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Toward the development of self-biased ferrite microwave devices

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Toward the development of self-biased ferrite
microwave devices
A Thesis Presented
by
Tomokazu Sakai
To
The Department of Electrical and Computer Engineering
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in
Electrical Engineering
Northeastern University
Boston, Massachusetts
August 20th 2008
3339331
2009
3339331
Abstract
Indium doped BaFe12-xInxO19 was prepared by a modified ceramic technique using
In2O3, BaCO3, and Fe2O3 followed by mechanical dispersion. The amount of Indium x
was controlled by x = 1.0, 1.5 and 2.0. The powder was screen printed on alumina
substrate using a suitable binder and in-plane oriented under a dc magnetic field of 15
kOe. The screen printed films were annealed at different durations to produce dense and
thick ferrite materials.
Scandium doped BaFe12-xScxO19 were produced by a modified chemical coprecipitation technique. The amount x of Scandium doping was varied by x=0.3, 0.5, 0.8
and 1.0. The size of platelets of BaFe12-xScxO19 was controlled by sintering temperature
and time. The screen printed and in-plane oriented films were annealed at different
temperatures to produce a dense and thick ferrite films.
To meet the industry requirements in telecommunication systems, a new type of
ferrite phase shifters should be able to work at Ka-band and higher frequencies. Barium
hexaferrite with high anisotropy field (HA) is the candidate for high frequency ferrite
phase shifter and we could control HA by doping Scandium and Indium. We designed
and fabricated a prototype of microstrip line phase shifter by using BaFe10.5In1.5O19 and it
worked at 33 GHz. We compared the data of phase shift with simulation.
i
NORTHEASTERN UNIVERSITY
Graduate School of Engineering
Thesis Title: Toward the development of self-biased ferrite microwave devices
Author: Tomokazu Sakai
Department: Electrical and Computer Engineering
Approved for Thesis Requirement for the Doctor of Philosophy Degree
______________________________________________
Thesis Advisor
Carmine Vittoria
____________________
Date
______________________________________________
Thesis Committee Member
Nian Sun
____________________
Date
______________________________________________
Thesis Committee Member
Katherine S. Ziemer
____________________
Date
______________________________________________
Thesis Committee Member
____________________
Date
______________________________________________
Department Chair
____________________
Date
Graduate School Notified of Acceptance:
______________________________________________
Director of the Graduate School
ii
____________________
Date
Acknowledgement
I would like to thank Prof. Carmine Vittoria who had been advising and encouraging
me all the time during my ph.D program. His deep knowledge of physics and electrical
engineering helped me to complete my ph.D. His sharp insight of physics was often
beyond my scope and it helped me to pursue my research of magnetic materials and
microwave device applications. I would also like to thank Prof. Vincent G. Harris who
kept supporting and advising me with his knowledge of magnetic materials. He always
shared his precious time with me and gave me the right direction of my research.
I would like to thank Dr. C. N. Chinnasamy and Dr. S. D. Yoon. Dr. Chinnsamy’s
chemical synthesis technique dramatically changed my research of magnetic materials.
At the same time, he supported and encouraged me with his warm heart and he always
devoted his time for my research problems. Dr. Yoon was my long term friend and he
recommended me to come to the research of magnetic materials and microwave devices.
He often gave me nice opinions for my research and I could be inspired from them. I
would thank all of colleagues in the Center of Microwaves and Magnetic Materials and
Integrated Circuits. They helped me a lot.
Finally I would thank my parents who encouraged and inspired me with their big and
warm hearts. Unfortunately my father passed away at March 18th 2007, but I believe that
he would be glad to hear from me that I earned ph.D. I would never forget their supports
and encouragements for the rest of my life.
iii
Table of contents
Title: Toward the development of self-biased ferrite microwave devices.
Abstract…………………………………………………………………………………….i
Approval…………………………………………………………………………………..ii
Acknowledgement………………………………………………………………………..iii
List of figures……………………………………………………………………………..vi
List of tables……………………………………………………………………………….x
Chapter 1: Introduction…………………………………………………………………1
References……………………………………………………………………4
Chapter 2: Background on the Magnetism of Ferrite Materials………..……………6
References…………………………………………………………………..18
Chapter 3: Instrumentation and Experimental Techniques…………………………28
Section 1: X-ray diffractometer………………………………………………………28
Section 2: Scanning Electron Microscope (SEM)
and Energy Dispersive X-ray Spectroscopy (EDX)…...………...………..31
Section 3: Vibration Sample Magnetometer (VSM)…...…………………………….35
Section 4: Planetary Ball Mill………………………………………………………...37
Section 5: Ferromagnetic Resonance (FMR)…………………………………………38
References…………………………………………………………………39
Chapter 4: Synthesis and Properties of BaFe12-xInxO19……………………………...56
Introduction…………………………………………………………………………...56
Section 1: Experiment………………………………………………………………..57
iv
Section 2: Results and Discussion…………………………...………………………58
Section 3: Conclusions……………………………………………………………….61
References………………………………………………………………...62
Chapter 5: Synthesis and Properties of BaFe12-xScxO19.............................................72
Introduction…………………………………………………………………………...72
Section 1: Experiment……………………………………………………………..…73
Section 2: Results and Discussion………………...…………………………………75
Section 3: Conclusions……………………………………………………………….78
References………………………………………………………………...78
Chapter 6: Synthesis and Properties of Perpendicular Oriented BaFe11In1.0O19 by
Conventional Ceramic Method.......................................................................................90
Introduction…………………………………………………………………………...90
Section 1: Experiment………………………………………………………………..90
Section 2: Results and Discussion…………………………...………………………92
Section 3: Conclusions……………………………………………………………….94
References………………………………………………………………...94
Chapter 7: Design and Fabrication of Phase Shifter………………………………..102
Introduction………………………………………………………………………….102
Section 1: Design and Simulation of Phase Shifter………………………...………102
Section 2: Results and Discussion……………………………………………..…...109
Section 3: Conclusions……………………………………………………………...110
References……………………………………………………………….110
Chapter 8: Summary and Conclusions………………………………………………122
v
List of figures
Figure 1.1.1: Prototype of phase shifter with BaFe10.5In1.5O19.
Figure 2.2.1 Unit cell of spinel.
Figure 2.2.2 Superexchanges in spinel.
Figure 2.2.3 Unit cell of BaFe12O19. From Alex Goldman, Modern Ferrite Technology.
Figure 2.2.4 Phase diagram of hexa-ferrite. From Soshin Chikazumi,
Physics of ferromagnetism 2nd edition.
Figure 2.2.5 Crystal structure of cubic spinel drawn taking in [111] as c-axis.
From Soshin Chikazumi, Physics of ferromagnetism 2nd edition.
Figure 2.2.6 Atomic arrangement of R-layer. From Soshin Chikazumi,
Physics of ferromagnetism 2nd edition.
Figure 2.2.7 Atomic arrangement of M-type crystal structure. From Soshin
Chikazumi, Physics of ferromagnetism 2nd edition.
Figure 3.1.1. Bragg’s condition.
Figure 3.1.2. Schematic picture of X-ray diffractometer.
Figure 3.1.3. X-ray diffractometer.
Figure 3.1.4. Miller Indices.
Figure 3.1.5. Fourth index i.
Figure 3.1.6. Schematic picture of X-ray diffractometer.
Figure 3.2.1. Schematic picture of SEM.
Figure 3.2.2. Energy gaps.
Figure 3.3.1. Block diagram of Vibrating Sample Magnetometer.
Figure 3.3.2. VSM.
Figure 3.3.3. Hysteresis curve.
vi
Figure 3.4.1. Schematic picture of ball milling.
Figure 3.4.2. Pulverisette 6.
Figure 3.5.1. (a). Magnet, RF source and Wave guide for FMR.
Figure 3.5.1. (b). Lock-in Amplifier, Modulation drive and
Power supply for FMR.
Figure 4.2.1-(a) XRD of the BaFe11In1O19
Figure 4.2.1-(b) XRD of the oriented BaFe10.5In1.5O19.
Figure 4.2.2-(a) Scanning electron micrograph of the BaFe11In1O19
(left) bulk and (right) after ball milling.
Figure 4.2.2-(b) Scanning electron micrograph of the BaFe10.5In1.5O19
(left) bulk (right) after ball milling.
Figure 4.2.2-(c) Scanning electron micrographs of the BaFe10In2.0O19
(left) bulk (right) after ball milling.
Figure 4.2.3-(a) EDAX spectra for x = 1.0.
Figure 4.2.3-(b) EDAX spectra for x = 1.5.
Figure 4.2.3-(c) EDAX spectra for x = 2.0.
Figure 4.2.4 Scanning electron micrograph of the screen printed,
in-plane oriented BaFe11In1O19 thick films sintered
at (above) 1000 °C and (below) 1100 °C for 1 hour.
Figure 4.2.5 Saturation magnetization versus the doping of Indium.
Figure 4.2.6. ∆H versus Frequencies.
Figure 4.2.7. HA versus Indium doping.
Figure 4.2.8. Resonance frequencies versus applied fields for BaFe11In1O19 film.
Figure 5.2.1-(a): XRD of BaFe11.2Sc0.8O19.
Figure 5.2.1-(b): XRD of in-planed oriented sample of BaFe11.7Sc0.3O19.
Figure 5.2.2-(a): EDAX for x=0.3.
vii
Figure 5.2.2-(b): EDAX for x=0.5
Figure 5.2.2-(c): EDAX for x=0.8
Figure 5.2.2-(d): EDAX for x=1.0
Figure 5.2.3-(a): SEM images of BaFe11.7Sc0.3O19 at high magnification
Figure 5.2.3-(b): SEM images of BaFe11.7Sc0.3O19 at low magnification
Figure 5.2.4: dispersed particles of BaFe11.2Sc0.8O19 after ball milling
Figure 5.2.5-(a): Sc=0.3 in-plane oriented sample before annealing.
Figure 5.2.5-(b): Sc=0.3 annealed at 1100oC for 2hr.
Figure 5.2.6: saturation magnetization versus doping amount.
Figure 5.2.7: Linewidth versus Frequencies.
Figure 5.2.8: Saturation magnetization versus the doping of Scandium.
Figure: 5.2.9: Resonance frequencies versus applied fields for BaFe11.2Sc0.8O19 film.
Figure 6.2.1-(a): XRDof BaFe11Sc1O19.
Figure 6.2.1-(b): EDAX spectra of BaFe11Sc1O19.
Figure 6.2.2-(a): SEM image of surface of BaFe11Sc1O19
after sintered at 1250oC for 10hrs.
Figure 6.2.2-(b): SEM image of surface of BaFe11Sc1O19
after ball milled for 10 hours.
Figure 6.2.3: Perpendicular orientation device and press.
Figure 6.2.4: Hysteresis loop of the compact annealed at 1100oC for 2hours.
Solid line is that external magnetic field is perpendicular to the plane of the
sample and dashed line is parallel to the plane.
Figure 6.2.5: SEM image of the surface of compact annealed at 1100o for 2 hours.
Figure 7.1.1: Geometry of ferrite film.
Figure 7.1.2: Schematic image of a ferrite phase shifter.
viii
Figure 7.1.3: VSM of BaFe10.5In1.5O19.
Figure 7.1.4 (a): Phase differences from 1000 Oe to 100Oe.
Figure 7.1.4 (b): Phase differences from 50 Oe to -120Oe.
Figure 7.1.4 (c): Phase differences from -140 Oe to -300Oe.
Figure 7.1.4 (d): Phase differences from -400 Oe to -1000Oe.
Figure 7.2.1(a): S21 at 1000Oe.
Figure 7.2.1(b): S21 at 0Oe.
Figure 7.2.1(c): S21 at -160Oe.
Figure 7.2.1(d): S21 at 180Oe.
Figure 7.2.1(e): S21 at -1000Oe.
Figure 7.2.2 (a): real phase change measurement from 1000Oe to100Oe.
Figure 7.2.2 (b): real phase change measurement from 50Oe to -120Oe.
Figure 7.2.2 (c): real phase change measurement from -140Oe to -300Oe.
Figure 7.2.2 (d): real phase change measurement from -400Oe to -1000Oe.
ix
List of tables
Table 2.2.1 Magnetic properties of M-type ferrite. From Soshin Chikazumi,
Physics of ferromagnetism 2nd edition.
Table 3.1.1. 24 equivalent planes for the hexagonal structure.
Table 4.2.1-(a): Magnetic property of BaFe11In1O19.
Table 4.2.1-(b): Magnetic property of BaFe10.5In1.5O19.
Table 4.2.1-(c): Magnetic property of BaFe10In2O19.
Table 5.2.1-(a): Magnetic property of BaFe11.7Sc0.3O19.
Table 5.2.1-(b): Magnetic property of BaFe11.5Sc0.5O19.
Table 5.2.1-(c): Magnetic property of BaFe11.2Sc0.8O19.
Table 5.2.1-(d): Magnetic property of BaFe10Sc1.0O19.
Table 6.2.1: Magnetic properties of oriented compacts at different annealed condition.
x
Chapter 1: Introduction
Microwave applications [1] of ferrite materials are quite important nowadays in
telecommunication systems because ferrites are usually oxide materials that can operate
at high frequencies. Over the last 50 years, many microwave devices have utilized the
magnetic phenomena at microwave resonance and are now commercially available.
However, many practical microwave challenges remain, such as: miniaturization, broader
relative frequency bandwidths, higher operating frequencies, and reduced costs.
The behavior of all microwave ferrite devices can be explained in terms of the
following magnetic effects [1].
1. Faraday rotation: The rotation of the plane of polarization of a TEM wave as it
propagates through a ferrite in the direction of the magnetization.
2. Ferromagnetic resonance (FMR): Strong absorption can occur only when a
polarized RF magnetic field is perpendicular to the direction of static
magnetization.
3. Nonlinear effects: The amplification and frequency doubling are possible and
subsidiary losses can occur at higher power levels.
4. Spin waves: The short-wavelength waves of magnetization can propagate at any
angle with respect to the direction of static magnetization. If the wavelength of
such a wave is comparable to the dimensions of the ferrite sample, it is called a
standing magnetostatic wave (MSW).
Ferrite phase shifters generally take advantage of the ability to control the
permeability of a waveguiding medium to alter the phase velocity of a microwave signal
1
passing through it. In general, the change in permeability changes the phase velocity and
it changes the insertion phase. Ferrite phase shifters can be first categorized as reciprocal
or nonreciprocal phase shifters. Reciprocal phase shifters imply that the microwave
signal is the same propagation directions, but for the nonreciprocal phase shifters the
microwave signal depends on propagation direction. Secondary they are categorized as
driven or latching phase shifters.
Phase shifters operating at high frequencies are expected to be fabricated in
commercial use in these days for high speed communication system. The usual phase
shifters utilized by garnet and spinel ferrites are practically not applicable above 10 GHz
because of no magnetic anisotropy field (HA). If indeed those ferrites are used at high
frequencies (above 10 GHz), a large biased magnetic fields are required. On the other
hand, hexaferrites appear to be potential candidates for high frequency applications with
their high anisotropy field (HA). By the virtue of the high HA of hexaferrites FMR
frequency is easily shifted to high frequency bands.
The anisotropy field of BaFe12O19 (typical M-type hexaferrite) is ~ 17000 Oe which
imply frequencies of operating above 50 GHz. For frequencies, below 50 GHz and above
10 GHz we must reduce the high anisotropy field down to below 17000 Oe. We have
developed a new hexaferrite system with relatively low losses or FMR linewidth. We
substituted In3+ or Sc3+ for Fe3+ in BaFe12O19 [2]-[4]. In3+ and Sc3+ help to reduce HA to as
low as 2000 Oe. These Sc- and In-doped Barium ferrites may be useful to Ka band
frequencies of operation. Sc-doped Barium ferrite was synthesized by modified coprecipitation and In-doped Barium ferrite was produced by conventional sintering
technique. The ferrite powder was screen printed on alumina substrate and was oriented
2
with c-axis in the plane of the ferrite slab. We then fabricated a prototype phase shifter
utilizing a slab of BaFe10.5In1.5O19, shown in Fig. 1.1.1.
The phase shifter fabrication will be discussed in Chapter 7, and discuss our model
of the operation of the fabricated phase shifter. We utilized two magnetic effects in our
model: hysteresis curve of in-plane oriented sample [5] and ferromagnetic resonance
(FMR) [6]. From the hysteresis curve we deduced the magnetic susceptibility (χ) as a
function of the external magnetic field. The relative susceptibility is related to the
relative permeability (µ) as µ=1+4πχ. The hysteresis curve provides the information
about µ directly with the dc magnetic field. As such, we can determine at what magnetic
field is the maximum change in µ. On the other hand, FMR data gives us the information
of how µ changes with microwave frequencies with external magnetic field, µ=µ (ω). At
FMR frequency, the microwave loss is at a maximum and we should avoid at frequency
of operation. Usually the frequencies above the FMR frequency are utilized for phase
shift, but we can also use frequencies below FMR frequency. Phase shift is simply given
by θ = βl =
ωl
c
εµ where l is the length of microstrip line, for example, usually ∆θ or
phase shift results from the change of µ. The change of permeability µ plays an important
role in the design of phase shifter.
This dissertation is devoted to synthesis, characterization of Indium and Scandium
doped Barium ferrites, design and fabrication of ferrite phase shifter using in-plane
oriented BaFe10.5In1.5O19. Chapter 2 discusses the magnetic properties of hexaferrite
materials in general as well as ferromagnetic resonance which is very important
phenomenon in ferrite devices. Chapter 3 is devoted to characterization of ferrite
materials. Chapter 4 presents the synthesis of Indium doped Barium hexaferrite by
3
modified conventional sintering method and in-plane orientation. Chapter 5 also presents
the synthesis of Scandium doped Barium hexaferrite by modified co-precipitation and inplane orientation.
Chapter 6 concludes with the synthesis of BaFe11Sc1O19 by the
conventional sintering method and c-axis orientation. The design and simulation of ferrite
phase shifter at Ka band is discussed in Chapter 7. Chapter 8 summarizes our research
and discusses about the future ferrite device work.
References
[1] J. Douglas Adam, Lionel E. Davis, Gerald F. Dionne, Ernst F. Schloemann and
Steven N. Stitzer, IEEE TRANSACTIONS ON MICROWAVE THEORY AND
TECHNIQUES, VOL. 50, NO. 3 (2002).
[2] Gerald F. Dionne and James F. Fitzgerald, J. Appl. Phys. Vol. 70, No.10 (1991)
[3] C. N. Chinnasamy, T. Sakai, S. Sivasubramanian, Aria F. Yang, C. Vittoria and V. G.
Harris, J. Appl. Phys. 103, 07F710 (2008)
[4] T. Sakai, C. N. Chinnasamy, S. D. Yoon, A. Geiler, C. Vittoria and V. G. Harris, J.
Appl. Phys. 103, 07E515 (2008)
[5] Alex Goldman, Modern ferrite technology, 2nd edition, page 376-382, Springer (2006)
[6] C. Vittoria, Microwave properties of Magnetic films (World Scientific, Singapore,
1993).
4
Alumina substrate
Silver paint
Figure 1.1.1: Prototype of phase shifter with BaFe10.5In1.5O19
5
Chapter 2: Background on the Magnetism of ferrite materials
The exchange interaction of energy between two isolated ions [1] can be expressed as
r r
r
H ij = −2 J ij S i ⋅ S j , where S i is the spin of an ion.
(2.1.1)
Total exchange interaction energy of a magnetic sample will be
r r
H = −∑ H ij = −∑ J ij S i ⋅ S j .
i, j
i≠ j
(2.1.2)
i, j
i≠ j
r
For 3d transition atoms the orbital momentum L is almost quenched and the spin-orbit
coupling is smaller than 4f atoms [2]. The atomic magnetic moment for 3d atoms is
written as
r
r
mi = gµ B S i ,
( g = 2 ).
(2.1.3)
We may now express H in terms of the magnetic moment as
r r
r
r
H = −∑ nij mi ⋅ m j = −∑ mi ⋅ ∑ nij m j or
i, j
i≠ j
r r
H = − ∑ mi ⋅ H i ,
(2.1.4)
i≠ j
i
r
r
where H i = ∑ nij m j , where
(2.1.5)
i≠ j
i
nij is a local molecular field coefficient reduced to one atomic magnetic moment.
r
H i is considered as a local field. It is time fluctuating and depends on the instantaneous
r
value of the considered magnetic moment mi . The time average < H > T is
r
r r
r
< H > T = ∑ < mi ⋅ H i > T = ∑ < mi > T < H i > T ,
i
i
r
r
r
where < H i > T = ∑ nij < m j > T ≡ H m .
i≠ j
6
(2.1.6)
r
H m is called the molecular field [3].
r
r
r
H m is also written as H m = WM , where
r
r
r
M = N < mi > T . M is the magnetization per unit volume and N is the number of atoms
per unit volume.
We briefly discuss about ferromagnetism in this section. The simplest description of
ferromagnetism is the Langevin model that is classical model based on Boltzmann
r
distribution. An atom with moment m0 that makes an angle θ with the applied magnetic
r
r r
field H has a potential energy − m0 ⋅ H = − m0 H cos θ . By the use of the Boltzmann
distribution, the portion of magnetic moments whose direction is in the solid angle
dΩ = 2π sin θdθ is
 m H cos θ 
2π sin θdθ
exp 0
k BT


