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8/15/2019 Electrochemical Potential
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Spin Transport in Epitaxial Heusler Alloy/
III-V Semiconductor Heterostructures
Kevin D. Christie, Chad Geppert, Tim Peterson, Changjiang Liu,
Gordon Stecklein, Paul A. Crowell School of Physics and AstronomyUniversity of Minnesota
Sahil J. Patel, Mihir Pendharkar, Chris J. Palmstrøm
Dept. of Electrical and Computer Engineering, Dept. of MaterialsUniversity of California Santa Barbara
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Outline
• Why lateral spin valves
• Why Heuslers: the Co2FexMn1-xSi family
• Progress in semiconductor lateral spin valves
• Improvements in high temperature performance
• Microwave detection of spin accumulation
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Lateral spin valve
− injector
detector
≈50% ≈ 5 μm
• Allows the study of spin-physics in wide array of materials systems
• ferromagnetic contacts (Fe, Co, Py, Co2MnSi, etc.)
• metallic channels (Al, Cu, Ag, etc.); ≪ 1 % • semiconducting channels (GaAs, Si, Ge, graphene, etc.)
• Can quantify injection rates, detection efficiencies, spin-lifetimes,
etc.
3
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The non-local measurement
e-
V
S
Dm
• No charge current flows in F2.
• The electrochemical potential is measured for
each state of F2 (seemingly straight-forward).• The (less than 100%) polarization of F2 reduces
the signal from the ideal value.
• F2 draws a spin current. This can perturb N
(irrelevant in this system)
F1 F2
NS
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Outline
• Why lateral spin valves
• Why Heuslers: the Co2FexMn1-xSi family
• Progress in semiconductor lateral spin valves
• Improvements in high temperature performance
• Microwave detection of spin accumulation
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Co2MnSi – a potential half-metal
CoMn
Si
• Predicted to be a half-metal with a relatively large minoritygap
• Lattice-matched to GaAs
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Co2MnSi – a potential half-metal
CoMn
Si
• Predicted to be a half-metal with a relatively large minority gap
• Lattice-matched to GaAs
• Spin injection will work [see Dong et al., Appl. Phys. Lett. 86, 102107
(2006) for Co2MnGe/GaAs]
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General idea: Fermi level in a rigid band model
Co2MnSi Co2FeSiCo2Mn0.5Fe0.5Si
• Can we tune the Fermi level through the minority spin gap?
B. Balke et al., Solid State Communications 150, 529 –532 (2010).
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Heusler alloy: Co2MnSi
L21 ordered
= 985 K
= 5.65 Å
Co
Mn
Si Cap
GaAs
Co2MnSi
(STEM courtesy of Paul Voyles, UW Madison)
Near perfect lattice
match to GaAs
Co2MnSi
=4.97
9
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Useful features of these alloys
• As indicated by work on MTJ’s, the tunneling polarization is
high; Co2MnSi is half-metallic or nearly so.
• As suggested by the cartoons on the previous viewgraphs,
the density of states at the Fermi level is relatively small.
This is a corollary to the fact that
changes so rapidly with
composition.
• Grown on (100) GaAs, they have a very large in-plane
uniaxial anisotropy. This turns out to be of practical utility.
• The LLG damping is particularly small for Co2MnSi
(~ 0.003 at high temperatures)
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Outline
• Why lateral spin valves
• Why Heuslers: the Co2FexMn1-xSi family
• Progress in semiconductor lateral spin valves
• Improvements in high temperature performance
• Microwave detection of spin accumulation
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FM/n -GaAs Heterostructures
(15 nm)(15 nm)
n n+ : GaAs
(5 nm)
n : GaAs
n ~ 3 x 1016 cm-3
i -GaAs [001]
(~ 2500 nm)
n+ : GaAs n ~ 5 x 1018/cm3FM : Co2MnSi or Fe
cap
FM n-GaAs
0.7 eV
12 nm
e
n e r g y
depth
w/o graded doping
(~ 100 nm)
w/ graded
doping
• Epitaxially grown along [001]
• Fe polarization at Fermi level ≈40% • Co2MnSi proposed to be half-metallic
• Surface-induced FM anisotropy
• Graded doping used to ‘thin’
natural forming Schottky barrier
• Interface states lead to complex
bias dependence
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Lateral spin valve
13
drift diffusion onlydiffusion
-250 0 250
0
20
40
60
80
100
DV(
m V)
Field (Oe)
Co2MnSi
Fe
-250 0 250
-400
-200
0
D V
(
m V )
Field (Oe)
Co2MnSi
Fe
unbiased (non-local) biased (non-local)
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The full time of flight experiment: add drift
∗ =0.79
• Solid curves are the analytic solution
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Non-local Hanle fitting
-600 -300 0 300 600
0
50
100
150
-600 -300 0 300 600
1140
1520
760
DV
( m V)
Field (Oe)
380 A/cm2
60 K 760 A/cm2
120 K
90 K
60 K
30 K
Field (Oe)
• Multiple biases at each temperature fit with a single set of parameters
• Hanle curves with ‘lobes’ allow extraction of diffusion constant
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0 30 60 90 120 1500
6
12
18
24
Temperature (K)
Diffusionconstant( m m/ns
2)
0
3
6
9
12
SpinLifetime(ns
)
17
Spin lifetime and diffusion constant
Einstein
free-fit
• Allowing to be a fitting parameter yields values in agreement withthe Einstein relation: spin and charge diffusion constants are thesame.
