close

Вход

Забыли?

вход по аккаунту

?

Wireless Microwave Detection Using Magnetic Tunnel Junctions

код для вставкиСкачать
UNIVERSITY OF CALIFORNIA,
IRVINE
Wireless Microwave Detection
Using Magnetic Tunnel Junctions
THESIS
submitted in partial satisfaction of the requirements
for the degree of
MASTER OF SCIENCE
in Physics
by
Brian J. Youngblood
Thesis Committee:
Professor Ilya N. Krivorotov, Chair
Professor Philip G. Collins
Professor Michael Dennin
2012
UMI Number: 1529208
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 1529208
Published by ProQuest LLC (2012). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against
unauthorized copying under Title 17, United States Code
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
c 2012 Brian J. Youngblood
TABLE OF CONTENTS
Page
LIST OF FIGURES
iii
ACKNOWLEDGMENTS
v
ABSTRACT OF THE THESIS
vi
1 Magnetization Dynamics
3
2 Spin Transfer Torques
8
3 Magnetic Tunnel Junctions
17
4 Tunneling Magnetoresistance
23
5 Spin Transfer Assisted FMR
5.1 FMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Conventional FMR Measurement . . . . . . . . . . . . . . . . . . . .
5.3 STFMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
27
28
29
6 Detector Design
33
7 Results
39
Bibliography
52
ii
LIST OF FIGURES
Page
1.1
Damped magnetization dynamics. . . . . . . . . . . . . . . . . . . . .
5
1.2
Torque contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
3.1
Schematic of free and fixed magnetic layers. . . . . . . . . . . . . . .
18
3.2
Typee A MTJ layer structure. . . . . . . . . . . . . . . . . . . . . . .
20
3.3
Type B MTJ layer structure. . . . . . . . . . . . . . . . . . . . . . . .
21
3.4
Type A MTJ Resistance vs. Field. . . . . . . . . . . . . . . . . . . .
21
3.5
Type B MTJ Resistance vs. Field. . . . . . . . . . . . . . . . . . . .
22
4.1
Spin-dependent band structure of a ferromagnet. . . . . . . . . . . . .
25
5.1
Free and fixed magnetic layers of an MTJ . . . . . . . . . . . . . . .
30
6.1
Schematic circuit diagram of an MTJ microwave detector . . . . . . .
34
6.2
Diagram of a bias-tee . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
6.3
Coplanar waveguide cross-section . . . . . . . . . . . . . . . . . . . .
35
6.4
Microwave detector components . . . . . . . . . . . . . . . . . . . . .
37
6.5
Dimensions of the assembled detector . . . . . . . . . . . . . . . . . .
38
7.1
Response of a type A sample to a direct microwave input . . . . . . .
40
7.2
Response of a Type A detector . . . . . . . . . . . . . . . . . . . . .
42
7.3
Response of a Type B detector . . . . . . . . . . . . . . . . . . . . . .
43
iii
7.4
Response of the best detector. . . . . . . . . . . . . . . . . . . . . . .
44
7.5
Response of a Type B detector to a direct microwave input . . . . . .
45
7.6
Power response of a GaAs Diode . . . . . . . . . . . . . . . . . . . . .
46
7.7
Diagram of spin-torque vectors
46
. . . . . . . . . . . . . . . . . . . . .
iv
ACKNOWLEDGMENTS
I want to first express my gratitude to my research advisor, Professor Ilya Krivorotov.
He has informed each step of this work and helped me to understand the physics that
makes it possible and to see its further applications. He has listened to my ideas,
both good and bad, and helped me to recognize the obstacles I was ignorant of and
the implications I had not thought of. In the way he runs our group and through
his personal example Prof. Krivorotov has made me a much better practitioner of
physics and of science than I could have otherwise been.
I also offer my thanks to the other members of my committee, Professors Philip Collins
and Michael Denin both for their time and review of my thesis and for teaching me
about undergraduate instruction and continuum mechanics, respectively.
My thanks also go to my labmates in the Krivorotov Group, especially Jian Zhu,
Graham Rowlands, and Yu-Jin Chen for technical advice and assistance in carrying
out experiments.
I thank my father Robert, for instilling and fostering both curiosity and a spirit of
investigation in me. Finally, my deepest thanks go to my wife Marlette, for all of her
support.
RDECOM-TARDEC, NSF, the Western Institute of Nanotechnology, and the GAANN
fellowship program provided financial support for this work.
v
ABSTRACT OF THE THESIS
Wireless Microwave Detection
Using Magnetic Tunnel Junctions
By
Brian J. Youngblood
Master of Science in Physics
University of California, Irvine, 2012
Professor Ilya N. Krivorotov, Chair
I report on experiments demonstrating the detection of airborne microwave radiation
using a magnetic tunnel junction as the sensing element. The detection is based on the
technique of spin-torque assisted ferromagnetic resonance. In our version of this technique the RF current induced in an antenna by the microwave radiation is fed into the
tunnel junction. The ac voltage across the junction is rectified by oscillations in the
tunneling magnetoresistance of the junction which are caused by spin transfer torque
due to the injected current. Compact coplanar waveguide antennas and non-magnetic,
microwave-transparent, reusable device/antenna holder enclosures were designed and
and assembled to carry out these experiments. Junctions with two different material
layer structures were tested and compared. One of the tested structures gave superior sensitivities higher than those reported in the literature for similar devices and
comparable to the sensitivities of commercial, diode-based microwave sensors.
vi
Introduction
The use of conduction electrons to control the magnetic state of a material has broad
applications from information storage and processing to sensors and microwave communication. Together, these technologies are often called spin electronics or spintronics. This thesis is concerned with the use of a magnetic tunnel junction as the
sensing element in a passive detector for microwave radiation. Unlike an electromagnetic signal confined in a transmission line like a waveguide or cable, a radiated
signal decays very quickly so a relatively sensitive detector is needed to measure it in
technolgically relevant situations. Also, while a measure of control over source and
cable impedances is possible when a source is connected directly to a detector, allowing improved matching and better overall detection efficiency, the impedance of air
is fixed and some way is needed to couple microwave signals to the sensing element.
The design presented here includes a compact antenna suitable for this purpose. The
detector is based on a measurement technique called spin torque assisted ferromagnetic resonance (STFMR)[1]. Other work has explored the use of tunnel junctions
as sensing elements [2],[3],[4], but until now wireless detection of microwaves using a
magnetic tunnel junction has not been demonstrated. We also demonstrate an improvement in maximum detector sensitivity over the best sensitivities reported in the
literature [4].
In this thesis I will describe the principles behind the operation of the magnetic
1
tunnel junction microwave detector, its design, and measurements obtained using
two different layer designs for the tunnel junction.
2
Chapter 1
Magnetization Dynamics
Magnetization dynamics are governed by the Landau-Lifshitz-Gilbert-Slonczewski
equation:
~ = −γ0 M
~ × Ĥef f +
∂t M
α ~
~ + η µB I M̂ × (M̂ × P̂ )
M × ∂t M
Ms
eV
(1.1)
where γ0 is the gyromagnetic ratio for an electron, Ms is the saturation magneti~ is treated as uniform
zation of the ferromagnet being studied.The magnetization M
(macrospin approximation) and of constant magnitude. In this equation the effec~ ef f is the gradient of the free energy of the system with respect to the
tive field H
orientation of the magnetization. That is
~ ef f = dF = ∇M F
H
~
dM
(1.2)
Typically, one includes terms in the effective field for contributions due to applied
~ ef f is given by
field, anisotropy, exchange field, and demagnetization so that H
~ ef f = H
~ app + 2Ku (n̂ · M
~ )n̂ + 2Aex ∇2 M
~ +H
~ demag
H
2
µ0 Ms
µ0 Ms2
3
(1.3)
where it is assumed that the anisotropy in the ferromagnet is uniaxial with coefficient
Ku and direction n̂, in the following we will usually write such a uniaxial anisotropy
~ and the anisotropy direction.
field as n̂Hk cos θ where θ is the angle between M
~ demag is the demagnetizing field arising from magnetic poles accumulated on the
H
surface of an object, such as a ferromagnetic layer. We approximate this field as
~ · û where û is the unit vector normal to the surface of the
being proportional to M
~ demag is
layer and also the direction of the demagnetizing field. This simple form of H
only strictly true for an ellipsoid but it is close to true for thin ferromagnets. For the
thin layers we deal with Hdemag = M/2 in SI units (Hdemag = 2πM in cgs).