dN =
.
π
 m0 H cos θ 
∫0 exp k BT 2π sin θdθ
(2.1.7)
r
r
The measured magnetization m along the field H per atom is equal to the average of
m0 H cos θ .
 m0 Hu 

du
m
u
exp
0
∫−1
π
k
T
 B  , where u = cos θ . (2.1.8)
m = ∫ m0 cos θdN =
0
1
 m0 Hu 
∫−1 exp k BT du
1
m is also written as
m = k BT
1
m H 
∂ ln Z
, where Z = ∫ exp 0 u du
−1
∂H
 k BT 
r
Therefore, magnetization M is given by
r
r
M = M 0 L( x) .
7
(2.1.9)
L( x) is called Langevin function L( x) = coth x −
mH
1
, where x = 0 . In the molecular
k BT
x
r
r
r
field theory H is changed to H + WM . The total magnetization is given by
r
r  m ( H + WM ) 
 .
M = M 0 L 0
k
T

B

(2.1.10)
The Langevin function method for ferromagnetism originated from classical physics.
Let the ground state in the absence of a magnetic field be defined by the quantum number
J.
The degeneracy is 2J+1 and each state is characterized by J , M J
Jˆ Z J , M J = M J J , M J
such that
with M J = J , J − 1, J − 2, , , , ,− J − 1,− J . When we apply a
magnetic field, the ground state is split into 2J+1 levels. These energy levels are the
eigenstates of the perturbing Hamiltonian, Hˆ = −mˆ z H z = − g J µ B Jˆ Z H Z , where g J is the
Lande′ g-factor.
At temperature T=0, only the ground state is occupied and the
magnetization per atom is m = g J µ B J .
At T ≠ 0 , the probability pi of occupation of each state of energy Ei is given by
Boltzmann’s law,
 − Ei 

exp
k BT 

pi =
.
 − Ei 
∑i exp k T 
 B 
(2.1.11)
The value of magnetization per atom at T ≠ 0 is
g µ H M
g J µ B M exp J B Z
k BT
M =− J

< m > T = ∑ mi pi =
J
g µ H M 
i
exp J B Z 
∑
k BT
M =− J


J
∑
8


.
(2.1.12)
We define x =
gJ µB H Z J
, < m >T is given by
k BT
M
 M
exp x 
J
 J .
< m > T = g J µ B J M = − JJ
 M
exp x 
∑
 J 
M =− J
J
∑
We define f ( x) =
J
∑e
xM
J
(2.1.13)
, so that f (x) is given by
M =− J
 2J +1 
sinh 
x
x
x 2
x 2J 

 J
 J 
J

.
−x 
J
f ( x) = e 1 + e +  e  +, , , ,  e 
=


 x 
 
  
sinh 


 2J 
(2.1.14)
 2J + 1
 2J +1  1
 x 
coth 
x −
coth   .
∴ < m >T = g J µ B J 
 2J
 2J
 2 J 
 2J
(2.1.15)
m0 = g J µ B J is called saturation moment at T = 0 and Brillouin function is given by
 2J + 1
 2J + 1  1
 x 
B( x) = 
coth 
x −
coth   , where
 2J
 2J
 2 J 
 2J
coth x is expanded as coth x =
(2.1.16)
1 x
+ + O( x 3 ) .
x 3
2
2
< m > T 1  2 J + 1   1  
J +1
Finally
= 
x.
 −
 x =
m0
3  2 J   2 J  
3J
(2.1.17)
The total magnetization is then
N < m >T =
gµ JH
N ( J + 1)
H
( gµ B J ) B
=C ,
k BT
T
3J
2
2
Ng J J ( J + 1) µ B
where C =
is called the Curie constant.
3k B
9
(2.1.18)
N < m >T C
=
is the well known Curie’s law [4].
H
T
The two functions L( x ) and BJ ( x) are connected in the lim BJ ( x) = L( x) .
J →∞
Ferrimagnetism is based on the theory of antiferromagnetism [5]-[6] investigated
by Nee′l .
r
r
Consider two sublattices with localized magnetic moments, M A and M B
r
r
where M A ≠ M B . Let W be the molecular field coefficient between the two sublattices
r
r
r
and W AA = αW and WBB = βW . When magnetic field H 0 is applied, H A and H B are
given by
2
r
r
r
N AmA
CA r
HA =
( H 0 + αWM A − WM B ) where C A =
,
3k B
T
(2.1.19)
2
r
r
r
C r
N m
and H B = B ( H 0 − WM A + βWM B ) where C B = B B .
3k B
T
(2.1.20)
r
The total magnetization M is then
r
r
r
M = MA + MB =
1
χ
is given by
1
χ
=
r
r
(C A + C B )T − C AC BW (α + β + 2)
H
H
=
χ
0
0.
T 2 − TW (αC A + β C B ) − C A C BW 2 (1 − αβ )
T +θ p
C
+
γ
(2.1.22)
T −θ
where C = C A + C B , θ = W (2 + α + β )
(2.1.21)
C AC B
C A + CB
2
2
C AC B
γ =W
{C A (1 + α ) − C B (1 + β )}2 and θ p = W 2C AC B − αC A − βC B .
3
C A + CB
(C A + C B )
2
10
At high temperatures,
1
χ
=
T +θ p
C
. T = −θ p is called the asymptotic Curie point. The
ordering temperature TC (Curie temperature) is defined as the temperature where
1
χ
passes through zero which means that χ becomes infinite.
Ferrites have three typical structures, spinel, garnet and hexagonal. We start with
spinel ferrites in this section.
Spinel was originally the name of a mineral with the chemical formula MgAl2O4.
Ferrimagnetic spinels have the same crystal structure as the spinel but cations are
replaced by ions of the transition elements. The general chemical formula is PQ2X4. In
the simple spinel, P ions are divalent ions and Q ions are trivalent ones. The oxygen ions,
that are large compared to the cations, form essentially a face-centered cubic lattice. The
unit cell of the spinel consists of eight molecules of PQ2X4, that is 32 oxygen ions. The
cations occupy interstitial positions and there are two different types, A and B. Magnetic
ion of A site is surrounded by four oxygen ions located at the corners of a tetrahedron.
Such an interstice is called a tetrahedral or A site. Another magnetic ion is surrounded by
six oxygen ions placed at the vertices of an octahedron. That is called octahedral or B
site. As shown in Figure-2.2.1, 8A sites and 16Bsites are occupied per unit cell. The
length of an edge of the unit cell is about 8Å. If the 8 P ions occupy the A sites and 16 Q
ions occupy the B sites, the structure is called a normal spinel. On the other hand, if B
sites are occupied half by divalent and half by trivalent ions, the structure is called an
inverse spinel. Almost all of the simple spinels that are ferrimagnetic have the inverse
arrangement.
11
The superexchange interaction between two cations via an intermediate oxygen ion is
enhanced if these ions are collinear and if their separations are not too large. The
varieties of superexchange interaction are shown in Figure 2.2.2. Figure 2.2.2(a) depicts
that both the angle and distances between ions are favorable for superexchange. From
Figs. (b), (c), (d) and (e) show superexchange is not enhanced. We can conclude that the
interaction shown in Figure 2.2.2(a) is stronger than the other interactions and A site is
weakest in all cases.
Ferrites having hexagonal crystal structure [7]-[8] are called hexagonal ferrite or
hexaferrite. Hexagonal ferrites are interesting and exhibit important properties such as
high saturation magnetization and very large magnetocrystalline uniaxial anisotropy. The
hexagonal ferrites are categorized by the compositions and Figure 2.2.3 shows the unit
cell of Barium hexagonal ferrites.
Phase diagram in Figure 2.2.4 shows growth
conditions of M-type, Y-type, W-type and Z-type Barium hexaferrites. The simplest type
is M-type Barium hexaferrite and the composition is BaFe12O19. We will dope BaFe12O19
with Scandium and Indium in order to reduce magnetocrystalline anisotropy.
The crystal structure of M-type hexagonal ferrite is very complex, and it may be
decomposed into small building blocks referred to as S and R blocks. The S block is
closely related to the spinel structure. As a matter of fact, although the spinel ferrite has
cubic structure, a unit cell of spinel ferrite can be rhombohedral or hexagonal in shape. If
we plot the spinel structure in a specific way such that [111] axis is along the vertical
direction and substitute Me2+ with Fe3+, we then obtain the S block as a unit cell of spinel
structure shown in Figure 2.2.5. The chemical formula of the S block is Fe3+6O2-8 which
means that S block is positively charged. The composition of R block is Fe6O8 and the
12
atomic arrangement of R block is shown in Figure 2.2.6. The total atomic arrangement of
M-type crystal structure is shown in Figure 2.2.7. The layers denoted S*and R* are the
atomic arrangement when the S and R blocks an rotated by 180o about the c-axis. The
lattice constant of BaFe12O19 was measured to be a ≈ 5.89 Å and c ≈ 23.2 Å, respectively.
The magnetic properties of the M-type hexaferrite are listed in Table 2.2.1. The
saturation magnetization of Barium ferrite is 4780 Gauss at room temperature and the
Curie temperature is about 450oC. The magnetocrystalline anisotropy field is 17000 Oe.
Usually, M-type ferrites are used as permanent magnetic materials [9] and magnetic
recording media [10].
r r
The Heisenberg exchange energy depends on the scalar product S i ⋅ S j . As such,
the magnetization of ferromagnetic and ferrimagnetic specimens has been considered to
be isotropic. However experimentally it is found that the magnetization tends to align
along certain axes or directions. This effect is known as crystalline anisotropy. It is clear
that much smaller fields are required to magnetize crystals to saturation along certain
directions than along others. The axes along which the magnetization tends to lie are
called easy directions. On the other hand, the axes along which it is most difficult to
produce saturation are called hard directions.
Crystalline anisotropy energy called magnetocrystalline energy is defined as the work
required making the magnetization lie along a certain direction compared to an easy
direction. If the work is carried at constant temperature, magnetocrystalline energy is
actually a free energy. From the first law of thermodynamics,
dU = dQ − dW = −dW ,
(2.3.1)
dF = −dW − SdT = − dW ,
(2.3.2)
13
F final − Finitial = − ∫ dW .
(2.3.3)
The magnetic anisotropy also describes the dependence of the internal energy on the
direction of spontaneous magnetization. In fact, the magnetic anisotropy energy term has
the same symmetry as the crystal structure of the material. The simplest case is uniaxial
magnetic anisotropy. BaFe12O19 exhibits uniaxial anisotropy with the stable direction of
spontaneous magnetization (or easy axis) parallel to the c-axis of the crystal at room
temperature. We can express the anisotropic energy as follows.
E A = K u1 sin 2 θ + K u 2 sin 4 θ + K u 3 sin 6 θ + K u 4 sin 6 θ cos 6ϕ + ⋅ ⋅ ⋅ ⋅ ⋅ ,
(2.3.4)
where θ is measured from c-axis and φ is the azimuthal angle of the magnetization in the
plane perpendicular to the c-axis. The higher order terms are small and their values are
not reliably known. The anisotropy energy increases with increasing angle θ so that EA is
minimum at θ = 0. In other words, the spontaneous magnetization is stable when it is
parallel to the c-axis. Such an axis is called an axis of easy magnetization or easy axis. If
these constants are negative, the anisotropy energy is maximum for M along the c-axis so
that it becomes unstable. Such an axis is called an axis of hard magnetization or hard
axis.
For cubic crystals such as iron and nickel, the anisotropy can be expressed in terms of
direction cosines (α1, α2, α3) of the magnetization vector with respect to the three cubic
edges. The anisotropy energy is given by
EA = K1(α21α22 + α22α23 + α23α21) + K2α21α22 α23 + ………
(2.3.5)
One of the methods to measure Ha is to measure the torque. The torque produced by
the action of the applied field is measured. The anisotropy coefficients are determined by
14
fitting a theoretical torque curve to the measured values. Another method to measure Ha
is to utilize ferromagnetic resonance. It is discussed in the following section 4.
According to Van Vleck [11], we can consider the coupling between metal ions to be
anisotropic. In the usual calculation of the exchange energy the spin-orbit coupling (L-S
coupling) is neglected. When the spin-orbit interaction is considered as a perturbation,
we have the term.
r r r r
2
 λ  3( S i ⋅ rij )( S j ⋅ rij )
J

