Spin Transport in Epitaxial Heusler Alloy/ III-V...
Transcript of Spin Transport in Epitaxial Heusler Alloy/ III-V...
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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 Astronomy University of Minnesota
Sahil J. Patel, Mihir Pendharkar, Chris J. Palmstrøm Dept. of Electrical and Computer Engineering, Dept. of Materials University 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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7/31/2015 Heusler Workshop, Minneapolis
Lateral spin valve
𝑒−
injector detector
𝑝𝑖𝑛𝑗 ≈ 50%
𝜆𝑠 ≈ 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.); 𝑝 ≪ 1%
• semiconducting channels (GaAs, Si, Ge, graphene, etc.)
• Can quantify injection rates, detection efficiencies, spin-lifetimes, etc.
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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
N
m
S m
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7/31/2015 Heusler Workshop, Minneapolis
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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7/31/2015 Heusler Workshop, Minneapolis
Co2MnSi – a potential half-metal
Co
Mn
Si
• Predicted to be a half-metal with a relatively large minority
gap
• Lattice-matched to GaAs
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Co2MnSi – a potential half-metal
Co
Mn
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 Co2FeSi Co2Mn0.5Fe0.5Si
• 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
𝑇𝑐 = 985 K
𝑎 = 5.65 Å
Co
Mn
Si Cap
GaAs
𝟐 𝐧𝐦
Co2MnSi
(STEM courtesy of Paul Voyles, UW Madison)
Near perfect lattice match to GaAs
Co2MnSi
𝑀𝑠𝑎𝑡 = 4.97𝜇𝐵
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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 𝐸𝐹 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/cm3 FM : Co2MnSi or Fe
cap
FM n-GaAs
0.7 eV
12 nm
ene
rgy
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
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𝑯
drift diffusion only diffusion
-250 0 250
0
20
40
60
80
100
DV
(m
V)
Field (Oe)
Co2MnSi
Fe
-250 0 250
-400
-200
0
DV
(m
V)
Field (Oe)
Co2MnSi
Fe
unbiased (non-local) biased (non-local)
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𝐷 diffusion constant 𝜏𝑠 spin lifetime 𝑝 fractional number polarization 𝐸 electric field 𝜈 mobility 𝛾 gyromagnetic ratio
𝐵 magnetic field
Continuity equation for spin (diffusive regime):
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Spin drift-diffusion model
relaxation injection
rate
Larmor precession drift & diffusion
𝜕𝑝
𝜕𝑡= 𝜈𝐸
𝜕𝑝
𝜕𝑥+ 𝐷
𝜕2𝑝
𝜕𝑥2 − 𝛾𝐵 × 𝑝 −
𝑝
𝜏𝑠 + 𝑝 0
steady state
0 = 𝐷
(Einstein relation)
𝑒𝐷 = 𝜈 𝑛𝜕𝜇
𝜕𝑛
𝜈 drift mobility 𝑛 carrier concentration 𝜕𝜇/𝜕𝑛 bulk modulus
DIFFUSION CONSTANT – Same for spin and charge?
𝜏𝑠
(Dyakonov-Perel)
𝜏𝑠−1 ∝ 𝛼2𝜀3𝜏𝑝
𝜀 electron energy 𝛼 spin-orbit prefactor (Dresselhaus) 𝜏𝑝 momentum relaxation time
SPIN LIFETIME – Reasonable values for n-GaAs?
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The full time of flight experiment: add drift
𝑔∗ = 0.79
• Solid curves are the analytic solution
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Non-local Hanle fitting
𝑒−
𝐵
𝑧 𝑦
𝑥
V
2.5 μm
-500 0 500-20
0
20
40
60
DV
(m
V)
Field (Oe)
𝑇 = 90 K
-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)
Diffu
sio
n c
onsta
nt (m
m/n
s2)
0
3
6
9
12
Sp
in L
ife
tim
e (
ns)
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Spin lifetime and diffusion constant
Einstein
free-fit
• Allowing 𝐷 to be a fitting parameter yields values in agreement with the Einstein relation: spin and charge diffusion constants are the
same.