The second term of (1.1) represents the damping or tendency for the magnetization
direction to return to the direction of the effective field. This results in a trajectory of
the magnetization direction which is a contracting spiral about the effective field as
shown in Fig.1.1. The damping constant α is an experimentally determined property
of a material, though efforts have been made to compute it theoretically. For most
ferromagnets the damping time determined by the damping term is on the order
of 1ns. Broadly, the damping is due to spin-orbit coupling to the lattice [5]. In
the absence of this damping the magnetization would precess uniformly around the
effective field.
The last term in (1.1) represents the pseudo-torque acting on the magnetization due
to interaction with a spin polarized current (polarized in the direction of the unit
vector P̂ ). Section 2 discusses the origin of this contribution but the main point is
that this spin torque term can act opposite to the damping (see Fig.1.2) and if the
current is sufficiently large it will cause the magnetization to switch to its other stable
orientation (parallel or anti-parallel to the effective field). Expanding (1.1) to first
4
Figure 1.1: Damped magnetization dynamics. In this case the effective field is in the
+ẑ direction and the magnetization is initially aligned with the +x̂ axis.
Figure 1.2: Schematic of the action of the damping torque (Tdamp ) and the spin torque
(Tst ).
5
order in the small damping constant α [6] gives
~ =M
~ × γ0 H
~ ef f + M
~ × (−αγ0 H
~ ef f +
∂t M
ηµB I
P̂ )
V
(1.4)
~ × M̂ × (M̂ × P̂ ) = 0 for any P̂ . Considering a magnetization
if we use the fact that M
~ initially oriented nearly parallel to both the effective field H
~ ef f and the incoming
M
conduction electron polarization direction P̂ means that the first term in (1.4) is
approximately zero and we are left with
~ =M
~ × M
~ × (−αγ0 H
~ ef f + ηµB I P̂ )
∂t M
V
(1.5)
~ also allows us to rewrite this in
and our assumption about the initial direction of M
a scalar form as
∂t θ = −αγ0 Hef f +
ηµB I
V
(1.6)
The condition for switching is ∂t θ = 0, giving a critical switching current of [7],[8]
Icrit =
Ms
2e α
Vµ0 Ms (Happ + Hk +
)
h̄ η
2
(1.7)
Here we have chosen a particular form for Hef f which includes the applied, anisotropy,
and demagnetization fields. The anisotropy is uniaxial and we are considering switch~ ,H
~ app ,and H
~ k are all aligned so that any factors
ing starting from a condtion where M
of cos θ, where θ is the angle between the magnetization and the various fields, are
equal to one. The same expression for Icrit can be obtained by averaging the rate
~ about H
~ ef f and finding the
of change in energy over a small angle precession of M
condition for energetic instability [9].
Magnetization switching due to spin-transfer torque from a conduction current was
predicted in [6], and observed for all-metal spin valve [9] and magnetic tunnel junction
6
[10] trilayer structures at similar current densities of order 107 A/cm2 .
Of course, currents smaller than the critical current also modify the dynamics of the
magnetization by stabilizing the precession and increasing the damping time. The
effect of alternating currents will be described in Chapter 5. This effect is the basis
for the measurements described in this thesis.
7
Chapter 2
Spin Transfer Torques
Spin transfer torques arise from the transfer of spin angular momentum from a spin
polarized current of conduction electrons to a ferromagnet, this transfer of angular
momentum results in motion of the ferromagnet’s average magnetization. This effect
was predicted independently by Slonczewski [6] and Berger [11]. Consider a (1D)
electron wave function normally (x̂ propagation direction) incident on a planar ferromagnet (assumed to be single domain and magnetized in the ẑ direction) from a
material whose band structure is spin-independent. At the interface the barrier for
minority (spin down) states is greater than the barrier for majority (spin up) states.
The incident electron wave function has the form [7]
θ
θ
eikx x
cos( )| ↑> +sin( )| ↓>
ψin = √
2
2
Ω
!
(2.1)
The reflected wave function has the form
θ
e−ikx x
θ
ψr = √
r↑ cos( )| ↑> +r↓ sin( )| ↓>
2
2
Ω
!
8
(2.2)
While the transmitted wave function has the form
!
1
θ
θ
ψt = √
eikx,↑ x t↑ cos( )| ↑> +eikx,↓ x t↓ sin( )| ↓>
2
2
Ω
(2.3)
where kx is the wave vector x-component in the spin-independent medium and kx,σ
are the spin resolved components in the ferromagnet. These wave functions can be
immediately modified to reflect the 3D case by multiplying their terms by
~
e±φ/2 eq~·R
(2.4)
where the upper (+) sign is chosen for | ↑> terms and − is chosen for | ↓> terms and
~ is the transverse
~q is the transverse parts of the full wave function k vector and R
position vector. The angles θ,φ give the orientation of the spin polarization direction
of the electron with respect to the magnetization of the ferromagnet. For parabolic,
free electron-like band structure in the ferromagnet and nonmagnetic region, the spin
dependence of the transmission and reflection coefficients is determined by the spin
dependence of the Fermi wave vector according to
tσ =
2kx
kx + kx,σ
(2.5)
rσ =
kx − kx,σ
kx + kx,σ
(2.6)
where we have assumed that q 2 ≤ (kF,σ )2 .
Computing the incident, reflected, and transmitted spin currents according to
Qxx
h̄2 k
=
2Re(ab∗ )
2mΩ
(2.7)
h̄2 k
2Im(ab∗ )
2mΩ
(2.8)
Qyx =
9
Qzx =
h̄2 k
(|a|2 − |b|2 )
2mΩ
(2.9)
where a,b are the ↑,↓ coefficients of the wave function gives
Qi,xx
h̄2
=
kx sin θ cos φ
2m
(2.10)
Qi,yx
h̄2
=
kx sin θ sin φ
2m
(2.11)
for the components of the incident current transverse to the ferromagnet’s magnetization. The same components are given by
Qr,xx =
h̄2
kx sin θRe[r↑∗ r↓ eiφ ]
4m
(2.12)
Qr,yx =
h̄2
kx sin θIm[r↑∗ r↓ eiφ ]
4m
(2.13)
Qt,xx =
h̄2 kx,↑ + kx,↓
sin θRe[t∗↑ t↓ eiφ ei(kx,↓ −kx,↑ )x ]
4m
2
(2.14)
Qt,yx =
h̄2 kx,↑ + kx,↓
sin θIm[t∗↑ t↓ eiφ ei(kx,↓ −kx,↑ )x ]
4m
2
(2.15)
for the reflected current and by
for the transmitted current. We have left out the component Qzx parallel to the
magnetization because Qi,zx = Qt,zx − Qr,zx exactly, indicating that no angular momentum is transferred to the ferromagnet from this component of the spin current.
If we take
wσ = cσ + idσ
(2.16)
w↑∗ w↓ = (c↑ c↓ − d↑ d↓ ) + i(c↑ d↓ + c↓ d↑ )
(2.17)
where w can be r or t. Then
10
From this equation we can see that when the reflection and transmission amplitudes
are the same for up and down spin states the product in (2.17) is real and the reflected
and transmitted spin currents have exactly the the same form (the factor exp[i(kx,↓ −
kx,↑ )x] in the transmitted current must be unity if the reflection and transmission
amplitudes and therefore kx,↑ and kx,↓ are the same) as the incident spin current (and
must sum to the same value since |r|2 + |t|2 = 1). This would mean that no spin
angular momentum at all would be transferred to the ferromagnet. When reflection
and transmission amplitudes differ for different spins then there is transfer, this is
called the contribution to the spin-transfer torque due to spin filtering.