r 2
 ∆E 
rij
(2.3.6)
where λ is L-S coupling constant and ∆E is the energy difference between ground and
excited states.
In order to understand the concept of FMR, we return to the image of electron as
spinning top. In the case of a real top, the top will precess around an axis in line with the
gravitational vector under the influence of gravity. The axis of the spinning orbits around
forming a cone. In electric precession, the aligning force is a static D.C. field orienting
the unpaired spins of ferromagnetic atoms or ions (Figure 2.4.1).
When the frequency of transverse excitation is in phase, we say that the system is in
resonance. The maximum transfer of energy takes place at this frequency. The spinning
electron is the top. The restoring force is D.C. field. The transverse excitation is the high
frequency electromagnetic field oscillation.
There are two ways [2] to calculate FMR conditions. One way is Smit and Beljers
Formulation and the other way is to calculate the FMR condition from internal magnetic
fields [2]. This formulation is so convenient and important that we can calculate
permeability easily. In the Smit and Beljers Formulation, Free energy F is expressed as a
15
function of directional cosines α1, α2 and α3, i.e. F = F (α1, α2, α3). α1, α2 and α3 are given
by
α1 = sin θ cos ϕ , α2 = sin θ sin ϕ , α3 = cosθ
(2.4.1)
In another word, F is written by the function of θ and φ, i.e.
F = F (θ,φ)
(2.4.2)
At the equilibrium state, the free energy has maxima or minima. Mathematically we can
write the situation as follows.
∂F ∂F
=
=0
∂θ ∂ϕ
(2.4.3)
From (1.7.3) we can get θ = θ 0 at which the free energy is stable. With this condition
and the equation of motion, then we can get the resonance condition derived by Smit and
Belgers in 1954. The equation is given by
ω2 ∂2F ∂2F ∂2F
1
=[ 2
−
]
,
2
2
2
∂θ ∂ϕ
∂θ∂ϕ M 0 sin 2 θ
γ
(2.4.4)
where M 0 is static magnetization.
This calculation may sometimes have mathematical singularities which originated from
geometry of sample position, not from physical properties. We can exclude such a
mathematical singularity by changing the geometry of sample positions relative to static
fields.
Carmine Vittoria calculated internal fields with special gradients in ordered magnetic
materials [2]. Van Vleck [11]-[12] proposed this formulation in 1937 on paramagnetic
seats, when the variables are the spin variables and not the magnetization. The special
gradient is defined by
16
− ∇ M = −iˆ
∂
∂
∂
− ˆj
− kˆ
,
∂M z
∂M x
∂M y
(2.4.5)
where iˆ , ĵ , k̂ are unit vector for x, y and z direction respectively.
The free energy F is written in this case by a function of M x M y M z , i.e.
F = F (Mx,M y ,Mz )
(2.4.6)
r
The internal magnetic field H int will be calculated from (2.4.5) and (2.4.6).
r
∂F
∂F
∂F
H int = − ∇ M F = −iˆ
− ˆj
− kˆ
∂M x
∂M y
∂M z
(2.4.7)
r
We also know that H int is written as
r
r
r
H int = H DC + h ,
(2.4.8)
r
r
where H DC is internal static field and h is internal dynamic field.
r
r
r
In a similar way, the total moment can be written by M = M 0 + m
r
r
where M 0 is static and m is dynamic magnetization.
r
r r
1 dM
= M × H int
The equation of motion is
γ dt
(2.4.9)
(2.4.10)
Substitute (2.4.8) and (2.4.9) into (2.4.10), then we will get
r
r
r
r
r
r r
r r
1 dm
= ( M 0 × H DC ) + ( M 0 × h ) + (m × H DC ) + (m × h ) .
γ dt
(2.4.11)
r
r
The first term of (2.4.11) is zero because M 0 and H DC are parallel each other and we
ignore the fourth term because we are only dealing with linear theory. We calculate the
magnetic response of a magnetic material to an external perturbation of arbitrary strength.
There the final equation of motion is given by
17
r
r
r
r r
1 dm
= ( M 0 × h ) + (m × H DC )
γ dt
(2.4.12)
In Chapter 7: calculations will be performed and we will show how to calculate
susceptibility and permeability using eq. (2.4.12).
If we want to utilize Barium ferrite, we have to lower the large anisotropy without
losing the other magnetic properties of Barium ferrite. The only way to reduce the large
anisotropy down is to dope something not magnetic in Barium ferrite. We substitute Sc3+
and In3+ for Fe3+ by sintering and co-precipitation techniques. The Fe3+ in S block is
replaced by Sc3+ and In3+ and the net moment of the S block is lowered, but not zero.
There are several ways to dope Scandium [13]-[14] and Indium [15]-[16] into Barium
ferrite such as conventional sintering method, crystallization method, co-precipitation,,,
etc.
We chose the conventional sintering method for Indium doping and the co-
precipitation for Scandium doping in Barium ferrite. The conventional sintering method
for Indium doping is a challenging research because of the control of Indium oxide. The
co-precipitation for Scandium doping is totally a new research. We will discuss
conventional sintering method in Chapter 3.
References
[1] W. Heisenberg, Z. Physik, 49, 619 (1928)
[2] Carmine Vittoria, Microwave properties of magnetic films, World Scientific (1993).
[3] P. Weiss, J. Phys. 6, 661 (1907)
[4] Charles Kittel, Introduction to Solid State Physics 7th ed. (1996)
[5] L. Neel, Ann. dePhysiq. [12] 3, 137 (1948)
18
[6]P. W. Anderson, Phys. Rev., 79, 705 (1950)
[7] Soshin Chikazumi, Physics of Ferromagnetism 2nd edition, Clarendon Press, Oxford
(1997)
[8] Alex Goldman, Modern Ferrite Technology 2nd edition, Springer (2006)
[9] Joseph. J. Becker, IEEE Transactions on magnetics, VOL. MAG-4, NO.3 (1968)
[10] Tatsuo Fujiwara, IEEE Transactions on magnetics, VOL. MAG-21, NO. 5 (1985)
[11] J. H. Van Vleck, J. Chem. Phys., 9, 85 (1941)
[12] Van Vleck, the Theory of Electric and Magnetic Susceptibilities Clarendon Press,
Oxford (1965)
[13] T. Sakai, Yajie Chen, C. N. Chinnasamy, C. Vittoria and V. G. Harris, IEEE
Transactions on Magnetics, 42, NO. 10 (2006)
[14] T. Sakai, C. N. Chinnasamy, S. D. Yoon, A. Geiler, C. Vittoria and V. G. Harris, J.
Appl. Phys. 103, 1 (2008)
[15] G. F. Dionne and J. F. Fitzgerald, J. Appl. Phys., Vol. 70, No. 10, 15 November 1991
[16] C. N. Chinnasamy, T. Sakai, S. Sivasubramanian, Aria F. Yang, C. Vittoria and V. G.
Harris, J. Appl. Phys. 103, 07F710 (2008)
19
Figure 2.2.1 Unit cell of spinel
20
Figure 2.2.2 Superexchanges in spinel
21
Figure 2.2.3 Unit cell of BaFe12O19. From Alex Goldman, Modern Ferrite Technology
22
Figure 2.2.4 Phase diagram of hexa-ferrite. From Soshin Chikazumi,
Physics of ferromagnetism 2nd edition.
23
Figure 2.2.5 Crystal structure of cubic spinel drawn taking in [111] as c-axis.
From Soshin Chikazumi, Physics of ferromagnetism 2nd edition.
24
Figure 2.2.6 Atomic arrangement of R-layer. From Soshin Chikazumi,
Physics of ferromagnetism 2nd edition.
25
Figure 2.2.7 Atomic arrangement of M-type crystal structure. From Soshin
Chikazumi, Physics of ferromagnetism 2nd edition.
26
Table 2.2.1 Magnetic properties of M-type ferrite. From Soshin Chikazumi,
Physics of ferromagnetism 2nd edition.
27
Chapter 3: Instrumentation and Experimental Techniques
Section 1: X-ray Diffractometer [1]-[2]
X-ray diffraction is based on Bragg’s condition. Bragg’s condition is nothing more
than the condition of interference between incident light and scattered light from layers in
crystals. Figure 3.1.1 schematically shows the interference among 3 layers. We derive
the interference condition between the light reflected at surface and the one scattered
from the first layer. The difference of traveling distance to detector after reflected at
surface and scattered at first layer is 2d sin θ . If 2d sin θ is
λ
2
× 2n = nλ , where λ is a
wave length, then the interference must be strongest. If 2d sin θ is
1
× (2n + 1) = λ (n + ) ,
2
2
λ
the interference must be weakest. The Bragg’s condition is the strongest case,
2d sin θ = nλ
(3.1.1)
The sample in Figure 3.1.2 is single crystal, powder or thin film. The powder is mounted
on XRD sample holder and is placed in X-ray diffractometer. The incident X-ray shown
in Figure 3.1.2 is scattered by a lot of tiny crystals in the sample and the scattered X-ray
makes interference pattern (See Figure 3.1.2 below). The interference pattern is different
for each sample. Usually the interference pattern is plotted for a graph instead of circular
ring. The Y-axis is intensity and X-axis is 2θ. The graph is usually compared with data
base [2] and we can analyze phase of sample and particle size from the graph. We used
Gigaku Ultima III shown in Figure 3.1.3.
28
XRD source is produced by high energy electron beam toward a cooled metal target.
The electrons collide inelastically with a metal target and they kick out the targeted
electrons. The targeted electrons are excited from their ground state and they fall to a
ground state. This energy gap produces X-rays. Most experiments use monochromatic
incident beam. The wavelength for Cu is Kα=1.54056 Å.
A crystal is a three dimensional repetition of some unit of atoms or molecules. The
v v v
scheme of repetition is designated by three vectors, a1 , a 2 , a3 called the crystal axes shown
in Figure 3.1.4.
They have only the magnitude and direction of the repeating
displacements. Unit cell is the smallest volume in a crystal and the volume is given
r r r
by Vunit = a1 ⋅ (a 2 × a3 ) . We consider diffraction in terms of a set of crystallographic plane,
hkl. By the set of crystallographic plane, hkl, we mean that a set of parallel equidistant
r r r
a1 a 2 a3
planes and the next nearest makes intercepts
, , on the three crystallographic axes.
h k l
The integers hkl are called Miller indices. We define reciprocal vectors as follows.
r r
r r
r r
r
r
r
a 2 × a3
a3 × a1
a1 × a 2
r r
b1 = r r r , b2 = r r r , b3 = r r r where ai ⋅ b j = δ ij .
a1 ⋅ (a 2 × a3 )
a1 ⋅ (a 2 × a3 )
a1 ⋅ (a 2 × a3 )
(3.1.2)
r
We then define a normal vector N hkl to the hkl plane with Miller indices and reciprocal
vectors.
r
r
r
r
r
N hkl = hb1 + kb2 + lb3 . With N hkl , we can calculate unit vector normal to the plane as
r
N hkl
nˆ = r .
N hkl
(3.1.3)
The spacing of planes d hkl is given by
29
d hkl
r
r
r
r r
a1 ⋅ nˆ a 2 ⋅ nˆ a3 ⋅ nˆ a1 N hkl
1
=
=
=
=
r = r .
h
k
l
h N hkl
N hkl
(3.1.4)
r
We now recognize that the inverse of N hkl is the spacing of planes.
The spacings of Cubic and Hexagonal structures are given by
Cubic: d hkl =
Hexagonal:
a
2
2
h +k +l
d hkl =
2
r
r
r
where a1 = a2 = a3 = a and angles α 23 = α 31 = α 12 = 90 o
1
(
2
4 h + hk + k
3a 2
2
)+ l
where
2
r
r
r
a1 = a2 = a, a3 = c
and
angles
c2
α 23 = α 31 90 o ,α 12 = 120 o .
(3.1.5)
In the hexagonal structure, fourth index i is convenient (See Figure 3.1.5.). Since there
are three equivalent axes at 120o to one another, it is arbitrary which two are chosen for a1
and a2. The fourth index i is the one with respect to the axis a ′ . From the geometry of
lines at 60o to one another, the intercepts by an hkl-plane satisfy the relation.
1
1
1
=
+
.
 − a ′   a1   a 2 

