .5 ).
Using the
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16
*
m o b ility y s ex/m , we can w rite the real and im aginary p a rts o f
as fo llo w s :
<
=
ney(ojx+yB )
--------------------- 9 - 5 -
k
coe0 [l+ (to x + y B o )
]
( 2 . 20 )
k"
ney_______
-
w£0 [l+(a)T+yB0 ) 2]
where the charge o f the c a rrie rs has been replaced by q = -e fo r
e le c tro n s .
E.
M icroscopic Form o f yQ
The model fo r "^developed above contains the q u a n tity xQ> the
s t a t ic o r dc magnetic s u s c e p t ib ilit y , which is the r a tio o f the
m agnetization to the a p p lie d f i e ld in the s t a t ic case, x0 = M0/ ^ 0 *
(
In th is s e c tio n we w i l l develop the m icroscopic form o f
The magnetic moment
the to ta l angular momentum
o f an atom is given
x0-
by y = J where J is
o f the ion and g is the Landd fa c to r .
For
the manganese io n , the o r b ita l angular momentum L = 0, so th a t 3 =
2+
the spin angular momentum.
The g -fa c to r o f Mn
fre e -e le c tro n value o f g =2.00.
is very close to the
Once the to ta l angular
momentum o f
an ion is known, the energy le v e ls in a magnetic f i e ld are given by
E0
=
Mjg „ 0„ BH
where Mj is the component o f J along the f i e ld d ir e c tio n and
is the Bohr magneton.
The populations o f these d if f e r e n t energy
le v e ls are determined s t a t i s t i c a l l y through the Boltzmann fa c to r
exp(MjgyQyBH/kgT) where kg is the Boltzmann co n sta n t.
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(2.21)
Qpt
= 2m
17
The m agnetization o f a system is obtained by sim ply summing a ll
o f the magnetic moments
ft
=
I
,
(2.22)
so th a t fo r a system w ith N magnetic io n s , the m agnetization is
I M0gpov xP<Mj9 V B H/kBT)
M =
N — ------------------------------------------
I
,
(2.23)
e x p ( M jg p iiBH/kBT)
where the sum is over a ll values o f Mj from -J to +J.
Equation (2.23)
may be w ritte n
M =
NgyoyBJ B j(y )
(2.24)
where B j(y ) is the B r illo u in fu n c tio n , given by [13]
B
Ojj(y
UJ)
=
~ 1j- [ ( J+%)coth(J+%)y - %coth Jgy] ,
(2.25)
where
y
=
gJu0yBH/kBT .
(2.26)
For most experim ental c o n d itio n s y << 1 and the B r illo u in fu n c tio n
may be approximated by a h y p e rb o lic cotangent fu n c tio n , in which case
Equation (2.24) reduces to
Ny J (d + l)g 2yRH
H ■
°
3kBT
'
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(2 ' 27)
18
C
Since x0 = M/H, the dc s u s c e p tib ility is given by
xo
Nyop2yB
3kgT
’
"
(2.28)
where we have defined p as the e ffe c tiv e number o f Bohr magnetons per
io n ,
P
sg [J ( J + l) ]55
.
(2.29)
I f we now d e fin e an e ffe c tiv e d ip o le moment per ion
Fg-p-p
=
PUg
>
( 2.30)
the s ta tic s u s c e p t ib ility is given by
=
xo
(
NyoPe f f
3kBT
‘
( 2 - 31)
Note th a t N, the number o f magnetic d ip o le s per u n it volume can be
ca lc u la te d .
For a face-centered cubic DMS,
N =
4x/a3
(2.32)
where x is the fr a c tio n o f manganese in the m a te ria l and aQ is the
la t t i c e parameter, which is i t s e l f a fu n c tio n o f x.
The fa c to r o f 4
is due to the 4 atoms making up the fee u n it c e ll.
The form o f Equation (2.31) above is known as the Curie law,
p re d ic tin g a 1/T dependence fo r x0 -
The measured m agnetization fo r
DMS is a c tu a lly b e tte r described using a Curie-Weiss form o f the
s u s c p e tib ility where the temperature is replaced by an e ffe c tiv e
tem perature, T ^ ^ = T + 0, where e is known as the Weiss constant.
The Weiss constants obtained by f i t t i n g the observed m agnetization to
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19
a Curie-Weiss law are negative fo r DMS.
This in d ic a te s th a t the in t e r ­
a ctio n between neighboring manganese ions is a n ti ferrom agnetic in
nature.
This a n ti ferrom agnetic in te ra c tio n tends to reduce the size
o f the e ffe c tiv e Bohr magneton, thus reducing o r s a tu ra tin g the
observed m agnetization below the value expected fo r a summation over
n o n -in te ra c tin g spins.
The e ffe c tiv e temperature and the spin
s a tu ra tio n have been incorporated in to a theory d e scrib ing the
m agnetization in CdMnTe by Gaj e t al_. [1 4 ].
('
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20
c
CHAPTER I I I - MATERIALS AND EQUIPMENT
A.
M a te ria ls
D ilu te d magnetic semiconductors (DMS) are I I - V I compound
semiconductors such as HgTe and CdSe where some o f the group I I ions
have been replaced s u b s titu tio n a lly by magnetic io n s , u s u a lly manganese
[1 -4 ].
The presence o f the manganese leads to a number o f in te re s tin g
phenomena.
In Figure 3 .1 , prepared by P rofessor W. G ir ia t from the
In s t it u t e o f S c ie n t if ic Research ( I . V . I . C . ) , Caracas, Venezuela, we
show sch e m a tic a lly the p o ssib le DMS w ith manganese as the magnetic io n .
(
As can be seen, the manganese goes in to the l a t t i c e w ith varying
degrees o f success.
Other magnetic io n s , such as iro n and c o b a lt,
also may be s u b s titu tio n a lly placed in the l a t t i c e , but are much less
m is c ib le in the host m a te ria l.
As a consequence, these o th e r DMS are
lim ite d to a t most, several percent o f the magnetic io n .
DMS are in te re s tin g m a te ria ls fo r several reasons.
The
presence o f the magnetic ions causes changes in the band s tru c tu re o f
the host m a te ria l.
On the o th e r hand, the magnetic p ro p e rtie s
themselves are o b vio u sly a ffe c te d .
In a d d itio n , the exchange in t e r ­
a c tio n between the fre e e le c tro n s and the lo c a liz e d e le ctro n s
com prising the manganese ion in flu e n ce s the e le c tr ic a l and o p tic a l
p ro p e rtie s in these a llo y s .
We hope to c o n trib u te to the knowledge o f
the magnetic p ro p e rtie s o f DMS by p ro v id in g a system atic study o f the
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21
CdTe
Cub
ZnTe
HgTe
J. 0.75
MnTe
HgS
HgSe
MnSe
CdSe
0.50' ■
H ex
0.35 ■■
Cub
MnS
■ 0.45
CdS
Hex
. .0 \0 s
Cub,
ZnSe
Figure 3 .1 .
ZnS
The II-V I-M n fa m ily o f DMS. The m is c ib ilit y and c ry s ta l
s tru c tu re o f th e .v a rio u s compounds are shown.
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22
dynamic magnetic s u s c e p tib ility in these m a te ria ls .
I t is c le a r th a t
an understanding o f the magnetic p ro p e rtie s o f DMS is im p o rta n t, not
o n ly in i t s own r ig h t , but also in th a t i t bears on o th e r p ro p e rtie s
through the exchange in te r a c tio n .
In th is se ctio n we w i l l discuss several p ro p e rtie s o f DMS th a t
are a ffe c te d by the presence o f the magnetic ions.
describe the c ry s ta l s tru c tu re o f DMS.
We w i l l f i r s t
Then we w il l discuss the band
s tru c tu re and how i t changes w ith the a d d itio n o f manganese.
then present the magnetic p ro p e rtie s o f these m a te ria ls .
We w ill
And, f i n a l l y ,
we w i l l b r ie f ly discuss the exchange in te ra c tio n and how i t a ffe c ts
the e le c t r ic a l and o p tic a l p ro p e rtie s o f DMS.
1.
C rystal P ro p ertie s
One o f the major problems in attem pting to prepare a llo y s occurs
when the c o n s titu e n ts have d if fe r in g c ry s ta l s tru c tu re s .
case o f Hg,
U nlike the
Cd Te, where both HgTe and CdTe have the same z in c blende
1" A
/\
s tru c tu re , and compounds are p o ssib le w ith any value o f x from 0 to 1,
DMS are hampered by the fa c t th a t none o f the sta b le phases o f Mn-VI
compounds have e ith e r the zinc blende o r the hexagonal s tru c tu re s
formed by the I I - V I non-magnetic "h o s ts ."
As shown in Table 3 .1 , the
manganese chalcogenides form in the NiAs o r NaCl s tru c tu re s .
This
in c o m p a tib ility o f c ry s ta l s tru c tu re prevents DMS from being produced
w ith values o f x much g re a te r than 0 .5 , w ith the exception o f the
te llu r id e s , where higher com positions are p o s s ib le .
D iffe re nce s in io n ic r a d ii between the various cations present
in DMS lead to a la t t i c e parameter th a t va rie s w ith manganese
co n ce n tra tio n .
The r a d ii are lis t e d in Table 3.2 [1 5 ].
Since, fo r
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23
Table 3 .1.
C rystal p ro p e rtie s o f I I - V I and Mn-VI compounds.
m .p .( °C)
Eq (300 K)
a(A)
S tru ctu re
MnTe
1165
1.25
4.1475
6.710
NiAs
MnSe
1510
2.50
5.462
NaCl
MnS
1530
3.20
5.223
NaCl
HgTe
670
-0.15
6.460
Cub
HgSe
779
-0 .1 0
6.084
Cub
HgS
825
-0 .1 7
5.851
Cub
CdTe
1098
1.44
6.481
Cub
CdSe
1265
1.67
4.2985
7.0150
Hex
CdS
1405
2.41
4.1368
6.7163
Hex
ZnTe
1293
2.26
6.1037
Cub
ZnSe
1526
2.70
5.6687
Cub
ZnS
1722
3.60
5.4093
Cub
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24
Table 3 .2.
Io n ic r a d ii o f ca tio n s in DMS.
Ion
Io n ic Radius
Mn2+
Zn2+
Cd2+
Hg2+
0.80 A
0.74 A
0.97 A
1.10 A
(
Table 3 .3.
Temperature o f the m e lt used to grow s in g le -c ry s ta l DMS.
HgMnTe
Typical temp,
o f the m elt
750-780
HgMnSe
900
CdMnTe
CdMnSe
ZnMnTe
1120-1150
1320-1350
1320-1350
(°c)
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25
example, the radius o f Mn
is between th a t o f Cd
and Zn
P’b
, i t is
not s u rp ris in g th a t the la t t i c e parameter o f Cd-based DMS shrinks upon
2+
the in tro d u c tio n o f Mn
w h ile th a t o f Zn-based compounds expands.
Because o f i t s va ryin g l a t t i c e parameter, CdMnTe has been used as a
su b stra te fo r e p ita x ia l growth o f o th e r m a te ria ls [1 6 ].
Figure 3.2
shows the l a t t i c e constant v a r ia tio n fo r CdMnTe and ZnMnTe [1 7 ].
Note th a t i f we e x tra p o la te to x = 1, i . e . , to pure MnTe, both
compounds p o in t to a f i c t i t i o u s , zinc blende form o f MnTe having a
o
la t t ic e constant o f 6.34 A.
2.
Band S tru c tu re
One o f the most in te r e s tin g and useful p ro p e rtie s o f DMS is
th a t the band gap can be va rie d by in tro d u c in g manganese in to the
system.
The a d d itio n o f manganese in to CdTe, a wide-gap m a te ria l, fo r
example produces an even la rg e r gap.
For the compounds th a t are
i n i t i a l l y zero-gap sem iconductors, the manganese causes a p o s itiv e gap
to open.
As can be seen from Table 3 .1 , the host compounds based on
cadmium and zinc are a ll wide-gap m a te ria ls w ith room-temperature gaps
ranging from 1.44 eV f o r CdTe to 3.6 eV fo r ZnS.
band gap fo r Cd,
1“ A
Figure 3.3 shows the
Mn Te as a fu n c tio n o f manganese co n cen tra tio n x [1 8 ].
/\
By about x = 0.35, the gap has become la rg e enough th a t o p tic a l
transm ission a t the red end o f the v is ib le spectrum begins.
With
2+
fu r th e r increase o f Mn , the m a te ria l becomes in c re a s in g ly tra n s -
p a ren t, re ta in in g i t s red c o lo r because o f absorption by the Mn
i t s e l f a t an e x c ita tio n energy o f about 2 eV.
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2+
26
6.50
6.40
o< 6.30
6.20
6.10
0.2
0.4
0.6
0.8
X(M ole fraction)
Figure 3 .2 .
L a ttic e co n sta n t as a fu n c tio n o f manganese concentration
f o r Cdi_xMnx Te and Zni_xMnx Te. E x tra p o la tio n to x = 1.0
in d ic a te s a f i c t i t i o u s zinc blende form o f MnTe w ith a
la t t i c e co n sta n t o f 6.34 A .
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0
0.1
0.2
0.3
0.4
0.5
Composition
Figure 3 .3.
Band gap energy o f Cd, J in Te as determined by the e xcito n
energy.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
^
The w idth o f the band gap is also dependent, to some e x te n t, on
the temperature [1 9 ], as is the e x c ita tio n energy o f the manganese ion
[2 0 ].
The e ffe c t o f the l a t t e r may be seen by the naked eye by sim ply
co o lin g a 50% sample o f CdMnTe to liq u id n itro g e n tem perature.
The
c o lo r changes from b r ig h t red to orange as the e x c ita tio n energy
increases.
The mercury chalcogenides are "negative-gap" ( i . e . ,
E (r6 ) - E ( r 8 ) < 0) o r "zero-gap" semiconductors w ith room temperature
band gaps ranging from -0.10 eV fo r HgSe to -0 .1 7 fo r HgS.
S ubsti­
tu tin g manganese f o r mercury causes th is negative gap to decrease
u n t i l , a t some c o n c e n tra tio n , the Tg and Tg bands become degenerate,
as shown in Figure 3.4 fo r Hg,
1 " A
Mn Te.
X
Further increase in the
manganese co n ce n tra tio n opens the gap.
(
The a b i l i t y to c o n tro l the band gap by c o n tr o llin g the composi­
tio n o f the m a te ria l is a c h a r a c te r is tic th a t promises to be very
u s e fu l.
From th is p o in t o f view , there is c u rre n tly considerable
in te r e s t in HgMnTe f o r in fra re d d e te c to r a p p lic a tio n s [2 1 ].
3.
Magnetic P roperties
The presence o f magnetic ions in the DMS leads to a number o f
in te re s tin g magnetic p ro p e rtie s .
on the ca tio n s u b la ttic e s ite s .
2+
e le ctro n s o f the Mn
The ions are randomly d is trib u te d
5
The h a l f - f i l l e d 3d o u te r s h e ll o f
ion is h ig h ly lo c a liz e d a t the io n ic p o s itio n .
Each ion has a magnetic moment equal to fiv e Bohr magnetons since
the e le c tro n s a lig n w ith a ll fiv e spins p a r a lle l.
The magnetic
p ro p e rtie s o f DMS are determined by these lo c a liz e d magnetic moments
and the in te ra c tio n s among them.
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29
c
zero - gap
positive
gap
h.h.
0.06
0 .1 0
0.14
X (M n content)
Figure 3 .4 .
Band gap o f Hgi_xMnx Te as a fu n c tio n o f com position. The
sem im etal-to-sem iconductor tr a n s itio n occurs when the r 6
and r 8 bands become degenerate a t about x = 0.07. The
s p in - o r b it s p li t t in g is given by A, c .b . re fe rs to the
conduction band and l . h . and h .h . denote the l i g h t hole
and heavy hole bands, re sp e ctive ly-.
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30
Using magnetic s u s c e p t ib ility and s p e c ific heat measurements,
several in v e s tig a to rs have mapped o u t magnetic phase diagrams fo r
DMS [2 2 -2 7 ].
The diagram f o r CdMnTe is shown in Figure 3 .5 .
diagrams fo r o th e r DMS are remarkably s im ila r .
The
The m a te ria l e x is ts in
three phases; paramagnetic, spin glass and a n ti fe rro m a gn e tic, but there
is s t i l l some confusion as to what the terms im ply and to e x a c tly what
happens when the m a te ria l undergoes a phase tr a n s itio n .
In the paramagnetic range, the magnetic moments are randomly
a lig n e d .
In the presence o f a dc magnetic f i e l d , the moments tend to
a lig n themselves w ith the dc f i e l d .
At high tem peratures, the magnetic
s u s c e p t ib ility can be described q u ite w ell by assuming a Curie-Weiss
type o f behavior:
where C is a co n sta n t, T is the temperature and ew is the Weiss
co n sta n t.
However, a t low tem peratures, the s u s c e p t ib ility ra p id ly
increases above the value p re d icte d by e x tra p o la tin g Equation ( 3 .1 ) ,
re v e a lin g an enhanced form o f paramagnetism r e la tiv e to Equation (3 .1 )
(see, e .g ., [2 8 ]) .
The m agnetization f o r high applied f ie ld s , which
is p ro p o rtio n a l to the average s p in , fo llo w s a B r illo u in fu n c tio n ,
in d ic a tin g th a t the system is heading f o r eventual spin alignm ent
s a tu ra tio n as the f i e ld increases.
The behavior o f the low temperature s p e c ific heat and the
presence o f a c h a r a c te r is tic cusp in the low f i e ld magnetic s u s c e p ti­
b i l i t y lead to the conclusion th a t above x = 0.17, DMS form a spin
glass phase a t low tem peratures.
In a spin g la s s , the magnetic moments
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50
P : Fbramagnetic
A : Antiferromagnetic
S .* Spin-glass
40
mixed,
crystal
phases
i—
20
0
0.2
0.4
0.6
0.8
1.0
X
Figure 3.5.
Magnetic phase diagram fo r CdMnTe.
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32
are "fro ze n " in random o rie n ta tio n s and are unable to re a c t to a small
dc f i e ld .
The tr a n s itio n to th is phase is n o t, however, a sharp one.
Escorne and Mauger [29] have suggested th a t although la rg e -s c a le
fre e z in g o f the spins begins a t the tr a n s itio n ( i . e . , cusp) temper­
a tu re , "loose" spins and small paramagnetic c lu s te rs may e x is t
considerably below th is tem perature.
In a d d itio n , sm a ll-sca le
c lu s te rin g may also occur considerably above the tr a n s itio n temper­
a tu re , leading to a smearing o u t o f the tr a n s itio n .
2+
A t the highest Mn
romagnetic phase occurs.
c o n c e n tra tio n s , a tr a n s itio n to an a n t if e r ­
In a ll p r o b a b ility , however, th is phase,
w h ile co n ta in in g larg e c lu s te rs o f a n tife rro m a g n e tic a lly ordered
sp in s, does not contain the tru e long-range order c h a r a c te r is tic o f
c la s s ic a l antiferrom agnets.
This conclusion is in fe rre d from the
w idth o f magnetic peaks observed in neutron s c a tte rin g experiments on
DMS [3 0 ].
4.
Exchange In te ra c tio n
One o f the most im po rta n t consequences o f the presence o f
magnetic ions in DMS is the e xiste nce o f a s p in -s p in exchange
in te ra c tio n between the lo c a liz e d 3d
e le c tro n s and the band e le c tro n s .
One way in which th is exchange in te ra c tio n m anifests i t s e l f is through
changes in in fra re d magnetooptical p ro p e rtie s .
When placed in a
magnetic f i e l d , the energy bands o f c ry s ta ls s p l i t in to ladders o f
Landau le v e ls , each o f which is fu r th e r s p l i t in to spin-up and
spin-down s u b -le v e ls .
Due to the presence o f exchange, th is
s p in - s p lit tin g becomes temperature-dependent in DMS, causing the
e n tire Landau le v e l scheme, and thus the magnetotransmission s p e c tra ,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
to depend s tro n g ly on the tem perature.
The extrem ely larg e spin
V
s p li t t in g can, in f a c t , a lt e r the usual Landau le v e l sequence [3 1 ],
and in some cases can a llo w a m a g ne tica lly induced sem im etal-tosemiconductor tr a n s itio n in zero-gap DMS [3 2 ].
Not o n ly does the exchange in te ra c tio n r e s u lt in la rg e spin
s p li t t in g o f the band le v e ls , but also the e x cito n le v e ls are s im ila r ly
s p lit.
The d iffe re n c e in d is p e rs io n near the e x cito n le v e l f o r l ig h t
o f opposite c ir c u la r p o la riz a tio n s causes g ig a n tic Faraday r o ta tio n ,
e x p e c ia lly a t low temperatures [18] (see Figure 3 .6 ).
Note th a t th is
la rg e Faraday r o ta tio n , which may reach values o f over l°/G -cm , is due
to the e x c ito n s p l i t t i n g , and is not to be confused w ith the ro ta tio n
discussed in Chapter V, below, which is caused by EPR.
The e x c ito n -
based Faraday ro ta tio n discussed here has p o te n tia l uses in several
(
o p tic a l device a p p lic a tio n s .
Other fe a tu re s o f DMS whose o rig in s may be traced to the
exchange in te r a c tio n in c lu d e a la rg e negative magnetoresistance in
HgMnTe [33] and the e xiste nce o f bound magnetic polarons in CdMnTe
[34] and CdMnSe [3 5 ], in which there is c u rre n tly intense research
a c t iv it y .
B.
DMS are u s u a lly grown using the Bridgman process.
C rysta l Growth
S to ic h io ­
m e tric q u a n titie s o f the p u r ifie d c o n s titu e n t elements are placed in
a q u a rtz ampule which is then evacuated and sealed o f f .
The ampule
is placed v e r t ic a lly in a fu rn a ce , the temperature slo w ly ra ise d to
the a p p ro p ria te growing temperature and then the furnace is slow ly
I
ra is e d , causing a tem perature g ra d ie n t to pass along the in g o t.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
34
i
0.2
,
0.3
0.5
o>
0.15
0.0 5
0.02
"g
0.01
u.
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
Energy ( eV )
Figure 3 .6 .
Exciton Faraday r o ta tio n in CdMnTe a t 77 K f o r several
d if f e r e n t com positions.
\
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35
ampules are drawn to a fin e p o in t, so th a t c r y s ta liz a tio n (which s ta rts
from the bottom up) can begin in as small an area as p o s s ib le . This
acts as a seed fo r the
remaindero f the in g o t.
Using m o d ific a tio n s
th is process we have succeeded in growing Hg,
1“X
Cd,
1“ X
Mn Te, Cd,
X
X“ X
Mn Se and Zn,
X
m a te ria ls such as Hg,
i" x
X
X“ X
Mn Se,
X
Mn Te, as w ell as some non-magnetic
X“ X X
Cd Te andHg,
x
Mn Te, Hg,
of
x“ x
Cd Te, ,.Se .
x
l j
y
The procedure f o r growing the mercury-based DMS has been
described elsewhere [5 ], but th a t used to produce the cadmium- and
zinc-based m a te ria ls needs to be discussed.
m a te ria ls involved are shown in Table 3 .1.
The m e ltin g p o in ts o f the
Before the fu rn a c e -ra is in g
begins, the m a te ria ls are heated to a temperature somewhat above the
m e ltin g p o in t as shown in Table 3 .3.
When growing mercury compounds, the prim ary problem is the
danger o f the ampule ru p tu rin g due to the high vapor pressure o f the
mercury.
The most dangerous time occurs during the synthesis o f HgTe
o r HgSe, which is a h ig h ly exothermic re a c tio n .
During th is period
the temperature in s id e the ampule may be con sid e ra bly higher than th a t
o u tsid e .
In growing cadmium and zinc compounds, the problems are due
m ainly to the elevated temperatures re q u ire d .
soften a t 1300 - 1350°C.