So far we have considered only a single electron mode incident on the ferromagnetic
barrier. In order to go further we have to consider a distribution f~(~k) of incident
electrons at the interface and some of their correlations [12]. Considering only the
electrons moving to the right, the incident spin current is given by


Z
h̄~k 
d3 k
~ i = h̄
f~(~
k)~
σ
]
⊗
T
r
Q
2 kx >0 (2π)3
m
(2.18)
The reflected current is given by
h̄ Z d3 k
~
Qr =
T r[R† f~R(~k)~σ ] ⊗ v~r (~k)]
2 (2π)3
(2.19)
and the transmitted current is given by
h̄ Z d3 k
~
Qt =
T r[T† f~T(~k)~σ ] ⊗ v~t (~k)]
2 (2π)3
(2.20)
In these equations v~r and v~t are the spin averaged velocities of reflected and trans-
11
mitted electrons and the transmission and reflection matrices are given by

ik~↑ ·~
r
k)e
 t↑ (~
T̂ = 


0
~
t↓ (~k)eik↓ ·~r
0
R̂ = 

0
~
r↓ (~k)eik·~r
0
(2.21)


~
k)eik·~r
 r↑ (~






(2.22)
Integrating over the distribution reveals that although there could have been a contribution to the spin-transfer torque due to reorientation of the electron polarization
upon reflection from the interface, the phase change due to this reorientation is randomized over the surfaces of integration (energies up to the Fermi surface) so that
such a contribution averages to zero. The spin-transfer contribution that does remain
after integration over the Fermi surface is due to the precession of the spins of the
transmitted electrons about the magnetization direction as they travel through the
ferromagnet. This change in momentum is expressed by the exp[i(kx,↓ − kx,↑ )x] factor
in (2.14),(2.15) for the single electron case. The same information is contained in the
transmission matrix (2.21) for the electron distribution case. Integrating gives the
expression
Qt,xx = Qi,xx
2 Z kF,↓
kx,↓ + kx,↑
|t↑ (q)t↓ (q)|
dqq
2
kF 0
2|kx |
for the total transmitted transverse spin current where q =
q
(2.23)
kF2 − kx2 . At large x (far
from the interface) this becomes [12]
Qt,xx = 2Qi,xx
kF,↑ kF,↓ kx,↓ + kx,↑
1
|t↑ (0)t↓ (0)|
.
2
kF
2kF
(kx,↑ − kx,↓ )x
(2.24)
This shows that the transmitted spin current transverse to the magnetization decays
with distance into the ferromagnet and we have already seen that the spin current
parallel to the magnetization does not change so the spin angular momentum is being
12
transferred to the ferromagnet’s magnetization.
Calculating the quantity
Z
~i + Q
~r − Q
~ t ) = τst,||
dAx̂ · (Q
(2.25)
which is the total in-plane spin transfer torque acting on the ferromagnet, gives
~ i,⊥
τst,|| ≈ Ax̂ · Q
(2.26)
since the transmitted and reflected spin currents for Fermi surface states are collinear
with the magentization of the ferromagnet [7]. This result indicates that spin angular
momentum (the transverse component) was lost in the interaction with the barrier.
This is the spin angular momentum which produces an effective torque on the magnetization in the ferromagnet. If an unpolarized (coefficients of | ↑> and | ↓> states
equal) electron wave function is incident on a barrier like the one described, the transmitted wave function ψt is spin polarized since the spin component transverse to the
ferromagnet’s magnetization will be absorbed. This will be the way that we obtain a
spin polarized current of electrons, by passing an unpolarized current through a ferromagnet. This is the purpose of the second magnetic layer in the magnetic trilayers
presented in section 3. The arguments above apply to an interface between a normal
metal and a ferromagnet. Magnetic tunnel junctions include insulator/ferromagnet
interfaces so that the reflection and transmission coefficients r↑,↓ ,t↑,↓ are different and
(2.26) no longer holds quantitatively. However, the fact of spin polarized currents
applying an in-plane torque to the magnetization of a ferromagnet remains.
To treat the spin transfer torque in the case of a magnetic tunnel junction we will
follow the scattering theory presented in [13]. We have introduced the idea that spin
polarization of the condition electrons will be achieved by a ferromagnet so that we
13
will be discussing a trilayer consisting of a ferromagnet on either side of an insulator.
The combined scattering matrices for right going electrons are
#
"
ŝA,→
Tb
=
T̂1
(1 − Rb0 R̂2 )(1 − R̂10 Rb )
(2.27)
Tb R̂10 Tb0
Rb0
+
=
T̂20
0
0
0
(1 − Rb R̂2 ) (1 − R̂1 Rb )(1 − R̂2 Rb )
#
"
ŝB,→
(2.28)
while the components for left going electrons are given by
Tb0 R̂2 Tb
Rb
=
+
T̂1
(1 − Rb R̂20 ) (1 − R̂10 Rb )(1 − R̂2 Rb0 )
(2.29)
Tb0
T̂20
=
(1 − Rb0 R̂1 )(1 − R̂20 Rb )
(2.30)
"
ŝA,←
#
#
"
ŝB,←
(0 )
Here, R̂i ,T̂i
(0 )
are the reflection and transmission matrices (like (2.22),(2.21)) for the
(0 )
(0 )
interfaces 1,2 between the ferromagnets and the insulator. Rb ,Tb are the reflection
and transmission matrices for the insulating barrier but since the insulator’s band
structure is independent of spin they are proportional to the 2×2 identity matrix. By
defining the normalized magnetizations of the two ferromagnets (m
~ 1 ,m
~ 2 ) it is possible
to further approximate (by taking the impurity scattering in the insulating barrier to
be zero ⇒ Rb = 0) the scattering matrices in terms of these two vectors as
−
ŝA,→ = tb (t+
~ 1)
1 + t1 σ̂ · m
(2.31)
−
−
~ 1 ×m
~ 2 ) (2.32)
~ 1 ·m
~ 2 ) + σ̂ · (r1− tb t+
~ 1 + r1+ tb t−
~ 2 − ir1− tb t−
ŝB,→ = (r1+ tb t+
2m
2m
2m
2 + r1 tb t2 m
−
−
ŝA,← = (r2+ tb t+
~ 1 ·m
~ 2 ) + σ̂ · (r2− tb t+
~ 1 + r2+ tb t−
~ 2 − ir2− tb t−
~ 1 ×m
~ 2 ) (2.33)
1 + r2 tb t1 m
1m
1m
1m
−
ŝB,← = tb (t+
~ 2)
2 + t2 σ̂ · m
(2.34)
where t±
i = (ti,↑ ± ti,↓ )/2 and ti,σ is the transmission amplitude for the spin σ at the
14
interface i. We can use these approximations for the spin scattering matrices in the
following expression [13] for the spin current
~ =
Q
X
1 Z
~js (E, ~q, ~q0 )
dE
(2π)3
q,q 0
(2.35)
with
~js = 2T rσ [σ̂Im(ŝA,→ ŝ†A,← f1 (E) − ŝB,→ ŝ†B,← f2 (E + eV )]
(2.36)
where fi are the electron distribution functions of the two ferromagnets and V is the
bias voltage applied across the multilayer. To determine the torque from this spin
current on the magnetization of ferromagnet 2 we use the earlier determination that
the entire transverse component of the spin current is absorbed as a torque, this gives
~τ = ~js − (~js · m
~ 2 )m
~2
(2.37)
for the normalized torque. If we now put (2.36) into (2.37) we get two torque components
~n|| = t2b T1− T2+ (f1 − f2 )m
~ 2 × (m
~1×m
~ 2)
(2.38)
~n⊥ = 2t2b Re(T1− r2− f1 + T2− r1− f2 )m
~1×m
~2
(2.39)
where Ti± = |ti,↑ |2 ± |ti,↓ |2 . This result shows that for a magnetic tunnel junction
there is both an in-plane or Slonczewski (2.38) and an out of plane or field-like (2.39)
spin torque acting on the magnetization of the second ferromagnet.
An alternative layer-by-layer nonequilibrium Green’s function approach [14] related
to the microscopic approach to magnetoresistance [15] discussed in Chapter 4, which
uses the true Bloch wave functions of the propagating electrons rather than a free
electron approximation, predicts that the small fluctuations of thickness in real samples suppress the out of plane field-like torque for small biasing voltages. In addition,
15
the numerical calculations in this work indicate that the spin-torque acting on the
ferromagnet’s magnetization (expressed as the decay of conduction electron spin components perpendicular to the magnetization) arises from majority propagating states
interfering coherently with minority evanescent states in the ferromagnet. It should
be noted that the magnetization of the second ferromagnet was initially perpendicular
to the interface planes for these calculations in contrast to the usual cases where the
magnetizations of both ferromagnetic layers are nearly in the plane of the interfaces.