    
 i  h  k 
(3.1.6)
From which h + k + i = 0 . Suppose we choose to use h and i .
2
h 2 + hi + i 2 = h + h(− h − k ) + (− h − k ) = h 2 + hk + k 2 .
(3.1.7)
This is the same as d hkl given by (3.1.5). As an example, consider the plane 132. The
fourth index i is i = −4 ≡ 4 . We will write the index as 13 4 2 . Table 3.1.1. shows 24
equivalent planes for the hexagonal structure.
The diffractometer is schematically shown in Figure-3.1.6. The powder sample is
a specific sample holder and put it on the position O. Monochromatic radiation diverges
30
from the entrance slit E and the diffracted radiation from the sample O is collected by a
narrow receiving slit R. The distances EO and OR are equal. The radiation passed by the
receiving slit R is detected by Geiger counter or crystal scintillation counter.
Finally we discuss about errors of diffractometer by measuring powder samples. The
errors of measurement are the followings.
1.) Displacement of the samples surface away from the center of the instrument.
2.) Imperfect focusing resulting from a flat-faced sample.
3.) Penetration of the beam. The diffraction takes place below the sample surface.
4.) With chart recording, the peak displacement results from use of long time constant.
Solutions for errors of 1.) - 4.) are given as follows.
1.) A displacement of the sample surface by the amount ∆y requires a correction as
∆d ∆y
=
cos 2 θ .
d
R
2.) It can be minimized by shortening the effective length of the sample or by using a
curved sample surface with an average curvature chosen for high angle reflections.
3.) It is minimized by using as thin a sample as intensity requirements will allow.
4.) It produces a displacement of the peak ∆θ .
We should take care of this
displacement when we analyze the measurement.
Section 2: Scanning Electron Microscope (SEM)
and Energy Dispersive X-ray Spectroscopy (EDX) [3]
SEM is schematically shown in Figure 3.2.1. It is analogous to the reflected light
microscope. The reflected light microscope forms an image from light reflected from a
31
sample surface, but SEM uses electrons for image formation. Electrons have much
shorter wavelength than light photons and shorter wavelengths are capable of generating
higher resolution information.
Another difference between light and scanning electron imaging concerns the depth of
field. SEM micrographs maintain the three dimensional appearance of textured surfaces.
Depth of field is further suppressed in both macro-photography and photo-micrography
as magnification is increased.
SEM consists of four systems:
1.) The illumination/imaging system.
2.) The information system.
3.) The display system.
4.) The vacuum system.
1.) It produces the electron beam and directs the beam onto the sample.
2.) It has the data released by the sample during electron bombardment and detects
that discriminate among and analyze the information signals.
3.) It consists of one or two cathode-ray tubes for observing and photographing the
surface of interest.
4.) It removes gases from the microscope column that would otherwise interfere with
high resolution imaging.
Magnetic lenses are responsible for focus and magnification of the image (See Figure
3.2.1.). Focus is achieved by changing the current passing through the final lens and
changing its focal length.
32
SEM magnification is the ratio of the size of the display area on the CRT to the
distance the probe is scanned. Direct readouts of magnification are usually accompanied
by micron markers from which dimensions may be measured.
The rate at which the beam passes over the specimen is called the scan speed. Very
rapid scan rates produce a static or nearly static image and are similar to conventional TV
images. Extremely slow scan rates are used to photograph the image. As a matter of fact,
slower scan rates improve image clarity because the electrons have sufficient time to
interact with the specimen.
Astigmation is an optical aberration caused by minute flaws or inhomogeneities in the
magnetic lens’ coiling. The asymmetry is corrected by incorporating stigmeters in the
final lens. They are weak lenses which exert a magnetic field having a magnitude equal
to but opposite from that of the asymmetric field produced by the final lens.
Inelastic (electron - electron) collisions between the beam electrons and the specimen
electrons produce the secondary electron imaging signal. Multiple inelastic collisions
result in the excitation of many specimen atoms to different levels of potential. On the
other hand, inelastic (electron - nucleus) collisions, a primary electron strikes the nucleus
of a specimen atom and rebounds with a negligible loss of energy and a slight angular
deflection (Rutherford scattering). The same electron enters and exits the specimen.
Therefore, it is referred to as a backscattered electron. If the mean atomic weight (Z) of
the specimen is low (for example plastics), the probability of a backscattering event is
lower than if the specimen is of higher Z. Backscattered electron imaging provides a
means of distinguishing zones of different atomic number within a composite specimen
because each zone will exhibit a different contrast level.
33
The excitation volume, synonymous with information depth and depth of penetration,
defines the volume where data signals originate and is a function of the atomic density of
the specimen and accelerating voltage. High Z specimens prohibit deep penetration of
the beam and low Z specimens offer little resistance to the incident beam. The depth of
penetration, d , is related to atomic number Z atomic and accelerating voltage V given by
d∝
WV 2
where W is atomic weight and ρ is the density of elements.
Z atomic ρ
SEM has an equipment of spectrometer capable of detecting X-rays emitted by the
specimen during electron beam excitation. This equipment is called EDX. The X-ray
carries characteristic energy and wavelength which will reveal the elemental composition
of the specimen. The limitation of X-ray analysis includes the inability to analyze light
elements, such as C, N, O, under typical laboratory conditions.
The origin of X-ray signals is coming from the energy gap between ground state and
an excited state. If the excited atom ejects an inner shell electron, an outer shell electron
fills the vacancy and emits an X-ray having energy equal to the difference between two
electron shell. K-shell electrons are closest to the nucleus and therefore are more tightly
bound than L, M, N shell electrons. A given shell is subdivided into α and β levels such
as K α , K β , Lα , Lβ , M α , M β ,,etc. K α arises from L to K shell transition and have the
highest rate of emission. Therefore it forms more prominent peaks than other transitions.
K β arises from M to K transition. The probability of this transition is lower than that of
L to K transition because the distance between shells are larger. On the other hand, K β
X-ray has higher energy than K α X-ray. These energy differences are shown in Figure
3.2.2. The final shell of interest is M shell. From Figure 3.2.2, M α line arises from N to
34
M shell transition. It is the least energetic X-rays and is detected only form elements
heavier than Lanthanum (Z = 57).
Section 3: Vibration Sample Magnetometer (VSM) [4]
We analyzed magnetic properties of ferrite samples with Vibration Sample
Magnetometer (VSM). The block diagram of VSM is shown in Figure 3.3.1.
The
principle of VSM is as follows. If a sample of any material is placed in a uniform
magnetic field created between electromagnets, a dipole moment will be induced. When
the sample vibrates with mechanical sinusoidal motion, a sinusoidal electrical signal can
then be induced in suitable placed at pick-up coils. The signal has the same frequency of
vibration and its amplitude will be proportional to the magnetic moment, amplitude, and
relative position with respect to the pick-up coils system. The sample is fixed to a small
sample holder located at the end of a sample rod mounted in an electromechanical
transducer. The transducer is driven by a power amplifier which itself is driven by an
oscillator at a frequency of 80 ~ 90 Hz. The sample vibrates along the Z axis
perpendicular to the magnetizing field. It induces a signal in the pick-up coil system that
is fed to a differential amplifier. The output of the differential amplifier is subsequently
fed into a tuned amplifier and an internal lock-in amplifier that receives a reference signal
supplied by the oscillator.
The output of this lock-in amplifier is a DC signal
proportional to the magnetic moment of the sample being studied. The electromechanical
transducer can move along X, Y and Z directions in order to find the saddle point (which
Calibration of the vibrating sample magnetometer is done by measuring the signal of a
35
pure Ni standard of known the saturation magnetic moment placed in the saddle point).
Our VSM from ADE Technology is shown in Figure 3.3.2. The frequency of the vibrator
is 80 Hz and the magnetic field that it can produce is 12.5 kOe.
VSM is used to investigate the magnetization process of magnetic samples with
hysteresis loop shown in Figure 3.3.3. The hysteresis loop starts from a demagnetized
state (M=H=0). The magnetization increases along the curve OABC and finally reaches
the saturation magnetization, normally denoted by Ms. In the region OA the process of
magnetization is reversible. The slop of OA is called the initial susceptibility χ initial .
After this region, the process of magnetization is no longer reversible. If the magnetic
field is decreased from the saturated state C, the magnetization M gradually decreases
along the curve CD. At H=0, the curve reaches the non-zero value Ms. It is called
remanence. The increase of H in a negative direction further results in M=0 where it is at
E. The absolute value of this point is called coercive force or coercivity (Hc=OE). The
portion DE is often referred to as a demagnetizing curve. Further increase of H field in a
negative direction reaches the negative saturation magnetization. If the field is reversed
again to positive direction, the magnetization changes along FGC. The closed loop
CDEFGC is called hysteresis loop.
Consider the work necessary to magnetize ferro- and ferri-magnetic materials.
Suppose that the magnetization is changed from M and M + δM under the action of
magnetic field H parallel to M . The work necessary to magnetize a unit volume of
magnetic sample is given by δW = HδM . Then the work required to magnetize a unit
volume from M1 to M2 is given by
36
M2
W=
r
r
H
⋅
d
M
(J/m3).
∫
M1
After one full circuit of hysteresis loop, the potential energy must return to its original
value, so that the resultant work must appear as heat. The heat is called hysteresis loss
and is given by
r
r
W = ∫ H ⋅ dM
which is equivalent to the area of inside the hysteresis loop.
Finally we can categorize magnetic materials as “soft” and “hard” materials. Soft
magnetic materials have low coercivity and small hysteresis loss. They are used for the
cores of transformers, motors and generators. On the other hand, hard magnetic materials
have high coercivity, high remanence and large hysteresis loss. Those materials are
utilized to permanent magnets and loudspeakers.
Section 4: Planetary Ball Mill
In Planetary Ball Mills [5]-[6], the combination of the material to be ground takes
place primarily through the high-energy impact of grinding balls. To achieve this, the
grinding bowl containing the material to be ground and grinding balls rotates around its
own axis on a main disk whilst rotating rapidly in the opposite direction. At a certain
speed, with this configuration, the centrifugal force causes the ground sample material
and grinding balls to separate from the inner wall of the grinding bowl. The grinding balls
then cross the bowl at high speed and further grind the sample material by impact against
37
the opposite bowl wall. In addition impact between the balls themselves on the sample
material adds to the size reduction process. Schematic picture is shown in Figure 3.4.1.
Fritsch Pulverisette 6 was used for planetary ball milling shown in Figure 3.4.2. The
Pulverisette 6 is a high-performance Planetary Ball Mill with a single grinding bowl
mount and practical, easily adjustable imbalance compensation. It is particularly easy use
and high-energy effect up to 650 rpm. This ensures a constantly high grinding
performance with extremely low space requirements for loss-free grinding results even in
suspension. The electronic timer adjustable to one second and the programmable,
automated reversing feature ensure precise, consistent reproducibility and grinding of
even the smallest samples. At the same time, the Pulverisette 6 is ideally suited for
mechanical alloying or for mixing and perfect homogeneity of emulsions and pastes.
Section 5: Ferromagnetic Resonance (FMR)
FMR [7] is a spectroscopic technique to detect the magnetization of ferromagnetic
materials. It was unknowingly discovered by V. K. Arkad'yev when he observed the
absorption of UHF radiation by ferromagnetic materials in 1911.
A qualitative
explanation of FMR along with an explanation of the results from Arkad'yev was offered
up by Ya. G. Dorfman in 1923 when he suggested that the optical transitions due to
Zeeman splitting could provide a way to study ferromagnetic structure. FMR is very
similar to nuclear magnetic resonance except FMR probes the magnetic moment of
electrons and NMR probes the magnetic moment of atomic nuclei.
38
FMR arises from the precessional motion of the magnetization in an external magnetic
field. The magnetic field puts a torque on the magnetization which causes the magnetic
moment to precess.
The precessional frequency depends on the orientation of the
material and the strength of the magnetic field.
The basic setup for an FMR experiment is a microwave waveguide with an
electromagnet. The resonant cavity is fixed at a frequency in some band (our case is Ka
band). A detector is placed at the end of the cavity to detect the microwaves. The
magnetic sample is placed between the poles of the electromagnet and the magnetic field
is swept while the intensity of the microwaves is detected.
When the precession
frequency and the resonant cavity frequency are the same, absorption increases indicated
by a decrease in intensity in the detector.
FMR setting is shown in Figure 3.5.1 (a) and (b). The frequency range of RF source
in Figure 3.5.1 (a) is from 27 GHz to 40 GHz that covers Ka band. Our FMR system is
to sweep the magnetic field at fixed frequency. The maximum magnetic field was about
15kOe.
References
[1] B.D. Cullity and S.R. Stock, Elements of X-Ray Diffraction, Addison-Welsley
Publishing Co. (1978).
[2] B. E. Warrem, X-ray diffraction, Addison-Welsley Publishing Co. (1969).
[3] Barbra L. Gabriel, SEM: A user’s manual for materials science, American society for
metals, Metals Park, Ohio 44073 (1985).
[4] Alex Goldman, Modern Ferrite Technology 2nd edition, Springer (2006).
39
[5] M. Abdellaoui and E. Gaffet, Acta Metallurgica et Materialia, Vol. 43, Issue 3, 1087
(1995).
[6] P. P. Chattopadhyay, I. Manna, S.Talapatra and S. K. Pabi, Materials Chemistry and
Physics, Volume68, Issues 1-3, Pages 85-94 (2001).
[7] Carmine Vittoria, Microwave properties of magnetic film, World Scientific (1993)
40
Diffracted beam
Incident beam
Diffraction angle
Crystal
Figure 3.1.1. Bragg’s condition.
41
Diffracted beam
2θ
Sample
Incident beam
Figure 3.1.2. Schematic picture of X-ray diffractometer.
42
Figure 3.1.3. X-ray diffractometer.
43
Figure 3.1.4. Miller Indices.
44
Figure 3.1.5. Fourth index i
45
Table 3.1.1. 24 equivalent planes for the hexagonal structure.
46
Figure 3.1.6. Schematic picture of X-ray diffractometer.
47
Figure 3.2.1. Schematic picture of SEM.
48
Figure 3.2.2. Energy gaps.
49
Figure 3.3.1. Block diagram of Vibrating Sample Magnetometer.
50
Vibrator head
Sample position
Sample holder
Coil
Figure 3.3.2. VSM.
51
Figure 3.3.3. Hysteresis curve.
52
Figure 3.4.1. Schematic picture of ball milling.
53
Figure 3.4.2. Pulverisette 6
54
Lock-in Amplifier
Modulation drive
Power supply for
magnet
Figure 3.5.1. (a). Magnet, RF source and Wave guide for FMR.
RF source
Wave guide is attached here
Magnetic field
Gauss meter
Figure 3.5.1. (b). Lock-in Amplifier, Modulation drive and
Power supply for FMR.
55
Chapter 4: Synthesis and Properties of BaFe12-xInxO19
Introduction
In recent years, microwave magnetic materials have attracted considerable attention
due to its important role in millimeter wave applications (isolators, phase shifters,
circulators and related components) [1]-[4]. Hexagonal ferrites have been proposed as
one of the possible solutions to reduce the need for external high magnetic fields and the
low microwave losses (low ferromagnetic resonance (FMR) linewidth) in microwave
ferrite devices. One advantage of the hexaferrite is that the high anisotropy field can be
adjusted by appropriate substitution for Fe and Ba ions allowing for tuning the resonance
frequencies from 1-100 GHz. This degree of freedom makes the hexagonal ferrite a
choice material for many monolithic microwave integrated circuit (MMIC) applications
[5]. Magnetic properties (4πM and HA) can be systematically varied by substituting for
the Fe cations, Fe3+. Elements such as scandium (Sc), aluminum (Al) and indium (In) are
used to replace the Fe3+ ion in BaFe12O19 to produce microwave absorber, for example.
The substitution of In for Fe3+ has shown to provide reduction in the anisotropy field (HA)
of hexaferrite [6]-[8]. The design of circulators and phase shifters operating below 50
GHz requires the low anisotropy compared with the pure barium ferrite, high Nèel
temperature, low FMR line width and low sensitivity at room temperature. Also, the In
substitution will stabilize the valence state of Fe3+ and will avoid the high loss tangents
[9]-[10]. The anisotropic field can vary over a wide range as a function of x [6]. In
addition to the composition, shape, size and orientation of the particles have significant
effects on its microwave absorption properties. When the particle size is at or near the
56
single domain, the domain-wall resonance mechanism no longer exists and the natural
frequency of the particle increases slightly. Most of the publications in pure and doped
hexaferrite materials dealt with the preparation of thin films by pulsed laser deposition
and liquid phase epitaxy methods. In this paper, preparation, magnetic and microwave
characterization of In-substituted Ba ferrite (BaFe12-xInxO19) are presented using the
modified ceramic technique. The main goal of this work is to prepare materials with
magnetically aligned grains along the in-plane, while maintaining the moderate coercivity
for self-biased microwave device applications at low frequencies.
Section 1: Experiment
High purity BaCO3, Fe2O3, and In2O3 were used as raw materials. They are
weighed stoichiometrically and then mixed by using a low energy ball mill. The pressed
compact powders were pre-heated at 1100 °C, crushed and sintered. After it was crushed
again and sieved, it finally went through an annealing process. In order to obtain single
phase crystallographic characteristics and magnetic properties, a post thermal annealing
was required. Samples were heated in air at a rate of 5 °C/min. The temperature is then
maintained between 1000-1150 °C for 10 hours, cooled to room temperature.
The