Quartz i t s e l f begins to
Special precautions must be taken, then, when
growing CdMnSe and ZnMnTe to prevent the ampule from exploding.
An
a d d itio n a l problem a ris e s due to the la rg e amount o f manganese o fte n
used in the cadmium and z in c compounds.
A t elevated temperatures,
manganese tends to a tta c k q u a rtz , and care must be taken to prevent i t
from sim ply e a tin g through the ampule from the in s id e .
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36
We have had some success w ith growing Cd,
1“ X
by using the method o u tlin e d in Figure 3 .7 .
Mn Se and Zn,
X
i" X
Mn Te
X
The p u r ifie d elements are
placed in a c ru c ib le made o f boron n it r id e , one o f the most in e r t
m a te ria ls a v a ila b le .
The c ru c ib le is placed in a th ic k -w a lle d quartz
ampule, thus preventing the
w ith the q u a rtz.
manganese from coming in to d ir e c t contact
The sealed ampule is placed in a g ra p h ite c ru c ib le
holder which is then t i g h t l y packed w ith pure g ra p h ite powder.
This
is designed to prevent the ampule from expanding when i t becomes s o ft.
The c ru c ib le h o ld e r is placed in a furnace and baked a t 1000°C under
vacuum to remove any oxygen adsorbed on the g ra p h ite powder, which
would tend to d e v it r if y the quartz a t higher tem peratures.
The system
is f i n a l l y pressurized to approxim ately 4 atm w ith argon to counter­
balance the pressure in s id e the ampule, the temperature is raised to
about 1350°C, and the Bridgman process is completed by ra is in g the
furnace.
There is c u rre n tly some question as to how w e ll the furnace
which was a v a ila b le to us was c h a ra cte rize d , and there is a possi­
b i l i t y th a t the actual temperature we have been using may have been as
much as 100°C h ig h e r than we thought.
This could e x p la in , to some
degree, several ra th e r dram atic fa ilu r e s th a t have occurred.
In a d d itio n to the c ry s ta ls we have grown, we have received a
number
of
samples
from
o th e r
researchers.
P rofessor W. G ir ia t
from I.V .I.C . has provided a la rg e number o f wide-gap samples and
Professor R. R. Galazka from the In s titu t e o f Physics o f the P olish
Academy o f Sciences has supplied some o f the HgMnSe and CdMnTe c ry s ta ls
used in th is in v e s tig a tio n .
Due to the extrem ely high m elting points
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37
t
Graphite powder
Graphite crucible holder
Quartz ampule
BN crucible
Thermocouple well
Figure 3 .7 .
O u tlin e o f the procedure used to grow ZnMnTe and CdMnSe
c r y s ta ls . BN denotes boron n it r id e . The e n tire assembly
is placed in s id e a Bridgman furnace.
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38
o f ZnSe and ZnS, the DMS provided by G ir ia t based on these compounds
were s in te re d ra th e r than s in g le - c r y s ta l.
F in a lly , we have received
a few samples from Dr. Reynolds o f W right-P atterson A ir Force Base,
Dayton, Ohio, and from Eagle-P icher In d u s trie s , In c ., Miami, Oklahoma.
The s in g le -c ry s ta l o r s in te re d m a te ria ls are prepared fo r
experiments as fo llo w s :
The a ctual manganese co n te n t is determined
by d e n s ity measurements in the mercury- and cadmium-based compounds.
Since the d e n s ity o f manganese is so close to th a t o f z in c , th is
method has in s u f f ic ie n t s e n s it iv it y fo r the zinc compounds.
For these
m a te ria ls , x -ra y powder measurements o f the la t t ic e parameter are
used [1 7 ].
In the case o f CdMnTe, the manganese co n cen tra tio n is
u s u a lly is o tr o p ic both r a d ia lly and lo n g itu d in a lly and very n e a rly
equal to the value expected from the s ta r tin g in g re d ie n ts .
The zinc
compounds and the o th e r cadmium compounds may o r may not be e q u a lly
homogeneous:
we have not examined a s u f f ic ie n t q u a n tity o f these
m a te ria ls to draw a r e lia b le co n clu sion .
However, our powder samples
are taken from a small enough area fo r any macroscopic manganese
co n cen tra tio n g ra d ie n t not to be a problem.
The value o f x is
determined e ith e r from the piece o f m a te ria l i t s e l f before i t is
powdered o r from an a d jacent piece.
For the mercury-based m a te ria ls ,
however, a t le a s t p a r t ia lly due to the la rg e d iffe re n c e in io n ic
r a d ii, lo n g itu d in a l co n cen tra tio n g ra d ie n ts are p a r tic u la r ly se rio u s.
D ensity measurements must then be made on each in d iv id u a l slab s tu d ie d .
The wide-gap DMS were u s u a lly stu d ied in the form o f fin e
powders (d < 62 ym), f o r reasons which w i l l be discussed in Chapter V.
The zero-gap m a te ria ls were c u t in to th in slabs on the order o f 500 ym
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39
th ic k .
The slabs were then placed on an i r i s w ith the edges sealed
w ith h ig h ly conductive s ilv e r paste to prevent microwave leakage
around the sample during transm ission measurements.
the Hg-based compounds, the slabs were annealed.
P rio r to studying
HgMnTe samples were
annealed in Hg vapor a t about 250°C in an e f f o r t to reduce the mercury
vacancies, which acts as acceptors and render the as-grown m a te ria l
p -typ e .
HgMnSe is always n-type due to the presence o f e ith e r
i n t e r s t i t i a l mercury o r selenium vo id s.
By annealing a t 200°C in
dynamic vacuum, the s to ic h io m e try is re sto re d (o r a t le a s t v a s tly
improved) and the e le c tro n co n ce n tra tio n is consequently lowered by
about an order o f magnitude.
C.
Experimental Apparatus
Microwaves generated by a k ly s tro n a t a frequency o f 35 GHz
tra v e l through two arms.
One arm, co n ta in in g the sample, passes
a x ia lly through a superconducting so le n o id .
The o th e r, c a lle d the
reference arm, bypasses the sample and subsequently re jo in s the sample
arm, r e s u ltin g in in te rfe re n c e between the two s ig n a ls .
When the
reference arm is closed, the sign a l reaching the d e te c to r is sim ply
the power tra n s m itte d through the sample.
With the reference arm open,
the two s ig n a ls in te r fe r e , p ro v id in g a means o f determ ining the phase
v a ria tio n o f the tra n s m itte d s ig n a l.
When the magnetic fie ld -in d u c e d
phase changes are la rg e , the d e te c to r o u tp u t shows o s c illa tio n s as a
fu n c tio n o f the magnetic f i e l d corresponding to a succession o f
c o n s tru c tiv e and d e s tru c tiv e in te rfe re n c e s o f the two signal tr a in s .
This enables us to measure the change in phase o f the microwaves due
to the sample as a fu n c tio n o f magnetic f i e ld in a p a r tic u la r ly
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40
s tra ig h tfo rw a rd manner.
In a d d itio n , the reference arm can be used
as an a m p lifie r when the sample signal is much sm aller than the
reference sig n a l [6 ].
The spectrom eter is illu s t r a t e d in Figure 3.8.
The sample arm signal is am plitude modulated a t 1000 Hz using
a f e r r i t e m odulator.
The modulator is driven by a sine wave produced
in t e r n a lly by a lo c k -in a m p lifie r and passed through an audio
a m p lifie r .
Modulation o f the sample arm signal is done to increase
the s ig n a l-to -n o is e r a tio and to e lim in a te from the in te rfe re n c e
signal th a t p a rt caused s o le ly by the unmodulated reference arm.
The
o u tp u t from the s ilic o n diode d e te c to r is fed to the lo c k - in a m p lifie r
and then to the Y -axis o f an X-Y recorder.
The X-axis in p u t comes
from the magnet power supply and is d ir e c t ly p ro p o rtio n a l to the f i e ld .
The spectrom eter contains a c ir c u la r p o la riz e r above ( i . e . ,
before) the sample, which is used to o b ta in the desired in c id e n t
p o la riz a tio n .
Immediately below ( i . e . , a fte r ) the sample there is a
c irc u la r - to - r e c ta n g u la r waveguide tr a n s itio n , which connects to the
U -turn o f the microwave c i r c u i t and the e x it waveguide leading to the
d e te c to r.
A ro ta tin g j o i n t precedes the c ir c u la r p o la r iz e r , a llo w in g
c o n tro l o f the o rie n ta tio n o f the in c id e n t lin e a r p o la riz a tio n .
This
fe a tu re is p a r tic u la r ly im portant in the case o f measuring small
values o f Faraday ro ta tio n and e l l i p t i c i t y , as described in Chapter V
and in the Appendix.
The magnet is a superconducting solenoid capable o f fie ld s o f up
to 6 T.
The sample holder is is o la te d from the magnet helium bath by
an in s e r t dewar which perm its measurement to be taken a t temperatures
above 4.2 K.
A manganin heater w ire (R ^ 3fi/cm) o f to ta l re sista nce
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41
Lock-In
Amplifier
Klystron
Audio
Amplifier
Wave
Meter \ - r
X -Y
Recorder
Diode
Detector
Attenuator
f
t
Isolator
20db
On-Off
Switch
Phase ^
Shifter 1
Oscilloscope
Reference Arm
Isolator
Isolator
Attenuator
Modulator
Sample Arm
To Lock-In
Amplifier
Rotating
Joint
Attenuator
OMT
Polarizer
S
' s’
Cylindrical
Waveguide
Sample
Holder
Figure 3 .8 .
/V\t
J i
Superconducting
Solenoid
Transition
(Cylindrical-to-Rectangular
Waveguide)
Diagram o f the microwave spectrom eter used in the
experiments.
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42
|
300 n is wound around the sample h o ld e r.
The temperature is measured
by a s ilic o n diode which was c a lib ra te d a gainst a germanium r e s is to r .
The system allow s measurements to be taken a t temperatures ranging
from 1.3 K (by pumping on the helium bath) to about 95 K.
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43
1
CHAPTER IV - ZERO-GAP AND NARROW-GAP DMS
Mercury chalcogenides are "zero-gap" o r "negative-gap" semi­
conductors since the Tg band is a c tu a lly lower in energy than the Tg
band (see Figure 3.4 f o r x = 0 ).
With the s u b s titu tio n o f manganese
f o r a fr a c tio n o f the mercury, the
band moves upward u n til a t some
co n ce n tra tio n (x = 0.06 f o r Hg, „MnvSe a t 4.2 K) the r c and r 0 bands
1 ““X
X
o
o
2+
F u rth e r increase o f Mn
opens the band gap, c re a tin g a
co in c id e .
"normal" narrow-gap m a te ria l, as shown in Figure 3.4 fo r x > 0.06.
The existence o f a zero-gap o r narrow-gap ensures th a t the
{,
m a te ria l w i l l have a high c o n d u c tiv ity , i . e . , th a t a r e la t iv e ly la rg e
number o f fre e charge c a rrie rs w i l l be present.
This high c o n d u c tiv ity
re s u lts in a small skin depth f o r electrom agnetic waves, which would
u s u a lly make i t d i f f i c u l t to study EPR.
However, under c e rta in
co n d itio n s (when the c a rrie rs are very m obile) a magnetic fie ld -in d u c e d
transparency can e x is t; known as "h e lic o n wave p ro p a g a tio n ."
As w il l
be shown, such h e lico n waves can be e x p lo ite d to study EPR, since they
can propagate w ith r e la t iv e ly l i t t l e
a tte n u a tio n , he lico ns can be
■ used to circum vent the skin depth problems in h e re n t in conventional
EPR stu d ies o f conductive samples.
Hg,
X*" X
Mn Se is a ttr a c t iv e f o r the study o f h e lic o n -e x c ite d EPR
X
because in th is m a te ria l the phenomenon is not com plicated by the
presence o f h o le s, as i t is in , e .g ., Hg,
J. “ A
Mn Te.
A
M u llin has studied
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44
(
the dynamic magnetic s u s c e p t ib ility in Hg,
1 "
Mn Se fo r a s in g le
a
a
manganese co n cen tra tio n o f x = 0.058, and was able to o b ta in both x0
and l ^ as fu n ctio n s o f temperature [2 8 ].
In p a r tic u la r , he observed
a very dram atic broadening o f the resonance lin e w ith decreasing
temperature.
Our purpose here is to extend the h e lic o n -e x c ite d EPR measure­
ments on HgMnSe to concentrations beyond th a t studied by Mull in .
study lo g ic a lly d iv id e s in to two s e c tio n s :
Our
the low concentration
l i m i t (x < 0 .0 0 5 ); and the inte rm e d iate concentrations (0.01 < x <
0 .1 0 ).
For the low concentrations we observe w e ll-re s o lv e d hyperfine
s tru c tu re in the EPR spectrum.
A t higher co n c e n tra tio n s , the sp in -
spin in te ra c tio n between the magnetic d ip o les broadens the hyperfine
lin e s and the EPR signal coallesces in to a s in g le lin e .
(
A t any one
tem perature, as the manganese co n cen tra tio n increases, th is s in g le
lin e continues to broaden.
This broadening e ffe c t c o n s titu te s a
p ra c tic a l lim ita tio n on h e lic o n -e x c ite d EPR, making the a n alysis
u n re lia b le fo r x > 0 .1 a t low temperatures.
In th is chapter we w il l f i r s t present the th e o re tic a l background
f o r electrom agnetic wave propagation in an e le c tro n plasma moving in a
la t t i c e which contains lo c a liz e d magnetic moments.
This w il l invo lve
a b r ie f fo rm u la tio n o f h e lico n wave propagation in a conducting,
paramagnetic medium.
We w i l l then present our experim ental re s u lts
fo r H g ^ M n ^ e .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
A.
Helicon Propagation in a Paramagnetic Medium
I
In an e a r lie r s e ctio n we form ulated the basic equations govern­
ing electrom agnetic wave propagation in a g y ro tro p ic medium.
Assuming
plane waves o f the form exp i( £ * r - iu t ) , we developed the wave equation
w ith the complex wave numbers
k+
=
to/c / K +n±
=
a + + ie + ,
(4 .1 )
where the propagation c o e ffic ie n ts are given by
<x+
-
-------
( l<+ l| n + |+ (K ;n |-K "n " )]1/2 ,
(4 .2 )
[ l<+ Mn+ |-(K |n + -K :"n + )]ly/2 ,
(4 .3 )
v/2 c
w ith the s in g le and double primes denoting the real and imaginary
(
p a rts , re s p e c tiv e ly , o f k+ and n+In terms o f the on e-e le ctro n Drude model, the d ie le c t r ic
fu n c tio n k + is given by
K±
1 +
”
P
OJ
T
1 -i ((0±U) ) t
(4 .4 )
2 *
is the l a t t i c e d ie le c t r ic constant,
= nq / m e q k ^ i s the
*fe
plasma frequency, n, q and m are the fre e c a r r ie r co n c e n tra tio n ,
where
charge and e ffe c tiv e mass, re s p e c tiv e ly , t is the re la x a tio n time and
o>c = qB/m
is the c y c lo tro n frequency.
the fre e c a rrie rs are e le c tro n s , w < 0.
For m a te ria ls lik e HgMnSe where
At microwave frequencies and
magnetic fie ld s exceeding a few kilo g a u ss, the parameters in k
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fo r
46
g o o d -q u a lity HgMnSe samples s a tis fy the fo llo w in g r e la tio n s :
l»c l »
| o)ct | »
U) ,
2
ui >> luiu I .
p
1 C1
1 ,
(4 .5 )
These re la tio n s h ip s c o n s titu te what is known as the "h e lic o n l i m i t "
[3 5 ].
In th is l i m i t the propagation constants may be approximated by
ct+
^
/nunjQ/B
1 + j x|
’+
(4 .6 )
a
f
'
e_
^
/nwy0/B
where we have s u b s titu te d 1
1
1 + 2 x+
+ x+ f o r
>5> $+
n+.
In these expressions we have
not s p e c ifie d the m icroscopic form o f x> b u t have assumed th a t x «
as is reasonable f o r paramagnetic systems.
1>
Equations (4 .6 ) in d ic a te
th a t the (+) p o la riz a tio n propagates w ith r e la t iv e ly l i t t l e
damping
w h ile the ( - ) p o la riz a tio n is s tro n g ly attenuated and almost t o t a lly
re fle c te d .
From the form o f a+ above we see th a t a t fie ld s away from
EPR ( i . e . , where
x|» x+ «
1) the d isp e rsio n is s tro n g ly dependent on
the e le c tro n co n cen tra tio n n, and may thus be used to determine th is
parameter.
With n known, the damping constant e+ gives a measure o f
|u> t | = yB, where y is the e le c tro n ic m o b ility .
Thus measurements o f
the h e lico n d isp e rsio n and damping away from EPR provide a co n ta ctle ss
method o f determ ining the e le c t r ic a l p ro p e rtie s o f the m a te ria l, which
may then be used to c a lc u la te the s u s c e p tib ility x*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
One very in te r e s tin g aspect o f Equations (4 .6 ) is th a t in the
expressions f o r a+ and 3+ the e le c tro n co n cen tra tio n appears as a
m u lt ip lic a t iv e fa c to r o f x | and x+» re s p e c tiv e ly .
For example, i t can
be seen from Equations (4 .6 ) fo r 3+ th a t the c o n trib u tio n o f the
magnetic resonance to the h e lico n damping is p ro p o rtio n a l to the
product v/n x+*
The e le c tro n s thus a c tu a lly serve to enhance the
stre n g th o f the resonant EPR in te r a c tio n , so th a t by incre a sing the
e le c tro n c o n c e n tra tio n , the resonance absorption i t s e l f increases.
B.
Experimental Results
In th is s e c tio n , we w i l l present the re s u lts o f h e lic o n -e x c ite d
EPR stu d ies in Hg.
Mn Se f o r values o f x < 0 .1 .
X
We have d iv id e d the
dynamic magnetic s u s c e p t ib ility re s u lts in to two s e c tio n s :
the very
low manganese co n ce n tra tio n data, where fin e and h yp erfin e s tru c tu re
must be taken in to account, and the h igher co n cen tra tio n data, where
the s tru c tu re is smeared o u t due to broadening, so th a t the simple
tw o -le ve l system is adequate.
H elicon transm ission stu d ies enable us to make co n ta ctle ss
measurements o f the e le c t r ic a l parameters o f the m a te ria l.
The
technique which we s h a ll use is Rayleigh in te rfe ro m e try [8 ] , in which
one beam o f microwaves passes through the sample and then in te rfe re s
w ith a reference beam bypassing the sample (see Figure 3 .8 ).
By
s h if tin g the phase o f the reference beam, in fo rm a tio n on the phase
o f the tra n s m itte d beam is obtained which y ie ld s a+ , the d isp e rsion
c o e ffic ie n t.
The am plitude o f the in te rfe ro g ra m gives in fo rm a tio n on
the a tte n u a tio n c o e ffic ie n t 3+ .
gram, obtained f o r Hg.
1" X
An example o f a Rayleigh in t e r fe r o ­
Mn Se w ith x = 0.0003 a t 4.2 K is shown in
X
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
i
(/)
C
3
180
.ri
o
<
o
270
cn
UJ
o
z
UJ
ce
90
UJ
u_
a:
UJ
Iz
2.0
M AGNETIC
Figure 4 .1 .
3.0
4.0
5.0
6.0
FIE LD (tesla)
Rayleigh in te rfe ro g ra m fo r HgMnSe a t 4.2 K. x = 3 • lO- 4 .
The fo u r traces were taken w ith the phase o f the reference
arm s e t a t 0 °, 90°, 180° and 270°. The dotted lin e
corresponds to the in te rfe ro g ra m envelope.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
Figure 4 .1 .
The non-monotonic behavior o f the inte rfe rog ra m envelope
(d o tte d lin e s in Figure 4 .1 ) is due to the presence o f Fabry-Perot
dimensional e ffe c ts .
We l i s t in Table 4.1 the Hg^_xMnxSe samples which we have
studied and t h e ir e le c tr ic a l parameters obtained from an a n alysis o f
the h e lico n data.
The high temperature in fo rm a tio n may have been
taken a t temperatures between 75 K and 95 K, depending on the sample.
As can be seen from Table 4 .1 , the e le c tro n concentration remains
n e a rly constant fo r HgMnSe in th is temperature range, in d ic a tin g
e x tr in s ic c o n d u c tiv ity .
There is a small but system atic decrease,
however, in the m o b ility o f the e le c tro n s as the sample is heated.
This drop in m o b ility is in agreement w ith dc e le c tr ic a l studies on
th is m a te ria l
[3 7 ].
band gap o f Hg,
1" A
As was mentioned in the previous s e c tio n , the
Mn Se opens above about 6% manganese co n cen tra tio n .
X
The opening o f the gap re s u lts in a s ig n ific a n t drop in the e le c tro n
co n ce n tra tio n , as can be seen fo r the 7% and 9% samples in Table 4 .1 .
1.
a.
EPR and Dynamic Magnetic S u s c e p tib ility
2+
Low Mn
Concentrations (x < 0 .0 0 5 ).
For manganese concen­
tra tio n s below about % a t. % a simple tw o -le v e l spin system is
inadequate to describe the observed EPR.
fin e and h y p e rfin e s tru c tu re as w e ll.
We must be concerned w ith
In the low co n cen tra tio n s, the
manganese ions can be assumed to be independent o f each o th e r, a ctin g
as is o la te d paramagnets in the HgSe host la t t i c e .
The most s tr ik in g aspect o f the low -x data is the presence o f
s ix w e ll-re s o lv e d h yp e rfin e lin e s as shown in Figure 4 .2 .
By measuring
the s p li t t in g between the lin e s , we have obtained a value o f 60 G fo r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
Table 4 .1 .
E le c tr ic a l p ro p e rtie s o f the Hg-j_xMnxSe samples used in
th is in v e s tig a tio n .
4.2 K
Sample
2+
Mn
Cone, x
High T
High T
y(m2/Vs)
n ( x l0 23/m3)
y(m2/V s)
.9
11.6
1.3
10.6
n ( x l0 23/m3)
4.2 K
S 25 B2
0
S 32 B2
5 x 10‘ 5
8.7
7.6
• • •
• • •
S 27 C2
3 x 10"4
2.5
9.3
2.4
7.2
S 33 D2
8 x 10"4
1.6
7.4
• • •
• • •
S 33 B2
3 x 10"3
5.2
8.5
5.3
7.4
S 34 B1
7 x 10"3
1.8
9.6
1.7
9.1
S 14 A
2 x 10“ 2
1.0
7.0
1.0
7.0
S 19 B3
3 x 10“ 2
3.6
9.5
3.6
8.0
S 18 E9
5 x 1 0 '2
2.4
10.5
2.1
7.4
S 23 2A
7 x 10"2
.2
7.0
.2
2.7
2194 D2
9 x 10“ 2
.4
4.4
.4
2.3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
i
'90
o
_l
<
2
o
CO
Ll I
o
z:
lj
o:
UJ
u_
cn
UJ
i—
MAGNETIC
Figure 4 .2 .
FIELD (tesla)
Rayleigh in te rfe ro g ra m f o r HgMnSe w ith x = 3 • 10_tf a t
2.5 K showing h yp e rfin e s tru c tu re in the EPR spectrum.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52
A, the h y p e rfin e s p lit t in g constant.
This agrees w ell w ith the values
2+
obtained by conventional EPR measurements f o r Mn
in CdTe [3 8 ,3 9 ].
Fine s tru c tu re s p lit t in g remained unresolved in a ll o f our EPR
2+
data o f HgMnSe regardless o f Mn
co n cen tra tio n and magnetic f i e ld
o rie n ta tio n w ith respect to the c ry s ta l axes.
We ascribe the absence
o f fin e s tru c tu re to the presence o f the h ig h ly mobile e le ctro n s in
the c r y s ta l.