The Type B tunnel junctions described in this thesis (see Chapter 3) are, however,
more like the ones in [14].
16
Chapter 3
Magnetic Tunnel Junctions
Magnetic tunnel junctions (MTJs) are trilayers consisting of an insulator sandwiched
between two ferromagnets, often referred to as an F/I/F structure. The detectors
described in this thesis are based on an MTJ sensing element. As stated at the
end of section 2 we obtain a spin polarized current to apply spin transfer torque
to a magnetic layer by passing the current through another magnetic layer. The
magnetizations of the two layers must be non-collinear for any torque to be applied
so the question arises of how to cause the magnetizations of the two layers to behave
differently under applied magnetic fields. This is accomplished in a variety of ways,
one way is to make one ferromagnetic layer (the fixed layer) thicker so that it does not
respond as easily to external fields. Another way is to have the fixed layer in close
proximity to an antiferromagnet such as IrMn or PtMn, the exchange interaction
between the antiferromagnetic layer and the ferromagnetic layer keeps the latter in
place. In the case of the MTJs used for our detectors both methods are used. The
ferromagnetic layer that is not constrained is called a free layer (see Fig. 3.1).
The first reported MTJ was developed by Julliere [16] in 1975. These devices were
17
Figure 3.1: Schematic showing free and fixed magnetic layers and how the spin torque
acts in an MTJ.
Fe/Ge/Co trilayers but the experiments showing a dependence of their resistance on
the relative orientation of the ferromagnets were never reproduced. Later, Slonczewski
[17] studied Fe/C/Fe trilayers theoretically (see Chapter 4) but the effect has not been
observed in this structure. The first successful magnetic tunnel junctions [18] were
based on NiO barriers. Currently, tunnel junctions are based on either AlOx (usually
Al2 O3 ) or MgO barriers [19]. The highest reported TMR ratio (see Chapter 4) for
an MgO based junction is 604% at 300K (1010% at 5K)[20]. The current best TMR
ratios of alumina barriers are significantly lower at 81% for room temperature (107%
at 4.2K) [21]. The reason for this is that the crystalline MgO barrier, in combination
with lattice matched ferromagnetic layers (such as CoFe) supports coherent tunneling
of spin polarized conduction electrons while AlOx barriers, which are amorphous, do
not. Coherent tunneling refers to the idea that for sufficiently perfect materials and
interfaces impurity and interface scattering can be ignored, allowing quantum features
of the tunneling process to emerge. More specifically, this can be taken to mean that
the component of electron momentum parallel to the barrier is conserved. In the case
of MgO tunnel junctions, theoretical studies [15],[22] indicate that, due to a small
density of states, the conductance of the barrier for minority electron states with
momenta nearly perpendicular to the barrier surface (that is, the electrons that are
propagating) is much lower than that of majority states with the same momenta (this
is dicussed in more detail in Chapter 4). The dependence of polarization on density of
states is shown in (4.3), we can see that the barrier acts to increase spin polarization
18
for propagating states because it acts like a half metal for those states. Equation
(4.2) shows that this increased polarization due to the crystalline barrier increases
the TMR ratio for MTJs based on materials like MgO.
Experimental support for the explanation of the higher TMR values for MgO tunnel
junctions described above comes from a recent study [23] that compares junctions
with barriers composed of AlOx , MgO, and a symmetric AlOx -MgO bilayer. This
study found that the half AlOx junction had a TMR of 78%, like that of a pure AlOx
junction instead of some intermediate value closer to the TMR of the MgO junctions
(323%) which they fabricated. If the latter had been true it would suggest that some
property of the barrier materials not related to coherent transport was responsible
for the decrease in TMR. The observed results can be interpreted to mean that
the presence of the disordered AlOx layer prevented coherent transport and thereby
suppressed the TMR ratio. However, experimental considerations required that the
combined AlOx -MgO barrier was about twice as thick as the pure barriers so the
diminished TMR might be attributed to the increased thickness. In the range of
thicknesses between 1.2nm and 2.6nm corresponding to the thicknesses of the pure
barriers and the combined barrier resistance increases exponentially with thickness
for both AlOx (approximately) and MgO while the TMR decreases by only about 20%
for MgO and decreases quickly to around 1% for AlOx [24],[25]. From this we can
see that the AlOx -MgO barrier does not behave like a simple combination or thicker
version of the pure barriers and the coherent tunneling explanation is supported.
For the detectors studied in this thesis, two different types of MTJs (which I will refer
to as Type A and Type B) were used. Both are MgO tunnel junctions with CoFeB
fixed and free layers. The Type A junctions, whose full layer structure is shown
schematically in Fig. 3.2, are fairly standard MTJs (all samples were fabricated by
J.A. Katine of Hitachi Global Storage Systems) with a free layer magnetization that is
19
entirely in the plane of the layer. The Type B junctions (Fig. 3.3) are the product of
an at least partially successful attempt to produce MTJs with a free layer magnetized
out of plane.
Figure 3.2: Type A MTJ layer structure: 3 [nm] Ta / 40 CuN / 3 Ta / 40 CuN / 3
Ta / 10 Ru / 5 Ta / 16 PtMn / 2.5 Co70Fe30 / 0.85 Ru / 2.4 Co60Fe20B20 / MgO
/ 1.83 Co60Fe20B20 / 2 Cu / 5 Ta / 10 Cu / 5 Ru / 3 Ta
The resistance of most Type A MTJs was between 300Ω and 350Ω at zero applied
field. The resistance versus applied field plot of a typical Type A junction is shown in
Fig. 3.4. For Type B junctions, resistances at zero applied field were higher, mostly
ranging from 600Ω to 620Ω. A resistance vs. field plot for a Type B junction is shown
in Fig. 3.5.
20
Figure 3.3: Type B MTJ layer structure.
Figure 3.4: Type A MTJ Resistance vs. Field.
21
Figure 3.5: Type B MTJ Resistance vs. Field.
22
Chapter 4
Tunneling Magnetoresistance
There is another consequence of the spin polarization of the conduction current. The
argument at the end of the previous chapter shows that the current transmitted
through a ferromagnet depends on the relative orientation of the incident electron
polarization direction and the ferromagnet’s magnetization. Therefore the resistance
of a trilayer (spin valve or magnetic tunnel junction) depends on the relative orientation of the ferromagnetic layers. When one layer’s magnetization is relatively
stationary then the resistance of the trilayer depends on the magnitude of an external field (when the external field is applied in some direction other than parallel to
the magnetization of the fixed layer). When the trilayer is a magnetic tunnel juction
this variable resistance is called the junction’s tunneling magnetoresistance and is
often defined as
T MR =
RAP − RP
RP
(4.1)
Here RAP stands for the resistance of the trilayer when the magnetizations of the
ferromagnetic layers are oriented anti-parallel to each other and RP stands for the
resistance when they are parallel.
23
According to a model developed by Julliere [16] the value of the TMR ratio can be
obtained in terms of the polarization coefficients of the two layers as
T MR =
2P1 P2
1 + P1 P2
(4.2)
In Julliere’s model P1 and P2 are given by the ratio
P =
N↑ (EF ) − N↓ (EF )
N↑ (EF ) + N↓ (EF )
(4.3)
where N (E) is the number density of states as a function of energy. For magnetic
MTJs, Slonczewski proposed an expression for tunneling polarization modified to
include interface effects as follows [[26]]:
P =
k↑ − k↓ k02 − k↑ k ↓
·
.
k↑ + k↓ k02 − k↑ k ↓
(4.4)
This expression is consistent with (4.3) when the parabolic dispersion relations
2mEσ
h̄2
(4.5)
2m(EF − V )
h̄2
(4.6)
kσ2 =
k0 =
are assumed (see Fig.4.1).