sintered compact samples were milled using a planetary ball mill. Since the In2O3 melts
at low temperature, it will easily accelerate grain growth through its own fluxing action
and different mole ratio of In substitution in hexaferrite has different sintering
temperature [11]. The milled particles were screen printed on a dielectric (Al2O3)
substrate with a thickness of about 0.5 – 1.0 mm and in-plane oriented using an epoxy
and hardener under the external dc magnetic field of 15 kOe. The screen printed and in57
plane oriented green compact was annealed at different temperatures to make highly
dense thick films for further characterization.
The crystallographic phase of the particles was analyzed using a θ−2θ x-ray powder
diffraction (XRD) (Rigaku–Cu-Kα radiation) technique. The surface morphology of the
particles was examined by scanning electron microscopy (SEM, Hitachi S-4100).
Chemical
analyses
were
carried
out
using
an
induction
coupled
plasma
spectrophotometer (ICP 20P VG Elemental Plasma Quad2) and as well as SEM-EDAX
facility. The magnetic properties were measured using a vibrating sample magnetometer
(VSM, ADE Technologies). Ferromagnetic resonance (FMR) measurements were
performed in both out-of-plane and in-plane FMR conditions by using a TE102 rectangular
cavity at room temperature. The FMR data allows us to calculate the effective
magnetization, anisotropy field, and FMR linewidth (∆HFMR).
Section 2: Results and Discussion
XRD patterns in Figure 4.2.1 confirmed the formation of pure single phase In
substituted Ba-hexaferrite with magnetoplumbite structure [12]. Chemical and SEMEDAX analysis showed that the samples had the required stochiometric ratios of Ba, Fe
and In as expected. The scanning electron micrograph shown in Figure 4.2.2-(a)-(c) of
the BaFe12-xInxO19 sample sintered at 1150 °C showed the formation of the larger grains,
which was about a few microns and had better inter grain connectivity. They also showed
the BaFe12-xInxO19 particles after ball milling with elongated thin platelets shape. The
58
average size of the particles was about 1-1.5 µm. EDAX spectra shown in Figure 4.2.3
confirmed that every samples produced by ceramic method had uniform composition.
The ball milled particles were screen printed on alumina (Al2O3) substrate using a
suitable binder and hardener. The loading factor, i.e., the binder and particle ratio is 70:30.
This ratio was suitable because if the amount of binder was large, density of the particles
was poor. Also, if the amount of binder was small, the orientation of the particles was
difficult because of its high viscosity. A maximum dc magnetic field of 15 kOe was
employed to orient the particles along the basal plane direction. The screen printed films
were then annealed at different temperatures to produce a dense and thick film. Figure
4.2.1-(b) indicated that the samples were oriented in c-plane and this orientation was
called basal plane orientation that was distinguished by c-axis orientation. Figure 4.2.4
showed the cross section of the BaFe11In1O19 film sintered at 1000 and 1100 °C for 1 hour
respectively. The structure of the film revealed to contain elongated grains with the short
axis parallel to the c-axis. Some pores remained visible. Table 4.2.1-(a)-(c) represented
magnetic properties for the in-plane oriented and annealed BaFe12-xInxO19 film at two
different temperatures, at 1000oC and 1100oC for 1hour. Table 4.2.1-(a)-(c) shows that
when x is relatively high, the squareness (in-plane) decreases. At x = 1.0, these films
exhibited low coercivity of 557 Oe but high hysteresis loop squareness ratio of 0.93.
This property provides these thick films potential for self-bias of ferrite devices. After
annealing at 1000oC for 1hr, the squareness was the same as before annealing, but
coercivity was increased because binders among particles before annealing were fired at
high temperature and the rooms where the binders were filled made porosities in the film.
Therefore the corecivity was increased. When the sintering temperature was increased
59
from 1000 to 1100 °C, the coercivity decreased to 1067 Oe and the squareness was
greater than 0.9. At 1100oC, the porosity made at 1000oC was occupied by grain growth
and coercivity decreased. At x = 1.5 and 2.0, squareness of these films decreased. Table
4.2.1-(b) and (c) also shows the same phenomenological effects. The coercivity of the
films was increased at 1000oC and then it was reduced at 1100oC. This is explained by
the same argument mentioned as the case for x = 1.0. Figure 4.2.5 shows that saturation
magnetization 4πMs is deceasing with the amount of Indium doping. This phenomenon
is quite obvious because cations of Fe3+ producing magnetic moments are replaced and
substituted by non magnetic In3+.
FMR measurements were performed by applying a swept dc magnetic field parallel to
the film plane, i.e., parallel FMR configuration. The frequency was fixed during each
field sweep and the measurements were taken for a wide range of frequencies from 28 to
40 GHz. When Hext was parallel to the film, the FMR condition is given as follows [13]:
ω
=
γ
( H ext + H A )( H ext + H A + 4π M S ) ,
where ω =2πf, and γ = 2π(g×1.4×106) Hz/Oe. Figure 4.2.6 shows the variation of FMR
derivative linewidth (∆H) with frequency over a range of 28-40 GHz for the BaFe12xInxO19
of thick films. A minimum linewidth of 800 Oe was realized for x=1.5 of at 28
GHz. The linewidths for x=1.0 and x=1.5 were small compared to the polycrystalline
compacts (typically > 2000 Oe). However, for x=2.0 the linewidths were broad and may
be applicable for microwave applications. On the other hand, the linewidths for x=1.0 and
1.5 can be further improved by increasing the density of the film. The density of these
films was about 3.6 ~ 3.8 g/cm3 compared with to 5.2 g/cm3 for single crystal.
60
By the FMR condition above, we deduced the anisotropy field assuming g= 2, see
Figure 4.2.7. The anisotropy field decreased with increasing amount of Indium doping,
as we expected. From x=1.0 to x=1.5, HA decreased by about 26%. However for x=1.5
to x=2.0, HA was reduced by about 50%. For x=1.0 to x=2.0, HA is reduced about 68%.
We recognize from this percentage reduction that the reduction of HA is sensitive for
x=1.5.
Finally, we determined experimentally the value of g (Lande spectroscopic splitting)
factor from the FMR relation between resonant frequencies versus resonance field was
1.91 at x=1.0 (shown in Figure 4.2.8 as a representative). We deduced g=2.01 at x=1.5
and 1.95 at x=1.97. These are in good agreement with g =2 for the bulk samples [14][15].
Section 3: Conclusions
Chemical synthesis of pure phase In doped barium hexa-ferrite platelets were prepared
by a modified conventional ceramic method. The size of the particles was controlled by
the mechanical alloying. The in-plane oriented, screen printed thick films showed a
squareness ratio of about 0.9 and a minimum linewidth of 800 Oe for x=1.5 and 900 Oe
for x=1.0 at 28 GHz samples. The saturation magnetization decreased with increasing In
ion substitution. The high squareness ratio, coercivity and narrow FMR linewidth
depended strongly on the sintering temperature and the resulting density of the film.
61
References
[1] J. J. Smit and H. P. J Wijn, Ferrites (Philips techn. Library, Eindhovan, 1959).
[2] V. G. Harris etal, J. Appl. Phys. 99, 08M911 (2006) and references therein.
[3] Y. Y. Song, S. Kalarickal, and C. E. Patton, J. Appl. Phys. 94, 5103 (2003).
[4] S. D. Yoon, C. Vittoria, and S. A. Oliver J. Appl. Phys. 92 (2002) 6733.
[5] M. Abe, T. Itoh, Y. Tamayura, Y. Gotoh, and M. Gomi, IEEE Trans. Magn. MAG-23,
3736 (1987).
[6] P. Shi, S. D. Yoon, X. Zuo, I. Kozulin, S. A. Oliver, and C. Vittoria, J. Appl. Phys. 87,
4981 (2000).
[7] G. Albanese and A. Deriu, Ceramurgia Int. 5, 3 (1979).
[8] G. F. Dionne and J. F. Fitzgerald J. Appl. Phys. 70, 6140 (1991).
[9] P. Röschmann, M. Lemke, W. Tolksdorf, and F. Welz, Mat. Res. Bull. 19, 385 (1984).
[10] K. Haneda and H. Kojima, J.J. Appl. Phys. 12, 355 (1973).
[11] C. N. Chinnasamy, T. Sakai, S. Sivasubramanian, Aria F. Yang, C. Vittoria,
and V. G. Harris, JOURNAL OF APPLIED PHYSICS 103, 07F710 (2008)
[12] JCPDS-PDF 27-1029.
[13] C. Vittoria, Microwave properties of Magnetic films (World Scientific, Singapore,
1993).
[14] Landolt-Börnstein. Numerical data and Functional relationships in Science and
Technology, edited by K.-H. Hellwege and A. M. Hellwege (Springer, Berlin, 1970), Vol
4, Part B, p. 573.
[15] J. Smit and H. G. Beljers, Philips. Res. Rep. 10, 113 (1955).
62
20
(107)
63
(2010)
40
60
2θ(degree)
(403)
(2014)
(3010)
(203)
(304)
(1011)
(108)
40
60
2θ(degree)
(409)
(2012)
(2013)
(300)
(209)
(202)
(205)
(206)
(104)
Intensity (a.u.)
20
80
Figure 4.2.1-(a) XRD of the BaFe11In1O19
80
Figure 4.2.1-(b) XRD of the oriented BaFe10.5In1.5O19
(3111)
(318)
(1018)
(3012)
(3010)
(2013)
(219)
(2012)
(2010)
(211)
(109)
(202)
(112)
(218)
(409)
(1118)
(403)
(405)
(2111)
(2014)
(228)
(0020)
(2115)
(300)
(1110)
(1116)
(220)
(217)
(108)
(203)
(106)
(006)
(116)
(205)
(206)
(2110)
(209)
(1011)
(1010)
(104)
(102)
(101)
(317)
(304)
(110)
Intensity
(008)
(107)
(114)
Figure 4.2.2-(a) Scanning electron micrograph of the BaFe11In1O19 (left) bulk and (right)
after ball milling.
Figure 4.2.2-(b) Scanning electron micrograph of the BaFe10.5In1.5O19 (left) bulk (right)
after ball milling
Figure 4.2.2-(c) Scanning electron micrographs of the BaFe10In2.0O19 (left) bulk (right)
after ball milling
64
Figure 4.2.3-(a) EDAX spectra for x = 1.0
Figure 4.2.3-(b) EDAX spectra for x = 1.5
Figure 4.2.3-(c) EDAX spectra for x = 2.0
65
Easy axis
Easy axis
Figure 4.2.4 Scanning electron micrograph of the screen printed, in-plane oriented
BaFe11In1O19 thick films sintered at (above) 1000 °C and (below) 1100 °C for 1 hour.
66
x=1.0
Squareness
(in-plane)
Squareness
(out of plane)
Before
annealing
0.93
0.11
Coercivity
(in-plane)
Coercivity
(out of plane)
557 Oe
1130 Oe
1000oC for
0.93
0.17
1150 Oe
1hr
1100oC for
093
0.10
1067 Oe
1hr
Table 4.2.1-(a): Magnetic property of BaFe11In1O19.
1540 Oe
668 Oe
x=1.5
Squareness
(in-plane)
Squareness
(out of plane)
Coercivity
(in-plane)
Coercivity
(out of plane)
Before
annealing
0.82
0.14
260 Oe
430 Oe
1000oC for
0.86
0.22
386 Oe
1hr
1100oC for
0.84
0.14
165 Oe
1hr
Table 4.2.1-(b): Magnetic property of BaFe10.5In1.5O19.
545 Oe
357 Oe
x=2.0
Squareness
(in-plane)
Squareness
(out of plane)
Coercivity
(in-plane)
Coercivity
(out of plane)
Before
annealing
0.50
0.14
76 Oe
248 Oe
1000oC for
0.60
0.20
153 Oe
1hr
1100oC for
0.51
0.16
90 Oe
1hr
Table 4.2.1-(c): Magnetic property of BaFe10In2O19.
246 Oe
67
175 Oe
4πMs (kG)
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
Before sintering
o
sintered at 1000 C for 1hr
o
sintered at 1100 C for 1hr
1.0
1.2 1.4 1.6 1.8
x (Indium doping)
2.0
Figure 4.2.5 Saturation magnetization versus the doping of Indium
68
2.8
2.6
2.4
∆H (kOe)
2.2
x=1.0
x=1.5
x=2.0
2.0
1.8
1.6
1.4
1.2
1.0
0.8
28
30
32
34
GHz
Figure 4.2.6. ∆H versus Frequencies.
69
36
38
40
10
HA(kOe)
9
8
7
6
5
4
3
1.0
1.5
x(Indium doping)
Figure 4.2.7. HA versus Indium doping.
70
2.0
Figure 4.2.8. Resonance frequencies versus applied fields for BaFe11In1O19 film.
71
Chapter 5: Synthesis and Properties of BaFe12-xScxO19
Introduction
The large uniaxial magnetocrystalline anisotropy field in hexagonal ferrites with Mtype structure (e.g. MeFe12O19, where Me=Ba, Sr and Pb) acts as an internal magnetic
field that provides for ferromagnetic resonance (FMR) to occur in the microwave and
millimeter frequency bands thus allowing for their incorporation in passive microwave
devices such as circulators, phase shifters and isolators[1]-[3]. Since hexagonal ferrites
have a high anisotropic field, their resonance frequencies are high. One advantage of the
hexaferrite is that the magnetic properties (4πM and HA) can be systematically varied by
substituting for the Fe cations. Elements such as Sc, Ga, Al and In are used to replace the
Fe3+ ion in BaFe12O19 to shift the FMR as low as1 GHz, or as high as100 GHz
frequencies. In particular, the substitution of scandium (Sc) for Fe3+ has been shown to
provide a reduction in the anisotropy field (HA) of hexaferrite thereby lowering the FMR
frequency to X-band and below[4]-[5].
The design of X-band circulators and phase shifters requires the low anisotropy field
compared with the pure barium ferrite (HA~17 kOe), high Néel temperature, high
remanence and saturation magnetization, and low FMR linewidth (<300 Oe). The Sc
substitution will stabilize the valence state of Fe3+ and will avoid the high loss tangents[6].
The anisotropic field can vary over a wide range as a function of the level of
substitution[7]. In addition to the composition, shape, size, and thickness, orientation of
the particles have a significant effect on the microwave absorption properties. Most of
72
the published research in pure and doped hexaferrite materials dealt with the preparation
of thin films and as well as out-of-plane (easy axis of magnetization is perpendicular to
the film plane) oriented bulk materials processed by conventional ceramic methods. This
method induces sintering and aggregation of particles, the hexaferrite must then be
grounded extensively to reduce the particle size close to the single domain size. The
milling process generally yields nonhomogeneous mixtures on a microscopic scale and
introduces lattice strains and defects in the material. In order to obtain uniform sized
hexaferrite particles, various techniques such as glass crystallization[8], sol-gel method[9],
co-precipitation[10], miroemulsion mediated process[11] and aerosol synthesis
technique[12] have been developed.
Since the single domain size of the barium
hexaferrite is about 1 µm [13], preparing the size and shape controlled particles using the
bottom-up approach is more desirable than the conventional ceramic method. Here, we
prepared the Sc doped hexaferrites BaFe12-xScxO19 (x = 0.3, 0.5, 0.8 and 1.0) by using the
modified co-precipitation method. The particles were screen printed, in-plane oriented
and annealed as thick films and studied their structural, magnetic and microwave
properties.
Section 1: Experiment
The BaFe12-xScxO19 particle processing experiments were carried out using the iron
(III) chloride hexahydrate (FeCl3.6H2O, 99.9%, Sigma Aldrich), barium chloride
(BaCl2.2H2O,
99.9%,
Sigma
Aldrich)
and
Scandium
(III)
acetate
hydrate
(CH3CO2)3Sc.xH2O, 99.9%) as raw materials and dissolved in distilled water with the
required ratio.
The mixed metal precursor solution was introduced slowly into the
73
mixture of NaOH-Na2CO3 alkaline solution. When an alkaline solution was added, an
intermediate precursor containing BaFe12-xScxO19 were formed.
The particles were
thoroughly washed several times with distilled water and then filtered. The filtered
intermediate particles were dried at 100 °C for 12 hours. In order to obtain single phase
crystallographic characteristics and magnetic properties, a post thermal annealing was
required. Samples were heated in air at a rate of about 6 °C/min. The temperature was
then maintained at 1000-1100 °C for 5 hours, after which a natural cooling was carried
out. The sintered samples were dispersed either using a roller mill or a planetary ball mill
while maintaining the particle shape.
The hexagonal platelet shaped particles were
suspended within an epoxy and screen printed on a dielectric substrate (Al2O3) with a
thickness of about 0.25-0.5 mm. Particles in the still green film were oriented along the
in-plane direction under an external dc magnetic field of 15 kOe. The screen printed and
in-plane oriented green compact was annealed at various temperatures to make highly
dense thick films for further characterization. Due to the space constraints we are
herewith presenting the data for x=0.3, 0.5, 0.8 and 1.0.
The crystallographic phase of the particles was analyzed using the θ−2θ x-ray
powder diffraction (XRD) (Rigaku – Cu-Kα radiation, λ= 1.54506 Å) technique. The
surface morphology of the particles and films was examined by scanning electron
microscopy (SEM, Hitachi S-4100). Chemical analyses have been carried out using an
induction coupled plasma spectrophotometer (ICP 20P VG Elemental Plasma Quad2) as
well with a SEM-EDAX facility.
The magnetic properties were measured using a
vibrating sample magnetometer (VSM, ADE Technologies). Ferromagnetic resonance
(FMR) measurements were performed in both out-of-plane and in-plane FMR conditions
74
by using a TE10 rectangular waveguide at room temperature at Ka-band frequencies. The
FMR data allowed us to calculate the effective magnetization, anisotropy field, Lande
spectroscopic splitting factor and FMR linewidth.
Section 2: Results and Discussion
The x-ray diffraction pattern X-ray of BaFe11.2Sc0.8O19 in Figure 5.2.1 confirmed the
formation of pure single phase Sc doped Ba-hexaferrite having the magnetoplumbite
structure[14]. Chemical analysis and SEM-EDAX analysis showed that the samples had
the required stochiometric ratios of Ba, Fe and Sc shown in Figure 5.2.2-(a) ~ (d). SEM
images of representative BaFe11.7Sc0.3O19 particles prepared by the present method shows
homogeneous hexagonal platelets, with average diameter of ~ 0.9 µm (Figure 5.2.3-(a)
and (b)). The sizes of the platelets were controlled by the sintering temperature. Figure
5.2.4 shows the dispersed particles of BaFe11.2Sc0.8O19 after ball milling with the
hexagonal platelet shape retained. This morphology is highly desired in achieving particle
orientation in the films. The dispersed particles were screen printed on alumina (Al2O3)
substrate using a suitable binder and hardener. At present the loading factor, i.e., the
binder to particle mass ratio was 70:30. A dc magnetic field of 15 kOe was employed to
orient the particles along the in-plane (basal plane) direction shown in Figure 5.2.1-(b).
The screen printed films were then sintered at different temperatures to produce a dense
and thick film. The hysteresis loops in Figure 5.2.5-(a) for the as-prepared and screen
printed, in-plane oriented BaFe11.7Sc0.3O19 film show a squareness ratio (S = Mr/Ms) of
0.88, a coercivity of 241 Oe, and the saturation magnetic moment (4πMs) of 3700 Gauss.
75
After sintering at 1100 °C for 2 hours the film became hard and dense and the in-plane
orientation was stabilized without deteriorating the magnetic properties as shown in
Figure 5.2.5-(b). Similar experiments were carried out for the BaFe12-xScxO19 (where
x=0.5, 0.8 and 1.0) thick films. Table 5.2.1-(a) ~ (d) shows the squareness and coercivity
at different temperatures.
At higher sintering temperatures, the squareness starts to
decrease and the coercivity increases. The saturation magnetic moment (4πMs) shown in
Figure 5.2.6 decreased with increasing substitutions of Sc due to the occupation of non
magnetic Sc at the octahedral sites (4fVI) belonging to the R structural block of barium
hexaferrite. As a part of the Sc ions 4fVI – 12k interactions, a decrease in magnetic
moment have been observed due to the antiferromagnetic order among up and down
sublattices, so that 12k ions with different number of magnetic 4fVI neighbors have
different magnetization[15]. We also speculate that the number of Sc ions occupying the
R structural block may influence the sintering temperature to keep improved in-plane
orientation.
FMR measurements were performed by applying a swept dc magnetic field parallel
to the film plane, i.e., parallel FMR configuration. The frequency was fixed during each