I t has been shown in the case o f d ilu te a llo y s o f
magnetic ions in metals ( e .g ., Mg:Gd) th a t the fin e s tru c tu re o f the
3+
Gd
ion collapses as a r e s u lt o f the s p in -s p in exchange in te ra c tio n
w ith the conduction e le c tro n s [4 0 ].
In th is process, re fe rre d to as
"exchange n a rro w ing ," encounters w ith fre e e le ctro n s cause the
s a t e l li t e fin e s tru c tu re liv e s to weaken o r disappear com pletely by
" s c a tte rin g in " to the c e n tra l lin e .
In our case (Mn
2+
) th is would
mean th a t the exchange narrowing process due to the fre e e le c tro n s
causes the - j *-*■ + j tr a n s itio n to grow a t the expense o f the
5
- f ^
~
3
3
1
1
3
3 5
and 2 ^ 2
tr a n s itio n s .
I t is also
po ssib le th a t the random paths o f the omnipresent m obile e le c tro n s tend
to screen o r smear o u t the c ry s ta l f ie ld s perceived by the manganese
ion s.
That the e lim in a tio n o f fin e s tru c tu re in the EPR spectrum is
due to the
presence o f the e le c tro n s is supported by the fa c t th a t in
in s u la tin g
Cd, „Mn Te (see Chapter V I) and in undoped Hg. Mn Te
1“ X
X
1“ X
X
pi o
(n ^ 2 x 10 / m ) [4 1 ], samples w ith e q u a lly low manganese concentra­
tio n s e x h ib it w e ll-re s o lv e d fin e s tru c tu re .
We show some o f the data
f o r HgMnTe in Figure 4.3 where a m ixture o f fin e and h y p e rfin e s tr u c ­
tu re is present.
The absence o f fin e s tru c tu re in HgMnSe is an
in te r e s tin g example o f where an e le c tr ic a l p ro p e rty , the fre e c a r r ie r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
II
HgMnTe
Z
o
CO
CO
CO
z
<
cr
M A G N E T IC FIE L D ( T )
Figure 4 .3 .
EPR spectrum o f undoped HgMnTe showing an incom pletely
resolved m ixture o f fin e and hyp erfin e s tru c tu re .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
co n ce n tra tio n , m odifies a magnetic one, the dynamic magnetic suscept­
t
ib ilit y .
Once the e le c tr ic a l parameters have been determined from the
p a rts o f the in te rfe ro g ra m away from EPR, they may be used to q u a n tita ­
t iv e ly c a lc u la te the real and im aginary p a rts o f the dynamic magnetic
s u s c e p tib ility [8 ].
In Figures 4.4 and 4.5 we show the re a l and
imaginary p a rts o f the s u s c e p t ib ility , re s p e c tiv e ly , fo r a sample w ith
x = 0.0003 w ith the dc f i e ld a pplied along the [100] d ire c tio n a t
temperatures from 2.5 K to 40 K.
N eglecting the unresolved fin e
s tru c tu re , the hyp erfin e peaks o f x+ may be represented as the sum o f
s ix terms, each behaving according to the Bloch equations and each
having a d if fe r e n t nuclear quantum number.
Equation (2.14) fo r x"
then becomes (in the form o f Equation (2 .15))
5/2
<
‘
r
V
T2
Z
— r -5 — r r r
•
m = -5/2 1 + <“ - V > T2
I
mj
(4 -7)
where
=
“o
ge(B+mjA)-2mQ .
(4 .8 )
I
Here A is the hyp erfin e s p lit t in g co nstant.
Equation (4 .7 ) fo r x+
assumes th a t we are s t i l l in the lin e a r p o rtio n o f the H vs B curve,
where M is the m agnetization o f the sample.
Note in Figure 4 .5 , th a t
even a t th is low value o f x , the in d iv id u a l lin e s broaden as the
temperature f a l l s .
While the resonance is stronger a t 2.5 K, the
hyperfine peaks in Figure 4.5 are o n ly about 50% resolved.
A t 10 K,
in c o n tra s t, although the in d iv id u a l lin e s are weaker, they are about
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
1
0.5
40 K
0.0
r\
-0.5
0.0:
A
A
O
2
10K
A
/
v
-0.5
m
H
0.
UJ
o
CO
A I. T -T “
Xi “
-0.5
UJ
cc
I
I
2.5 K |
I
-1.5 h\
I
\
I
\
i
\
I
2.0
"
\ i
w
1.0
\
\
\
\
A/ \
\
1 \ / ‘
\V II *+ ■ I I1
I
•
i
i
4— t----- 1i
i
i
i
\ 1
T T
\
i
u\ /
V
\
i
1
\ I
\ /
i
i
i - V A
I
-
I
/ .-N " ' A
\ 1
v ./;
I
I
3
\\
!
I \\ ;I
-
-
/ V77 V / A
V
/ '
^-v _____'
! \
4.2 K
____ f
^
0.0
CO
<
v
\
-0.5
/
/
'
0.0i
V
A
A
/
\/
-
1
1.23
1.24
1.25
M A G N E T IC
Figure 4 .4 .
1.26
1.27
F IE L D ( T )
Real p a rt o f the dynamic magnetic s u s c e p t ib ility fo r
HgMnSe w ith x = 3 • 10_t+ a t several tem peratures. The
curves have been displaced v e r t ic a lly f o r c l a r i t y .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
1.8
t\
i
I
i
i
l
I
i
i
i
I
i
i
2.5 K
1.6
1.4
O
O
1.2
\
09
hQ_
UJ
O
to
13
to
>-
cr
1.0
i
a
0.8
a
i\
i \
CD
;
0.6
“ ■i !
'V
i I
H \ i
! I
0.4
0.2
j
"
ii
I
i
i
!
i
1
»•
!
!V
I
i
i « /I 1
/ !
\
I
i
i
1
ii
I !
\
i
.
i
I
l/\
a \\
i
i
11
!
/A ' j A U /
.
\
\
i
i
A
i
i
i i
i i
\ i
i !
/
/
i
!
i
i
i
iU
I i i
I I
I I
I I
i■ 1
i
M
'i
! 1 ii
ii
11
<
z
<
1!i
I! i
I
I! M
;i
/ X
II
I I
I I
I!
1 i i
*I \ i
ii
1
f\
M
i
ti
4.2 K\|
\
\
I
I
i
i
i
i
I
I
i
i
ii
\
i!
A\
IM \
!/'
i i I i i I \ { Ji/ \ \ V/i i ill
1l1'i
•' 1 \ I I I
40K< [
I
I
1
/ i
I ...\
/.•
—•
‘- i
1.23
__
1.24
M A G N E TIC
Figure 4 .5 .
I
i
'
I
\
Vsi
^v-7 i//V rv n U '-\
/ /
0.0
I
•••••
\ V
I____________ I____________ K
1.25
F IE L D
1.26
1.27
(T )
Imaginary p a rt o f the dynamic magnetic s u s c e p t ib ility fo r
HgMnSe w ith x = 3 • 10_tf a t several tem peratures.
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57
80% resolved.
As the temperature is ra ise d fu r th e r , the am plitude
continues to decrease, but the re s o lu tio n increases u n til the e n tire
fe a tu re vanishes a t about 90 K.
In te g ra tin g x+ over B, o r e q u iv a le n tly over coQ y ie ld s a constant
times xQ fo r a ll the spins independent o f 7^.
From Equation (2.14) we
have
/
x+dB +
/
V
o
T2
~2~2
du0
=
*»x0
(4 .8 )
=
6.91 x 1011 xQ
Thus the area under the x" curves in Figure 4 .5 is a measure o f x0 fo r
th a t given tem perature.
I f we assume th a t the ions are n o n in te ra c tin g
2+
(which is a good assumption fo r these very low Mn
c o n c e n tra tio n s ),
the s t a t ic s u s c e p t ib ility is given by
■■
*o
2
■
(4 -9)
where N$ is the number o f spins per u n it volume, yQ and kg are the
p e rm e a b ility o f fre e space and the Boltzmann c o n s ta n t, re s p e c tiv e ly , T
is the temperature and
is the e ffe c tiv e magnetic moment o f the
manganese io n , which we take to be y ^
= 5 y g ( f iv e unpaired
e le c tro n s , each c o n trib u tin g one Bohr magneton).
So once we have
found xQ by in te g r a tin g , Equation (4 .9 ) can be used to c a lc u la te Ng
and thus x , the mole fr a c tio n o f manganese in the c r y s ta l.
This is
very useful f o r the low co n ce n tra tio n s, since o th e r methods o f d e te r­
mining com positions a t such low values o f x ( e .g ., d e n sity measurements)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58
become u n re lia b le .
Having a method to determine the manganese content
in a p a r tic u la r sample is e s p e c ia lly im portant in Bridgman c ry s ta ls o f
the mercury compounds, where lo n g itu d in a l concentration gradients are
p a th o lo g ic a lly high.
For example:
in Sample S32B2, fo r which x was
-5
nom inally equal to 3 x 10, xQ measurements gave a value
-5
o f 5 * 10 .
Figure 4.6 shows the temperature dependence o f the s ta tic s u s c e p tib il2+
i t y fo r the low Mn
concentration samples.
The s tr a ig h t lin e s im ply
Curie law behavior fo r these c o n ce n tra tio n s, in keeping w ith our e a rlie r
assumption o f n o n -in te ra c tin g sp in s.
the in te g ra tio n
over
c u ttin g o u t the
area under the curve and sim ply weighing the paper on
a precise balance.
areas.
(
v
Two methods were used to perform
in Equation (4 .8 ).
The second
The f i r s t method involved
used a planim eter designed to measure
The two methods agreed to b e tte r than one percent.
Using the microwave h e lico n transm ission technique we were able
to observe the EPR w ith i t s s ix h yp erfin e peaks in samples w ith mangan-5
ese co ncentrations as low
as x =5*10
.
For th is lowest concentration
sample, the resonance was
barely measurable a t 4.2 K, and only by
reducing the temperature to about 1.3 K could r e lia b ly accurate data
be taken.
2+
To examine lower Mn
co n c e n tra tio n s , th ic k e r samples would
be needed, which would r e s u lt in less microwave transm ission.
A more
s e n s itiv e d e te c to r and/or the use o f quarter-wave pla tes [42] would
then be necessary to d e te c t the s ig n a l.
In th is low concentration range, the s u s c e p tib ility is d ir e c t ly
p ro p o rtio n a l to the number o f spins present in the sample.
As x
increases, the s u s c e p tib ility increases, as shown fo r x" in Figure 4 .7 .
('
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
8.0
5x10
7.0 -
-4
•O
x
6 .0
>
I-
GO
t
4.0
Ld
O
3
3.0
GO
8 x 10
LU
C /)
cr
LU
>
2
3 x 10
0.0
0
5
10
15
20
25
TEMPERATURE (K)
Figure 4 .6 .
Temperature dependence o f the inverse s ta tic s u s c e p tib ility
fo r several lo w -co n cen tra tio n samples. The s tr a ig h t lin e s
in d ic a te C u rie -lik e behavior.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
i
X= 3-10",
T = 2.5 K
1.6
1.4
O
O
x
>
ICD
I-
QL
UJ
<J>
GO
ID
CO
>
o:
<
z
o
<
2
0.8
-5
X = 5 • 10
T = 1.3 K
0.6
0.4
0.2
0.0
’ 1.22
1.23
1.24
M A G N E T IC
Figure 4 .7 .
1.25
1.26
1.27
1.28
F IE L D ( T )
Imaginary s u s c e p t ib ility fo r samples w ith x = 3 • 10-l+ a t
2.5 K and x = 5 • 10"5 a t 1.3 K showing th a t x is d ir e c t ly
p ro p o rtio n a l to x in th is co n cen tra tio n range.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
^
Had the two samples been measured a t the same tem perature, the
d iffe re n c e would be even more s t r ik in g .
When discussing Equation (4 .6 ) fo r B+ above, i t was pointed out
th a t the stre n g th o f the EPR absorption was a c tu a lly enhanced by the
presence o f a la rg e number o f e le c tro n s .
As was mentioned in Chapter
I I I , the HgMnSe samples are annealed, which lowers the e le c tro n
c o n c e n tra tio n .
HgMnSe, however, p a th o lo g ic a lly tends to lose i t s
annealed p ro p e rtie s , o fte n q u ite ra p id ly .
In one sample the e le c tro n
co n ce n tra tio n increased by a fa c to r o f fo u r o v e rn ig h t.
In Figure 4.8
we show the EPR in te rfe ro g ra m before and a fte r th is change in e le c tro n
c o n c e n tra tio n .
The increased value o f n is evidenced by the reduced
h e lic o n period o f Figure 4.8b.
Since the number o f spins is the same,
the measured s u s c e p t ib ility must, o f course, be the same.
{
Note,
however, th a t the s tre n g th o f the resonance is d ra m a tic a lly increased
in the case corresponding to the la rg e r n.
We b e lie ve th a t th is is
the f i r s t time th a t th is enhancement o f EPR by an increase in the
e le c tro n co n cen tra tio n has been unambiguously demonstrated e x p e ri­
m e n ta lly .
F in a lly , w ith so few spins present in these low co n cen tra tio n
samples, the a n ti ferrom agnetic in te ra c tio n between them is not re a d ily
apparent.
But i t is im p o rta n t to n o tic e th a t even in th is d ilu te l i m i t
we can already begin to observe the lin e broadening process th a t w il l
la t e r ( a t higher values o f x) become com pletely dominant.
As has
already been pointed o u t, the h yp e rfin e lin e s broaden (as evidenced by
a decrease in re s o lu tio n ) as the temperature decreases.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2 July 1981
I July 1981
z
o
2
z
<
<r
H
in
1.0
l.l
1.2
1.3
MAGNETIC
Figure 4 .8 .
Rayleigh interferogram s fo r a sample w ith x = 3 • 10-l> on two consecutive days showing the
enhancement o f EPR due to an increase in the e le c tro n co n ce n tra tio n . The two in te r fe r o ­
grams were taken on the same sample a t the same temperature. The increased e le c tro n
co n cen tra tio n is evidenced by the decreased h e lico n period in 4.8 b.
ro
63
2+
Interm ediate Mn
b.
Concentrations (0.005 < x < 0 .1 0 ).
increases above 0.005, the s ix hyp erfin e lin e s broaden to form a s in g le
lin e due to in te ra c tio n s between the manganese ion s.
With fu r th e r
increase in the manganese c o n te n t, th is broadening becomes very
dra m atic, and is accompanied by a gradual decrease in the resonance
s tre n g th .
Since HgMnSe w ith less than 10% manganese contains a la rg e
number o f h ig h ly mobile e le c tro n s , we can continue to employ the method
o f h e lic o n -e x c ite d EPR to study the dynamic magnetic s u s c e p tib ility in
these samples.
A t concentrations near 10%, however, the resonance a t
low temperatures becomes too broad and too weak fo r q u a n tita tiv e
measurement, thus e s ta b lis h in g a p ra c tic a l l i m i t f o r the usefulness o f
the h e lico n method.
(
Typical h e lico n Rayleigh in te rfe re n c e data fo r a 2% sample a t
75 K are shown in Figure 4 .9 .
From the data we can c a lc u la te the real
and im aginary p a rts o f the dynamic magnetic s u s c e p tib ility [8 ].
We
show the c a lc u la te d values f o r th is 2% sample a t several temperatures
in Figures 4.10 and 4.11.
As the temperature is ra ise d above 4.2 K,
the resonance lin e both weakens and narrows in a manner s im ila r to th a t
observed by M u llin e t al_. f o r a 6% sample [2 8 ].
The weakening o f the
resonance w ith in cre a sin g temperature is due to the normal temperature
dependence o f xQ.
The la rg e lin e w id th a t low temperatures in d ic a te s
th a t the exchange in te r a c tio n between the manganese ions is already
q u ite strong a t x = 0.02.
This exchange in te ra c tio n is fo rm a lly
represented through the s p in -s p in re la x a tio n time
in Equation (2.14).
The EPR lin e is seen to be Lorentzian in n a tu re, w ith the d is p e rs iv e
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
As x
2 % HgMnSe
T =75 K
cn
,90
0.4
0.6
1.4
0.8
MAGNETIC
Figure 4 .9.
F IE L D
(T )
Rayleigh in te rfe ro g ra m fo r a HgMnSe sample w ith x = 0.
a t 75 K.
(
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
65
0.20
2 % HgMnSe
•
0.15
4.2 K
O 30 K
SUSCEPTIBILITY
0.10
0.05
0.00
REAL
-0 .0 5
-0.10
-0.15
-
0.20
1.10
1.15
1.20
MAGNETIC
Figure 4.10.
I
.25
.30
.35
40
FIELD ( T )
Real p a rt o f the dynamic magnetic s u s c e p t ib ility fo r a 2%
HgMnSe sample. The p o in ts are measured data and the lin e s
are the best f i t s obtained by f i t t i n g the real and imag­
in a ry p a rts sim ultaneously.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
0.35
2 % HgMnSe
0.30
>
h-
0 .2 5
_J
m
a.
0 .2 0
>
(T
0.15
LJ
u
V)
(
<
Z
o
<
2
0.10
0.05
0.00
1.10
1.15
1.20
1.25
1.30
.35
.40
MAGNETIC FIELD ( T )
Figure 4.11.
Imaginary p a rt o f the dynamic magnetic s u s c e p tib ility fo r
a 2% HgMnSe sample. The p o in ts are data and the lin e s
are computer f i t s .
('
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
e ffe c ts (re a l p a rt o f the s u s c e p tib ility ) extending fo r several k ilo -
(
gauss from the center o f the resonance w h ile the a b sorptive e ffe c ts
(im aginary p a rt) have a considerably narrower range.
By f i t t i n g
Equation (2.14) fo r x+ to our data (we f i t both the
real and im aginary p a rts s im u lta n e o u s ly ), we get values o f x0 and l ^ .
In Figures 4.10 and 4.11 the p o in ts represent the measured values o f
the dynamic magnetic s u s c e p t ib ility , obtained from the Rayleigh data
such as th a t shown in Figure 4.9 fo r the 21 sample a t 75 K.
The s o lid
lin e s are the "be st f i t " th e o re tic a l values o f x 1 and x" obtained w ith
the same parameters xQ and T
We id e n tify the parameter xQ as the dc o r s t a t ic magnetic
s u s c e p t ib ility .
U sually s t a t ic s u s c e p tib ility measurements are made
a t fie ld s o f a few gauss, whereas ours are made a t 1.25 T.
(
Thus our
s u s c e p t ib ility must, s t r i c t l y speaking, be understood as a measure o f
the m agnetization (M = xQH) a t th a t la rg e f i e l d , and corresponds to
the lo w - fie ld x0 o n ly in the range where M is lin e a r w ith H.
The
inverse o f our x0 is shown in Figure 4.12 as a fu n c tio n o f temperature
f o r x = 0.05.
Comparison w ith Figure 4.6 reveals th a t, w hile in the
case o f very low manganese concentrations we had seen C u rie -lik e
behavior in d ic a tin g l i t t l e
io n ic in te ra c tio n (Figure 4 .6 ) , fo r the
higher concentrations there is a s ig n ific a n t amount o f in te ra c tio n
between the ion s.
This in te ra c tio n is evidenced by the c h a ra c te ris tic
down-turn in the inverse s u s c e p tib ility which is seen in a ll DMS
s u s c e p tib ility stu d ies [4 ].
This fe a tu re has been ascribed by others
to the tendency o f the ions to form spin c lu s te rs as the temperature
is decreased [2 2 ].
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68
1400
5 % HgMnSe
1200
1000
>_J
9
8 00
Q.
LU
O
CO
3
CO
600
LU
to
cr
LU
>
z
-
400
200
0
20
40
60
80
100
TEMPERATURE ( K )
Figure 4.12.
Inverse s t a t ic s u s c e p t ib ility as a fu n c tio n o f temperature
fo r a 5% HgMnSe sample. The lin e is a guide fo r the eyes.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
In the range where x is a few p e rce n t, the c o n trib u tio n o f x to
the microwave a b sorption becomes extrem ely la rg e a t low temperatures
due to the ra p id ly in cre a sin g value o f xQ-
We i ll u s t r a t e the magnitude
o f th is e ffe c t in Figure 4.13 where the EPR is seen to com pletely
e xtin g u is h the Rayleigh transm ission around 1.25 T.
the data f o r a 2% sample a t 1.3 K.
Figure 4.13 shows
This to ta l e x tin c tio n o f the
he lico n sign a l by the EPR was observed in samples w ith values o f x from
0.003 to 0.02 a t low tem peratures.
In the extrem ely d ilu t e manganese co n cen tra tio n range, we re c a ll
th a t the s u s c e p t ib ility was d ir e c t ly p ro p o rtio n a l to x.
manganese was added, both xQ and x+ increased.
As more
Above about 2%
manganese, however, the in te r a c tio n between the ions becomes in cre a s­
in g ly im p o rta n t, and due to the a n ti ferrom agnetic nature o f th is
in te r a c tio n , xQ no longer increases as fa s t as x.
Since, in a d d itio n ,
the increase o f x is accompanied by a broadening o f the resonance, th is
leads to the behavior shown in Figure 4.14, i llu s t r a t in g th a t the
resonance s tre n g th va rie s in v e rs e ly w ith co n cen tra tio n above about 2%.
Note the sharp c o n tra s t between th is behavior fo r 2% and 5% samples a t
4.2 K, and th a t shown in Figure 4.7 f o r the very d ilu te l i m i t .
When the manganese co n cen tra tio n is increased above 6%, HgMnSe
undergoes a zero-gap semiconductor to open-gap semiconductor tr a n s i­
tio n .
This increase o f x is accompanied by a ra th e r ra p id disappearance
o f the h e lic o n -e x c ite d EPR, so th a t in the open-gap range the he lico n
method becomes p ro g re s s iv e ly less u s e fu l.
three cooperating fa c to rs .
This behavior is caused by
Above a c e rta in co n cen tra tio n (roughly
x = 0 .0 2 ), as more manganese is added, the a n ti ferrom agnetic
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
2 % HgMnSe
T = 1.3 K
Z
<
cn
h-
90
0.9
1.2
1.0
MAGNETIC
Figure 4.13.
1.3
1.4
1.5
FIELD ( T )
Rayleigh in te rfe ro g ra m fo r a 2% HgMnSe sample a t 1.3 K.
The a b sorp tive tra c e (phase = 0°) is com pletely e x tin ­
guished by EPR.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
J
0.35
HgMnSe
T=4.2 K
0.30
0.25
>
ICD
IQ. 0.20
lii
O
C/5
15
CO
>-
cr
•(
<
z
§
2
0.10
0.05
0.00
1.10
1.20
1.30
1.40
MAGNETIC FIELD ( T )
Figure 4.14.
Imaginary s u s c e p t ib ility fo r samples w ith x = 0.02 and
0.05 a t 4.2 K showing th a t x is in v e rs e ly p ro p o rtio n a l
to x in th is range.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
72
in te r a c tio n between the ions tends to lower the value o f xQ i t s e l f ,
thus making the resonance weaker.
In a d d itio n , as x incre a se s, the
re la x a tio n time T2 decreases, r e s u ltin g in broader lin e s .
F in a lly , as
was illu s t r a t e d in Figure 4 .8 , the in te n s ity o f EPR observed by the
h e lico n method is p ro p o rtio n a l to v^n, where n is the e le c tro n concen­
t r a t io n , and in the open-gap region (x > 0.06) the e le c tro n concentra­
tio n is much lower (see Table 4 .1 ).
Thus the combination o f a weak,
broad form o f x+ and a lower e le c tro n concentration leads to EPR
sig n a ls th a t are b a re ly d is c e rn ib le using the h e lico n method.
4.15 shows the resonance f o r a 9% sample a t 4, 8 and 40 K.
Figure
Note the
sharp c o n tra s t between the low temperature behavior in Figure 4.15 and
th a t shown in Figure 4.13 where the signal is t o t a l l y e xtinguished by
EPR.