A more accurate and detailed picture of TMR, applicable to magnetic tunnel junctions
with epitaxial interfaces such as Fe/MgO/Fe, was developed in [15]. In this model the
Bloch states of the electrons (near the Fermi level) in the first ferromagnet are used
instead of free electron states as the incident states on the barrier. Bulk band structure
calculations [27] show that the majority (↑) and minority (↓) electrons have four states
available near the Fermi level in Fe. One of these, labeled ∆1 , is only available to
24
Figure 4.1: The spin-dependent parabolic approximation of a ferromagnet’s band
structure.
majority electrons and has spd hybridization, the others all have pd hybridization or
are d states. In [15] Butler and co-workers use a layered Korringa-Kohn-Rostoker
method [28] to calculate the density of states for each state of both majority and
minority electrons propagating through an MgO barrier as a function of penetration
into the barrier. Their analysis is specific to modes propagating normal to the barrier,
but these are the modes that dominate transport. They find that the details of the
band structure have a significant effect on understanding the conductance of the
tunnel junction. Specifically, the density of ∆1 states decays much more slowly than
those of the other states as it traverses the barrier and since this state is only available
to majority electrons these are conducted much more readily than minority electrons.
When the magnetizations of the ferromagnetic layers are oriented parallel to each
other majority states remain majority states throughout the trilayer but when the
magnetizations are oriented anti-parallel to each other the states which start out as
majority states on one side of the barrier are minority states on the other side and vice
versa. This means that when the magnetizations are antiparallel the ∆1 state is not
available in the second ferromagnet and is in fact completely reflected. This greatly
25
reduces the conductance of the trilayer (it now nearly matches the conductance for
minority states alone) in the antiparallel state and explains the partial half metal
behavior of the tunneling barrier mentioned in Chapter 2 and the large TMR ratio of
this type of tunnel junction. The conductance for the minority states is not affected
much by the relative orientation of the ferromagnetic layers.
The dependence of the trilayer resistance on the angle θ between the magnetizations
of the two ferromagnets is not yet completely understood. For simplicity, it is the
conductance G that is usually expressed and this value is modeled and given to fair
accuracy by [17],[29]:
G(θ) =
GP − GAP
(1 + P1 P2 cos θ)
2
where Pi are the spin polarization factors given by Eq.(4.4).
26
(4.7)
Chapter 5
Spin Transfer Assisted FMR
In this section we will first consider FMR in general and its conventional measurement
and then describe spin torque assisted FMR measurements.
5.1
FMR
Earlier, in section 2, we discussed how the Landau-Lifshitz-Gilbert equation of motion
~ × ∂t M
~
~ = −γ0 M
~ ×H
~ ef f + α M
∂t M
Ms
(5.1)
(where we have suppressed the spin transfer term) describes a precessional motion of
the magnetization of a ferromagnet. As mentioned before, in the absence of damping
(5.1) describes stable circular precession. The frequency of such a precession is (for
a spherical sample) given by the Larmor frequency ω = γHef f . Once it has been
resonantly excited, this precession can be detected in different ways, two of which are
described in more detail below. The resonance spectrum can yield information about
the saturation magnetization, damping constant, magnetic anisotropy, spin-torque
27
vector, and bias response of a sample.
5.2
Conventional FMR Measurement
For most of their history ferromagnetic resonance measurements have been made by
determining the microwave absorption of a ferromagnetic sample in a DC magnetic
field. The quantity determined directly is the imaginary component of the magnetic
susceptibility so we would like to make the connection to magnetization precession.
To do this we follow Kittel’s [30] derivation and consider a ferromagnetic ellipsoid
with its axes aligned with a Cartesian coordinate system and a DC magnetic field
applied along its longest (ẑ) axis. Microwave radiation is incident on the ellipsoid such
that the RF magnetic field is aligned perpendicular to the DC field (along the x̂ axis).
It is this oscillating magnetic field which drives the precession of the magnetization.
In this situation the applied magnetic field has the form
~ app = ẑHDC + x̂HRF eiωt
H
(5.2)
To take the shape of the sample into account we have to include the demagneti~ ef f of (5.1). In this treatment we will leave out the effect of
zation fields in the H
anisotropy, but if included it would cause a change in the FMR resonance frequency.
The components of the magnetic field within the sample are then given by
Hx0 = Hx − Nx Mx
(5.3)
Hy0 = −Ny My
(5.4)
Hz0 = Hz − Nz Mz
(5.5)
28
Ignoring damping (which does not modify the resonance frequency significantly for
~ app ,Hz = ẑ · H
~ app the components
physically realistic values of α) and taking Hx = x̂· H
of (5.1) become
∂t Mx = γ[Hz + (Ny − Nz )Mz ]My
(5.6)
∂t My = γ[Mz Hx − (Nx − Nz )Mx Mz − Mx Hz ]
(5.7)
∂t Mz ≈ 0
(5.8)
Solving these equations gives the susceptibility
χx =
Mz
1
Mx
=
Hx
Hz + (Nx − Nz )Mz 1 − ( ωω0 )
(5.9)
with the resonant frequency
q
ω0 = γ [Hz + (Ny − Nz )Mz ][Hz + (Nx − Nz )Mz ]
(5.10)
When a sample is placed in a microwave cavity its microwave absorption can be
measured. For these types of measurements it is usually the magnetic field that is
varied (since the frequency cannot be varied over a wide range in a microwave cavity).
The resonant frequency can be observed from this measurement and if the geometry
of the sample is well known then the magnetization Mz can be easily determined.
5.3
STFMR
Spin transfer (or torque) assisted ferromagnetic resonance (abbreviated STFMR)
[1],[31] is an all electrical technique for driving electrically detectable signals of ferromagnetic resonance. Briefly, the spin torque (section 2) due to a subcritical alter-
29
nating current drives a precession of the magnetization about the effective field. This
results in an oscillation of the resistance of a spin valve or MTJ as the magnetization
of the free layer is forced toward or away from alignment with the fixed layer magnetization depending on the instantaneous polarity of the RF current (see section 4).
The product of this oscillating resistance with the alternating current that produces
it is a rectified voltage whose average is measured as a DC signal (see Fig. 5.1).
Specifically, the resistance in a trilayer can be expressed [1] as the expansion
Figure 5.1: Schematic showing free and fixed magnetic layers and how the spin torque
acts in an MTJ.
∆Rnf ein2πf t )
(5.11)
1
Vdc =< Irf cos(2πf t)R(t) >= Irf |∆Rf | cos(δf )
2
(5.12)
R(t) = R0 + ∆R(t) = R0 + Re(
X
n
Then by Ohm’s law
Where f is the δf is the phase of the resistance with respect to the current.
30
In terms of a DC bias (I,V ), Vdc can be approximated as [32]
1 ∂ 2V 2
1 ∂ 2 V h̄γ0 sin θ
2
(εk S(ω) − ε⊥ Ω⊥ A(ω))
+
× Irf
I
4 ∂I 2 rf 2 ∂θ∂I 4eMs Vσ
(5.13)
where
"
εk,⊥
#
2e/h̄ dτk,⊥
=
sin(θ) dI
(5.14)
are dimensionless differential torques and S(ω) and A(ω) are symmetric and anti
symmetric lorentzians given by
S(ω) =
A(ω) =
1
1+
(ω−ωm )2
σ2
(ω − ωm )
S(ω)
σ
(5.15)
(5.16)
In these equations ωm is the resonance precession frequency of the magnetization,Ω⊥ =
γ(4πMef f + H)/ωm for an elliptical thin film. σ is the line width of the STFMR resonance peak. It is given by [32]
σ=
γτk (V, θ)
αωm
(Ω⊥ + Ω−1
⊥ ) − cot(θ)
2
2Ms V
(5.17)
From this equation it is clear that the damping constant α can be obtained from an
STFMR measurement of the line width at V = 0 giving
αef f =
2σ
ωm (Ω⊥ + Ω−1
⊥ )
(5.18)
Equation (5.13) shows that by fitting the symmetric and antisymmetric components of
an STFMR voltage vs.frequency spectrum the contributions of the in-plane and out of
plane spin torque components found in Chapter 2 can be determined experimentally.
In the case of STFMR it is a spin polarized current and not an external magnetic field
31
that oscillates and causes resonant motion of the magnetization, the process described
depends entirely on the spin transfer term in (1.1). In an STFMR measurement, both
the frequency of the current and the magnitude and sign of the applied DC current
are easy to vary. Usually the current frequency is swept at a constant field to obtain
an FMR spectrum. Using this technique, samples much smaller than those accessible
by the conventional absorption method can be measured. An STFMR measurement
on a magnetic tunnel junction is the basis of the microwave detectors described in
this thesis.