field sweep and the measurements were taken from 28 to 40 GHz. When Hext is parallel
to the film, the FMR condition is given as follows[16]:
ω
= ( H ext + H A )( H ext + H A + 4πM S )
γ
,
where ω =2πf, and γ= 2π(g×1.4×106) Hz/Oe. Figure 5.2.7 shows the variation of FMR
derivative linewidth (∆H) as a function of frequency over a range of 28-40 GHz for the
Sc-substituted samples. A minimum linewidth of 800 Oe and 1500 Oe were realized for
the x=0.3 and 0.8 films, respectively. The broadening of the linewidth is also not linearly
76
proportional to the frequency as shown in Figure 5.2.7 which is usually observed for
single crystals and epitaxial films[17]. This is due to the large role of extrinsic loss
mechanisms (for example, presence of porosity) that often do not have a linear
relationship with frequency[18]. Hence, it is possible to produce in-plane oriented thick
films at low cost using the present method.
The variation of HA is shown in Figure 5.2.8. The plot for HA versus x is almost linear
and this is in agreement with the result of single crystal [19]. At x=1.0 HA is about
5000Oe and there is still capability of substituting Scandium in Barium ferrite.
Compared with Indium substituted Barium hexaferrite, the slope of doping Scandium
(see Figure 4.2.7 and Figure 5.2.8) is steeper so that Scandium doping for Barium ferrite
is effective as well as sensitive. From x=0.3 to x=0.5 HA decreased 15%. From x=0.5 to
x=0.8, it is about 20%. From x=0.8 to x=1.0, it reduced about 35%. From x=0.3 to
x=1.0, HA is reduced about 60%. These percentages confirm that Scandium substitutions
are more effective than Indium doping.
The linewidth can be further reduced by improving the in-plane orientation and
density of the film. The density of these films was about 3.6 ~ 3.8 g/cm3, same as the
case of Indium substituted films. Experimental values of g (Lande spectroscopic splitting
factor) shown in Figure 5.2.9 (BaFe11.2Sc0.8O19) were deduced from the relation between
resonant frequencies versus resonance field for the screen printed films and was found to
be 1.92 for x=0.3, 1.97 for x=0.5, 2.04 for x=0.8 and 2.01 for x=1.0. This is in good
agreement with the value g =2 found for bulk samples[20].
77
Section 3: Conclusions
Large scale chemical synthesis of pure phase Sc doped barium hexaferrite platelets
were prepared by a modified coprecipitation method. The size of the platelets was
controlled by the sintering temperature. The in-plane oriented, screen printed thick films
showed a squareness ratio of about 0.88 and a minimum linewidth of 800 Oe for the
x=0.3 sample.
The saturation magnetization decreased with increasing Sc ion
substitution. Scandium substitution for Barium hexaferrite is more effective than Indium
substitution in changing HA.
References
[1] V. G. Harris et al., J. Appl. Phys. 99, 08M911 (2006) and references therein.
[2] J. Smit and H. P. J Wijn, Ferrites (Philips Techn. Library, Eindhovan, 1959).
[3] C. E. Patton, IEEE Trans. on Magn. 24, 2024 (1988).
[4] T. M. Perekalina and V. P. Cheparin, Sov. Phys. Solid State 9, 2524 (1968).
[5] P. Shi, S. D. Yoon, X. Zuo, I. Kozulin, S. A. Oliver, and C. Vittoria, J. Appl. Phys. 87,
4981(2000).
[6] D. B. Nicholson, Hewlett-Packard J. 41, 59 (1990).
[7] K. Haneda and H. Kojima, Jpn. J. Appl. Phys. 12, 355 (1973).
[8] B. T. Shirk and W. R. Buessem, J. Am. Ceram. Soc. 53, 192 (1970).
[9] C. Surig, K. A. Hempel, and D. Bonnenberg, Appl. Phys. Lett. 63, 2836 (1993).
[10] K. Haneda and H. Kojima, J. Am. Ceramic. Soc. 57, 68 (1974).
[11]V. Pillai, P. Kumar and D. O. Shah, J. Magn. Magn. Mater. 116, 299 (1992)
78
[12] W. A. Kaczmarek, B. W. Ninham, and A. Calka, J. Appl. Phys. 70, 5909 (1991).
[13] C. D. Mee and J. C. Jeschke, J. Appl. Phys. 34, 1271 (1963).
[14] JCPDS-PDF 27-1029.
[15] G. Albanese, A. Deriu, E. Lucchini and G. Slokar, IEEE Trans. Magn. MAG-17,
2639 (1981).
[16] C. Vittoria, Microwave Properties of Magnetic Films (World Scientific, Singapore,
1993).
[17] W. Platow, A. N. Anisimov, G. L. Dunifer, M. Farle, and K. Baberschke, Phys. Rev.
B 58, 5611 (1998).
[18] B. Lax and K. Button, Microwave ferrites and ferrimagnetics, (McGraw-Hill, New
York (1962), Ch. 5, p. 200.
[19] Dean B. Nicholson, Hewlett Packard Journal (1990) p. 59
[20] Landolt-Börnstein. Numerical data and Functional relationships in Science and
Technology, edited by K.-H. Hellwege and A. M. Hellwege (Springer, Berlin, 1970), Vol
4, Part B, p. 573
79
20
(300)
(304)
80
(202)
(203)
40
60
2θ(degree)
(409)
(403)
(106)
(2014)
(3010)
(3012)
(209)
(109)
(104)
(1018)
(405)
(2013)
(2010)
(1010)
(1011)
(205)
(107)
(101)
(102)
Intensity (a.u.)
(206)
(108)
Figure 5.2.1-(a): XRD of BaFe11.2Sc0.8O19
(2012)
80
Figure 5.2.1-(b): XRD of in-planed oriented sample of BaFe11.7Sc0.3O19.
Figure 5.2.2-(a): EDAX for x=0.3
Figure 5.2.2-(b): EDAX for x=0.5
Figure 5.2.2-(c): EDAX for x=0.8
Figure 5.2.2-(d): EDAX for x=1.0
81
Figure 5.2.3-(a): SEM images of BaFe11.7Sc0.3O19 at high magnification.
Figure 5.2.3-(b): SEM images of BaFe11.7Sc0.3O19 at low magnification.
82
Figure 5.2.4: dispersed particles of BaFe11.2Sc0.8O19 after ball milling.
83
Figure 5.2.5-(a): Sc=0.3 in-plane oriented sample before annealing.
4πM(kG)
4
2
0
-2
S(parallel) = 0.88
S(perpendicular) = 0.06
Hc(parallel) = 257.83 Oe
Hc(perpendicular) = 388.05 Oe
-4
-15
-10
-5
0
5
H(kOe)
10
15
Figure 5.2.5-(b): Sc=0.3 annealed at 1100oC for 2hr.
84
x=0.3
Squareness
(in-plane)
Squareness
(out of plane)
Before
annealing
0.88
0.7
241Oe
384Oe
0.87
0.88
0.06
0.06
250Oe
258Oe
385Oe
388Oe
700oC for 2hr
1100oC for
2hr
Coercivity
(in-plane)
Coercivity
(out of plane)
Table 5.2.1-(a): Magnetic property of BaFe11.7Sc0.3O19.
x=0.5
Squareness
(in-plane)
Squareness
(out of plane)
Before
annealing
0.76
0.32
1445Oe
1593
0.73
0.66
0.37
0.42
1624Oe
2290Oe
1700Oe
2287Oe
700oC for 2hr
1100oC for
2hr
Coercivity
(in-plane)
Coercivity
(out of plane)
Table 5.2.1-(b): Magnetic property of BaFe11.5Sc0.5O19.
X=0.8
Squareness
(in-plane)
Squareness
(out of plane)
Before
annealing
0.78
0.22
Coercivity
(in-plane)
Coercivity
(out of plane)
930Oe
970Oe
700oC for 2hr
0.78
0.22
992Oe
1100oC for
0.66
0.35
2545Oe
2hr
Table 5.2.1-(c): Magnetic property of BaFe11.2Sc0.8O19.
923Oe
2010Oe
x=1.0
Squareness
(in-plane)
Squareness
(out of plane)
Before
annealing
0.64
0.26
441Oe
457Oe
0.6
0.56
0.31
0.33
521Oe
604Oe
550Oe
600Oe
700oC for 2hr
1100oC for
2hr
Coercivity
(in-plane)
Table 5.2.1-(d): Magnetic property of BaFe10Sc1.0O19.
85
Coercivity
(out of plane)
3800
Before annealing
o
annealed at 700 C
o
annealed at 1100 C
3700
4πMs(G)
3600
3500
3400
3300
3200
3100
3000
2900
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
x(scandium doping)
Figure 5.2.6: saturation magnetization versus doping amount.
86
∆H(kOe)
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
x=0.3
x=0.5
x=0.8
x=1.0
28
30
32
34 36
GHz
Figure 5.2.7: Linewidth versus Frequencies.
87
38
40
13
12
HA (kOe)
11
10
9
8
7
6
5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
x(Scandium doping)
Figure 5.2.8: Saturation magnetization versus the doping of Scandium.
88
GHz
41
40
39
38
g=2.04
37
36
35
34
33
32
11.5 12.0 12.5 13.0 13.5 14.0 14.5
H(kOe)
Figure: 5.2.9: Resonance frequencies versus applied fields for BaFe11.2Sc0.8O19 film.
89
Chapter 6: Synthesis and Properties of Perpendicular Oriented
BaFe11In1.0O19 by Conventional Ceramic Method
Introduction
Barium ferrite doped by scandium [1] has great potential as a self-biased ferrite
material for nonreciprocal passive device applications below 18 GHz [2]-[4]. This
frequency range is commonly utilized in industries for applications in radar and wireless
communication technologies [5]-[6]. The main goal in processing this material,
BaFe11ScO19, for circulator device applications is to maintain high saturation
magnetization and high squareness (Mr/Ms) with the c-axis aligned perpendicular to the
plane of the compact.
In addition to these magnetic and structural properties, the
materials should have a minimal microwave loss, i.e. a ferromagnetic resonance (FMR)
linewidth (∆H) of < 500 Oe, at the targeted frequencies. We describe the processing of
pure phase powders, compaction within a high magnetic field, and optimal sintering
condition to obtain highly textured compacts having uniaxial magnetic properties.
Hysteresis loop squareness was measured to be 0.83 and the FMR derivative linewidth
was 1000 Oe at 9.5 GHz.
Section 1: Experiment
We first obtained a pure phase Sc-doped barium hexaferrite by using conventional
ceramic processing technique. Chemicals of BaCO3, Fe2O3, and Sc2O3, having the right
90
molar ratio, was blended with alcohol in a mortar and pestle for 30 ~ 40 minutes. After
the alcohol evaporated away, the mixture was pressed to make a solid compact in a die
with 3000 psi. The compact was sintered in air at 1000oC for 10 hours. The sintered
compact was grinded in motor and pestle and the grinded powder was pressed again in a
die with same pressure. The compact was sintered at 1100oC for 10 hours. The same
process was repeated one more time at 1200oC for 10 hours. The first 2 sintering process
is called calcination. The usual temperature of calcining for ferrites was about 900oC
~1100oC. The reason for calcining was to start the process of forming the ferrite lattice.
This process is essentially one of interdiffusing the substituent oxides into a chemically
and crystallographically uniform structure. The driving force for the interdiffusion is the
concentration gradient. The material in the center of each of the oxide particles
experienced difficulty diffusing through the ferrite since the diffusion distances become
larger.
The final sintered compact was grinded finely and was measured by X-ray
diffractometer (Philips Xpert Cu Kα radiation). The surface morphology and composition
analysis were measured by SEM and EDAX system attached with SEM facility (Hitachi
S-4800 with EDAX system). It was then put in a planetary ball mill (Pulverissette 6)
used with agate bowl and balls. The mass ratio of agate balls and ground ferrite powder
was 8 : 1 and milling speed and time were 400rpm and 10 hours. The alcohol was used
as a media in the ball mill.
The magnetic field (~ 10 kOe) was applied to orient the ferrite particles perpendicular
to the plane in a cylinder. During the orientation the powder in a cylinder was pressed at
3000 psi at the same time. The oriented compacts were annealed or sintered at different
91
temperatures and DC magnetic properties of the compacts were measured with Vibrating
Sample Magnetometer (ADE Technology).
The microwave properties were characterizing Ferromagnetic resonance technique.
The resonance condition for perpendicular FMR is given by
ω
= H ext + H A − 4πM
γ
where ω =2πf, and γ = 2π(g×1.4×106) Hz/Oe.
Section 2: Results and Discussion
Figure 6.2.1-(a) shows that after sintering at 1250oC for 10hrs, BaFe11Sc1O19 has a
pure phase of Barium hexaferrite. Chemical composition analysis with EDAX shown in
Figure 6.2.1-(b) confirmed that the final sintered powder has a right molecular
composition. Surface morphology of BaFe11ScO19 after sintered at 1250oC for 10hrs is
shown in Figure 6.2.2-(a). We see in Figure 6.2.2-(a) that some platelets were grown in a
shape of hexagon and particle size of these particles were about 2 ~ 4 µm. Other particles
were about 5 ~7 µm.
The as-prepared single phase powders were ball milled using agate balls to reduce the
average particle size to 2µm ~ 3µm shown in Figure 6.2.2-(b). The single domain size of
BaFe11ScO19 was about 1µm [7] and we have found in previous studies [8] that particles
having diameters in the range 2µm ~ 3µm allowed for effective crystallographic
orientation in an applied magnetic field. In this procedure a variety of agate balls having
diameters ranging from 5mm to 12 mm were used. As seen in Figure 6.2.2-(b), the size
92
of the particles ranged from 0.5µm to 3µm. It is common for ball milled powders to
exhibit a wide range of particle sizes. The milled powder was mixed with alcohol and
ultrasonically dispersed to minimize the agglomeration of particles. The particles with
alcohol were then introduced to a die in preparation for field alignment and compaction.
In the field compaction, the plunger and seat were made of FeCo alloy that allowed
for the focus of the magnetic field through the sample. The die was wrapped with a large
number of turns of copper coils that generate 12 kOe magnetic fields for the orientation
during compaction as shown in figure 6.2.3. A pressure of 3000 psi was applied for the
powder during the orientation. The oriented specimen was then sintered at a range of
sintering temperatures from 1000oC to 1150oC and time of 2 hours and 5hours. The
compacts were annealed in the air and were cooled naturally.
Table 6.2.1 indicated that the compact annealed at 1100oC for 2hours exhibited high
squareness and also had good orientation. Hysteresis loop is shown in Figure 6.2.4. The
saturation magnetization (4πMs) was estimated as 1800 G. From Table 6.2.1, the case f
or 1050oC and 2 hours and 5 hours sintering revealed to us that longer annealing times
damaged the orientation. This effect is explained as follows. Heat helps to grow the
particle grains and the grain growth occupies the pores in the compact. As such, we have
ideal orientation as shown in Figure 6.2.5. After the optimal condition, the grain keeps
growing and neighbor’s grains have no room to grow.
Continual growth implies
deformation and, hence, breaking of the orientation. In our case, the optimal condition
for annealing was 1100oC for 2 hours.
In-plane FMR measurements with an applied (in plane) magnetic field of 7800Oe
indicated that for the optimally prepared sample the resonant frequency was 9.53 GHz.
93
FMR linewidth ∆H was measured to be 1000Oe. Although this value is relatively high in
comparison to samples prepared by pulsed laser deposition and liquid phase epitaxy [9],
it is low in comparison to polycrystalline compacts.
Section 3: Conclusions
Sc-doped Barium hexaferrite powders were synthesized by a conventional ceramic
method and subjected to field compaction and sintering. The samples had a hysteresis
loop squareness of 0.83 that is required for self-biased applications at frequencies below
20 GHz. The high remanence arises from well-oriented platelet particles, while the high
coercivity arises from small particles, copious grain boundaries, and porosity. X-band
FMR measurement showed a linewidth of 1000Oe. Although this is low compared to
most polycrystalline compacts, continued refinement of the process is required to reduce
this value to below 500Oe.
References
[1] G. F. Dionne and J. F. Fitzgerald, “Magnetic hysteresis properties of BaFe12-xInx
ceramic ferrites with c-axis oriented grains,” J. Apple. Phys., vol. 70, pp. 6140 – pp.
6141, 1991.
[2] A. Gruskova, “Magnetic properties of substituted barium ferrite powders,” IEEE
Transaction on Magnetics, vol. 30, no. 2, pp. 639 – pp. 641 1994.
[3] S. Capraro, J. P. Chatelon, M. Le Berre, T. Rouiller, H. Joisten, D. Barbier and J. J.
Rousseau, “Thick barium ferrite films use for passive isolators,” Phys. Stat. Sol. (c), vol.
1, no. 12, pp.3373 – pp. 3377, 2004.
[4] D. B. Nicholson, R. J. Matreci, M. J. Levernier, “26.5 to 75 GHz preselected mixers
based on magnetically tunable barium ferrite filters,” Hewlett-Packard Journal, vol. , pp.
94
59 – pp. 62, 1990.
[5] M. A. Tsankov and L. G. Milenova, “Design of self-biased hexaferrite waveguide
circulators,” J. Appl. Phys., vol. 73, pp. 7018 – pp. 7020, 1993.
[6] C. K. Queck and L.E. Davis, “Self-biased hexagonal ferrite coupled line circulators,”
Electronics. Lett., vol. 39, no. 22, pp. 1595 – pp. 1599, 2003.
[7] J. Dho, E. K. Lee, J. Y. Park and N. H. Hur, “Effects of the grain boundary on the
coercivity of barium ferrite BaFe12O19,” Journal of Magnetism and Magnetic Materials,
vol. 285, pp. 164 – pp. 166, 2005.
[8] Y. Chen, T. Sakai, T. Chen, S. D. Yoon, C. Vittoria and V. G. Harris, “Screen printed
thick self-biased, low-loss, barium hexaferrite films by hot-press sintering”, J. Appl.
Phys, in press, 2006.
[9] P. Shi, S. D. Yoon, X. Zuo, I. Kozulin, S. A. Oliver and C. Vittoria, “Microwave
properties of pulsed laser deposited Sc-doped barium hexaferrite films,” J. Appl. Phys.,
vol. 87, pp. 4981 – pp.4983, 2000.
95
20
40
2θ(degree)
60
96
80
Figure 6.2.1-(a): XRDof BaFe11Sc1O19.
Figure 6.2.1-(b): EDAX spectra of BaFe11Sc1O19.
(0020)
(1118)
(405)
(228)
(3012)
(3010)
(219)
(2010)
(211)
(1010)
(108)
(116)
(112)
(206)
(409)
(2115)
(403)
(317)
(2111)
(2014)
(2012)
(218)
(209)
(300)
(1011)
(109)
(106)
(006)
(101)
(102)
(220)
(217)
(205)
(304)
(203)
(110)
Intensity (a.u)
(107)
(114)
Figure 6.2.2-(a): SEM image of surface of BaFe11Sc1O19
after sintered at 1250oC for 10hrs.
Figure 6.2.2-(b): SEM image of surface of BaFe11Sc1O19
after ball milled for 10 hours.
97
Squareness
(easy axis)
Squareness
(hard axis)
Coercivity
(out of plane)
Oe
Corcivity
(in-plane)
Oe
1050oC for 2hr
0.80
0.26
2250
1744
1100oC for 2hr
0.83
0.24
2347
1792
1150oC for 2hr
0.82
0.28
2288
1768
1050oC for 5hr
0.82
0.29
2576
2027
Sintering
Temperature (oC)
Table 6.2.1: Magnetic properties of oriented compacts at different annealed condition.
98
Orientation device
Press device
1200 turns of copper
wires
Figure 6.2.3: Perpendicular orientation device and press.
99
Figure 6.2.4: Hysteresis loop of the compact annealed at 1100oC for 2hours.
Solid line is that external magnetic field is perpendicular to the plane of the
sample and dashed line is parallel to the plane.
100
Figure 6.2.5: SEM image of the surface of compact annealed at 1100o for 2 hours.
101
Chapter 7: Design and Fabrication of Phase Shifter
Introduction
The ferrite phase shifter [1]-[3] is utilized as a component of a microwave circuit in
telecommunication and radar system. Nowadays, companies are seeking high frequency
tunable phase shifters and they are targeting Ka and higher band phase shifters. Spinel
and Garnet ferrites require high bias magnetic fields for Ka-band phase shifter
applications and they are not ideal materials for the purpose.
On the other hand,
hexaferrites are an ideal materials for Ka and higher bands. It has high anisotropy field
(HA) and by the existence of the high HA FMR frequencies are shifted to higher
frequencies. However, HA of pure Barium hexaferrite is too high and pure Barium ferrite
is not applicable for some needs as it is. Reducing the high HA of pure Barium ferrite is
required and it can be accomplished by the doping of Sc and In in pure Barium ferrite as
in previous chapters. In this chapter we fabricate and test a phase shifter with Indium
doped Barium ferrite.
Section 1: Design and Simulation of Phase Shifter
The phase, θ, of a wave is calculated by θ = βl =
ω
c
εµ eff (Gaussian unit) where ε is
permittivity about 20 statfarads/cm, l is the length of microstrip within the oriented ferrite
and ω is angular frequency (ω=2πf). Effective permeability µeff is dependent on the
102
frequencyω, i.e. ω= µeff (ω). The quality and performance of a magnetic phase shifter is
due to µeff and phase changes ∆θ come from µeff.
In order to derive µeff we will first calculate FMR condition [4]-[5] of in-plane oriented
sample. Free energy F of the geometry shown in Figure 7.1.1 is given by
2
F = − M y H + 2πM z − K1
M 2y
.
M 2s
(7.1.1)
r
r
∂
∂
∂
H int ernal is calculated as H int ernal = −∇ M F , where ∇ M = iˆ
+ ˆj
+ kˆ
.
∂M x
∂M y
∂M z
For the definition of the gradient see [Vittoria]
r
My