In a d d itio n , the a n a ly s is o f the helicon EPR e ffe c t is complicated
by the fa c t th a t the w idth o f the EPR lin e is now comparable to the
he lico n p e rio d .
We conclude th e re fo re th a t the h e lico n method o f
e x c itin g and measuring EPR becomes u n re lia b le a t low temperatures fo r
the open-gap m a te ria ls .
EPR measurements on powder samples [43] may
prove to c o n s titu te a more p ra c tic a l technique fo r the study o f th is
co n ce n tra tio n range.
2.
EPR Linew idth
The w idth o f the resonance lin e in HgMnSe depends both on the
2+
Mn
co n cen tra tio n and on the tem perature.
For the low concentrations
where h yp e rfin e s p li t t in g is p re sen t, the in d iv id u a l h yp e rfin e lin e s
are separated by about 60 G (w ith the w idth o f the in d iv id u a l lin e s
being less than the s e p a ra tio n ), leading to an EPR spectrum o f to ta l
w idth about 350 G.
As the amount o f manganese is increased, the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
9% HgMnSe
Z
o
cn
00
5
cn
z
<
cc.
I-
T = 40 K
0.8
1.0
1.2
MAGNETIC
Figure 4.15.
1.4
1.6
i.8
2.0
FIELD ( T )
Rayleigh in te rfe ro g ra m traces fo r a 9% HgMnSe sample a t
4 K, 8 K and 40 K. The arrow marks the EPR p o s itio n .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
in d iv id u a l lin e s become broader than th e ir se p ara tio n , and the whole
spectrum coalesces in to a s in g le lin e whose w idth depends s tro n g ly on
the temperature and can be very much w ider than 350 G.
However, a t
high tem peratures, th is s in g le lin e narrows d ra m a tic a lly and can
a c tu a lly be less than the 350 G w id th o f the o v e ra ll h y p e rfin e spectrum.
Figure 4.16 compares x" f o r a 2% sample a t 75 K w ith x" fo r a 0.03%
sample a t 2.5 K, i ll u s t r a t i n g th is e ffe c t.
We ascribe th is behavior
to m otional narrowing [1 0 ].
The normal temperature dependence o f the EPR lin e w id th fo r a 5%
sample is shown in Figure 4.17.
The la rg e increase in lin e w id th a t
low temperatures has been reported in a ll o th e r DMS (see next c h a p te r),
and seems to be a u n ive rsa l fe a tu re c h a ra c te ris tic o f these m a te ria ls .
As has also been observed in o th e r DMS, the EPR lin e w id th increases as
the manganese c o n c e n tra tio n is increased a t a constant tem perature.
This increase, shown in Figure 4.18 a t 4.2 K, appears to be n e a rly
lin e a r w ith x.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
Figure 4.15.
Imaginary p a rt o f the s u s c e p tib ility fo r samples o f
HgMnSe w ith x = 0.02 a t 75 K and x = 3 • 10_1+ a t 2.5 K.
The v e r tic a l scale is a r b itr a r y , showing th a t the lin e ­
w idth ( f u l l w idth a t h a lf max) a t high temperatures can
a c tu a lly be less than the sum o f the s ix h yperfine peaks.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
>
_J
GO
hU
(f)
ID
a>
o
o
tn
</>
u.
O
w
(
O
CD
<
1.23
1.24
1.25
1.26
1.27
MAGNETIC FIELD ( T )
Figure 4.16.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
c
1.6 r -
5 % HgMnSe
o
JC.
u_
<
X
I-
<
0.8
X
(
IQ
^
0.6
_l
_1
X
u_
0.4
0.2
0.0
0
20
40
60
80
100
TEMPERATURE ( K )
Figure 4.17.
Linew idth ( f u l l w idth a t h a lf max) fo r a 5% HgMnSe sample
as a fu n c tio n o f tem perature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
2.0
HgMnSe
T = 4.2 K
Ll.
_J
<
X
X
I-
0
0.8
5
_J
_l
3
0.6
u.
0.4
0.2
0.0
COMPOSITION
Figure 4.18.
(%
Mn )
Linew idth a t 4 .2 K f o r Hgi_xMnxSe as a fu n c tio n o f mangan­
ese co n cen tra tio n x.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
£
CHAPTER V - WIDE-GAP MATERIALS
The d ilu te d magnetic semiconductors based on cadmium and zinc
compounds are wide-gap m a te ria ls , w ith energy gaps ranging from 1.6 eV
f o r CdTe to 3.6 eV fo r ZnS.
The existence o f th is larg e gap insures
th a t there are p r a c tic a lly no fre e c a r r ie r s a t low tem peratures, thus
rendering the m a te ria ls tra n sp a re n t to microwaves.
Under these
c o n d itio n s the d ie le c tr ic p e r m it t iv it y is a co n sta n t, t =
and
any microwave absorption o r d is p e rs io n e ffe c ts observed are due to the
in te r a c tio n o f the microwave magnetic f i e l d w ith the manganese ions in
(
the m a te ria l.
Thus we are provided w ith a remarkably uncomplicated
system in which to study EPR and i t s e ffe c ts .
In th is se ctio n we w i l l present m o d ific a tio n s which must be made
in the theory o f the dynamic magnetic s u s c e p t ib ility in order to b e tte r
e xp la in the experim ental re s u lts we have observed.
We w ill also
describe the method we have used to o b ta in our data and the advantages
i t enjoys over conventional EPR measurements.
In the experimental
se ctio n we w i l l present our r e s u lts , comparing them to the p re d ic tio n s
o f both the o r ig in a l Bloch model as o u tlin e d in
a
and the m odified version d e ta ile d in th is s e c tio n .
previous se ctio n
We w il l concentrate
On CdMnTe p r im a r ily , presenting re s u lts over the e n tire range o f
compositions p o s s ib le (x < 0 .7 ).
In a d d itio n we w il l s e le c t one
com position, x = 0 .1 , and w i l l c a rry o u t measurements on the o th e r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
^
wide-gap DMS w ith th a t value o f x to see how EPR o f Mn
2+
depends on the
host m a te r ia l.
A.
1.
Theory
M odified Bloch Model o f Dynamic Magnetic S u s c e p tib ility
In the previous chapter d ealing w ith zero-gap DMS, we developed
the theory o f the dynamic magnetic s u s c e p tib ility using the Bloch
model.
Since a ll o f our re s u lts were obtained fo r r e la t iv e ly low
manganese co n cen tra tio n samples, x < 0 .1 , the EPR lin e s were narrow and
the Bloch model was adequate.
For the wide-gap m a te ria ls we have studied samples w ith up to
68% manganese.
2+
As the amount o f Mn
is increased, the EPR lin e
broadens d ra m a tic a lly a t low tem peratures, u n til i t is no longer
(
observable (see, e .g ., [2 3 ]), as shown in Figure 5 .1.
This increase in
lin e w id th is due to a ra p id decrease in re la x a tio n time which re s u lts
from in c re a s in g exchange coupling between spins as x increases.
In the
case o f very s h o rt re la x a tio n tim es, o r e q u iv a le n tly , very broad EPR
lin e s , the Bloch model is no longer able to
adequately exp la in the
observed re s u lts and must be m odified [1 0 ].
In d e riv in g the o r ig in a l Bloch equations i t was
uT2
»
assumed th a t
1, i . e . , th a t the re la x a tio n process wasslow enough so th a t the
e q u ilib riu m m agnetization "seen" by the s p in s , ( i . e . , the m agnetization
to which these spins re la x ) is the tru e dc m agnetization MQz, which a t
low fie ld s -c a n be w ritte n x0Hqz .
the case where wT «
1.
Consider now the opposite extreme:
Because the re la x a tio n process is so f a s t, the
spins "see" the instantaneous magnetic f i e l d
as " s ta tic "
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
X
<
S
<
X
Cd,
_i
x
Ll.
.40
50
100
.53
150
200
.60
250
300
TEMPERATURE ( K )
Figure 5 .1 .
Linew idth ( f u l l w idth a t h a lf max) o f Cd^Mn^-Te as a
fu n c tio n o f temperature f o r several com positions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
because they s c a tte r before the to ta l f i e ld has a chance to change
p e rc e p tib ly .
The ft^ above is the magnetic f i e ld o f the microwaves.
The e q u ilib riu m m agnetization fo r the spins is th e re fo re the magnetiza­
tio n determined by the instantaneous ft, ft = xQftj and a fte r s c a tte rin g
the spins w i l l re la x to th is m agnetization.
An equation o f motion
recognizing th is manner o f re la x a tio n is [10]
(5 .1 )
where now ft = to ta l f i e l d = ftQ + ft^ w ith ftQ taken along the z - d ir e c ti on.
Note here th a t th is model considers the re la x a tio n process as is o tro p ic ,
i . e . , i t does not d is tin g u is h between T^ and T^.
Separating Equation
(5 .1 ) in to i t s components, we have
(
dMx
fM -H 1
_
Y(My H0-HzHy )
dt
.
dt
y
( - mx
W
x
-
) -
dMz
v < V y - MyHx>
dt
X
I
X
T
f v v
I T
(5 .2 )
fMz_xoHol
- \
T
We may w r ite Hq = u)q/ y where y is given as b e fo re:
y = ge/2m.
Assum­
ing the standard e "1ait time dependence fo r the m a g ne tiza tio n, the
d if fe r e n t ia t io n leads to
=
v c y v x o iv y
-
fMx_xoHx
(5 .3 )
M - y _H
■iuM
y
-
y(-M H +x„H H ) ' ' x o Ao o x '
y “Q y
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
83
Combining the equations f o r Mx and My gives
M -x H
-iuM ±
=
±yH0 [iM±- i x 0H±]
±
o ±
(5 .4 )
where M+ are am plitudes o f c ir c u la r ly p o la riz e d vectors in the x-y
plane:
K
and s im ila r ly f o r H+.
=
M+ ^ (x + iy ) ,
- /2
(5 .5 )
S olving Equation (5 .4 ) f o r M+ y ie ld s
-ia)T+iYHoT+l
X0H± [l± ia )oT]
(5 .6 )
1 -i (to+uo )T
Separating Equation (5 .6 ) in to i t s real and im aginary parts and d iv id ­
ing by H+, we a r r iv e a t the dynamic s u s c e p t ib ility :
M,
x±
=
h;
=
Xo [1+uo ( w q)T ]
ix_o)T
l+(u)+(o0 ) 2T2
1+(u)+o)0 ) 2T2
(5 .7 )
In comparing Equation (5 .7 ) w ith the s u s c e p t ib ility obtained from the
unmodified Bloch model (Equation ( 4 .8 ) ) , several d iffe re n c e s become
apparent.
As has already been pointed o u t, the present form assumes
s c a tte rin g to be is o t r o p ic , i . e . , i t does not d is tin g u is h between the
s p in - la ttic e re la x a tio n tim e
and the s p in -s p in re la x a tio n tim e Tg.
A more ta n g ib le change becomes n o tice a b le a t low and zero dc magnetic
f ie ld s .
The m odified form o f the dynamic magnetic s u s c e p tib ility
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
^
contains an a d d itio n a l "1" in the numerator o f x 1 and u instead o f cjq
in the numerator o f x"> so th a t n e ith e r the re a l nor the im aginary
p a rts o f x vanish a t zero dc f i e ld .
This in d ic a te s the presence o f
EPR absorption and d is p e rs io n even a t zero f i e ld .
As the value o f the
re la x a tio n time decreases, the "1" in x 1 e v e n tu a lly becomes the
dominant term.
Note, however, th a t fo r the case wT > 1 the p re d ic tio n s
o f the two models move c lo s e r and c lo s e r together as uoT increases.
The
behavior o f x as obtained by both the standard as w ell as the m odified
Bloch models is shown in Figure 5.2 fo r the case o f very broad lin e s .
As w il l be shown s h o r tly , using th is m odified form o f the Bloch theory
we have been able to e x p la in our data q u ite w e ll except fo r the highest
values o f manganese co n ce n tra tio n a t low temperatures.
2.
Faraday R otation and E l l i p t i c i t y
One o f the g re a te s t d if f i c u l t i e s in perform ing an EPR experiment
on DMS w ith in te rm e d ia te and high manganese concentrations is the
problem o f the very la rg e lin e w id th discussed above.
In a conventional
EPR experiment based on microwave a b sorp tio n , the resonance lin e in
these m a te ria ls broadens u n t il i t is no longer observable.
This
f a ilu r e o f the conventional technique is e s p e c ia lly u n fo rtu n ate in th a t
i t occurs as the spin glass region is approached.
Ju st when the
re s u lts become most in te r e s tin g , the e ffe c t by which they could be
studied disappears.
In order to overcome th is problem, we have developed a microwave
transm ission technique s e n s itiv e to both the d is p e rs iv e and a b sorp tive
aspects o f EPR.
The method is based on the Faraday r o ta tio n and
c
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85
Figure 5 .2 .
Comparison o f the real and imaginary parts o f the
dynamic magnetic s u s c e p tib ility as p re dicte d by the
Bloch and m odified-B loch th e o rie s .
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X
—
Bloch
—
Modified
Bloch
a
Figure 5.2.
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87
Faraday e l l i p t i c i t y th a t occurs as the microwaves pass through the
sample in the presence o f a magnetic f ie ld .
To describe our procedure, we must discuss wave propagation in
the m a te ria l.
From Section I I , we have the wave v e c to r given by
k±
where
atu re s.
=
c
^1+x±
% c v/* 7 ( 1+isx±)
(5 .8 )
remains constant and is o tr o p ic fo r wide-gap DMS a t low temper­
Separating k+ in to i t s re a l and im aginary p a rts gives
k+
a’+, + iS.+ 9
(5 .9 )
a'+
Consider a lin e a r ly p o la riz e d wave in c id e n t on the sample.
D ifferences in the ab sorp tio n c o e ffic ie n t B fo r the two c ir c u la r
p o la riz a tio n s cause the tra n s m itte d wave to be e l l i p t i c a l l y p o la riz e d .
This magnetic c ir c u la r dichroism is c a lle d Faraday e l l i p t i c i t y .
Likew ise, d iffe re n c e s in the d isp e rsio n c o e ffic ie n t a lead to Faraday
ro ta tio n where the major axis o f the tra n s m itte d wave is ro ta te d .
These e ffe c ts are shown in Figure 5 .3 .
For a sample o f thickness d,
the Faraday ro ta tio n 0p and Faraday e l l i p t i c i t y ep may be w ritte n
(5.10)
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
?Q V>*
\
A
\> e
_ *\0^ -i \,o
ro ^v.W \^e
,a
\vtfe
89
Sp
= \
(S+-B_ )d
( 5 . 11 )
=
where ep is the r a tio o f the minor to major axes o f the tra n s m itte d
wave.
S u b s titu tin g Equation (5 .7 ) f o r the s u s c e p tib ility in to the
above equations gives us the fo llo w in g a n a ly tic expressions fo r the
Faraday e ffe c ts :
0
F
-
i a
I <1 X - v
2 c
a xo
2 , 2 r 2 ,2 2 ,2 1n
I N I
1 “ 1J
— 2- - - - - - - - - - - - - - - - - 2- - - - - - - - - - - n . ( 2 2 \,2 ,2 , , 2,2
[l+(co -w0 )T 1 + 4(d0T
(5 i p )
3,3
d
e
F =
^o^
^
x°
n H J - jy ?
+
•
(5 a 3 )
Examination o f Equations (5.12) and (5.13) reveals several
in te re s tin g fe a tu re s .
From the numerator o f Equation (5.12) we see
th a t 6p = 0 when
A
2 - to2T2 - 1
=
0
(5.14)
or
to2
=
to2 - -^2"
i . e . , a t fie ld s lower than toQ = to.
,
(5.15)
I t is im portant to p o in t o u t th a t
the o r ig in a l ( i . e . , unm odified) Bloch model p re d ic ts th a t ep goes
through zero ( i . e . , x+ = x'_) o n ly fo r w
Figure 5 .2.
> to, as can be seen in
I f we now consider the low f i e ld form o f the Faraday
ro ta tio n , i . e . , when toQ «
to and toQ « y , we have
»p ' ? K v v "
.
•
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<5-16>
90
Thus when toT becomes less than one, the low f i e ld 0p w il l change sig n .
This change o f sign o f low f i e ld Faraday ro ta tio n f o r very s h o rt
re la x a tio n times is again not p re d icte d by the o r ig in a l Bloch model.
Since both 6p and ep have the same dependence on the sample
thickness and on x0 > by ta k in g the r a tio o f the e ffe c ts , we o b ta in
something which is independent o f these parameters:
e7 = “ O
F
cj T
h i
~
- u)qT - 1
•
(5.17)
One f in a l aspect o f the present study o f Faraday e ffe c ts remains
to be discussed.
Our measurements on slabs reveal lin e d is to r tio n s due
to geom etrical in te rfe re n c e .
This is e a s ily understood when we
re a liz e th a t as x' changes, the " o p tic a l le n g th " o f the sample changes,
seeking—o r moving away from --a Fabry-Perot resonance.
We found th a t
these e ffe c ts could be avoided by using samples in powder form.
This
procedure, however, has the disadvantage in th a t the thickness o f the
sample d must be replaced by an e ffe c tiv e thickness dgpp.
We c a lc u la te
dgpp as fo llo w s :
de f f
pA
(5.18)
where M is the mass o f the powder, A is the c ro s s -s e c tio n a l area o f
the waveguide and p is the d e n s ity o f the m a te ria l which is a fu n c tio n
o f the manganese co n ce n tra tio n x.
The e ffe c tiv e thickness corresponds
to the thickness o f an e q u iv a le n t s o lid sample o f the same m a te ria l
com pletely f i l l i n g
the cross s e c tio n o f the waveguide.
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91
B.
Experimental Results
In th is se ctio n we w i l l present our re s u lts f o r CcL
J. “ X
Mn Te over
X
the e n tir e a v a ila b le range o f manganese concentrations (x < .7 ) .
We
w i l l d iv id e these data in to three se ctio ns f o r convenience o f presen­
ta tio n .
For the low values o f x , coT »
1 and the o r ig in a l Bloch model
can be used to adequately describe the Faraday e ffe c ts we observe.
As
the manganese co n te n t is increased, the re la x a tio n tim e decreases
ra p id ly and the m odified form o f the Bloch theory must be used.
F in a lly , a t low temperatures and the h ig h e st values o f manganese
c o n c e n tra tio n , th e re emerge c e rta in new fe a tu re s which even the
m odified form o f the Bloch model f a i l s to e x p la in .
These new fe a tu re s
may in f a c t be present in the o th e r cases as w e ll, but t h e ir presence
is masked by the much la r g e r , normal paramagnetic behavior.
a d d itio n , we w i l l present data fo r the o th e r wide-gap DMS:
Cd1 Mn S, Zn.
i“ a
X
1"X
c o n c e n tra tio n :
Mn Te, Zn.
X
X“ X
x = 0 .1 .
Mn Se, and Z.
X
X X
In
Cd,
1 "X
Mn Se,
X
Mn S, a ll f o r one manganese
X
Thus we w i l l have presented in fo rm a tio n
about one DMS over i t s e n tir e range o f com position and about one
co n ce n tra tio n f o r a ll wide-gap DMS.
1.
Cd,
Mn Te:
X“ X
X
The "Bloch Model" Region
For low con cen tra tio n s o f manganese (x < 0 .1 5 ), CdMnTe is
paramagnetic a t a l l tem peratures.
In th is re g io n , EPR is c h a ra c te r­
ized by s tro n g , r e la t iv e ly narrow lin e s .
O seroff has s u c c e s s fu lly
made conventional EPR measurements on DMS in th is range [2 3 ,2 4 ].
to the la rg e e ffe c ts , our s e n s itiv e measurement techniques are not
necessary f o r the observation o f EPR.
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Due
92
When the e ffe c ts are la rg e , we can observe them using lin e a r
p o la riz a tio n w ith the d e te c to r/a n a ly z e r s e t a t 0 °, 45°, 90°, and 135°
from the in c id e n t p o la r iz a tio n .
Data o f th is type is shown in
Figure 5.4 fo r a 10% CdMnTe sample.
As can be seen in the Appendix,
the Faraday e ffe c ts may be e x tra cte d from the lin e a r p o la riz a tio n data.
This w i l l serve to i ll u s t r a t e , in the co n te xt where EPR is w e llunderstood, the techniques which we must use la t e r .
We show the
Faraday r o ta tio n and e l l i p t i c i t y in Figures 5.5 and 5.6 fo r the 10%
sample a t several tem peratures.
As the sample is warmed, the reson­
ance narrows and weakens due to an incre a sing re la x a tio n time and a
decreasing s t a t ic s u s c e p t ib ilit y , xQ» re s p e c tiv e ly .
Figure 5.7
shows I / T 2 as a fu n c tio n o f temperature f o r the 10% sample.
Since the
lin e w id th o f the resonance is in v e rs e ly p ro p o rtio n a l to the re la x a tio n
(
tim e , th is is e q u iv a le n t to a graph o f lin e w id th versus tem perature.
The inverse s t a t ic s u s c e p t ib ilit y , l / x Q> is shown in Figure 5 .8.
By
e x tra p o la tin g from the high temperature data, we o b ta in a Weiss
24-
constant o f 0^ = -21 K fo r th is Mn
co n c e n tra tio n .
The negative
value o f the Weiss constant reveals th a t the in te ra c tio n between the
manganese ions is a n ti fe rro m a gn e tic.
The values o f 7^ and x0 shown in Figures 5.7 and 5.8 were
obtained by computer f i t t i n g the data to the o r ig in a l Bloch equations
as developed in Chapter I I .
In th is range o f manganese co n c e n tra tio n s ,
m o d ific a tio n o f the Bloch model is unnecessary since wT »
1.
F it t in g
to the m odified equations y ie ld e d id e n tic a l parameters, w ith the
q u a lity o f the f i t being n e a rly the same.
("
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93
(
10% CdMnTe
T = 4.2 K
Z
o
cn
v>
z
cn
y = 45
Z
<
(T
I-
y = 135
y = 90
0.6
1.0
1.4
1.8
MAGNETIC FIELD ( T )
Figure 5 .4 .
Linear p o la riz a tio n data fo r 10% CdMnTe a t 4.2 K. y is
the angle between the in c id e n t p o la riz a tio n and the
d e te c to r/a n a ly z e r.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
i
0.15
10 % CdMnTe
4.2 K
Z
o
i-
s
o
<r
1
q:
<
£
0.8
1.0
1.2
1.4
1.6
1.8
MAGNETIC FIELD ( T )
Figure 5 .5 .
Faraday ro ta tio n fo r a 10% CdMnTe sample a t several temper­
a tu re s . Points are measured data. Lines are the best f i t s
obtained by computer f i t t i n g the ro ta tio n and e ll i p t i c i t y
sim ultaneously.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
0.22
10% CdMnTe
• 4.2 K
0.20
0.18
□ 32 K
0.16
£
0.14
O
£L 0.12
_J
-I
UJ
0.10
5
Q
< 0.08
<E
12
0.06
0.04
0.02
0.00
0.6
0.8
1.0
1.2
1.4
1.6
1.8
MAGNETIC FIELD ( T )
Figure 5 .6 .
Faraday e l l i p t i c i t y f o r the 10% CdMnTe sample a t several
tem peratures. Points are data and lin e s are computer
f i ts .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
10% CdMnTe
o
O
x
0.9
T*
in
—
0.8
UJ
5
I-
0.7
Z
o
0.6
6
X
<
—I 0.5
LlI
tr
LtJ
0.4
V)
DC
g
0.3
Z
0.2
0.1
0.0
20
40
60
80
.100
TEMPERATURE ( K )
Figure 5 .7 .
Inverse re la x a tio n tim e fo r the 10% CdMnTe sample as a
fu n c tio n o f tem perature. The p o in ts correspond to re la x
a tio n times obtained as f i t t i n g parameters and the lin e
is a guide fo r the eyes.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
t
2000
10% CdMnTe
1800
1600
1400
I - 1200
Pr 1000
800
> 600
400
200
0
20
40
60
80
100
TEMPERATURE ( K )
Figure 5 .8 .