32
Chapter 6
Detector Design
As was mentioned earlier, the microwave detectors described in this thesis are based
on an STFMR measurement made on an MTJ. In addition to the magnetic multilayer
sample described in section 3, such a measurement requires a source of RF oscillating
current, a way of applying a (preferably tunable) DC magnetic field, a means of
separating DC and AC signals, and a way to measure the DC average of the rectified
voltage signal produced across the MTJ. It is the purpose of this section to describe
each of these components and the assembly of the whole device. A schematic circuit
diagram of the detector is given in Fig. 6.1 below.
The DC voltage across the MTJ is measured by connecting the top lead to the
AC+DC port of a bias-tee and the DC port of the bias-tee to the signal pin of an
SMA connector flange while the bottom lead of the MTJ is connected to the ground
of the flange and the chassis of the device. The voltage measurements were made
using a Keithley 2182A nanovoltmeter which can measure down to 1nV.
The separation of DC and AC signals in the final device is accomplished using a biastee. A bias-tee (equivalent circuit shown in Fig. 6.2) can take a combined AC and DC
33
Figure 6.1: Schematic circuit diagram of an MTJ microwave detector
input at its AC+DC port and output the components separately. For the final devices
a small, surface-mountable model SM-101 bias-tee from Picosecond Pulse Labs was
used. An earlier design using single or series connected inductors to suppress AC
signals did not work.
The DC magnetic field is provided by a permanent magnet affixed to a set screw.
This gives a constant field which can be adjusted to obtain the best possible response
from the magnetic tunnel junction. The magnet is a 3.175mm diameter × 3.175mm
long Nd2Fe14B magnet from MagCraft which has a nominal surface field of 4kG. Its
position in the detector allows fields between 0 and about 800G to be applied at the
MTJ. This covers the fields which give maximum response which are about 700G for
samples of type A and about 200G for samples of type B (see section 3).
34
Figure 6.2: Diagram of a bias-tee.
The source of RF current in these detectors is a coplanar waveguide (CPW) acting as
an antenna. This makes the detector capable of picking up ambient microwave radiation (of the correct polarization) and, via the MTJ, converting it to a measureable
DC voltage. The coplanar waveguide antenna is the aspect of the detector design we
had the most control over. The idea is to couple the microwave radiation to a signal
at the tunnel junction as efficiently as possible. This came down to trying to match
the impedance of the CPW to those of air and the MTJ as nearly as possible.
Figure 6.3: Cross-sectional view of a coplanar waveguide showing relevant dimensions
Analytically, the impedance of a grounded coplanar waveguide as depicted in Fig. 6.3
35
with a dielectric (r ) substrate of thickness h >> b = s + 2w is given by [33]:
60π
√
ef f
1
K(k)
K(k0 )
ef f =
κ=
K(k1 )
K(k10 )
1 + r κ
1+κ
(6.1)
(6.2)
K(k 0 ) K(k1 )
K(k) K(k10 )
(6.3)
k = s/b
(6.4)
√
1 − k2
(6.5)
tanh(πs/4h)
tanh(πb/4h)
(6.6)
k0 =
k1 =
+
k10 =
q
1 − k12
(6.7)
As indicated by these equations the characteristic impedance of the CPW increases
with increasing w or decreasing s. By modeling the coplanar waveguide structure
in the finite element calculation software CST Microwave Studio, we were able to
determine the parameters (s,w) that maximized the gain of the CPW antenna but
were still relatively easy to fabricate. For the .254mm thick Duroid 6002 substrate
that we used, the optimum values determined were s = 0.2mm and w = 0.1mm,
which in the modeling software gives an impedance of 76Ω. We found that increasing
w causes losses while decreasing s would lead to both losses and possible fabrication
difficulties. The analytical approximation above gives an impedance of 86Ω for the
same CPW dimensions. The discrepancy with the numerical result is explained by
the fact that our coplanar waveguide does not satisfy the condition h >> b.
An additional feature of this detector is an electrostatic discharge (ESD) protection
circuit designed to prevent damage to the delicate magnetic tunnel junction. The
36
Figure 6.4: Microwave detector components - (1) Coplanar waveguide antenna, (2)
MTJ Sample, (3) Bias-tee, (4) Brass screw holder, (5) Brass set-screw, (6) NdFeB
magnet, (7) K-connector flange
junction is susceptible to breakdown and shorting across its thin insulating layer
when exposed to large transient voltages. The ESD protection circuit consists of two
Schottky diodes connected in opposite directions which will shunt large voltages of
either polarity to ground.
The assembly of the detector’s components is shown in Fig. 6.4 and the major
dimensions of the design are shown in Fig. 6.5.
37
Figure 6.5: Dimensions of the assembled detector
38
Chapter 7
Results
Here we present the results of tests of the MTJ microwave detectors. First, in Fig.
7.1, is the voltage response of a Type A junction not mounted in a detector but
instead measured in a standard STFMR setup with the oscillating current applied
by a microwave signal generator (Agilent E8257D). In this case the power incident in
the tunnel junction is easy to compute using [2],[34]
Pinc =
1
2Z0
R + Z0
2
2
2
IRF
(7.1)
In our case the current applied was 0.1mA and the line impedance is 50Ω so the
power applied to the MTJ was 1.5µW. The important figure of merit for our devices
as microwave detectors is the sensitivity given by
=
V
Pinc
(7.2)
Using our peak voltage of 48µV in this equation gives a sensitivity of 32 mV/mW.
To explore the relationship between detector sensitivity and the parameters of the
39
Figure 7.1: Response of a type A sample to a directly(cable) fed microwave signal.
detectors we can follow [2] and rewrite the frequency dependent part of (5.13) as
"
dτk
dτ⊥ γ0 (Hz + 4πMef f )
dR
µB
2
Irf
S(ω) −
A(ω)
Vdc =
dθ 2h̄(Ms V)σ
dI
dI
ωm
#
(7.3)
where Hz is the component of the applied magnetic field parallel to the initial orientation of the free layer magnetization and θ is the angle between the magnetizations
of the two ferromagnetic layers before any RF current is applied. Mef f is an effective
out of plane anisotropy which must be determined experimentally from resistance vs.
field measurements with field applied perpendicular to the sample plane [32]. Now
we can write (7.2) as
"
dτk
dR
dτ⊥ γ0 (Hz + 4πMef f )
µB
Z0
=
S(ω) −
A(ω)
2
dθ 4h̄(Ms V)σ (R + Z0 ) ) dI
dI
ωm
#
(7.4)
Next we use
1
1 1
1
1 1
1
= (
+
)+ (
−
) cos θ
R
2 RP
RAP
2 RP
RAP
40
(7.5)
which expresses the sinusoidal angular dependence of TMR predicted in [17](see also
(4.7)) to obtain
R2
dR
=
(RAP − RP ) sin θ
dθ
2RP RAP
For the symmetric tunnel junctions we are studying we will treat
(7.6)
dτ⊥
dI
as negligible or
suppressed at zero bias in accordance with [14] and [32]. The differential torque in
the plane of the ferromagnet
dτk
dI
is given by
dτk
h̄ 2P R
=
sin θ
dI
4e 1 + P 2 RP
(7.7)
Here P = P1 (= P2 ) is the spin polarization of the ferromagnet, also expressible as
(see (4.1),(4.2))
s
P =
RAP − RP
RAP + RP
(7.8)
Putting (7.6) and (7.7) into (7.4) gives
=
RAP − RP µB
2P
R2
RZ0
sin2 θ
RP
2eVσ (R + Z0 )2 1 + P 2 RP RA P
(7.9)
From this equation we can see how the sensitivity of a tunnel junction depends on the
initial angle between the free and fixed layer magnetizations. This angle is generally
set by the direction and magnitude of the applied magnetic field so information about
θ is really information about the applied field. The sensitivity is maximized when
θ is approximately 90◦ [2] and this means that the external magnetic field must be
applied perpendicular to the fixed layer magnetization and be of sufficient magnitude
to saturate the free layer magnetization but not so strong that it rotates the fixed
layer magnetization. In terms of the resistance vs. applied field curves of Chapter
3 this occurs at fields where the derivative dR/dH is large, implying that dR/dθ is
large for large sensitivity, as expected from (7.4). Also, we can see that if the applied
field were zero,
dτk
dI
would be zero and only the
41
dτ⊥
dI
term could contribute to Vdc which
could only happen if there were a relatively large biasing voltage.