H int ernal = ˆj  H + 2 K1 2
M s

 ˆ
 + k (− 4πM s ) = ˆj (H + H A ) + kˆ(− 4πM s ) .

(7.1.2)
r
r
The static magnetization M 0 is given by M 0 = M s kˆ and the static part of internal
r
magnetic field is given by H int ernal 0 = ˆj (H + H A ) . We also have the microwave field and
the dynamical parts of magnetization and internal field are given by
r
r
m = m x iˆ + m y ˆj + m z kˆ and h = −4πm z kˆ . The dynamic equation of motion is
r
r
r
r
r
r
r
r r
1 dm
= M 0 + m × H0 + h = M0 × h + m + H0 .
γ dt
(
) (
) (
) (
)
(7.1.3)
This equation gives us
1 dm x
= −(H + H A )m z .
γ dt
(7.1.4)
1 dm y
= 0.
γ dt
(7.1.5)
1 dm z
= (H + H A + 4πM x )m x .
γ dt
(7.1.6)
103
If one writes mx and mz as m x = m x 0 e iωt and m z = m z 0 e iωt , then we have two equations as
follows:
i
ω
m x 0 + (H + H A )m z 0 = 0 .
γ
(7.1.7)
i
ω
m z 0 − (H + H A + 4πM s )m x 0 = 0 .
γ
(7.1.8)
From (7.1.7) and (7.1.8), we can get the FMR condition as
ω
=
γ
(H + H A )(H + H A + 4πM s ) .
(7.1.9)
r
In order to derive the magnetic susceptibility, h is rewritten as
r
h = hx iˆ + h y ˆj + (hz − 4πm z )kˆ .
(7.1.10)
Following the same path to derive the FMR condition, we have

H + HA
 hx 0  M s 
  = 2
 hz 0  Ω  − i ω

γ


 m
 x 0  .