Inverse s t a t ic s u s c e p tib ility fo r the 10% CdMnTe sample
as a fu n c tio n o f temperature. The p o in ts were obtained
as f i t t i n g parameters E xtra p o la tio n from the high
temperature p o in ts y ie ld s a Weiss constant o f ew = -21 K.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
f
2.
Cdj_xMnxTe:
The "M odified-B loch Model" Region
Above about 15% manganese, the q u a lity o f the f i t s obtained
using the unmodified Bloch model d e te rio ra te s r a p id ly a t low temper­
atures due to the ra p id decrease o f the re la x a tio n tim e.
In a d d itio n ,
as x increases, the resonance weakens and broadens u n til our simple
lin e a r p o la riz a tio n data (Figure 5 .4 ) no longer has s u ffic ie n t
re s o lu tio n to be m eaningful.
Thus we must go to the more s e n s itiv e
method o f measuring Faraday ro ta tio n and e l l i p t i c i t y which is described
in d e ta il in the Appendix.
B r ie f ly , the r o ta tio n is measured by observing a very small
p ro je c tio n o f the lin e a r ly p o la riz e d in c id e n t microwaves (p o la riz e r
and analyzer n e a rly — b u t not q u ite — p e rp e n d icu la r) fo r both f ie ld
(
d ire c tio n s .
E l l i p t i c i t y is obtained from h ig h ly e c c e n tric e ll i p t i c a l
p o la riz a tio n
(n e a rly — but no.t q u ite — lin e a r ) by d e te c tin g the minor
axis o f the e llip s e w h ile sweeping the f i e ld in both d ire c tio n s .
Using
th is more s e n s itiv e technique, we have been able to measure EPR and
it s e ffe c ts over the e n tir e range o f manganese concentrations and
temperatures.
As the manganese co n cen tra tio n is increased above about 15%,
the c o n trib u tio n o f x_ becomes in c re a s in g ly im po rta n t in the Faraday
ro ta tio n and e l l i p t i c i t y due to the la rg e w id th o f the EPR lin e s .
The
lin e shape o f the ro ta tio n changes d r a s tic a lly a t low temperatures.
In a d d itio n , the p o s itio n o f the resonance s h if t s to lower f ie ld s .
This s h i f t is e s p e c ia lly unambiguous in the e l l i p t i c i t y data.
The Faraday e l l i p t i c i t y data fo r a 22.5% sample a t 7 K is shown
in Figure 5.9.
Although the resonance is very broad (n e a rly 10 kG),
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
22 '2 % Cd Mn Te
Z
o
<o
to
S
CO
z
<
tr
i-
0.0
1.0
MAGNETIC
Figure 5 .9 .
2.0
FIELD
3.0
(T )
Faraday e l l i p t i c i t y data f o r a 22.5% CdMnTe sample a t 7 K.
The e l l i p t i c i t y is obtained from the d iffe re n c e between
the two tra c e s .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
i
22 '/2 % Cd MnTe
T =7K
0.0
1.0
2.0
3.0
MAGNETIC FIELD (T )
Figure 5.10.
Faraday ro ta tio n data f o r the 22.5% CdMnTe sample a t 7 K.
The ro ta tio n is obtained from the d iffe re n c e between the
two tra c e s .
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
7
1
the o v e ra ll shape o f the lin e is th a t o f
The Faraday ro ta tio n fo r
+
the same sample a t 7 K (Figure 5.10) may no longer be adequately
explained by x+ alone.
The lo w - fie ld r o ta tio n ( i . e . , below the
resonance p o s itio n ) is much sm aller than th a t a t fie ld s above the
resonance.
In a d d itio n , the zero-crossing
o f the ro ta tio n occurs a t
a f i e l d o f only 1.05 T ra th e r than the 1.25 T resonance p o s itio n .
As
the manganese co n cen tra tio n increases, o r as the temperature decreases,
the changes become even more s t r ik in g .
The p o s itio n o f the zero-
crossing moves to s t i l l lower fie ld s and the lo w - fie ld ro ta tio n becomes
sm a lle r, u n til a t ojT= 1, e changes sign a t B = 0 , and fo r urT < 1 i t
remains o f the same sign a t a ll f ie ld s .
o f the ro ta tio n
Figure 5.11 shows an overview
behavior fo r a sample w ith 30% manganese.
parameters used to f i t the data are lis t e d
s'
The
in Table 5 .1 .
The temper­
a tu re where the lo w - fie ld ro ta tio n becomes zero is f a i r l y easy to
measure e x p e rim e n ta lly and is shown in Figure 5.12 as a fu n c tio n o f
manganese c o n c e n tra tio n , x.
For our microwave frequency o f 35 GHz,
th is c o n d itio n (wT = 1) gives T = 4.5 x 10
-12
s.
Figure 5.13 shows
o th e r "is o -te m p o ra l" lin e s o f constant re la x a tio n time as obtained by
computer f i t t i n g the Faraday r o ta tio n data to the p re d ic tio n s o f the
m odified Bloch model.
The magnetic phase diagram fo r Cd1
is superimposed on Figures 5.12 and 5.13.
A“ X
Mn Te [22]
X
We show how the re la x a tio n
time v a rie s w ith temperature fo r several samples in Figure 5.14.
For the s m a lle st re la x a tio n times th a t gave reasonable f i t s ,
the m a te ria l is in the sp in -g la ss phase.
In a t r u ly frozen s ta te no
paramagnetic resonance e ffe c ts would occur since the frozen spins would
be unable to re a c t to the r f magnetic f i e ld .
However, according to
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T * 4K
T» 15 K
4-
•O
I.
s
■
0
1 °
fi:
20r
M
T-35K
TM7K
T»70K
§
3
MAGNETIC FIELD (T )
Figure 5.11.
Faraday r o ta tio n fo r a 30% CdMnTe sample a t several temperatures. The p o in ts are the
measured ro ta tio n s and the lin e s are the best f i t to the data. The f i t t i n g parameters
are lis t e d in Table 5.1.
^
O
ro
103
Table 5.1.
T
Parameters used to c o m p u te r-fit the Faraday ro ta tio n and
e l l i p t i c i t y data f o r the 30% CdMnTe sample.
xRot
XE11
TE11
gRot
gE ll
. 3 xl0 -11
.3 x l0 “ U
3.35
3.25
3 .0 x l0 ‘ 2
7
2.26
2.6
.35
.35
3.0
2.25
11
2.48
1.9
.45
2.9
2.25
15
2.14
—
.5
—
2.5
—
17
1.68
1.34
.65
.8
2.3
2.05
25
1.4
1.4
1.0
1.05
2.05
2.0
35
1.32
1.24
1.5
1.5
2.0
2.0
50
1.2
1.0
2.2
2.5
2.0
2.0
1.04
3.5
3.0
2.0
2.0
.8
4.5
- .0
2.0
2.0
70
90
.92
1.1
00
4
CO
1 .5 2 x l0 '3
TRot
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
100
90
80
70
60
Ld
<
cc.
UJ
50
UJ 40
30
20
0.0
Figure 5.12.
0.2
0.6
0.4
COMPOSITION ( X )
0.8
The temperature a t which the lo w - fie ld Faraday r o ta tio n
becomes zero as a fu n c tio n o f manganese co n cen tra tio n in
CdMnTe. This c o n d itio n ( odT = 1) corresponds to a re la x ­
a tio n tim e o f T = 4.5 * 10"12 s. The magnetic phase
diagram o f CdMnTe (see Figure 3.5) is superimposed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
100
-II
3x10
3 x IO"10 ^ ' O 10
90
xIO"
4.55x10"'^
80
70
UJ
Q£
3
3x 16 '2/
60
£
0C
UJ
CL
*12
50
2
UJ
i
b-
40
30
20
0.0
0.2
0.4
0.6
0.8
COMPOSITION ( X )
Figure 5.13.
Lines o f co n sta n t re la x a tio n time as determined by
computer f i t t i n g the Faraday ro ta tio n data. The magnetic
phase diagram o f CdMnTe is superimposed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
106
T
1
35 %
30 %
\1 % %
-▲ A
in
20
40
60
80
100
Temperature ( K )
Figure 5.14.
Inverse re la x a tio n time as a fu n c tio n o f temperature fo r
several CdMnTe samples. The re la x a tio n times were
obtained by computer f i t t i n g the Faraday ro ta tio n data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
A
Escorne and Mauger [1 9 ], in Cd,
1“ X
Mn Te loose o r unfrozen spins may
X
e x is t even in the s p in -g la s s phase.
By using the Faraday e l l i p t i c i t y d a ta , s im ila r re s u lts may be
obtained.
An overview o f the e l l i p t i c i t y data fo r the 30% sample is
presented in Figure 5.15.
We have n o t, however, been able to
sim ultaneously f i t both the ro ta tio n and the e l l i p t i c i t y using the same
values o f the parameters.
The discrepancy becomes la rg e r as the
manganese co n ce n tra tio n becomes la r g e r , i . e . , as we move to s h o rte r
re la x a tio n tim es.
We have chosen to emphasize the ro ta tio n data ra th e r
than the e l l i p t i c i t y fo r two reasons.
F ir s t , the ro ta tio n is obtained
from x ' » the d is p e rs iv e p a rt o f the s u s c e p t ib ility .
D ispersion e ffe c ts
are la rg e over a w id e r magnetic f i e ld range than are absorption
e ffe c ts .
{
Also the r o ta tio n curves contain more "fe a tu re s " ( e .g ., zero-
cro ssin g s, lo w - fie ld sign changes, e t c . ) , which tend to make the f i t s
more r e lia b le .
An a d d itio n a l fe a tu re o f EPR in the in te rm e d ia te co n cen tra tio n
range is the s h i f t o f the resonance p o s itio n to lower f ie ld s .
This
s h if t may be explained by the presence o f an e ffe c tiv e in te rn a l
f i e ld
[2 3 ], by a v a ria b le g -fa c to r [44] o r both to g e th e r [4 5 ].
We have
chosen to express the resonance s h if t by a llo w in g the g -fa c to r to vary
from i t s high-tem perature value o f 2.0
f o r several reasons.
By
a llo w in g g to vary we can ill u s t r a t e most c le a r ly the e x te n t to which
the data are described by the m odified Bloch model in i t s present form.
In a d d itio n , w h ile we have s u c c e s s fu lly f i t the ro ta tio n data using an
in te rn a l f i e l d , the f i t s
to the e l l i p t i c i t y have been less s a tis fa c to r y .
I t is c le a r th a t the f i t s can be fu r th e r improved by a d ju s tin g both g
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
7.0
D jO
T - 7K
60
60
ao
50
90
40
40
30
30
70
60
50
40
20
20
8
O
30
20
10
x
>- 00
O 140
00
160
300
160
T • 25 K
120
00
T » 70 K
250
14.0
100
12.0
60
200-
100
150
60
•60
60
100
40
40
SO
2.0
2.0
00
QO
20
3.0
40
50
00
00
1.0
20
30
4.0
50
00
00
20
30
40
5.0
MAGNETIC FIELD ( T )
Figure 5.15.
Faraday e l l i p t i c i t y f o r the 30% CdMnTe sample a t several temperatures. The p o in ts are the
measured e l l i p t i c i t i e s and the lin e s are the best f i t s to the data. The f i t t i n g param­
e ters are lis t e d in Table 5.1.
109
^
and the in te rn a l f i e ld .
I t also appears l ik e l y th a t a t le a s t
some o f
the parameters invo lve d (g , T, xQ and H ..^ ) may themselves be fu n c tio n s
o f the e x te rn a l magnetic f i e ld .
However, the in tro d u c tio n o f such
refinem ents in to the f i t t i n g procedure is not meaningful unless i t is
guided by a deeper understanding o f the physical s itu a tio n , which we
p re se n tly do n o t have.
Figure 5.16 shows the v a ria tio n o f the g -fa c to r
as obtained from the ro ta tio n data fo r samples w ith x = 0.17, 0.30 and
0.35.
The re s u lts from the e l l i p t i c i t y are s im ila r .
The Faraday e ffe c t method o f studying EPR also y ie ld s values
o f xQ» the dc magnetic s u s c e p t ib ility .
We have compared the re s u lts
w ith those obtained by conventional s u s c e p t ib ility measurements.
Although the data show the same temperature dependence o f the suscep­
t i b i l i t y , th e re is some disagreement in the absolute magnitude.
(v
obtained x0 by f i t t i n g
the am plitude o f the Faraday e ffe c ts .
We
The
am plitude is also determined by the length o f the m a te ria l, which in
the present case is the e ffe c tiv e length o f a powder sample.
I t is
p o ssib le th a t our method o f g e ttin g the e ffe c tiv e length could in t r o ­
duce some e r r o r in the value o f x
o
deduced from the data.
I t should
also be pointed out th a t the a v a ila b le dc measurements are themselves
not unambiguous, i . e . , the values o f xQ obtained by Galazka e t al_. [22]
d if f e r by a fa c to r o f roughly 1.5 from those o f O seroff [2 3 ].
Thus the
small departure o f our data, obtained by a new and in d ir e c t method,
from Galazka's re s u lts by a s im ila r fa c to r o f 1 .5 , is in fa c t q u ite
g r a tify in g .
We show our re s u lts and those o f Galazka e t al_. in
Figure 5.17.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
20
40
60
Temperature
Figure 5.16.
80
100
( K)
The Landd g -fa c to r as a fu n c tio n o f temperature fo r
several CdMnTe samples. The g -fa c to rs were obtained by
computer f i t t i n g the Faraday r o ta tio n data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I ll
i
1200
1000
cn
800
X
600
2C
400
(
200
0
0
20
40
60
80
100
TEMPERATURE( K )
Figure 5.17.
Inverse s t a t ic s u s c e p tib ility as a fu n c tio n o f temper­
atu re fo r the 30% CdMnTe sample. The p o in ts were
obtained by computer f i t t i n g our Faraday r o ta tio n data.
The s o lid lin e is the conventional s u s c e p tib ility
measurement made by Galazka e t a l .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
By using our Faraday e ffe c t technique we have been able to
extend the measured lim it s o f the EPR parameters w ell beyond those
obtained by O se ro ff.
The resonance s h if t s , whether due to in te rn a l
f ie ld s o r v a ria b le g -fa c to rs , th a t we measure are up to s ix times
g re a te r than the la rg e s t O seroff is able to observe.
In a d d itio n ,
the maximum lin e w id th s which p r io r EPR measurements were capable o f
re s o lv in g were an o rd er o f magnitude sm a lle r than those corresponding
to our measurements.
Thus the present method has determined re la x a ­
tio n time values s h o rte r by an order o f magnitude than the s h o rte s t
tim e accessible by the e a r lie r s tu d ie s .
3.
Cd,
Mn Te:
X " * />
Unexplained E ffe c ts
/\
We have not been able to s u c c e s s fu lly e x p la in our re s u lts fo r
the h ig h e st manganese concentrations a t low tem peratures.
As the
manganese content is increased, the a n ti ferrom agnetic in te ra c tio n
between the ions causes the
e ffe c ts o f EPR described above to decrease
g ra d u a lly , since the e ffe c t
due to oneion tends to cancel th a t o f i t s
neighbors.
As the o v e ra ll e ffe c ts become s m a lle r, a d if fe r e n t type
o f EPR behavior emerges.
This new phenomenon may also be present a t
lower manganese concentrations o r h ig h e r tem peratures, but i t s presence
is com pletely overshadowed by the much la rg e r Faraday e ffe c ts caused
by "norm al" EPR.
Faraday ro ta tio n in th is region o f co n cen tra tio n and temperature
is ch a racterize d by a sharp, alm ost discontinuous ris e from a near-zero
value to some p o s itiv e value a t 12.5 kG, i . e . , a t the p o s itio n o f EPR
corresponding to g = 2.
An
example o f th is behavior is shown in
Figure 5.18a fo r a sample w ith 45% manganese a t 8 K. The r o ta tio n
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
MICROWAVE
TRANSMISSION
T *2 3 K
0.0
05
2.0
23
MAGNETIC FIELD
Figure 5.18.
3.5
3.0
4.0
4.3
3.0
(T )
Faraday r o ta tio n data fo r a 45% CdMnTe sample a t several
tem peratures. The ro ta tio n is obtained from the d i f f e r ­
ence between the two lin e s .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
is given by the d iffe re n c e between the two tra c e s .
As the m a te ria l is
heated, the r o ta tio n shows a gradual r is e a t low fie ld s as p re dicte d
fo r very s h o rt re la x a tio n tim e s, w ith the sharp r is e a t 12.5 kG
p e rs is tin g (see Figure
5 .18b,c) u n t il the normal behavior becomes so
la rg e th a t the sharp r is e becomes unnoticeable.
The Faraday e l l i p t i c i t y in th is region also d isp la ys a behavior
markedly d if fe r e n t from th a t reported in the previous s e c tio n .
At low
tem peratures, the e l l i p t i c i t y spectrum c o n sists o f a very s m a ll, very
narrow lin e a t 12.5 kG, as shown in Figure 5.19a fo r a sample w ith 50%
manganese.
As w ith the r o ta tio n , when the sample is warmed up, the
e l l i p t i c i t y due to "norm al" EPR strengthens (as a broad lin e ) , but the
small narrow e ffe c t remains, serving to give the "norm al" broad lin e a
sharp peak (see Figure 5 .19b).
The above-described behavior o f the Faraday e ffe c ts occurred fo r
a ll samples stu d ied w ith x > 0 .4 .
sharp e ffe c ts were observed.
A t low tem peratures, only the sm a ll,
When the samples were heated, above 4 K,
the "normal" EPR behavior emerged, w ith the small e ffe c ts m odifying the
expected lin e shape.
E v e n tu a lly , a t high enough tem peratures, the
"norm al" behavior com pletely masked the small e ffe c ts .
In one sample,
the s m a ll, anomalous e ffe c ts were strong enough to remain observable
even when the normal e ffe c ts were q u ite la rg e .
Figures 5.20 and 5.21
show the Faraday ro ta tio n and e l l i p t i c i t y , re s p e c tiv e ly , fo r the sample
which, according to d e n s ity measurements, contained about 44%
manganese.
Conventional EPR measurements in DMS and o th e r paramagnetic
systems have also sometimes revealed the presence o f a s m a ll, sharp
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.25
5 0 % CdMnTe
T« 48 K
5 0 % CdMnTe
T» 8K
g
0.20
O
x
>-
O 10
O
x
>
IO 08
f0.
_l
_l
o
0.
0.15
_l
_1
UJ
<
<
UJ 0.6
0.10
o:
1
15
<
CE
If
0.4
0.05
0.2
0.00
0.0
1.0
2.0
3.0
4.0
5.0
MAGNETIC
Figure 5.19.
Faraday e l l i p t i c i t y fo r a 50% CdMnTe s
0.0
1.0
2.0
3.0
4.0
5.0
FIELD ( T )
iple a t two temperatures.
cn
116
v
1
Rotation
T = 4.2 K
5
co
z
<
a:
i-
c
0.0
0.5
1.0
1.5
2.0
2.5
3.0
MAGNETIC FIELD (T )
Figure 5.20.
Faraday ro ta tio n data fo r a 44% CdMnTe sample a t 4.2 K.
The ro ta tio n is obtained from the d iffe re n c e between the
tra c e s .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
Ellipticity
T = 4.2 K
5
(/)
z
<
01
0.0
1.0
2.0
3.0
MAGNETIC FIELD ( T )
Figure 5.21.
Faraday e l l i p t i c i t y data fo r a 44% CdMnTe sample a t
4.2 K. The e l l i p t i c i t y is obtained from the d iffe re n c e
between the tra ce s.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
resonance superimposed on a la r g e r , broad lin e .
As w ith our r e s u lts ,
o n ly the small resonance was present a t low temperatures and o n ly the
la rg e one was observable a t high tem peratures.
Seehra and S rin iva sa n ,
[46] studying MnO, ascribed the presence o f the small resonance to the
EPR o f precipates o f MngO^ in the m a te ria l.
e t a l.
S im ila r ly , Manoogian,
[47] and O se ro ff [48] r e fe r to c lu s te rs o r p re c ip ita te s o f
manganese as causing the e ffe c t in DMS.
These conventional EPR measurements are based on a b so rp tio n , and
thus are s e n s itiv e o n ly to x "-
0u r measurements o f x ' through the
Faraday r o ta tio n , however, appear to suggest a mechanism d if fe r e n t from
a sim ple EPR o f manganese p r e c ip ita te s .
While the e l l i p t i c i t y behavior
th a t we observe does d is p la y the behavior o f o rd in a ry EPR absorption
associated w ith a narrow resonance lin e , the discontinuous Faraday
ro ta tio n cannot be explained by assuming d is p e rs io n caused by the
behavior o f x 1 associated w ith such EPR.
We fe e l th a t the anomalous
behaviors o f both the ro ta tio n and the e l l i p t i c i t y are caused by the
same mechanism, and th a t they thus must be explained to g e th e r.
Further
study, e s p e c ia lly o f the x 1 e ffe c ts causing the Faraday r o ta tio n , w il l
be necessary before an adequate understanding o f th is behavior is
p o ssib le .
We have shown, then, a progression o f Faraday ro ta tio n and
e l l i p t i c i t y behavior as e ith e r the temperature o r manganese concentra­
tio n is v a rie d .
In d iscu ssin g the r o ta tio n , f o r example, we see a
progression from narrow x ^ - lik e behavior to w ider resonances, to
where the lo w - fie ld ro ta tio n changes s ig n , and e v e n tu a lly to the
s te p - lik e behavior discussed above.
In Figure 5.22 we o b ta in th is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
i
8.0
45 % Cd MnTe
7.0
6.0
ROTATION
x IOOO
A
60 K
5.0
4.0
3.0
FARADAY
2.0
0.0
-3.0
0.0
2.0
3.0
4.0
5.0
MAGNETIC FIELD ( T )
Figure 5.22.
Progression o f Faraday ro ta tio n behavior as illu s t r a t e d
by co o lin g a 45% CdMnTe sample. The p o in ts are the
measured ro ta tio n s and the lin e s are sim ply included fo r
c la r it y .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
r
■i
progression o f r o ta tio n behavior by c o o lin g a 45% sample.
The same
progression is shown in Figure 5.23, where here we m aintain the
temperature a t 4 K, but increase the manganese co n ce n tra tio n .
This
dram atic change in behavior is due to the steep drop in the re la x a tio n
time which, as can be seen from Figure 5.13, may be accomplished
e ith e r by low ering the temperature o r ra is in g the manganese concen­
tr a tio n .
Even the appearance o f the unexplained EPR e ffe c t can be
produced by e ith e r low ering T o r ra is in g x , h in tin g th a t although we
are p re s e n tly unable to adequately e x p la in i t , the second phenomenon
may be re la te d in some way to the re la x a tio n tim e.
A s im ila r progression o f behavior can be fo llo w e d in the
e l l i p t i c i t y , where the decrease in the re la x a tio n time produced e ith e r
by decreasing the tem perature, as shown in Figure 5.24, o r incre a sing
{
x s te a d ily broadens the ab sorp tio n peak.
In these f i r s t three s e c tio n s , then, we have taken one DMS,
Cd,
X“ X
Mn Te, and examined the behavior o f EPR as evidenced by the
X
Faraday ro ta tio n and e l l i p t i c i t y as a fu n c tio n o f manganese co n te n t.
Our focus was on r e la t iv e ly high concentrations and we have not
mentioned the presence o f fin e and h yp erfin e s tru c tu re in
spectrum.
the EPR
That to p ic , c h a r a c te r is tic o f the " is o la te d " spins
found
in the low -co n ce n tra tio n CdMnTe samples, w i l l be b r ie f ly discussed in
Chapter VI.
4.