• 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
DV
cd (
mV
)
Field (mT)
𝑇 = 30 K
𝑝 =𝑛↑ − 𝑛↓𝑛↑ + 𝑛↓
= 60%
𝐸𝑓 + 𝑒ΔV↓
𝐸𝑓 − 𝑒Δ𝑉↑
𝐸𝑓
DOS 𝑔(𝐸)
E
• We can set a lower bound for the spin-polarization if we assume a perfect detection efficiency (𝜂 = 1)
• The measured spin splitting Δ𝑉 is half of the Fermi energy 𝐸𝑓 = 5 meV
𝜂 = 1
𝑛↑(↓) = 𝑔 𝐸 𝑑𝐸𝐸𝑓±
𝑒𝜂𝑉↑ ↓
0
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Sign of the spin accumulation by Hanle measurements
-75 -50 -25 0 25 50 75
0
500
DV
(m
V)
Field (mT)-75 -50 -25 0 25 50 75
0
500
DV
(m
V)
Field (mT)
Sign of the spin polarization in the bulk GaAs can be determined in the presence of a hyperfine field
60 K
𝐵𝑁
Co2MnSi/GaAs Co2FeSi/GaAs
𝐵𝑡𝑜𝑡 = 𝐵 − 𝑏𝐻𝑆 ⋅ 𝐵
𝐵2𝐵
40 K
𝐵𝑁 majority spin accumulation
minority spin accumulation
Exploit hyperfine coupling:
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Co2Mn1-xFexSi: comparison with Fe
0 50 100 150-50
-25
0
25
50
75 Co
2MnSi
Co2Mn
0.7Fe
0.3Si
Co2FeSi
Fe
Spin
Accum
ula
tion (
%)
Temperature (K)
• Polarizations determined by “biased detector technique”
• Sign determined by hyperfine field
• Sign change in going from Co2MnSi to Co2FeSi is expected,
but overall sign is backwards
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Interlude: (Scalar) Spin EMF
• Expand chemical potentials w.r.t. 𝑝:
asymmetric shift: Δ𝜇𝑎𝑣𝑔
𝑝 0𝜀
𝜇↑
𝜇↓Δ𝜇𝑎𝑣𝑔
𝜀𝑝 = 0
𝜇0
DOS
• Current in each spin-channel:
spin-indep. mobility
chemical potentials
electrostatic potential
carrier densities
• Result:
spin-generated EMF
𝑘 =1
2𝑒(𝜕𝜇
𝜕𝑛 𝑛 +
𝜕2𝜇
𝜕𝑛2𝑛2) =
2
9
𝐸𝑓
𝑒
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Quadratic dependence
1 10
0.1
1
10
10075 K
60 K 45 K
Spin
-EM
F, D
VC
H (m
V)
Non-local, DVDH
(mV)
30 K
1 10
0.1
1
10
10075 K
60 K 45 K
Spin
-EM
F, D
VC
H (m
V)
Non-local, DVDH
(mV)
30 K
Δ𝑉𝐷𝐻 ∝ 𝑝
Δ𝑉𝐶𝐻 ∝ 𝑝2
slope = 2
• Log-log plot of magnitudes demonstrates quadratic dependence
• Deviation at large bias due to large E-field at injector (drift effects)
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Dual-injector experiment
anti-parallel
parallel A
H
C
C
D B
• Spins injected simultaneously at FM contacts B and D
• Clear spin valve signals observed at contact C
• Low-field features due to hyperfine interactions
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
Spin
EM
F, D
VC
H (m
V)
jB = j
D = 380 A/cm
2
x 2 60 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)
Nu
mbe
r p
ola
rizatio
n (
%)
Co2MnSi
(3.8 x 1016
/cm3)
Fe/n-GaAs
(5.5 x 1016
/cm3)
𝑝𝑖𝑛𝑗 =𝑛↑ − 𝑛↓𝑛↑ + 𝑛↓
• For 𝑝 > 0.3, need to account for ‘Thompson’ effect: 𝑘 = 𝑘 𝑝
• Results are independent of any assumptions about
interfacial spin injection/detection efficiencies
• This resolved the “three-terminal” discrepancy
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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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7/31/2015 Heusler Workshop, Minneapolis
What about room temperature?