H + H A + 4πM s  m z 0 

i
ω
γ
(7.1.11)

H + HA
Ms 
Therefore, we can get a susceptibility χ as χ = 2
Ω  −iω

γ



 . (7.1.12)

H + H A + 4πM s 

i
ω
γ
From this χ of (7.1.12), we can calculate the permeability µ as the following.
 χ xx
1 0 0



µ= [I] + 4π[χ] where [I ] =  0 1 0  and [ χ ] =  0
χ
0 0 1


 yx
 µ xx

µ = 0
µ
 zx
0 µ xz  1 + 4πχ xx
 
1 0 =
0


0 µ zz   4πχ zx
4πχ xz 

1
0

0 1 + 4πχ zz 
0 χ xz 

0 0 
0 χ zz 
(7.1.13)
0
104
(7.1.14)
µ xx = 1 +
4πM s (H + H A )
2
(H + H A )(H + H A + 4πM s ) − ω 2
γ
4πM s (H + H A + 4πM s )
µ zz = 1 +
2
(H + H A )(H + H A + 4πM s ) − ω 2
γ
4πM s i
µ xz = − µ zx =
,
(7.1.15)
, and
(7.1.16)
ω
γ
ω2
(H + H A )(H + H A + 4πM s ) − 2
γ
.
(7.1.17)
ω
ω ∆H
−i
for
and the calculations are as
γ
2
γ
The damping is included by substituting
follows.
µ xx = 1 +
µ xx = 1 +
4πM s (H + H A )
(H + H A )(H + H A + 4πM s ) −  ω − i ∆H
2
γ
2
,
(7.1.18)
2



ω
∆H 2 

4πM s (H + H A ) (H + H A )(H + H A + 4πM s ) −   +
4 

γ 

2
2
2

 ω  ∆H 2   ω∆H 

 (H + H A )(H + H A + 4πM s ) −   +
 +

4   γ 

γ 

4πM s i (H + H A )
−



ω∆H
γ
2
2
2
2 





ω
ω
∆
H
∆
H
 + 
 (H + H A )(H + H A + 4πM s ) −   +

4   γ 

γ 

µ xx = µ ′xx − iµ ′xx′
105
(7.1.19)
∴
µ ′xx = 1 +
2

 ω  ∆H 2 


4πM s (H + H A ) (H + H A )(H + H A + 4πM s ) −   +
4 

γ 

2
2
2

 ω  ∆H 2   ω∆H 

 (H + H A )(H + H A + 4πM s ) −   +
 +

4   γ 

γ 

4πM s i (H + H A )
µ ′xx′ =
ω∆H
γ
2
2

 ω  ∆H 2   ω∆H
 (H + H A )(H + H A + 4πM s ) −   +
 + 

γ
4

 
  γ



,
.
2
(7.1.20)
(7.1.21)
Similarly,
µ ′zz = 1 +
2

 ω  ∆H 2 


4πM s (H + H A + 4πM s ) (H + H A )(H + H A + 4πM s ) −   +
4 

γ 

2
2
2

 ω  ∆H 2   ω∆H 

 (H + H A )(H + H A + 4πM s ) −   +
 +

4   γ 

γ 

4πM s i (H + H A + 4πM s )
µ ′zz′ =
µ ′xz =
ω∆H
γ
2
2
2

 ω  ∆H 2   ω∆H 

 (H + H A )(H + H A + 4πM s ) −   +
 +

4   γ 

γ 

2
 ω  ∆H 2 
 ∆H  

4πM s 
  (H + H A )(H + H A + 4πM s ) −   +
4 
 2  
γ 

2
2
2
2 





ω
ω
∆
H
∆
H
 + 
 (H + H A )(H + H A + 4πM s ) −   +

4   γ 

γ 

106
, (7.1.22)
,
(7.1.23)
,
(7.1.24)
µ ′xz′ = −
2
 ω  
 ω  ∆H 2 

4πM s    (H + H A )(H + H A + 4πM s ) −   +
4 
 γ  
γ 

2
2
2

 ω  ∆H 2   ω∆H 

 (H + H A )(H + H A + 4πM s ) −   +
 +

4   γ 

γ 

.
(7.1.25)
Now µeff is given by the following relation,
µ eff
2
µ +µ
1  µ xx − µ zz  

xx
zz
=
± κ 1+ 
  , where κ = −iµ xz .

2
4
κ
 

′ − iµ eff
′′ .
We must keep in mind that µeff is complex, i.e. µ eff = µ eff
(7.1.26)
k (= β − iα ) is
calculated with µeff as follows,
2
 µ +µ
1  µ xx − µ zz  


xx
zz
k = β − iα =
ε 
 ± κ 1+ 
  , ε = 20.
c
2
4
κ


 

ω
(7.1.27)
∴

2 
ω  µ xx + µ zz 
1  µ xx − µ zz   

β = Re al
ε 
 ± κ 1+ 
 
c
2
4
κ


 

 

(7.1.28)
The phase θ is given by,

2 
1  µ xx − µ zz   
ω  µ xx + µ zz 

θ = βl = Re al
ε 
 ± κ 1+ 
  l .
c
2
4
κ



 



(7.1.29)
Design of phase shifter [6]-[9] is schematically shown in Figure 7.1.2. The in-plane
oriented BaFe10.5In1.5O19 [10]-[11] was inserted between two alumina substrates. The
thickness of the two alumina substrates was 0.5mm. The thickness of alumina substrate
on which oriented ferrite was screen printed was 0.25mm. The total thickness of alumina
and ferrite was 0.5mm. The surface of the screen printed ferrite was roughly polished
107
with very fine sand paper to make it. However, the surface is very fragile and easily
peeled from the alumina substrate. We had to be careful to polish the film surface with
fine sand paper. The density of the ferrite film was about 3.6g/cm3 ~ 3.7 g/cm3. The dc
magnetic field was applied for the direction of the in-plane orientation. We utilized the
magnetic property of the sample whose hysteresis curve is shown in Figure 7.1.3. The
microstrip line was designed to fit the characteristic impedance of 50 Ω [12]-[13]. The
oriented ferrite film saturated at 1000Oe and the external magnetic field was decreased
gradually from 1000Oe. Basically, we fixed the external field, Hext, and measure θ as a
function of frequency. The range of Hext was chosen so that the magnetization varied
from +4πMs to -4πMs through 0 gauss, as the hysteresis curve implied. Hence, we started
at Hext = +1000 Oe and varied it incrementally to -1000 Oe and returned to 1000 Oe. For
example, for Hext = ± 165 Oe, the magnetization was zero gauss. In this phase
measurement, the phase difference was calculated from the saturated point of the film at
1000 Oe which is the reference point of this phase analysis. At 1000 Oe the phase is
normalized and a phase difference was calculated with respect to reference point at
another field value of Hext. The simulated results are shown in Figure 7.1.4 (a) ~ (d). In
this simulation, we used the data of In = 1.5 sintered at 1100oC for 1hour with ∆H =
800Oe. In the simulation of the phase changes shown in Figure 7.1.4 (a) ~ (d) the
frequencies between 20GHz and 25GHz are recognized as the range of FMR frequencies.
The phase changes occur at 33GHz which is the frequency of interest above
′ =0.
antiresonance, µ eff
108
Section 2: Results and Discussion
The phase measurement was carried out with the network analyzer (Agilent
Technologies E8369A 45MHz – 50GHz).
We started saturating the ferrite film at
1000Oe and then decreased the external magnetic field gradually down to -1000 Oe. At 1000Oe the external magnetic field was reversed and increased to +1000 Oe. The
starting S21 is shown in Figure 7.2.1(a). Even if we carefully polished the surface of the
film with fine sand paper and normalized the S parameter [8], the noise signal was
significant, perhaps due to surface roughness. When the magnetic field was decreased to
0Oe as shown in Figure 7.2.1(b), we could recognize FMR signal around 23GHz. When
Hext reached -1000Oe, shown in Figure 7.2.1(e), S21 coincided with the S21 measurement
for Hext = +1000 Oe, as it should. The phase shift data are shown in Figure 7.2.2 (a) to
Figure 7.2.2 (d). We recognize that FMR frequency was at 23GHz. Maximum phase
changes occurred at 33GHz which is the frequency above the antiresonance. When Hext
was changed from 1000Oe to 500Oe, the phase change was only 3o. From 500 Oe to
400Oe, the phase change was 3.5o. At each point of Hext from 1000 Oe to -1000 Oe,
there is a factor of 100 differences between data and simulated data.
There are reasons for the factor of 100 differences. First of all, the surface of ferrite
film was not smooth enough and the signal reflection from the rough surface was severe.
Second reason is that the microstrip line on the ferrite film was not matched well with the
microstrip lines due to connectors. Third reason is that the density of ferrite was low
(about 3.6 g/cm3 ~ 3.7 g/cm3). At the point where the microstrip line on the ferrite and
109
the microstrip line are disconnected we used silver paint. Silver paint connection also
caused mismatching of lines.
Section 3: Conclusions
A new type of phase shifter with BaFe10.5In1.5O19 was fabricated and tested. We
simulated the phase changes and compared the simulation with phase change data.
Except for the factor of 100 in real data, the simulation and the real data were matched
that we confirmed that this new design and fabrication of phase shifter were applicable
with hexa-ferrites. We believe that from simulation results that practical phase shifters
are possible above antiresonance frequencies.
References
[1] Russian Physics Journal, Volume 9, Number 5 (1966). Page 39-42.
[2] Xu Zuo, Hoton How, Ping Shi, S. A. Oliver and Carmine Vittoria, IEEE
TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4 (2001).
[3] J. Douglas Adam, Lionel E. Davis, Gerald F. Dionne,Ernst F. Schloemann and Steven
N. Stitzer, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,
VOL. 50, NO. 3 (2002).
[4] Carmine Vittoria, Microwave properties of magnetic films, World Scientific (1993).
[5] Xu Zuo, ph.D thesis “Practical Electromagnetic Devices Using Hexaferrits”, (2002).
[6] Xu Zuo, P. Shi, S.A. Oliver, and C. Vittoria, "Single crystal hexaferrite phase shifter
at Ka-band", J. Appl. Phys. 91, 7622 (2002).
[7] Hoton How, Pin Shi, Carmine Vittoria, Leo C. Kempel and Keith D. Trott,
JOURNAL OF APPLIED PHYSICS, 87, NUMBER 9 (2000).
110
[8] CARL E. PATTON, IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 3,
(1988).
[9] R.W. Babbitt and R.A. Stern, IEEE TRANSACTIONS ON MAGNETICS, VOL.
MAG-15, NO. 6, (1979)
[10] C. N. Chinnasamy, T. Sakai, S. Sivasubramanian, Aria F. Yang, C. Vittoria,
and V. G. Harris, JOURNAL OF APPLIED PHYSICS 103, 07F710 (2008).
[11] W. H. Von Aulock, Handbook of Microwave Ferrite Materials, Academic, New
York, (1965).
[12] Terry Edwards, Foundations of for Microstrip Circuit Design, John Wiley & Sons
(1981).
[13] Carmine Vittoria, Elements of Microwave Networks, World of Scientific (1998).
111
z
Easy axis
r
H
y
x
.O
Figure 7.1.1: Geometry of ferrite film.
112
Orientation
Oriented and Screen
printed
BaFe10.5In1.5O19
Alumina substrate
Figure 7.1.2: Schematic image of a ferrite phase shifter.
113
Normalized 4πM (G)
Starting point at 1 kOe
1.0
0.5
0.0
-0.5
squareness(in-plane): 0.84
squareness(out of plane): 0.14
coercivity(in-plane): 165 Oe
coercivity(out of plane): 356 Oe
-1.0
-15
-10
-5
0
5
H(kOe)
Figure 7.1.3: VSM of BaFe10.5In1.5O19.
114
10
15
∆φ (degree)
600
400
200
0
-200
-400
-600
-800
-1000
-1200
-1400
1000 Oe (31.5 GHz)
500 Oe (29.8 GHz)
400 Oe (29.4 GHz)
300 Oe (29.0 GHz)
200 Oe (28.6 GHz)
100 Oe (28.5 GHz)
10
15
20
25
30
35
40
GHz
Figure 7.1.4 (a): Phase differences from 1000 Oe to 100Oe.
∆φ (degree)
800
600
400
200
0
-200
-400
-600
-800
-1000
-1200
-1400
50 (28.3 GHz)
0 (28.0 GHz)
-50 (27.1 GHz)
-100 (26.2 GHz)
-120 (23.7 GHz)
10 15 20 25 30 35 40 45
GHz
Figure 7.1.4 (b): Phase differences from 50 Oe to -120Oe.
115
∆φ (degree)
800
600
400
200
0
-200
-400
-600
-800
-1000
-1200
-1400
-140 (20.0 GHz)
-160 ( GHz)
-168 ( GHz)
-180 ( GHz)
-200 (22.0 GHz)
-300 (27.3 GHz)
10
15
20
25 30
GHz
35
40
Figure 7.1.4 (c): Phase differences from -140 Oe to -300Oe.
∆φ (degree)
600
400
200
0
-200
-400
-600
-800
-1000
-1200
-1400
-400 (29.4 GHz)
-500 ( 29.8GHz)
-1000 (31.5 GHz)
10
15
20
25 30
GHz
35
40
Figure 7.1.4 (d): Phase differences from -400 Oe to -1000Oe.
116
dB
2.0
1000Oe
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
15
20
25
30
GHz
35
40
Figure 7.2.1(a): S21 at 1000Oe.
2
0Oe
dB
1
0
-1
-2
-3
15
20
25
30
GHz
Figure 7.2.1(b): S21 at 0Oe.
117
35
40
2
-160Oe
dB
1
0
-1
-2
-3
15
20
25
30
GHz
35
40
35
40
Figure 7.2.1(c): S21 at -160Oe.
2
-180Oe
dB
1
0
-1
-2
-3
15
20
25
30
GHz
Figure 7.2.1(d): S21 at 180Oe.
118
dB
2.0
1.5 -1000Oe
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
15
20
25
30
GHz
Figure 7.2.1(e): S21 at -1000Oe.
119
35
40
Figure 7.2.2 (a): real phase change measurement from 1000Oe to100Oe.
Figure 7.2.2 (b): real phase change measurement from 50Oe to -120Oe.
120
Figure 7.2.2 (c): real phase change measurement from -140Oe to -300Oe.
Figure 7.2.2 (d): real phase change measurement from -400Oe to -1000Oe.
121
Chapter 8
Summary and Future work
Section 1: Material productions
Indium substitution for Barium ferrite was produced successfully by the modified
conventional sintering technique. The evaporation temperature of Indium oxide (which is
quite low) was controlled by this technique discussed in Chapter 4. We succeeded by
substituting Indium up to x=2.0 in BaFe12-xInxO19. In future work, the substitution of
Indium may be increased up to HA=0. At x=2.0, HA is about 3200Oe in Chapter 4. We
believe that there is room for improvement toward producing materials for HA ~ 1000 Oe.
Scandium doped Barium ferrite was produced by modified co-precipitation.
Differently from the conventional sintering method, co-precipitation produced a lot of
tiny single crystal Scandium doped Barium ferrites discussed in Chapter 5. Instead of
polycrystalline powder, the single crystal powder has several advantages as follows. The
production of Sc-doped Barium ferrite by the co-precipitation is quite simple and the
large amount of powder at one production is possible. There is no decomposition for
mechanical alloying.
We therefore can apply for any kinds of speed and time in
mechanical alloying and can control the particle size.
The future work of the co-
precipitation technique of Sc-doped Barium ferrite is to increase the amount of Scandium
substitution and analyze the decrease of the anisotropy. The co-precipitation technique
must be applied for any substitution such as Indium, Gallium.
122
Section 2: Phase shifter fabrication
Indium substituted Barium ferrite BaFe10.5In1.5O19 was used for a phase shifter device
fabrication in a microstrip line configuration. The Indium doped ferrite powder was
screen printed on alumina substrate with PVA binder and oriented in the in-plane
direction with 1.5T. The oriented sample was annealed at 1100oC for 1hour. This
sample was mounted on the phase shifter and analyzed with a network analyzer. The
data from network analyzer was compared with simulation of the phase shift. Although
the phase shift of simulation predicted considerable phase shifts for frequencies above
antiresonance, µ ′ = 0 , the data for phase shift was small.
The difference between
simulation and data was factor of 100. However, most importantly, both the simulation
and the data showed that phase shifts may be obtained above antiresonance frequency
which is a region of frequencies where insertion losses are relatively low. There are
several factors to explain the difference. The surface quality of screen printed sample
was not good. The microstrip line on the ferrite was not matched well with the other
microstrip lines connected to the network analyzer. Microwave “jump” wires would
have been helpful instead of silver paint in connecting two microstrip lines together. The
density of the ferrite film was low ~ 3.6 g/cm3 to 3.7 g/cm3.
In future work of phase shifter fabrication, we propose to use pressed samples instead
of screen printed samples in order to increase the crystal density. The pressed and
oriented samples have high density and we are able to polish the surface well. It also
helps the linewidth, ∆H, at FMR frequencies and reduces the reflection of the signal from
123
the surface. The microstrip line on the ferrite of the phase shifter must be fabricated
carefully to match characteristic impedance of 50Ω.
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