Other wide-gap DMS (x % 0 .1 )
While in the previous s e c tio n we discussed one DMS f o r a ll
p o ssib le values o f x , here we w i l l examine the EPR behavior o f a ll
(
wide-gap DMS f o r one p a r tic u la r manganese co n ce n tra tio n :
x %0 .1 .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
We
121
Cd MnTe
T = 4.2 K
O 20%
221 / 2 %
2 5 % (10.5 K )
30%
40%
68%
(.
2.0
3.0
MAGNETIC FIELD ( T )
Figure 5.23.
Progression o f Faraday r o ta tio n behavior as illu s t r a t e d by
incre a sing the manganese co n cen tra tio n in the CdMnTe
samples, a ll o f which are measured a t 4.2 K. The lin e s
are included fo r c l a r i t y .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
T
i
10.0
17 1/2% Cd MnTe
9.0
8.0
>-
7.0
O
t
_i
60
UJ
5.0
s
o
2
4.0
2
3.0
2.0
0.0
0.0
0.5
1.0
MAGNETIC
Figure 5.24.
1.5
2.0
2.5
FIELD ( T )
Progression o f the Faraday e l l i p t i c i t y behavior as
illu s t r a t e d by decreasing the temperature o f a 17.5%
CdMnTe sample. The lin e s are guides fo r the eyes.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.0
123
have measured EPR using the Faraday e ffe c ts technique on 10% samples
o f the fo llo w in g DMS in a d d itio n to CdMnTe:
ZnMnSe, and ZnMnS.
CdMnSe, CdMnS, ZnMnTe,
Since the wide band gap o f these m a te ria ls prevents
fre e c a r r ie r e ffe c ts a t low temperatures and since each sample contains
roughly the same percentage o f manganese, the behavior o f a ll the
m a te ria ls was q u a lita tiv e ly the same.
Table 5.2 l i s t s the parameters o f the m a te ria ls s tu d ie d .
Due
to the high temperatures needed to grow some o f the compounds, not a ll
o f the powdered samples were from s in g le c ry s ta l in g o ts .
Some were
prepared by s in te r in g , as in d ic a te d in the ta b le .
In a d d itio n to the 10% samples lis t e d above, we have studied
several o th e r manganese concentrations o f CdMnSe and ZnMnTe.
These
compounds behave in a manner very s im ila r to th a t o f CdMnTe fo r
(
comparable values o f x.
The Bloch model must be m odified as before in
order to account f o r the observed behavior.
In Figures 5.25 and 5.26, re s p e c tiv e ly , we show the Faraday
ro ta tio n and e l l i p t i c i t y fo r the 10% samples a t 4.2 K.
To f a c i li t a t e
comparison, we have p lo tte d the Faraday e ffe c ts per e ffe c tiv e c e n ti­
meter w ith the e ffe c tiv e length as described p re v io u s ly .
Although the
behavior is q u a lita tiv e ly the same fo r a ll o f the samples, several
trends become e v id e n t.
The resonances seem to be stro n g e r fo r the
cadmium compounds than fo r the z in c compounds.
In a d d itio n , the
lig h t e r the anion i s , the la rg e r the resonance appears; the s u lfid e s
show the s tro n g e st e ffe c ts , fo llo w e d by the se le n ide s, w ith the
te llu r id e s g iv in g the sm a lle st e ffe c t.
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124
Table 5.2.
M aterial
P ro p ertie s o f the wide-gap DMS used in th is in v e s tig a tio n .
Nominal x
Mass
Remarks
CdMnTe
0.10
1.242
s in g le -c ry s ta l
CdMnSe
0.085
0.225
s in g le -c ry s ta l
CdMnS
0.10
0.387
s in g le -c ry s ta l
ZnMnTe
0.10
0.675
s in g le -c ry s ta l
ZnMnSe
0.10
0.325
s in te re d
ZnMnS
0.12
0.362
s in te re d
(
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125
0.8
FARADAY
ROTATIO N/cm
0.6
0.4
ZnMnTe
CdMnTe
0.2
-
Zn Mn Se
Cd Mn Se
-0.4
Zn Mn S
0.6
-
-
Cd Mn S
0.8
1.4
MAGNETIC FIELD ( T )
Figure 5.25.
Faraday r o ta tio n a t 4.2 K fo r the wide-gap DMS w ith
x = 0 .1 . The lin e s correspond to the best f i t s to the
data w ith the ro ta tio n and e l l i p t i c i t y data being f i t
sim ultaneously.
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126
*
1
Cd Mn S
E
o
s
Zn Mn S
>
IO
I-
Q_
—I
_l
■Cd Mn Se
0.8
UJ
•ZnMn Se
CdMnTe
(
0.4
Zn Mn Te
0.2
0.0
MAGNETIC
Figure 5.26.
FIELD ( T )
Faraday e l l i p t i c i t y a t 4.2 K f o r the wide-gap DMS w ith
x = 0 .1 . The lin e s are the best f i t s to the data.
('
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127
/
There are d iffe re n c e s in lin e w id th as w e ll fo r the d if fe r e n t
types o f m a te ria l.
The cadmium-based DMS tend to have narrower EPR
resonances (see Figure 5.27) than those based on z in c .
And as was the
case fo r the s tre n g th o f the Faraday e ffe c ts , the sm a lle r the anion is ,
the narrower is the lin e w id th .
The s u lfid e lin e s are extrem ely sharp,
being less than 200 G by 90 K, w ith the selenide and t e llu r id e lin e w idths being in c re a s in g ly la rg e r.
As shown in Figures 5.25 - 5.27, the EPR behavior as evidenced
by the Faraday e ffe c ts is q u a lita tiv e ly the same fo r a ll o f the
samples.
This good agreement tends to in d ic a te th a t the magnetic
p ro p e rtie s in DMS depend weakly (b u t p e rc e p tib ly ) on the host la t t ic e .
(
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128
O
x
o
a>
to
UJ
2
hZn M nTe
Z
o 0.8
£
X
<
-I
S
06
Zn Mn Se
UJ
</)
oc
UJ
> 0.4
z
CdMnTe
ZnMnS
0.2
CdMnS
CdMnSe
0.0
20
40
60
80
100
TEMPERATURE ( K )
Figure 5.27.
Linew idth ( f u l l w id th a t h a lf max) fo r the wide-gap DMS
w ith x : 0.1 as a fu n c tio n o f temperature. The lin e s are
guides fo r the eyes.
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129
CHAPTER VI - MISCELLANEOUS TOPICS CONCERNING EPR IN DMS
In th is Chapter we w il l present re s u lts from a number o f b r ie f
experiments in v o lv in g various aspects o f EPR in d ilu te d magnetic semi­
conductors.
Most o f the experiments d e a lt w ith e ith e r a s in g le sample
or a lim ite d number, so th a t fu r th e r study was not p o ssib le.
A ll these
experiments are th e re fo re p re lim in a ry in n a tu re , but contain valuable
in fo rm a tio n which, in many insta nce s, may serve as a p o in t o f departure
fo r fu r th e r study.
I t is in th is s p i r i t th a t they are included as a
p a rt o f th is th e s is .
A.
Fine and H yperfine S tru c tu re in CdMnTe
Chapter V d e a lt w ith the study o f EPR in CdMnTe.
We focused
there p r im a r ily on EPR broadening and o th e r e ffe c ts o f the manganesemanganese in te r a c tio n , and we reported th e re fo re only on those samples
w ith manganese concentrations g re a te r than x = 0.01, i . e . , where there
was a s in g le resonance lin e .
For very low values o f x, however, both
fin e and h yp erfin e s tru c tu re should be d is c e rn ib le .
We show here how
these e ffe c ts m anifest themselves in the transm ission method which we
employ.
We have studied a Cd1 Mn Te sample w ith x nom inally equal to
i”X
-4
3 x 10 .
X
The sample was cleaved, which fo r CdMnTe means th a t in our
experiment ( i . e . , the Faraday geometry) the dc f i e ld was a p p lie d along
the [110] d ir e c tio n .
The microwave transm ission spectrum a t 4.2 K o f a
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130
Z
o
CO
CO
5
CO
z
<
q:
i-
MAGNETIC FIELD ( T )
Figure 6 .1 .
Microwave transm ission EPR spectrum f o r a Cdi_xMnxTe
s in g le -c ry s ta l slab w ith x = 3 • 10-1+ a t 4.2 K.
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131
y
s in g le -c ry s ta l slab is shown in Figure 6 .1 .
When both fin e and hyper-
fin e s tru c tu re are p re sen t, a to ta l o f t h i r t y lin e s are p o ssib le (see
Chapter I I ) .
We were not able to t o t a l l y resolve a ll t h i r t y .
Other researchers [38,39] have measured the fin e s tru c tu re
2+
s p li t t in g o f Mn
about 60 G.
in CdTe as about 30 G and the h yp erfin e s p lit t in g as
Our experim ental system is not s u ita b le fo r high re s o lu tio n
spectroscopy, and we have th e re fo re not attempted to resolve a ll t h i r t y
lin e s
q u a n tita tiv e ly . N evertheless, our measurements in d ic a te
the same
order o f magnitude f o r the fin e s tru c tu re s p lit t in g .
A fte r measuring the s in g le -c ry s ta l s la b , we powdered an adjacent
piece
o f the c r y s ta l. The r e s u ltin g spectrum is shown in Figure 6 .2 .
Since the powder grains are randomly o rie n te d , the c ry s ta l f i e ld
averages to zero, e lim in a tin g the fin e s tru c tu re s p li t t in g .
(
s ix h y p e rfin e
Only the
lin e s remain. We measured the hyp erfin e s p li t t in g as
58 G, in e x c e lle n t agreement w ith our HgMnSe data (see Chapter IV) and
the lit e r a t u r e on CdMnTe [3 8 ,3 9 ].
The data i l l u s t r a t e the com paratively long range o f EPR d is p e r­
s io n , whose cum ulative e ffe c t leads to the o v e ra ll character o f the
"background" on which the resonances are superposed.
n o t done t h is ,
determine the
Although we have
data such as those shown in Figure 6.2 can be used to
com position x by a p p ro p ria te in te g ra tio n o f the spectrum.
B.
"P h o to c o n d u c tiv ity " in Zero-Gap DMS
We have made a p re lim in a ry in v e s tig a tio n o f the e ffe c t o f
illu m in a tio n by microwaves on the dc c o n d u c tiv ity o f the zero-gap DMS
HgMnTe and HgMnSe as the magnetic f i e l d was swept over a wide range,
(
in c lu d in g the
c o n d itio n fo r EPR.
A small dc c u rre n t was passed through
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132
4
T= 1.3 K
Z
o
if)
if)
2
if)
z
<
a:
i-
MAGNETIC FIELD ( T )
Figure 6 .2 .
Microwave transm ission EPR spectrum fo r a powdered sample
o f Cdi_xMnxTe w ith x = 3 • 10-lt a t 4.2 K. Only the hyper­
fin e s tru c tu re is present.
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133
7
the sample.
Microwaves were in c id e n t on the sample, and as the magnetic
f i e l d was v a rie d , the voltage across the sample was measured.
Contacts
were made e ith e r w ith s ilv e r paste o r by s o ld e rin g to spots o f gold
e le c tro p la te d onto
the sample.
in the re s u lts fo r
the two types o f contacts.
Two e ffe c ts
L i t t l e , i f any, d iffe re n c e was observed
can lead to a magnetic f i e ld dependence
in the re s is ­
t i v i t y o f the sample as a fu n c tio n o f microwave illu m in a tio n .
A simple
b o lo m e tric heating o f the conduction e le ctron s by the microwaves could
occur.
As the magnetic f^ e ld is swept, the h e lico n waves e x cite d by
the in c id e n t microwaves propagate in the sample and dimensional FabryPerot (standing wave) resonances take place a t c e rta in f ie ld s .
Since
maximum microwave power is absorbed by the sample when a Fabry-Perot
resonance occurs, maximum heating w i l l take place each time the
(
magnetic f i e ld s a tis fie s the Fabry-Perot c o n d itio n .
This heating is
evidenced by a change in the m o b ility o f the c a r r ie r s , and hence a
change in the r e s is t iv i t y .
In a d d itio n , a spin-dependent heating can occur.
When the
co n d itio n s fo r EPR o f the manganese ions are met in a c r y s ta l, a
r e la tiv e maximum in microwave absorption occurs.
This a b so rp tio n ,
again, re s u lts in a d d itio n a l heating which, in tu r n , leads to m o b ility
changes in the c a r r ie r s .
Figure 6.3 shows our re s u lts fo r a 2.5% HgMnTe sample doped w ith
indium a t 4.2 K f o r d if fe r e n t amounts o f in c id e n t power.
The c u rre n t in
the disk-shaped sample was perpe n d icu la r to the a p p lie d magnetic f i e ld .
We can see both types o f e ffe c ts discussed above.
The broad peaks are
due to the spin-independent Fabry-Perot resonances, w h ile the sharp lin e
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134
i
2.5 % HgMnTe
T = 4.2 K
OdB
EPR
UJ
O
§
O
>
3dB
o
X
Q.
6dB
9dB
0.0
0.5
1.0
1.5
2.0
2.5
3.0
MAGNETIC FIELD ( T )
Figure 6 .3 .
P h o to co n d u ctivity sig n a l (v o lta g e across the sample) fo r a
2.5% HgMnTe sample doped w ith indium a t 4.2 K as a function
o f magnetic f i e ld . Data is shown f o r several d if fe r e n t
amounts o f in c id e n t power. The sharp change in r e s is t iv ­
i t y a t 1.25 T is due to EPR.
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135
T
a t 1.25 T corresponds to the manganese EPR.
L a te r work on HgMnTe by
W it t lin e t al_. [49] a lso showed a r e s is t iv i t y change due to EPR (see
Figure 5 .4 ), b u t was le ss able to d e te c t the spin-independent heating
e ffe c t s .
Our re s u lts obtained on HgMnSe were o f two c a te g o rie s .
Some o f
the microwave-induced changes in the dc c o n d u c tiv ity consisted o f peaks
th a t were p e rio d ic in B 2, in d ic a tiv e o f Fabry-Perot geom etrical
resonances s im ila r to those described fo r HgMnTe.
We also observed,
however, small o s c illa tio n s in the signal th a t were p e rio d ic in 1/B
(see Figure 6 .5 ).
We have p lo tte d the number o f the peak versus 1/B
in Figure 6.6 to emphasize th is p e r io d ic ity .
Such a p e r io d ic ity is
s tro n g ly suggestive o f Shubnikov-de Haas-type quantum o s c illa tio n s ,
i . e . , whatever the immediate reason, i t is in step w ith the crossing o f
(,
the Fermi le v e l by successive Landau le v e ls .
The h a lv in g o f the slope
may in f e r the onset o f spin s p li t t in g o f the peaks.
I f Shubnikov-
de Haas behavior is assumed, we o b ta in a c a r r ie r co n ce n tra tio n o f
4.5 x 10
23
/m
3
from the period o f the o s c illa tio n s which agrees w ell
w ith the value o f 3.6 x 10
23
/m
3
obtained fo r th is sample using the
h e lico n transm ission method.
I t is noteworthy th a t these microwave-induced o s c illa tio n s begin
a t r e la t iv e ly low f ie ld s :
w e ll-d e fin e d o s c illa t o r y behavior is already
d ir e c t ly observable a t 9 kG.
More work is needed to p ro p e rly under­
stand th is phenomenon which, however, appears to be very e x c itin g .
r
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136
1.8 % Hg MnTe
T = 4 .2 K
IxJ
O
<
b
EPR
§
P
0
1
Q_
2
3
4
MAGNETIC FIELD ( T )
Figure 6 .4 .
C
P h o to co n d u ctivity as observed by W it t lin e t al_. fo r a
1.8% HgMnTe sample a t 4.2 K as a fu n c tio n o f magnetic
f i e ld . The sharp change in r e s is t iv i t y a t 4.3 T is due
to EPR.
■
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137
39Vl“10A010Hd
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138
1
1.2
3 % Hg Mn Se
T = 4.2 K
0.9
A = 0.06
LlJ
0.8
u_
o
H
Ul
Z
o
0.7
<
0.6
Ll I
0.5
<f)
<r
UJ
>
0.4
A = 0.03
0.3
0.2
10
20
PHOTOCONDUCTIVITY PEAK NUMBER
Figure 6 .6 .
P h o to co n d u ctivity peak number from Figure 6.5 (peak a t
hig h e st f i e ld is number 1) p lo tte d versus 1/B. The abrupt
change in slope may in d ic a te the onset o f spin s p li t t in g .
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139
C.
Heating E ffe c ts in CdMnSe
One o f the 10% CdMnSe samples showed anomalous transm ission
re s u lts .
The transm ission c o e ffic ie n t o f the sample was s tro n g ly depen­
dent on the in c id e n t microwave power.
In a d d itio n , the actual lin e
shape o f the e n tir e magnetotransmission spectrum also depended on the
in c id e n t power.
The e ffe c t on the transm ission o f d if f e r e n t amounts o f
power in c id e n t on the sample is illu s t r a t e d in Figure 6 .7 .
Each trace
has fo u r times more in c id e n t power than the tra ce above i t .
I t is in te re s tin g to compare th is behavior to the e ffe c t o f
tem perature on the magnetotransmission
spectrum f o r th is sample. A ll
o f the tra ce s shown in Figure 6.7 were
taken a t 4.2 K. The same
behavior as th a t observed by in cre a sin g the in c id e n t power was obtained
by using o n ly a small amount o f in c id e n t power and p h y s ic a lly heating
the sample.
The behavior shown in the
bottom tra ce o f Figure 6.7
corresponds to th a t shown a t a temperature o f about
30 K w ith the same
amount o f in c id e n t power as th a t used to observe the top curve a t 4.2 K.
We conclude, th e re fo re , th a t th is power-induced e ffe c t should probably
be ascribed to he atin g .
The heating e ffe c t occurred o n ly in th is s in g le sample.
In an
attem pt to id e n t if y the source o f th is e f f e c t , a PIXE (Proton Induced
X-ray Emission) a n alysis was performed and revealed the presence o f
about 90 ppm by w eight o f g a lliu m .
acts as a shallow donor.
The g a lliu m , in th is m a te ria l,
In a d d itio n , room temperature and 77 K Hall
measurements gave a con cen tra tio n o f about 2 * 10
22
/m
3
[5 0 ].
Thus we
conclude th a t th is e ffe c t is somehow re la te d to the presence o f donors
in the sample.
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140
10 % Cd Mn Se
T = 4 .2 K
S = Sample Attenuator
D = Detector Attenuator
S = 3 0 D= 0
^ S = 2 4 D=6
S= 18 0=12
Z
o
co
CO
2
S= 12 D = I8
CO
z
<
a:
i-
S=6 D =24
S=0
0.0
1.0
2.0
D =3 0
3 .0
MAGNETIC FIELD ( T )
Figure 6 .7 .
Transmission spectra fo r a 10% CdMnSe sample a t 4.2 K show­
ing the e ffe c t o f d if fe r e n t amounts o f in c id e n t power.
Each tra c e has fo u r times more in c id e n t power than the one
above i t .
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141
▼
k
The broad background peak was also observed by Dobrowolska e t a l .
using a fa r in fra re d la s e r [5 0 ].
As w ith our data, the peak they
observed was temperature-dependent.
I f the observed behavior i s , indeed, due to h e a tin g , one question
imm ediately a ris e s :
What causes such heating in th is m a te ria l?
The
e ffe c t could be caused by Joule heating due to fre e c a r r ie r s , but th is
ra ise s a second question regarding the o r ig in o f these c a r r ie r s .
In a
wide-gap m a te ria l such as CdSe a t liq u id helium tem peratures, no i n t r i n ­
s ic c a rrie rs are expected.
The PIXE a n alysis revealed the presence o f
g a lliu m im p u ritie s which give r is e to shallow donor le v e ls , but the
io n iz a tio n energy o f these le v e ls is ca. 20 meV, i . e . , fa r exceeding
the a v a ila b le thermal energy (kT a t 4.2 equals 0.34 meV) o r the
microwave photon energy (hu a t 35 GHz equals .15 meV).
{
However, the presence o f fre e c a rrie rs a t a co n ce n tra tio n le v e l
o f n % 10
20 3
/m has been observed in fa r in fa re d c y c lo tro n resonance
experiments [51] in samples from the same in g o t.
I t has been argued by
Ich ig u ch i and Drew [52] th a t flu c tu a tio n s in manganese concentration
lead to lo c a l flu c tu a tio n s in the band edge which can e a s ily exceed
20 meV on the scale o f one Bohr o r b it o f a donor.
This could lead to
a s p ill- o v e r o f e le ctro n s which are bound a t a lo c a tio n characterized
by a s lig h t ly la rg e r gap, in to the conduction band a t a neighboring
lo c a tio n where the gap is s lig h t ly s m a lle r.
I t is also p o ssib le th a t
the energy o f the microwave photons a s s is ts the e le c tro n s in th is
io n iz in g (o r tu n n e lin g ) process.
We fe e l th a t th is is a very im portant problem.
r
To resolve the
many questions which i t poses, a sequence o f a d d itio n a l d e ta ile d and
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142
system atic experiments must be c a rrie d out which, however, exceed the
intended scope o f th is th e s is .
D.
H ysteresis E ffe c ts in CdMnTe
One o f the CdMnTe samples th a t we measured d iffe r e d from the
others in th a t i t showed a marked h yste re sis a t low tem peratures.
Microwave transm ission through the sample, which contained 25 at.%
manganese, depended not o n ly on the f i e ld d ir e c tio n , b u t on whether the
f i e ld was being swept up o r down.
Figure 6.8 shows the Faraday ro ta tio n data fo r th is sample a t
1.3 K.
The dc f i e ld was swept up in one d ire c tio n w ith the transm ission
producing the f i r s t s o lid tra c e .
tra c e .
Sweeping down re s u lte d in the dotted
The f i e ld was then swept up and down in the opposite d ir e c tio n ,
y ie ld in g the second s o lid and dotted tra c e s , re s p e c tiv e ly .
s is was most n o tice a b le a t the low est tem peratures.
The h ystere­
Once the sample
was warmed s ig n ific a n t ly above 4.2 K, the e ffe c ts disappeared.
We found th a t i t was p o ssib le to " tr a in " the sample.
As shown
in Figure 6 .9 , a fte r sweeping the f i e ld tw ice in the same d ir e c tio n ,
the d iffe re n c e s between the incre a sing f i e ld transm ission and the
decreasing f i e ld transm ission become le s s .
A fte r several more it e r a ­
tio n s (n o t shown in Figure 6 .9 , to preserve c l a r i t y ) , the d iffe re n c e s
become n e g lig ib le .
When adequate data was obtained f o r one f i e ld
d ir e c tio n , the " tr a in in g " process would be repeated f o r the o th e r
d ire c tio n .
There may be a connection between the observed h y s te re s is and
ir r e v e r s ib le e ffe c ts th a t are observed in the spin glass phase
(remanence, the d iffe re n c e between fie ld -c o o le d and z e ro -fie ld -c o o le d
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143
Figure 6 .8.
Faraday r o ta tio n data fo r a 25% CdMnTe sample a t 1.3 K.
The r o ta tio n is obtained from the d iffe re n c e between the
tra ce s. The s o lid lin e s in d ic a te increasing magnetic
fie ld s and the dotted lin e s correspond to decreasing
fie ld s .
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144
25%
CdM nTe
1. + Field
2 . -F ie ld
0.0
1.0
2.0
MAGNETIC FIELD ( T )
Figure 6 .8 .
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145
in the
same field
d ire c tio n .
I
'CM
(
N0ISSIWSNVU1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure
6.9.
Illu s tr a tio n
of
the
Q z
"tra in in g "
effect
U.
of
repeated
sweeps
CJ
146
7
m agnetization, e t c . ) .