0.0 0.2 0.4
0
50
100
150
200
DV
NL (m
V)
Iinj
(mA)
Idet
= 0
1 mA
10 mA
100 mA
250 nm separation, 150 K
• Δ𝑉𝑁𝐿 is linear in spin injection rate, 𝐼𝑖𝑛𝑗, with
fixed non-zero detector bias 𝐼𝑑𝑒𝑡
• Δ𝑉𝑁𝐿 becomes larger with detector bias 𝐼𝑑𝑒𝑡, which we interpret as a detector bias dependence of 𝜂 → 𝜂(𝐼𝑑𝑒𝑡)
𝑽𝑵𝑳
𝑰𝒊𝒏𝒋 𝑰𝒅𝒆𝒕
𝑯𝑺𝑽
Δ𝑉𝑁𝐿 = 𝜂(𝐼𝑑𝑒𝑡)𝑃(𝐼𝑖𝑛𝑗)𝑛
𝑒 𝜕𝜇
𝜕𝑛
• We also see saturation of Δ𝑉𝑁𝐿 at large 𝐼𝑑𝑒𝑡.
• Biased detector
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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 outR 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
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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
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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
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Temperature dependence
0 2 4
10
100
DV
NL (m
V)
Separation (mm)
25 K
50 K
100 K
150 K
200 K
250 K
300 K
𝑑𝑷
𝑑𝑡= 0 = −
𝑷
𝜏𝑠+ D𝛻2𝑷− 𝒗 𝛁𝑷 + 𝑭
We fit to the steady state solution of the spin drift-diffusion equation to extract 𝜏𝑠
relaxation diffusion drive drift
𝑽𝑵𝑳
𝐼𝑖𝑛𝑗
Channel (n-GaAs)
𝑴𝒊𝒏𝒋 𝑴𝒅𝒆𝒕
Detector
𝐶𝑜2𝐹𝑒𝑆𝑖
𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑜𝑛
𝐼𝑑𝑒𝑡
For 𝐼𝑖𝑛𝑗 ≫ 𝐼𝑑𝑒𝑡
By measuring the separation dependence, we extract the spin diffusion length 𝜆.
10 1000.01
0.1
1
10
fitt
ed
s (
ns)
Temperature (K)
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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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7/31/2015 Heusler Workshop, Minneapolis
What about Hanle measurements?
• Conventional wisdom: these become difficult or impossible
at 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
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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
Vo
lta
ge
(m
V)
Field (Oe)
I = 1 mA
5 50 mm2
Co2MnSi/n-GaAs
𝐻0
• Signal/Background ~10−4
• Impossible to extract spin
signal at room temperature in n-GaAs system
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What about Hanle measurements?
• Conventional wisdom: these become difficult or impossible
at 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 well
as the semiconductor.
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Solution: modulate the injector with FMR
V
𝐻0
𝑚𝑖𝑐𝑟𝑜𝑤𝑎𝑣𝑒
(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...
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Spin accumulation leads to an FMR peak in Δ𝑉
• 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
V
olta
ge
(m
V)
Field (Oe)
T = 100 K
I = 3 mA
f = 13 GHz
• At forward bias, the FMR signal is
dominated by spin accumulation
• Linewidth determined by 𝛼~0.003 for Co2MnSi at room temperature
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Modeling FMR spin detection
n-GaAs
𝐼𝑠: Spin injection current
𝜂: Detection efficiency
𝐷: Spin diffusion constant
𝜏𝑠: Spin lifetime
𝑉 = 𝜂𝐼𝑠 𝒎 𝑡 ∙𝑡
−∞
𝒔 (𝑡′)1
2𝜋𝐷(𝑡 − 𝑡′)𝑒−𝑡−𝑡′
𝜏𝑠 𝑑𝑡′
𝜑𝑖𝑛 𝜑𝑜𝑢𝑡: Precession cone angles
𝑉𝐹𝑀𝑅 = 𝜂𝐼𝑠1
2(𝜑𝑖𝑛
2 + 𝜑𝑜𝑢𝑡2)
𝜏𝑠2𝐷
1
2 1 + 𝜔2𝜏𝑠2+
1
2 1 + 𝜔2𝜏𝑠2 − 1
𝐒(𝐭′)
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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
VN
LS
V (m
V)
T (K)
VF
MR (
arb
. u
.)
0
300
600
900
0
200
400
600
• Agreement with spin-valve data for both Co2FeSi and Co2MnSi
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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
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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 𝜏𝑠 is short.