• Larger uncertainty at higher temperatures due to disappearance of
‘lobes’
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Estimates of the spin polarization
-50 0 50-2.5
-2.0
-1.5
-1.0
-0.5
0.0
DVcd
(mV)
Field (mT)
= 30 K
= ↑ ↓↑ + ↓ =60%
+ΔV↓
Δ↑
DOS ()
E
• We can set a lower bound for the spin-polarization if we assume a perfect
detection efficiency ( = 1)• The measured spin splitting Δ is half of the Fermi energy = 5 meV
= 1
↑(↓) = ±↑ ↓
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Sign of the spin accumulation by Hanle measurements
-75 -50 -25 0 25 50 75
0
500
D
V
( m V)
Field (mT)-75 -50 -25 0 25 50 75
0
500
D
V (
m V )
Field (mT)
Sign of the spin polarization in the bulk GaAs can be determined in thepresence of a hyperfine field
60 K
Co2MnSi/GaAs Co2FeSi/GaAs
= ⋅
40 K
majority spinaccumulation minority spinaccumulation
Exploit hyperfine coupling:
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Interlude: (Scalar) Spin EMF
• Expand chemical potentials w.r.t. :
asymmetric shift: Δ
0
↑
↓Δ
= 0
DOS
• Current in each spin-channel:
spin-indep.
mobility
chemical
potentials
electrostatic
potential
carrier
densities
• Result:
spin-generated EMF
= 12 ( +
) =
29
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Quadratic dependence
1 10
0.1
1
10
10075 K
60 K45 K
Sp
in-EMF,
D V
CH
( m V)
Non-local, DV DH (mV)
30 K
1 10
0.1
1
10
10075 K
60 K45 K
Sp
in-EMF,
D V
CH
( m V)
Non-local, DV DH (mV)
30 K
Δ ∝
Δ ∝
slope = 2
• Log-log plot of magnitudesdemonstrates quadratic dependence
• Deviation at large bias due to largeE-field at injector (drift effects)
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Dual-injector experiment
anti-parallel
parallelA
H
C
C
DB
• Spins injected simultaneously at FMcontacts B and D
• Clear spin valve signals observed atcontact C
• Low-field features due to hyperfineinteractions
Field
I. J. Vera-Marun et al ., Nature Phys. 8, 313 (2012).
hyperfine
-400 -200 0 200 400
0
25
50
75
100
125
150
SpinEMF,
D V
CH
( m V)
j B = j
D = 380 A/cm
2
x 260 K
30 K
Field (Oe)
45 K
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Polarization vs. Temperature
30 45 60 75 90 105 1200
20
40
60
Temperature (K)
Numberpolarization
(%)
Co2MnSi
(3.8 x 1016
/cm3
)
Fe/n
-GaAs(5.5 x 10
16/cm
3)
= ↑ ↓↑ + ↓
• For > 0 . 3, need to account for ‘Thompson’ effect: = • Results are independent of any assumptions about
interfacial spin injection/detection efficiencies
• This resolved the “three-terminal” discrepancy
O li
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Outline
• Why lateral spin valves
• Why Heuslers: the Co2FexMn1-xSi family
• Progress in semiconductor lateral spin valves
• Improvements in high temperature performance
• Microwave detection of spin accumulation
Wh t b t t t ?
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What about room temperature?
0.0 0.2 0.4
0
50
100
150
200
DVNL(
m V)
Iinj
(mA)
Idet
= 0
1 m A
10 m A
100 m A
250 nm separation, 150 K
• Δ is linear in spin injection rate, , withfixed non-zero detector bias
• Δ becomes larger with detector bias ,which we interpret as a detector bias
dependence of → ( )
Δ =() () • We also see saturation of Δ at large .
• Biased detector
C li ti T li AMR (TAMR)
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z
FM
GaAs
x
y
2
|| ||3 ( , )[ ( ) ( )]
(2 ) F N
edEd k T E k f E f E
K. Wang et al., PRB, 88, 054407 (2013)
A. Matos-Abiague et al., PRB, 80, 045312 (2009)
2 2 2
0 sin ( ) cos ( ) sin ( )in out R R R R
D D
2sin ( )[ ( , ) ( , ) cos(2 )]anisoT f g
( , ) R
Complication: Tunneling AMR (TAMR)
J. Moser et al., PRL, 99, 056601 (2007)
: Rashba spin-orbit coupling
constant
: Dresselhaus spin-orbit coupling
constant
[1,1,0]
m
R ifi ti f bi d d t t
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Ramifications for a biased detector
• The ratio of the uniaxial to fourfold anisotropies is larger in
Co2Mn1-xFexSi than in Fe. This makes the Heuslers very forgiving.