4 K (see Figure 3 .5 ).
A 25% CdMnTe sample is a spin glass below about
However, none o f the o th e r samples e x h ib ite d the
h yste re sis e ffe c t even though many o f them were measured in th e ir spin
glass phase.
We fe e l th a t th is is a very e x c itin g e ffe c t , m e ritin g
fu r th e r system atic stu d y, focused s p e c if ic a lly on remanence phenomena.
E.
EPR in ZnCoS
For the past several years there has been a la rg e e f f o r t to
extend the fa m ily o f DMS.
The m a jo rity o f th is e f f o r t has concentrated
on fin d in g s u ita b le hosts in to which manganese can be in s e rte d .
There
has also been some work done in an attem pt to fin d o th e r magnetic ions
which may be placed in the l a t t ic e .
samples co n ta in in g iro n [5 3 ].
^
EPR has been observed in HgTe
Iro n goes in to the HgTe la t t ic e much
less r e a d ily than does manganese, w ith the maximum amount being
probably about 2% [4 ].
Recently, attem pts w ith higher m e ltin g p o in t
hosts have increased th is th reshold to about 5% in CdFeTe [54] and 11%
in CdFeSe [5 5 ].
We have extended the DMS fa m ily fu r th e r by observing EPR in a
ZnS sample co n ta in in g 0.1% c o b a lt.
The sample was obtained from
Dr. Reynolds o f W right-P atterson AFB.
E a r lie r attem pts to introduce
c o b a lt in to the HgTe l a t t i c e , made in th is la b o ra to ry , fa ile d [5 6 ],
Our r e s u lts , then, in d ic a tin g th a t c o b a lt does e n te r the la t t ic e
s u b s titu tio n a lly in the case o f h ig h -m e ltin g -p o in t hosts are q u ite
e x c itin g .
I f the lim it s o f m is c ib ilit y are in fa c t s ig n ific a n t ly
higher than 0.1%, I I - V I compounds w ith c o b a lt w i l l c o n s titu te an
2+
im portant member o f the DMS fa m ily , since Co
(
V
Fe
2+
2+
, lik e Mn
but u n lik e
, has a permanent d ip o le moment in i t s ground s ta te .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
147
y
k-
6.10.
We show the resonance fo r a powder sample a t 4.2 K in Figure
2+
From the p o s itio n o f the lin e , we c a lc u la te d a Co
g -fa c to r o f
2.23 fo r ZnS, which is in e x c e lle n t agreement w ith values obtained
using conventional EPR techniques [5 7 ,5 8 ].
The valency o f Co
?+
suggests
th a t these ions occupy s u b s titu tio n a l s ite s in the zinc s u b la ttic e .
The resonance was very sharp and weakened ra p id ly as the sample was
warmed above 4.2 K.
Using the
techniques developed fo r small e ffe c ts in CdMnTe (see
previous chapter) we measured Faraday ro ta tio n and e l l i p t i c i t y fo r the
powder sample.
The r o ta tio n , shown in Figure 6.11 a t 4.2 K, illu s t r a t e s
the extreme sharpness o f the resonance.
In a d d itio n , the Faraday
e ffe c ts d isp la yed several small "resonances" a t fie ld s considerably
away from the main EPR a b sorp tio n .
(
This a d d itio n a l s tru c tu re , marked
by arrows in Figure 6 .1 1 , may be due to very larg e c ry s ta l f ie ld
s p lit t in g .
Because o f the non-Lorentzian lineshape o f the resonance, we
have n o t attempted a q u a n tita tiv e a n a ly s is o f the data to e x tra c t
and x0 > although th is should be p o ssib le w ith fu r th e r e f f o r t .
From
q u a lita tiv e exam ination o f the observed temperature dependence, however,
i t is c le a r th a t the lin e narrows (Tg increases) and x0 drops w ith
in cre a sin g tem perature.
F.
Study o f PbMnTe
One d ir e c tio n in which the extension o f the DMS fa m ily has
proceeded is the in tro d u c tio n o f manganese in to IV-V I compounds such as
PbTe and GeTe.
(
We have observed EPR in a 4% sample o f PbMnTe.
The
data, w h ile n o t o f s u f f ic ie n t q u a lity to be q u a n tita tiv e ly analyzed,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
148
Zn Co S
T = 4 .2 K
z
o
if)
if)
2
if)
Z
<
<r
i-
0.0
1.0
2.0
MAGNETIC FIELD ( T )
Figure 6.10.
D ire c t transm ission data fo r a sample o f Zni_xCoxS w ith
x = 1 • 10-3 a t 4.2 K. The sharp resonance occurred a t
1.12 T fo r our frequency o f 35 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
T
Z n Co S
T = 4 .2 K
Z
o
co
co
2
co
z
<
<r
h
0.6
1.0
1.4
1.8
MAGNETIC FIELD ( T )
Figure 6.11.
Faraday ro ta tio n data fo r the ZnCoS sample a t 4.2 K
showing the extreme sharpness o f the resonance and the
small a d d itio n a l s tru c tu re o f the spectrum.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
nevertheless illu s t r a t e s a very in te re s tin g phenomenon.
PbMnTe was s tro n g ly p -typ e .
Our sample o f
Because o f the sign o f the fre e c a r r ie r s ,
h e lico n waves now correspond to the ( - ) p o la riz a tio n .
s t i l l occurs fo r the (+) p o la r iz a tio n .
However, EPR
This co n tra sts w ith the s itu a ­
tio n encountered in h e lic o n -e x c ite d EPR, discussed in Chapter IV , where
both h e licons and EPR correspond to the same sense o f c ir c u la r p o la r i­
z a tio n .
Because o f the high absorption by the sample, we studied the
re fle c te d microwave signal ra th e r than the tra n sm itte d one.
r e fle c tio n signal is shown in Figure 6.12.
The
The lower tra c e is the ( - )
p o la riz a tio n and shows a d e c lin e in the re fle c te d power as the magnetic
f i e ld is swept, in d ic a tin g an incre a sing absorption as the helicon
c o n d itio n is b e tte r and b e tte r s a tis fie d .
This d e clin e in d ic a te s th a t
the transm ission ( i . e . , adm ittance) o f th is p o la riz a tio n in to the sample
is in c re a s in g .
The upper tra c e , which corresponds to the (+)
p o la riz a tio n , shows a slo w ly incre a sing r e fle c tio n s ig n a l, in d ic a tin g
th a t the o p a c ity o f the m a te ria l increases to th is p o la riz a tio n
(propagation approaches evanescence).
At the p o s itio n o f the manganese
EPR the microwaves are absorbed, thus reducing the otherw ise increasing
r e fle c tio n c o e ffic ie n t.
This is the only m a te ria l studied fo r which
the EPR occurs in the p o la riz a tio n opposite to th a t o f h e lico n waves.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
151
%
4% PbMnTe
T = 4.2 K
Z
o
. CRA - electrons
CRI - holes
h
O
UJ
_J
u_
UJ
2. CRI - electrons
CRA - holes
a:
0.0
1.0
2.0
3.0
MAGNETIC FIELD ( T )
Figure 6.12.
Microwave r e fle c tio n sign a l fo r a 4% sample o f PbMnTe a t
4.2 K. The resonance occurs in the p o la riz a tio n opposite
o f the one th a t sustains helicon waves.
('
V
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF REFERENCES
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
152
T
A
LIST OF REFERENCES
[1]
R. R. Galazka, "Semimagnetic Semiconductors Based on HgMnTe and
CdMnTe," Proc. 14th I n t . Conf. on the Phys. o f Semicond.,
Edinburgh, 1978, ed. by B. L. H. Wilson ( In s t, o f P h ys.C o nf.
Ser. No. 43) London (1978) p. 133.
[2]
J. A. Gaj, "Semimagnetic Semiconductors," Proc. 15th I n t . Conf.
on the Ph.ys. o f Semicond., Kyoto, 1980, ed. by S. Tanaka and
Y. Toyozawa (J . Phys. Soc. Japan 49 (1980) Supplement A)
Tokyo (1980) p. 797.
[3]
T. D ie t!, "Semimagnetic Semiconductors in Magnetic F ie ld s ,"
Proc. O ji In t. Sem. on Phys. in High Mag. F ie ld s , Hakone, Japan,
1980, ed. by S. Chikazumi and M. Miura (S pringer Ser. in S o lid S tate Sciences No. 24) B e rlin (1981) p. 344.
[4]
J. K. Furdyna, "D ilu te d Magnetic Semiconductors:
An In te rfa c e
o f Semiconductors and Magnetism," J. A ppl. Phys. 53, 7637
(1982).
[5]
R. T. Holm, "H elicon Transmission and H elico n-E xcite d E lectron
Paramagnetic Resonance in Hgi_xMnxTe," Ph.D. th e s is , Purdue
U n iv e rs ity (1973).
[6]
J. K. Furdyna, "Microwave Helicon In te rfe ro m e try in Semiconduc­
t o r Plasmas," Rev. S ci. In s tr . 37, 462 (1966).
[7]
R. E. Kremer and J. K. Furdyna, "EPR Measurements in Cdi_xMnxTe
Under Extreme Line Broadening Using Microwave Faraday R o ta tio n ,"
Phys. Rev. L e t t . , to be published.
[8 ]
R. T. Holm and J. K. Furdyna, "Microwave H elicon Propagation and
H elico n-E xcite d E le ctro n Paramagnetic Resonance in Hgi_xMnx Te,"
Phys. Rev. B 15, 844 (1977).
[9]
[10]
C. P. S lic h te r , P rin c ip le s o f Magnetic Resonance, (S pringer
Ser. in S o lid -S ta te Sciences No. 1) New York (1978).
A. Abragam, The P rin c ip le s o f Nuclear Magnetism,
s it y Press) London (1961).
(Oxford U niver­
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
153
[11]
M. Tinkham, Group Theory and Quantum Mechanics, (McGraw-Hill
Book Co.) New York (1964).
[12]
G. E. Pake and T. L. E s tle , The Physical P rin c ip le s o f E lectron
Paramagnetic Resonance, (F ro n tie rs in Phys. S e r., Benjamin)
Reading, Mass. (1973).
[13]
C. K it t e l , In tro d u c tio n to S o lid State P hysics, (John W iley and
Sons) New York (1976).
[14]
J. A. Gaj, R. Plane! and G. Fishman, "R e latio n o f MagnetoO ptical P ro p ertie s o f Free Excitons to Spin Alignment o f Mn2+
Ions in Cd]_xMnxTe," S o lid State Comm. 29, 435 (1979).
[15]
A. Pajaczkowska, "Physiochemical P ro p ertie s and C rystal Growth
o f AI ^BV I-MnBVI Systems," Prog. C ryst. Growth and Charact. _1,
289 (1978).
[16]
R.
E. Nahory, p riv a te communication.
[17]
J. K. Furdyna, W. G ir ia t , D. F. M itc h e ll and G. I . Sproule,
"The Dependence o f the L a ttic e Parameter and Density o f
Zni_xMnx Te on Composition, J. S o lid State Chem.," to be published.
[18]
J. A. Gaj, R. R. Galazka and M. Nawrocki, "G iant Exciton Faraday
R otation in Cd]_xMnx Te Mixed C ry s ta ls ," S o lid S tate Comm. 25^,
193 (1978).
[19]
R. A. Abreu, W. G ir ia t and M. P. Vecchi, "Temperature Dependence
o f the Absorption Edge in Cdi_xMnx Te," Phys. L e tt. 85A, 399
(1981).
[20]
M. M. M oriw aki, W. M. Becker, W. Gebhardt and R. R. Galazka,
"Temperature Dependence o f 1.98 eV Photoluminescence Band in
Cdi_xMnxTe Semiconductor A llo y s ," S o lid State Comm. 39, 367
(1981).
[21]
J. K. Furdyna, " E le c t r ic a l, O ptical and Magnetic P ro perties o f
Hgi-xMnxTe," Proc. U.S. Workshop on Phys. and Chem. o f HgCdTe,
M inneapolis, 1981, J. Vac. S ci. Tech. 21, 220 (1982).
[22]
R. R. Galazka, S. Nagata and P. H. Keesom, "Paramagnetic-Spin
G lass-Anti ferrom agnetic Phase T ra n s itio n s in Cdi_xMnxTe from
S p e c ific Heat and Magnetic S u s c e p tib ility Measurements," Phys.
Rev. B 22, 3344 (1980).
[23]
S. B. O s e ro ff, "Magnetic S u s c e p tib ility and EPR Measurements in
Concentrated Spin-G lasses: Cdi_xMnx Te and Cdi_xMnxSe," Phys.
Rev. B 25, 6584 (1982).
[24]
S. O seroff and F. Acker, "Magnetic S u s c e p tib ility on Semimag­
n e tic Sem iconductors," S o lid S tate Comm. 37, 19 (1980).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
154
[25]
S. Nagata, R. R. Galazka, D. P. M u llin , H. Akbarzadeh,
G. D. Khattak, J. K. Furdyna and P. H. Keesom, "Magnetic
S u s c e p tib ility , S p e c ific Heat, and the Spin Glass T ra n s itio n
in Hgi_xMnxTe," Phys. Rev. B 22, 3331 (1980).
[26]
G. D. K hattak, C. D. Amarasekara, S. Nagata, R. R. Galazka and
P. H. Keesom, "S p e c ific Heat, Magnetic S u s c e p tib ility and the
Spin-Glass T ra n s itio n in Hgi_xMnxSe," Phys. Rev. B 2^> 3553
(1981).
[27]
S. P.
[28]
D. P. M u llin , R. R. Galazka and J. K. Furdyna, "Microwave
Helicon Propagation and the Dynamic Magnetic S u s c e p tib ility in
H g i-xMnx Se," Phys. Rev. B 24, 355 (1981).
[29]
M. Escorne and A. Mauger, "Spin Glass versus A n ti ferrom agnetic
C lu ste rin g in C di-xM njJe," Phys. Rev. B 25, 4674 (1982).
[30]
T. M. Holden, G. D o llin g , V. F. Sears, J. K. Furdyna and
W. G ir ia t , "Magnetic C o rre la tio n s in Disordered MncZ n i-cTe
A llo y s ," S o lid State Comm. 40, 281 (1981).
[31]
G. Bastard, C. Rigaux and A. M y c ie ls k i, "G iant Spin S p lit tin g
Induced by Exchange In te ra c tio n s in Hgi_kMnkTe Mixed C ry s ta ls ,"
Phys. S ta t. S ol. (b) 79, 585 (1977).
[32]
P. Byszewski, K. Szlenk, J. Kossut and R. R. Galazka, "Energy
Levels a t r-P o in t in Hgi_xMnx Te in Intense Magnetic F ie ld s ,"
Phys. S ta t. S ol. (b) 95, 359 (1979).
[33]
A. M ycielski and J. M y c ie ls k i, "Acceptors in Semimagnetic
Semiconductors," Proc. 15th In t. Conf. on Phys. o f Semicond.,
Kyoto, 1980, ed. by S. Tanaka and Y. Toyozawa, (J. Phys. Soc.
Japan 49 (1980) Supplement A) Tokyo (1980) p. 807.
M c A llis te r and J. K. Furdyna, p riv a te communication.
[34]
A. G o ln ik, J. A. Gaj, M. Nawrocki, R. Planel and C. Benoit a la
Guillam e, "O p tica l Observation o f a Magnetic Molecule in
Cd]_xMnxTe," Proc. 15th I n t . Conf. on Phys. o f Semicond.,
Kyoto, 1980, ed. by S. Tanaka and Y. Toyozawa, (J. Phys. Soc.
Japan 49 (1980) Supplement A) Tokyo (1980) p. 819.
[35]
M. Nawrocki, R. P la n e l, G. Fishman and R. Galazka, "ExchangeInduced S p in -F lip Raman S c a tte rin g in a Semimagnetic Semi­
co n du ctor," Phys. Rev. L e tt. 46, 735 (1981).
[36]
E. D. P a lik and J. K. Furdyna, "In fra re d and Microwave Magnetoplasma E ffe c ts in Semiconductors," Rep. Prog. Phys. 33, 1193
(1970).
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
155
[37]
S. Takeyama and R. R. Galazka, "Band S tru c tu re o f Hgi_xMnxSe
from Anomalous Shubnikov-de Haas E ff e c t," Phys. S ta t. S ol. (b)
96, 413 (1979).
[38]
J. Lambe and C. K ik u c h i, "Paramagnetic Resonance o f CdTe:Mn2+
and CdS:Mn," Phys. Rev. 119, 1256 (1960).
[39]
K. Falkowski, "E le c tro n Paramagnetic Resonance o f CdTe:Mn2+,"
Acta Phys. Pol on. 32, 831 (1967).
[40]
P. H. Zimmermann, D. Davidov, R. Orbach, L. J. Tao and
J. Z itk o v a , "Exchange Narrowing o f Fine S tru c tu re in D ilu te
Magnetic A llo y s : Mn:Gd," Phys. Rev. B i5, 2783 (1972).
141]
H. K. Fun, Y. K. Agarwal, R. L. Mieher and J. K. Furdyna,
unpublished.
[42]
R. S. B razis and J. K. Furdyna, "In v e s tig a tio n o f the Microwave
Magnetoplasma Matching E ffe c t in Indium A ntim onide," J. A p p l.
Phys. 48, 4267 (1977).
[43]
J. E. S a n s o n e tti, D. P. M u llin , J. R. Dixon and J. K. Furdyna,
"E le c tro n Paramagnetic Resonance in Powdered Semiconductors and
Semimetals," J. Appl. Phys. 50, 5431 (1979).
[44]
S. B. O s e ro ff, R. Calvo, W. G ir ia t and Z. F is k , "Magnetic
P ro p e rtie s o f Cd;|_xMnxTe," S o lid State Comm. 35^, 539 (1980).
[453
D. J. Webb and S. M. Bhagat, "Comment on 'M agnetic S u s c e p tib ility
and EPR Measurements in Concentrated Spin Glasses: Cdi_xMnxTe
and Cdi-yMnySe, 1 (by S. B. O s e ro ff, Phys. Rev. B 25^, 6584 (1982)
(1 9 8 1 )), to be published in Phys. Rev. B (1983).
[463
M. S. Seehra and G. S rin iv a s a n , "E le c tro n Spin Resonance o f
Mn30tf Defects in MnO," J. Appl. Phys. 53, 8345 (1982).
[47]
A. Manoogian, B. W. Chan, R. Brun del Re, T. D onofrio and
J. C. W oolley, "E le c tro n Spin Resonance in CdxZnvMnzTe A llo y s ,"
J. Appl. Phys. 53, 8934 (1982).
[48]
S. B. O s e ro ff, p riv a te communication.
[49]
A. W it t lin , W. Knap, Z. Wilamowski and M. Grynberg, "Evidence
f o r the Spin-Dependent S c a tte rin g o f Conduction E lectrons on
Mn2+ Ions in Hgi.xMn-jJe and Cd^xMnxSe Mixed C ry s ta ls ," S o lid
S tate Comm. 36, 233 (1980).
[50]
M. Dobrowolska, H. D. Drew, J. K. Furdyna, T. Ic h ig u c h i,
A. Witowski and P. W o lff, " E le c tric -D ip o le Spin Resonance o f
Bound E le c tro n ic States in Cdi_xMnxSe," Phys. Rev. L e tt. 49,
845 (1982).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[51]
M. Dobrowolska, T. Ich ig u ch i and H. D. Drew, p riv a te communica­
tio n .
[52]
T. Ic h ig u c h i, H. D. Drew and J. K. Furdyna, "D~ Levels in
C di-xMnxSe, " Phys. Rev. L e tt. 50^, 612 (1983).
[531
Y. Guldner, C. Rigaux, M. Mennant, D. P. M u llin and
J. K. Furdyna, "Magnetooptical Evidence o f Exchange In te ra c tio n s
in Zero-Gap H g i-xFexTe Mixed C ry s ta ls ," S o lid State Comm. 33,
133 (1980).
[54]
W. G ir ia t , p riv a te communication.
[55]
U. Debska, p riv a te communication.
[56]
D. P. M u llin , "Microwave Studies o f SemimagneticSemiconductors,
Ph.D. th e s is , Purdue U n iv e rs ity (1980).
[57]
F. S. Hum, G. W. Ludwig, G. D. Watkins and H. H. Woodbury,
"Spin H am iltonian o f Co2+," Phys. Rev. L e tt. 5_, 468 (I9 6 0 ).
[58]
A. G. Anders, V. A. Moiseev and A. I . Zuyagin, "EPR Spectrum
o f Co2+ Ions in S ingle C rysta ls o f Hexagonal ZnS," Sov. Phys.S o lid S tate 11, 3059 (1970).
[59]
M. C. Wilson and G. F. H u ll, J r . , "On the Faraday E ffe c t a t
Microwave Frequencies," Phys. Rev. 74, 711 (1948).
[60]
A. K a s tle r, "Une Nouvelle Methode de Mesure deL 'e f f e t Zeeman.
L 'e f f e t de Resonance de la P o la ris a tio n R o ta to ire Magnetique
des Ondes H ertziennes," Acad. S c i. Compt. Rend. 228, 1640
(1949).
[61]
C. R yte r, R. L a croix and R. Extermann, " E ffe t Faraday des Ondes
C en tim e triq ue s," Helv. Phys. Acta 2[3, 539 (1950).
[62]
C. R yter and R. Extermann, " E ffe t Faraday des Ondes C enti­
m etriques. Phenomenes de Resonance," Physica J 7 , 440 (1951).
[63]
J. S o u tif-G u ic h e rd , "Etude de L 'e f f e t Faraday Paramagnetique,"
Ann. des Telecomm. 13, 169 (1958); 13, 222 (1958).
[64]
J. S o u tif-G u ic h e rd , "Paramagnetic Faraday E ffe c t," J. Appl.
Phys. 29, 256 (1958).
[65]
Y. Servant, "Etude de la R otation de Resonance Paramagnetique
{•lectronique du S u lfa te de Manganese Monohydrate dans la Bande
des 3000 MHz," Acad. S c i. Compt. Rend. 258, 1455 (1964).
[ 66]
Y. Servant, " C o n tr ib u tio n ^ L'Etude de L 'E ff e t Faraday H ertzien
Resonance Paramagnetique E le c tro n iq u e ," Ann. Phys. 4, 579 (1969)
with permission of the copyright owner. Further reproduction prohibited without permission.
157
[67]
Y. Servant, "Magneto-Microwave E ffe c ts Related to E lectron Spin
Resonance," Mag. Res. Rev. 4 , 1 (1975).
[ 68]
Y. Servant, "Magneto-Microwave E ffe c ts Related to E lectron
Paramagnetic Resonance," Physica 89B, 280 (1977).
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDICES
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix A.
A nalysis o f the Farada.y E ffe c t Data
In th is se ctio n we fo rm ulate a mathematical a n alysis o f a
generalized e ll i p t i c a l p o la riz a tio n in the Faraday geometry and then
examine the re s u lts fo r several special cases, i . e . , those cases which
we have used to measure Faraday r o ta tio n and e l l i p t i c i t y .
s p e c ify in g a coordinate system as shown in Figure A .I.
We begin by
The in c id e n t
microwave ra d ia tio n is lin e a r ly p o la riz e d w ith i t s f- v e c to r along y .
This ra d ia tio n passes through a c ir c u la r p o la riz e r made o f a se ctio n o f
e l l i p t i c a l waveguide ju s t long enough so th a t the f i e ld components
p o la riz e d p a ra lle l to the m ajor and minor axes are 90° o u t o f phase as
they emerge.
The o rie n ta tio n o f the c ir c u la r p o la riz e r is s p e c ifie d by
x 1 and y ' , corresponding to i t s axes o f symmetry, such th a t p o la riz a ­
tio n p a r a lle l to x ' is retarded by ir/2 radians r e la tiv e to p o la riz a tio n
p a ra lle l to y 1.
A fte r passing through the p o la r iz e r , the wave (w ith
i t s p o la riz a tio n determined by the p o la riz e r o r ie n ta tio n ) is in c id e n t
on the sample.