Tests on the full microwave detectors were run by placing the detectors at some
distance from a microwave horn antenna (AH-118 from Com-Power Corporation)
which was in turn connected to a microwave generator. The voltage reading from the
nanovoltmeter was recorded as the frequency of the microwave emissions was varied.
The next plot (Fig. 7.2) shows the output voltage at the applied field giving the best
signal for a typical detector with a Type A tunnel junction. This result was obtained
Figure 7.2: Response of a Type A detector
with an external field of about 650G applied and a signal generator power output of
15dBm.
Next, a figure (Fig. 7.3) showing the typical response of a Type B detector. Besides
42
Figure 7.3: Response of a Type B detector
the stronger response of the Type B detector we also note that the resonance is at
a lower frequency for this kind of MTJ. The constant external field applied for this
measurement was about 200G, lower than the field at which the best response for
Type A samples occurs.
The last figure (Fig. 7.4) shows the signal obtained from our best performing sample,
which was of Type B. As the figure shows, the response of this sample was atypically
strong, though the resonance frequency was the same as for other Type B samples.
This best performing sample was larger than the other Type B samples tested, measuring 210nm × 60nm while the other samples measured 150nm×70nm. Also, since
these tunnel junctions were designed to have equal Resistance-Area (RA) products
regardless of size, the MTJ in the detector of Fig.7.4 has a lower resistance (340Ω),
closer to the impedance of air.
43
Figure 7.4: Response of the best detector.
Finally, we show the response of a Type B sensing element under controlled conditions
with the microwave power applied directly to the detector via a set of titanium probes
in Fig.7.5. The RF power applied was -36dBm and the applied was 150 G.
The signal corresponds to a maximum sensitivity of 240mV/mW since a power of
0.25µW was applied. For comparison, the best sensitivity for an MTJ detector reported to date [4] was 170mV/mW and the sensitivity of the commercial diode we
used for calibration is quoted as 400mV/mW. We show the response of this GaAs
diode microwave detector (Agilent 8474B) to different input powers in Fig. 7.6. The
sensitivity we observed is well below the theoretical maximum of 10,000mV/mW
predicted in [2].
To explain why the Type B sensing elements have a stronger response we can examine
Fig. 7.5 and note the asymmetry of the resonance peak. We saw in Chapter 5 that an
44
Figure 7.5: Response of a Type B detector to a direct microwave input
asymmetric component of the spectrum is likely a signature of an out of plane spin
torque. Such an out of plane torque could cause the precession angle of the free layer
~ 2 about the effective field direction to be larger resulting in both a
magnetization M
lower resonant precession frequency and a larger change in resistance which would
result in a larger signal. The natural perpendicular to plane anisotropy of the free
layer that the Type B detectors were designed for would have the same effect. We still
have to explain how an observable out of plain spin torque could arise at zero bias (no
such torque was observed in [32] for an in plane free layer magnetization, though one
is predicted in [13]). Figure 7.7(b) illustrates how a partially out of plane free layer
magnetization can result in the stronger (Slonczewski) spin-torque component being
directed out of the plane while the field-like torque is in the plane. Note that this does
not happen in normal in-plane magnetized free layers (Fig.7.7(c)) or a completely out
of plane free layer magnetization (Fig.7.7(a)).
The picture we present here indicates that the spin-torque will be directed more out
~ 2 is with M
~ 1 . However, since the magnitudes
of the plane the more closely aligned M
45
Figure 7.6: Power response of a GaAs Diode
Figure 7.7: Diagram of spin-torque vectors: (a) Free layer magnetization perpendicular to plane, (b) Free layer magnetization out of plane, (c) Free layer magnetization
in plane
of both spin-torque components depend on sin θ where cos(θ) = M̂1 · M̂2 , the torque
~ 2 approaches M
~ 1 . If we restrict our attention to the case where M
~2
goes to zero as M
~ 1 are in the same x-z plane so that the field-like torque is completely in plane
and M
as in Fig. 7.7, the out of plane component of the Slonczewski spin-torque term is
46
proportional to sin(θ) cos(θ) so that its maximum value is obtained when the angle
~ 2 and M
~ 1 in the x-z plane is 45◦ .
between M
STFMR spectra obtained for other Type B tunnel junction samples [35] at various
bias voltages indicate that the antisymmetric component of the peaks is the result of
voltage induced magnetic anisotropy [36],[37],[38]. First, the spectra show a decrease
in the resonance frequency as positive bias voltage is increased. The response frequency increases for negative bias voltages. This is in direct agreement with [37] but
with much higher TMR junctions and is consistent with the results of other studies
where methods other than STFMR were used. The bias changes the electron density
at the interfaces in which in turn can modify the energy and therefore the occupancy
of the different 3d electron states in the ferromagnet. This changes the surface magnetic anisotropy and through the change in the anisotropy field changes the resonance
frequency according to a version of (5.11) modified to include anisotropy terms [30]
q
ω0 = γ [Hz + (Ny + Nya − Nz )Mz ][Hz + (Nx + Nxa − Nz )Mz ]
(7.10)
Nxa = −Hxa /Mx
(7.11)
Nya = −Hya /My
(7.12)
where
with H a the anisotropy field. Here ẑ is the initial direction of the magnetization and
we take ŷ to be out of the plane of the sample.
The voltage across the tunnel junction due to the oscillating RF current used to make
~ ef f
STFMR measurements induces anisotropy resulting in the addition of a term to H
in the first term of the Landau-Lifshitz-Gilbert equation for magnetization dynamics
47
(1.1). We rewrite this first term
~ = −γ0 M
~ ×H
~ ef f
∂t M
(7.13)
and separate the contribution of voltage induced anisotropy from the rest of the
~ 0 giving
effective field which we label H
ef f
0
~
~
~ = −γ0 (M
~ ×H
~ ef
∂t M
f + M × Hvia cos θ)
(7.14)
The voltage induced contribution to the anisotropy is uniaxial, hence the factor of
cos θ = Ĥvia · M̂ which makes the contribution zero when the sample is magnetized in
plane. Equation (7.14) also shows us that this contribution is zero when the sample
is magnetized completely perpendicular to the sample plane. The effect of voltage
induced anisotropy is therefore important in MTJs with a significant component of
magnetization perpendicular to the layer planes like our Type B junctions. This
torque due to voltage induced anisotrpy is inherently field-like and appears as an
anitsymmetric contribution to STFMR spectra that is not caused by current-induced
spin-torque and therefore appears at zero bias and is linear in applied DC bias to the
extent that the out of plane anisotropy responds linearly to voltage.
When the bias and therefore the standard perpendicular field-like torque are non-zero,
voltage induced anisotropy has an additional effect. To obtain (7.9) we treated
dτ⊥
dI
at
zero bias as negligible, an assumption that is supported by theory [14] and experiment
[32]. However, this is no longer true for non-zero bias and by examining (7.4) we see
that there is a factor of Ω⊥ = γ(Hz + 4πMef f )/ω0 multiplying this antisymmetric
term. Including both in plane and out of plane anisotropy [39] we can write
Ω0⊥ =
γ
(Hz + 4πMef f − Hk sin2 β)
ω0
48
(7.15)
where Hk is the in-plane anisotropy field strength and 4πMef f is the effective out of
plane anisotropy mentioned earlier in connection with (5.13), and β is the in plane
angle between the free layer’s magnetization and its anisotropy (easy) axis when no
currents are applied. We also assume that the fixed layer is aligned with the free layer
in-plane anisotropy. Voltage induced anisotropy therefore modifies the effect of the
current-induced spin-torque on the STFMR signal through its effect on Mef f as well
as contributing the wholly independent field-like term discussed above. When the in~ k is weak compared to the out of plane anisotropy
plane anisotropy represented by H
(which can be strengthened by increasing the bias) the effects of voltage modification
of anisotropy become increasingly significant.
49
Conclusions
In this thesis we have shown that it is possible to use magnetic tunnel junctions as
sensing elements in microwave radiation detectors. In addition, we show that the junctions’ sensitivity (240 mV/mW) approaches that of current commercial semiconductor
diode based detectors. An MTJ based detector has the feature of being intrinsically
frequency tunable, which semiconductor RF detectors lack. We have also shown that
the sensitivity of tunnel junctions with free layer magnetic anisotropy perpendicular
to the plane of the layer have enhanced sensitivity when compared to junctions with
in plane anisotropy. This enhancement is due to voltage induced anisotropy.