• Any contact rotation leads to a TAMR contribution to the“three-terminal”
signal; i.e. an additional field-dependent voltage at the detector. This is
large and only weakly temperature-dependent.
La Bella et al., PRL 83, 2989 (1999).
2-fold surface symmetry
D i ti g t t t
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Devices operating at room temperature
• Use of Co2FeSi as injector/detector
• Electron beam lithography• Performance today comparable to low-T performance as of a
few years ago (particularly size of non-local voltage)
• Spin diffusion length at 300 K is ~ 800 nm
T t d d
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Temperature dependence
0 2 4
10
100
DVNL
( m V)
Separation (mm)
25 K
50 K
100 K 150 K
200 K
250 K
300 K
= 0 =
+ D
+
We fit to the steady state solution of the spin
drift-diffusion equation to extract
relaxation diffusion drivedrift
Channel (n-GaAs)
Detector
For ≫
By measuring the separation dependence,we extract the spin diffusion length .
10 1000.01
0.1
1
10
fitted
s
(ns)
Temperature (K)
O tli
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Outline
• Why lateral spin valves
• Why Heuslers: the Co2FexMn1-xSi family
• Progress in semiconductor lateral spin valves
• Improvements in high temperature performance
• Microwave detection of spin accumulation
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Hanle measurement at room temperature fails
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Hanle measurement at room temperature fails
-4000 -2000 0 2000 4000
433.80
434.40
435.00
435.60
436.20
T = 300 K
Voltage(mV)
Field (Oe)
I = 1 mA
5 50 mm2
Co2MnSi/n-GaAs
• Signal/Background ~10− • Impossible to extract spin
signal at room temperature
in n-GaAs system
What about Hanle measurements?
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What about Hanle measurements?
• Conventional wisdom: these become difficult or impossibleat high temperatures because the lifetime “is too short”
• This is reinforced by the fact that the g-factor in GaAs
is so small (i.e. -0.44 insteady of 2)
• Ordinary magnetoresistance is very large
• Solution: use the Hanle concept (sensitivity to precession),
but exploit the fact that spins can precess in the FM as wellas the semiconductor.
Solution: modulate the injector with FMR
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Solution: modulate the injector with FMR
V
(15 nm)
(18 nm)
n n+ : GaAs
(5 nm)FM
i -GaAs [001]
n : GaAs
n ~ 3 x 1016 cm-3 (~ 2500 nm)
n+ : GaAs n ~ 5 x 1018/cm3
Cap
FM: Co2MnSi, Co2FeSi, Fe
• This is a three-terminal measurement
with microwave excitation
• Signal is the difference of the 3T
signal with and without microwave field
Skipping details...
Spin accumulation leads to an FMR peak in
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Spin accumulation leads to an FMR peak in Δ • A strong resonance peak is
observed (note the sign is
negative)
• The peak position is well
described by the Kittel’s
formula
2000 2200 2400 2600
-4
-3
-2
-1
Voltage
( m V)
Field (Oe)
T = 100 K
I = 3 mA
f = 13 GHz
• At forward bias, the FMR signal isdominated by spin accumulation
• Linewidth determined by ~0.003 for Co2MnSi at room temperature
Modeling FMR spin detection
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Modeling FMR spin detection
n-GaAs
: Spin injection current: Detection efficiency: Spin diffusion constant
:Spin lifetime
= ∙
−∞ (′) 12(′) −−
′
: Precession cone angles
= 12 ( + )2
1
2 1 +
+
1
2 1 +
1
(′)
Temperature dependence (comparison with NLSV)
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Temperature dependence (comparison with NLSV)
0 100 200 3000
1
2
3
VFMR
(Co2MnSi)
VFMR
(Co2FeSi)
VNLSV
(Co2MnSi)
VNLSV
(Co2FeSi)
0.0
1.5
3.0
4.5
V
NLSV
( m V)
T (K)
V
FMR
(arb.u.)
0
300
600
900
0
200
400
600
• Agreement with spin-valve data for both Co2FeSi and Co2MnSi
Frequency dependence
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Frequency dependence
• Spin lifetime extracted agrees with those obtained from spin-valve
measurements
• At high temperatures, this technique is much more sensitive than
the conventional spin valve approach
Summary
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Summary
• Co2Mn1-xFexSi is a very effective spin injector/detector
for GaAs
• The high polarization helps, although in our case the
highest polarizations measured are about 70%
• There are other features of these materials that are as“useful” as the high polarization
• Lateral spin valves useful as quantitative tools up to
room temperature
• Microwave detection of spin accumulation is a complementary
technique, particularly when is short .
Recommended