The signal tra n s m itte d through the sample is then
in c id e n t on a c ir c u la r - to - r e c ta n g u la r t r a n s itio n , which admits o n ly
th a t p o la riz a tio n which is p a r a lle l to x" and guides th is component o f
the signal to the d e te c to r.
The orthogonal component o f the tra n s ­
m itte d wave ( i . e . , th a t p o la riz a tio n which is p a r a lle l to y " ) is
absorbed by a vane in the waveguide.
We s t a r t by d e fin in g the t- v e c to r
o f the in c id e n t wave in the coordinates shown in Figure A .I.
E^ y cos wt
o
E ( x 's in e + y 'co s e)cos
o
cot .
(A. 1)
R eca llin g the behavior o f the c ir c u la r p o la r iz e r , we can w rite the wave
with permission of the copyright owner. Further reproduction prohibited without permission.
159
T
i.
y
X
Figure A .I.
Geometry o f the p o la riz a tio n apparatus. 0 is the angle
between the in c id e n t p o la riz a tio n and the o rie n ta tio n o f
the c ir c u la r p o la r iz e r , y is the angle between th is
o rie n ta tio n and th a t o f the d e te c to r.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
160
tra n s m itte d by i t as
?2 =
EQ[x 's in e co s (u t - |-) + y 'c o s e cos tot] .
Then by using complex n o ta tio n , we can re-express
(A .2)
in r o ta tin g
coordinates:
•
•
TT
- I t o t + 1 Tj-
E Re x 's in 0 e
o
- i t
+ y 'c o s 0 e~ “
EoR e [ix 's in 0 + y 'c o s 0 ] e
■itot
2 EQRe[ ( i x ' +y' )s in 0 + ( i x ' - y ' ) s i n 0 + ( ix '+ y ') c o s 0
- ( i x ‘ - y 1)cos 0] e
-itot
EQRe[i ( x ' - i y 1) ( s in 0+cos 0 ) + i ( x '+ iy ' ) (s in o+cos 0) ] e-1a)t
E Re i S ^ - s 1n (0
0
ft
'
E Re i
0
e_COS
(e -
V
-
'
e+ C OS (0
■itot
cos (e + J-}
' 4'
/2
■itot
+
(A. 3)
where we have defined the ro ta tin g coordinates e_ and e+ as
=
_
x '- i. y ‘
x '+ iy '
(A .4)
ft
ft
When the microwaves tra v e l through the sample, in the Faraday
geometry (j< || £ ) , the propagation constants d if f e r fo r the two c ir c u ­
l a r p o la riz a tio n s corresponding to the e+ and e_ components o f
Equation (A .3 ).
Thus the am plitude tra n s m itte d by the sample becomes
Z
]L
3
=
E Re i e_cos(e - | ) e
0
la
e
„,Z
Z
"
t t -\
_
- e+cos(e + |-)e
+
l a ,Z
_
e
+
a- i i o t
-
5
(A .5)
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161
where a+ and B+ are the phase and a tte n u a tio n c o e ffic ie n ts defined in
Equation (2 .1 1 ).
Only the p ro je c tio n o f t^ p a ra lle l to the d e te cto r
( i . e . , p a ra lle l to x") w i l l be detected.
So |t^| =
* x ">
R ecalling
Figure A .1 and Equation (A .4 ), we have
e
-x"
1
= — (cos y - i s in
y
_1 e" iv
)
ft
e+ *x
_1
(cos y + i sin y )
(A . 6 )
= — ely
ft
ft
where y is the angle between x' and x" as shown in Figure A .I .
The
am plitude reaching the d e te c to r is then
-6 Z
E.
4
=
E Re i
0
ft
cos(e - j )
e
- cos (e + j )
e
"
la Z
e
-B,z
e
"
e” Y
ia.z
. ■
e y
■iait
(A .7)
In an experim ent, the q u a n tity measured corresponds to the tim eaveraged power in c id e n t on the detecto* , which is given by
<P>
-
I Re
cos (0 - j )
-
I
E*
cos (e + j )
9
„
“ 26- Z
9
*
" 26+Z
cos (0 - 4) e
+ cos (e + 4) e
-B_Z -B+Z
t i(a _ -a + )z -2 iy
e
e
• Re e
i(a,-a )Z-2iYY
+ e
.
(A . 8 )
Note th a t
i( a _ - a +)z-2iY
Re e
i ( a +-a_)z-2iY'
+ e
2 COS[(a_-a+)z-2Y] •
(A .9)
In a d d itio n , i t is re a d ily seen from Equation (A . 6 ) th a t the amplitude
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
162
-e_z
o f the e_ p o la riz a tio n reaching the d e te c to r is given by cos(e - | ) e
-e .z
whii le th a t o f the e+ p o la riz a tio n is cos(e + ^-)e_ + . W ritin g
e
”
2
A
=
A
A,
+
=
- e .z
A
e
o+
l
"6 z
= — E cos (e - t ) e
at o
'•4-'
ft
=
9
.
-e z
— E cos (e + t ) e
,
yjr o
(A. 10)
Equation (A . 8 ) fo r the power becomes
<P>
=
A2 + A2 - 2A+A COS[(a -a +)z-2 y]
=
(A_+A+) 2s in 2$ + (A_-A+) 2cos2$ ,
(A .11)
where we have defined
$
= \
(a_~a+) z ~ T
-
9p - y •
(A .12)
Here 0p is the Faraday r o ta tio n .
Equation (A .11) is the general case fo r any values o f the
angles e and y in Figure A .I.
We now consider special cases which
correspond to the actual s e ttin g s used in our measurements.
In the
case o f low manganese concentrations (0.01 < x < 0 .1 5 ), the EPR was
r e la t iv e ly narrow and stro n g .
Because o f t h is , the Faraday ro ta tio n
and e l l i p t i c i t y were la rg e and q u ite easy to measure.
As the mangan­
ese content increased, the e ffe c ts became s m a lle r, and more s e n s itiv e
techniques had to be developed.
In the low co n cen tra tio n range, where the Faraday ro ta tio n 0p
is la rg e , the angle o f ro ta tio n was determined as fo llo w s .
The
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163
in c id e n t ra d ia tio n was lin e a r ly p o la riz e d and fo u r transm ission traces
were taken, w ith the r o ta tin g j o i n t adjusted so th a t the angle between
the d e te c to r and the in c id e n t p o la riz a tio n had the fo llo w in g values:
Y = 0 °, 45°, 90° and 135° (0° corresponds to the maximum s ig n a l, 45°
is a ha lf-po w e r p o in t, e t c . ) .
Figure A .2.
An example o f such data is shown in
The value o f the r o ta tio n was e x tra c te d from the data by
measuring the d iffe re n c e s between two tra c e s .
R e fe rrin g to the
coordinates shown in Figure A .1, we see th a t fo r the 45° tra c e and
the 135° tra c e ,
4- <PV
<P>W
y
-» /4
corresponds to ± tt/4 .
Then
(A.+A+ ) 2s in 2 (e F - J ) + (A_-A+ ) 2cos2 (e F -
"
-
(A_+A+ ) 2s in 2 (e + J )
-
( A _ - A + ) 2 c o s 2 { 0 f + J)
/
=
(A_+A+ ) 2 [s in 2 (eF - f ) - s i n 2 (eF + J )
+ (A_-A+) 2 [cos 2 (eF - 5 - c o s 2 (eF + J)
2A+A_ s in 2 (ep - J )-co s ‘ (eF - f ) - s i V ( e F + f)+ cos^(eF + J)
2A+A_ cos 2(ep + |) - c o s 2(ep - J)
(A .13)
4A+A_ s in 2eF
S im ila r ly , fo r the 0° tra c e and the 90° tra c e
y
= 0° and
tt
/2,
(
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
y =0 '
z
o
(A
CA
X = 45'
s
(A
Z
<
£K
I-
QO
0.4
2.0
0.8
MAGNETIC FIELD ( T )
Figure A .2.
Linear p o la riz a tio n data (e = 0°) w ith d if fe r e n t values fo r the angle between the
in c id e n t p o la riz a tio n and the d e te c to r (y = 0 °, 45°, 90°, 135°).
CD
165
I
re s p e c tiv e ly , and t h e ir d iffe re n c e is
4A+A_ cos 20p
.
(A .14)
Thus, by ta k in g the r a tio o f these d iffe re n c e s we can o b ta in the
Faraday ro ta tio n :
4A+A_ sin 20p
4A+A_ cos 20p
tan 20
(A .15)
F
Although in fo rm a tio n on the Faraday e l l i p t i c i t y
can be
e xtra cte d from data such as th a t shown in Figure A .2, in the study o f
low manganese co n c e n tra tio n s , we p re fe rre d to use data f o r c ir c u la r ly
p o la riz e d microwaves.
I t should be remembered th a t the actual cause
o f ep is c ir c u la r d ichroism , where one c ir c u la r p o la riz a tio n is
p r e fe r e n tia lly absorbed to the o th e r.
We can thus study th is e ffe c t
d ir e c t ly by observing the absorption o f the two opposite c ir c u la r
p o la riz a tio n s .
The two c ir c u la r p o la riz a tio n s correspond to 0 = ±
Figure A . l, w ith the CRA p o la riz a tio n having 0 = -
0 = +
in
and CRI having
S u b s titu tin g fo r 0 in Equation (A .10) gives
C
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166
fo r 0 = - j :
^
A
1
'M
= — E e
J2 0
fo r e = + J :
4
A
=
,
A
,
0 ,
A
=
-3
= — E e
y/2 0
0 ,
z
~
.
(A. 16)
The c ir c u la r dichroism is then
1 2 "^+ z
<P>9 = - u / 4
<PW
=
£n
4
2 j o J ______
I F2
2 0
- 2S- Z
2(3_-B.)z
=
£n e
=
4£p
,
(A .17)
where we have defined the Faraday e l l i p t i c i t y as Ep = |-(b _ - 3+ )z.
(
As the manganese content increases, the size o f the Faraday
ro ta tio n and e l l i p t i c i t y decreases.
In order to measure these sm aller
e ffe c ts , we have developed a more s e n s itiv e technique.
To measure 6p we use lin e a r in c id e n t p o la riz a tio n as before
( e = 0 in Equation (A .1 0 )).
However, we now use a value o f
y
very
close to 90° (the in c id e n t p o la riz a tio n is alm ost, but not q u ite ,
p e rpendicular to the d e te c to r), so th a t the d e te c to r measures o n ly a
small p ro je c tio n o f the in c id e n t s ig n a l.
be s u ita b ly increased (see Figure A .3 ).
The a m p lifie r gain can then
The angle yQ e 90 - y is
determined a t B = 0 by moving the ro ta tin g j o i n t so th a t the maximum
p ro je c tio n is obtained, i . e . , y = 0 ° (in c id e n t and detected p o la riz a ­
tio n s are c o llin e a r ) , and then a tte n u a tin g the signal u n til i t is
equal to y , the o r ig in a l p ro je c tio n .
Since fo r lin e a r p o la r iz a tio n ,
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Incident
polarization
detector
projection
maximum projection - y when
ottenuotion - XdB
Figure A. 3.
I llu s t r a t io n o f how the Faraday ro ta tio n was e x tra cte d from the data,
za tio n was lin e a r and values o f x and y were measured.
The in c id e n t p o la ricn
168
O
the sig n a l received by the d e te c to r va rie s as s in y , we then have
s in 2yo
=
[lO ^ 10]" 1
(A .18)
where x is the a tte n u a tio n in dB required to reduce the maximum signal
a t B = 0 to the s iz e o f the o r ig in a l p ro je c tio n .
Knowing y and x , we
can c a lc u la te the maximum power a v a ila b le ( in the same u n its as y ) a t
B = 0, i . e . ,
E2 e 2B° Z =
where bq is
y • 10x /1 ° ,
the a tte n u a tio n c o e ffic ie n t f o r
(A .19)
B = 0.Follow ing the same
procedure as th a t used in Equation (A .13), the d iffe re n c e between the
two traces in Figure A .3 is given by
<p>^
- <P>_Y =
O
0
2A+A_[ c o s
2(0
f
-
yo
) -
cos
2( e p+ Y 0 ) ]
.
(A . 20)
R e ca llin g th a t fo r lin e a r p o la r iz a tio n , e = 0 and s u b s titu tin g fo r A+ ,
we get
<p>+
0
-<p>
0
=
i o -(e +B+ )z
2 Eo e
[cos 2(6f -y0 )-cos 2 ( e p+Y0 ) ]
=
i o -(b + e,)z
2 Eo e
^2sin 2eF s in 2V
=
? -(e _ + e .)z
Eq e
s in 2yq s in 20F
.
(A .21)
Since th is technique is used fo r the case o f very weak e ffe c ts , we can
s a fe ly assume th a t
- 2b z
e
0
*
e
-(3 +S,)z
+
.
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(A .22)
169
T
A
2 “ 2Boz
Then, knowing yQ and Eq e
, we can c a lc u la te 9p.
With th is sensi­
tiv e technique we are e a s ily able to measure angles o f less than one
minute o f a rc.
F in a lly , we consider the e l l i p t i c i t y fo r the case o f high mangan­
ese co n cen tra tio n s.
By using a very small value o f 0 , the in c id e n t
p o la riz a tio n a t B = 0 is made to be a very e c c e n tric e llip s e ( i . e . , very
ne arly lin e a r ) .
The d e te c to r is s e t to measure the minor axis
a t B = 0 as shown in Figure A.4.
(y
= 90°)
The e c c e n tr ic ity o f the e ll i p t i c a l
p o la riz a tio n , tan 0 , is then obtained by moving the r o ta tin g j o i n t to
measure the major axis a t B = 0 and a tte n u a tin g the signal u n t il i t is
the same size as the minor axis was o r ig in a lly .
Then, i f the attenua­
tio n re q uire d was x dB,
tan 0
=
y -10
2
_2Bn Z
and E e
o
x/10
=
is obtained as b e fo re .
10
-x /10
(A .23)
Since the traces in Figure A .4
are made w ith the d e te c to r measuring the minor axis
2
2
= 9 0 °), we have
(y
2
2
$ = 0p - 90° and s in $ and cos $ become cos 0p and s in 0p, re s p e c tiv e ly .
S ta rtin g from Equations (A .10) and (A .11) we form ulate an a lte rn a te
expression f o r the power:
-3 z
<P>
=
Ao e
+A
-(3_+3+ )z
=
-(e_+e+ )z
e
-3 +z,
e
-B z
COS 0p +
A e
o
-A. e
-M -
-Jg(B -S .)z
+ k( 3_ - 3 .)z
A e
+Art e
o
o,
: “ -*s(3 - 3 .) z
+k{ 3 -3,)z-\
A e
-A e
o
o.
-eF
A. e
o_
+Ep'
+A e
o+
cos 0p+ A e
°_
. 2
sin 0r
2
cos 0r
(A .24)
s in 20r
-e l"-A
+ep'
. 2
e r Sin 0r
°+
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Detector
major axis = y when
attenuation s XdB
Figure A .4.
I llu s t r a t io n o f how the Faraday e l l i p t i c i t y was e xtra cte d from the data.
p o la riz a tio n was e l l i p t i c a l and values o f x and y were measured.
The in c id e n t
O
171
where we have again defined ep = J5(g_-e+ )z.
Expanding the exponentials
2
and keeping only terms to Ep, we have:
<P>
=
-(e _ + 6+)z
e
•U_+e+)z
=
1 ■ ef +
T
+ A
1 • eF +
T
- A
£F'
e
(A +A
vo
o,-'
1+/
1 + eF +
T
1 + ef +
T
(A -A 1
F1- o
o ,;
. 2
s in 0
cos er
. 2
sin e.
Epl
[A -A ) - e P(A„ +A )
^0
0 ,-' F'- o
o,
1+/
9
cos“ e.
(A .25)
C arrying o u t the m u ltip lic a tio n s and again keeping o n ly terms to Ep,
we a rriv e a t
<P>
=
- ( 6_+S+)z
e
(A
0_
+A ) 2 c o s 2 0,-+(A -A ) 2
0 /
F v 0_
0 +J
°+
= —
J?
0
(A .26)
+4 ( (Ao.+Ao 2+W
R eca llin g the d e fin itio n o f A
°_
F
J
2M V fl0+)
A„ +A„
s in 20p
(Equation (A .1 0 )), we can w rite
c o s (0 - f) + c o s (0 + J)
= — Eq c o s
/ ?
V.
/2
0
cos
+ s in
0
s in |- + cos
0
cos
- sin
0
s in ^
— E 2 — cos 0
/2 0 L J?.
E cos
o
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( A-27)
172
Li kewi se ,
Aq
- Aq+
Eq sin 0 .
=
(A .28)
S u b s titu tin g Equations (A .27) and (A .28) in to (A .26) y ie ld s
<P>
=
- ( 0_+8+ )z 2
e
Eq
[cos
2
2
2
2
2
e cos 0p+sin 0 sin 9p-20p cos 0 s in 0 + £p]
=
- ( 0_+ 0+)z 2
e
Eq
[cos
2
2
2
2
2
0 cos 0p+sin 0 s in 9p-ep s in 2© + £p] .
(A .29)
The two traces in Figure A .4 were made w ith opposite e l l i p t i c a l
p o la riz a tio n s
( i . e . , © (trace 1) = -© (tra ce 2 ) ) .
Thus we can w rite the
d iffe re n c e between the two traces as
<P>_Q-<P >+0
=
e
- ( 0_+ 0+ )z
2
?
Eq
[cos
2
2
2
(-e)cos Op+sin (-e )s in 0p-epSin(-2e)
+ ep-cos^(+e)cos^0p-sin^(+0)sin^0p+£psin(+2e)-£p]
-(6 + e .)z
=
e
?
E^
2ef s in 20 .
2
Since we have measured e and Eq e
-(e_+e+)z
e
-2eo z
(A .30)
, by once again assuming
-20 z
e
, we can o b ta in the Faraday e l l i p t i c i t y £p from the
d iffe re n c e between the two tra c e s .
I t should be noted th a t in reaching Equations (A .21) and (A .30)
we assumed th a t the two traces in Figure A .3 corresponded to
y (tra c e 1) = -y (tra c e 2) and in Figure A .4, © (trace 1) = - 0(tra c e 2 ).
This could be achieved by moving the ro ta tin g j o i n t in the f i r s t case
and by re a d ju s tin g the c ir c u la r p o la riz e r in the second.
In p ra c tic e ,
however, th is was accomplished by fix in g e ith e r the j o i n t o r the
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173
p o la riz e r and, in s te a d , re versing the magnetic f i e ld .
Since th is
reversed the sign o f 0p o r £p, ro ta tio n o r e l l i p t i c i t y could be
obtained by the same manner o f ta kin g the d iffe re n c e between the
re sp ective tra c e s .
Reversing the f i e ld was not only a more accurate
way to perform the measurement (no moving p a r ts ) , b u t in a d d itio n was
much s im p le r, both p h y s ic a lly and e m o tio n a lly .
(
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174
7
'I
Appendix B.
An H is to ric a l Note on the EPR Faraday E ffe c t
During the fin a l w r itin g o f th is th e s is , a lit e r a t u r e search
revealed th a t the method o f studying EPR through the Faraday ro ta tio n
and e l l i p t i c i t y has been used by e a r lie r researchers working w ith
paramagnetic s a lts .
While our own re s u lts regarding th is approach were
obtained independently, fo r the sake o f completeness we w il l present a
b r ie f h is to r ic a l survey o f the Faraday e ffe c t and o th e r microwave
"m agnetooptical 11 e ffe c ts employed in the study o f EPR.
The microwave Faraday e ffe c t associated w ith the Larmor preces­
sion o f magnetic spins was f i r s t observed in 1948 by Wilson and H u ll,
who studied the paramagnetic s a lts MnClg^F^O and MnSO^^O using
9 GHz microwaves [5 9 ].
T h e ir dc magnet was not la rg e enough to reach
the resonance c o n d itio n corresponding to th e ir microwave frequency, so
{
th a t the Faraday ro ta tio n they observed was n e a rly lin e a r w ith f i e ld
(the c o n d itio n u)Q «
to in our te rm in o lo g y).
Since they could not reach
the EPR c o n d itio n , they were sim ply te s tin g various m a te ria ls to see
whether any observable ro ta tio n was present.
In 1949 K a s tle r [60] suggested th a t the Faraday ro ta tio n
observed by Wilson and H ull might have the shape o f a d isp e rsio n curve
when the f i e ld sweep was extended to the v ic in i t y o f EPR.
The f i r s t
experimental measurements o f the Faraday ro ta tio n which included the
EPR region were made the next year by Ryter e t al_. [6 1 ,6 2 ].
Using
9.5 GHz microwaves, they measured ro ta tio n s o f about 3° in MnSO^H^O.
The most thorough work on the su b je ct was done by S o u tif-G uicherd
[6 3 ,6 4 ], whose th e s is d e a lt w ith EPR Faraday r o ta tio n .
She discussed
the e ffe c t using the m odified Bloch model and pointed o u t (as we have
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175
t
k
done) th a t the ro ta tio n changes sign a t fie ld s lower than the resonance
f i e ld fo r small wT.
Not u n til 1964 d id observers o b ta in simultaneous measurements o f
the Faraday ro ta tio n and e l l i p t i c i t y .
Servant [6 5 ], using 3 GHz
microwaves, stu d ied the r o ta tio n and e l l i p t i c i t y in MnSO^^O.
His
technique, described in d e ta il in h is th e s is [ 66] , involved e l l i p t i c a l
p o la riz a tio n w ith the d e te c to r o rie n te d s lig h t ly away in both d ire c ­
tio n s from the minor a xis o f the e llip s e .
f i e ld was swept in both d ire c tio n s .
For each o r ie n ta tio n , the
By m anipulating the re s u lta n t fo u r
tra c e s , he was able to e x tra c t both the r o ta tio n and the e l l i p t i c i t y .
Servant has subsequently extended h is studies o f the Faraday e ffe c t
associated w ith EPR to several o th e r paramagnetic s a lts [6 7 ,6 8 ].
I t should be pointed out th a t w h ile the techniques used in th is
(
e a r lie r work were s im ila r to those we have been using, there were
s ig n ific a n t d iffe re n c e s .
Our technique allow s us to measure the
e l l i p t i c i t y and ro ta tio n by sim ply re ve rsin g the dc f i e l d ; no change
o f p o la riz a tio n o r d e te c to r o rie n ta tio n is necessary.
E xp erim entally,
we have found th a t making these l a t t e r changes, and making them
re p ro d u c ib ly , is extrem ely d i f f i c u l t .
Thus, a method v^hich avoids
"moving p a rts " (changing e ith e r p o la riz a tio n o r d e te c to r o r ie n ta tio n )
should lead to more accurate r e s u lts .
In a d d itio n , although the m odified Bloch model was discussed fo r
the case o f small coT [6 4 ], and i t was suggested th a t the method could
be used fo r the case o f broad lin e s [ 68] , the paramagnetic s a lts used
in these e a r lie r stu d ies had re la x a tio n times long enough so th a t
goT »
1 and the lin e s were r e la t iv e ly narrow.
Our r e s u lts , which
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reached oiT ^ 0.1 and used microwaves o f higher frequency, to our
knowledge correspond to the s h o rte s t re la x a tio n times measured
q u a n tita tiv e ly in any m a te ria l.
(
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
177
VITA
Russell Eugene Kremer was born in Seward, Nebraska to Lorne and
Hazel (K ing) Kremer on May 10, 1954.
He was ra ised in M ilfo rd ,
Nebraska, and graduated from M ilfo rd High School in May 1972.
He
continued h is education a t Goshen C ollege, Goshen, Indiana and in
December 1975 received a Bachelor o f A rts degree in Physics.
The
fo llo w in g September, he entered Purdue U n iv e rs ity and received a Master
o f Science degree in May 1978 and the Doctor o f Philosophy degree in
May 1983.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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