According to theoretical models [2] for tunnel junctions similar to those used in our
Type A detectors there is considerable room for improvement in sensitivity for the
kinds of microwave sensors described here. Using MTJs with perpendicular magnetic
anisotropy like our Type B sensing elements may result in even higher sensitivity
especially in active, biased detectors for which voltage induced anisotropy and out of
plane spin transfer torque will play a greater role. The maximum sensitivity possible
in such an active detector will depend on the maximum biasing voltage the tunnel
junction can sustain without breaking down and has not been determined yet.
Besides improvements to the MTJ sensing elements, the microwave detectors described in this thesis would be improved significantly by better impedance matching
between air, antenna, and sensing element. This kind of matching could possibly
be achieved by a different antenna design or the inclusion of impedance matching
circuitry in the detector. One promising note in this regard is the fact that MTJs
are available with perpendicular anisotropy and impedances very much like that of
air. So far we have discussed only the sensitivity of the MTJ microwave detectors,
but to be technologically viable these detectors need to have not only high sensitivity,
50
but also low noise. Further work is needed to investigate the noise properties of tunnel junctions used as detectors and compare them to those of semiconductor diode
detectors.
51
Bibliography
[1] J. Sankey et al., “Spin-transfer-driven ferromagnetic resonance of individual
nanomagnets,” Physical Review Letters, vol. 96, p. 227601, 2006.
[2] C. Wang et al., “Sensitivity of spin-torque diodes for frequency tunable resonant
microwave detection,” Journal of Applied Physics, vol. 106, p. 053905, 2009.
[3] X. Fan et al., “Magnetic tunnel junction based microwave detector,” Applied
Physics Letters, vol. 95, p. 122501, 2009.
[4] S. Ishibashi et al., “Large diode sensitivity of CoFeB/MgO/CoFeB magnetic
tunnel junctions,” Applied Physics Express, vol. 3, p. 073001, 2010.
[5] C. Kittel, Introduction to Solid State Physics. John Wiley, 1996.
[6] J. Slonczewski, “Current-driven excitation of magnetic multilayers,” Journal of
Magnetism and Magnetic Materials, vol. 159, pp. L1–L7, 1996.
[7] D. Ralph and M. Stiles, “Spin transfer torques,” Journal of Magnetism and
Magnetic Materials, vol. 320, no. 7, pp. 1190–1216, 2008.
[8] J. Sun, “Spin angular momentum transfer in current-perpendicular nanomagnetic junctions,” IBM Journal of Research and Development, vol. 50, pp. 81–100,
2006.
[9] J. Katine et al., “Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars,” Physical Review Letters, vol. 84, pp. 3149–3152,
2000.
[10] G. Fuchs et al., “Spin-transfer effects in nanoscale magnetic tunnel junctions,”
Applied Physics Letters, vol. 85, pp. 1205–1207, 2004.
[11] L. Berger et al., “Emission of spin waves by a magnetic multilayer traversed by
a current,” Physical Review B, vol. 54, pp. 9353–9358, 1996.
[12] M. Stiles and A. Zangwill, “Anatomy of spin-transfer torque,” Physical Review
B, vol. 66, p. 014407, 2002.
[13] J. Xiao et al., “Spin-transfer torque in magnetic tunnel junctions: Scattering
theory,” Physical Review B, vol. 77, p. 224419, 2008.
52
[14] C. Heilinger and M.Stiles, “Ab initio studies of the spin-transfer torque in magnetic tunnel junctions,” Physical Review Letters, vol. 100, p. 186805, 2008.
[15] W. Butler et al., “Spin-dependent tunneling conductance of Fe—Mgo—Fe sandwiches,” Physical Review B, vol. 63, p. 054416, 2001.
[16] M. Julliere, “Tunneling between ferromagnetic films,” Physics Letters A, vol. 54,
no. 3, pp. 225–226, 1975.
[17] J. Slonczewski, “Conductance and exchange coupling of two ferromagnetics separated by a tunneling barrier,” Physical Review B, vol. 39, no. 10, pp. 6995–7001,
1989.
[18] S. Maekawa et al., “Electron tunneling between ferromagnetic films,” IEEE
Transactions on Magnetics, vol. MAG-18, pp. 707–708, 1982.
[19] S. Parkin et al., “Giant tunnelling magnetoresistance at room temperature with
MgO(100) tunnel barriers,” Nature Materials, vol. 3, pp. 862–867, 2004.
[20] S. Ikeda et al., “Tunnel magnetoresistance of 604Ta diffusion in cofeb/mgo/cofeb
pseudo-spin-valves annealed at high temperature,” Applied Physics Letters,
vol. 93, p. 082508, 2008.
[21] H. Wei et al., “80Al-O barrier magnetic tunnel junction with cofeb as free and
reference layers,” Journal of Applied Physics, vol. 101, p. 09B501, 2007.
[22] J. Mathon and A. Umerski, “Theory of tunneling magnetoresistance of an epitaxial Fe/MgO/Fe(001) junction,” Physical Review B, vol. 63, p. 220403(R),
2001.
[23] O. Schebaum et al., “Tunnel magnetoresistance in alumina,magnesia,and composite tunneling barrier and magnetic tunnel junctions,” ArXiv, vol. [cond-mat],
p. 1008.0761v3, 2010.
[24] J. Hayakawa et al., “Dependence of giant tunnel magnetoresistance of sputtered
CoFeB/MgO/CoFeB magnetic tunnel junctions on MgO barrier thickness and
annealing temperature,” Japanese Journal of Applied Physics, vol. 44, pp. L587–
L589, 2005.
[25] J. Du et al., “Investigation of magnetic tunneling junctions with wedge-shaped
barrier,” Journal of Applied Physics, vol. 91, pp. 8780–8782, 2002.
[26] J. Slonczewski, “Currents, torques, and polarization factors in magnetic tunnel
junctions,” Physical Review B, vol. 71, p. 024411, 2005.
[27] D. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids.
Plenum, 1986.
53
[28] J. MacLaren et al., “Layer kkr approach to bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Physical Review B, vol. 59,
pp. 5470–5478, 1999.
[29] F. Montaigne et al., “Angular dependence of tunnel magnetoresistance in magnetic tunnel junctions and specific aspects in spin-filtering devices,” Journal of
Applied Physics, vol. 108, p. 063912, 2010.
[30] C. Kittel, “On the theory of ferromagnetic resonance absorption,” Physical Review, vol. 73, no. 2, pp. 155–161, 1948.
[31] A. Tulapurkar et al., “Spin-torque diode effect in magnetic tunnel junction,”
Nature, vol. 438, pp. 339–342, 2005.
[32] J. Sankey et al., “Measurement of the spin-transfer-torque vector in magnetic
tunnel junctions,” Nature Physics, vol. 4, pp. 67–71, 2008.
[33] R. N. Simons, Coplanar Waveguide Circuits Components Systems. Wiley-IEEE
Press, 2001.
[34] D. M. Pozar, Microwave Engineering. Wiley, 2004.
[35] J. Zhu et al., “Voltage-induced ferromagnetic resonance in magnetic tunnel junctions,” Pysical Review Letters, vol. 108, p. 197203, 2012.
[36] T. Marayuma et al., “Large voltage-induced magnetic anisotropy change in a
few atomic layers of iron,” Nature Nanotechnology, vol. 4, pp. 158–161, 2009.
[37] T. Nozaki et al., “Voltage induced perpendicular magnetic anisotropy change in
magnetic tunnel junctions,” Applied Physics Letters, vol. 96, p. 022506, 2010.
[38] Y. Shiota et al., “Quantitative evaluation of voltage-induced magnetic anisotropy
change by magnetoresistance measurement,” Applied Physics Express, vol. 4,
p. 043005, 2011.
[39] C. Wang et al., “Bias and angular dependence of spin-transfer torque in magnetic
tunnel junctions,” Physical Review B, vol. 79, p. 224416, 2009.
54
Документ
Категория
Без категории
Просмотров
0
Размер файла
697 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа