spin transport in epitaxial heusler alloy/ iii-v...

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

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


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.

3


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


Outline







Co2MnSi – a potential half-metal

Co

Mn

Si

• Predicted to be a half-metal with a relatively large minority

gap

• Lattice-matched to GaAs


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]


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).


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

9


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)


Outline






7/31/2015 Heusler Workshop, Minneapolis 12

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


Lateral spin valve

13

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)


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):

14

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?


The full time of flight experiment: add drift

𝑔∗ = 0.79

• Solid curves are the analytic solution


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


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)

17

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’


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


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:


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


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


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)


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


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


Outline







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


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


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


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


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)


Outline







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


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


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.


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...


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


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′)


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


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

• 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.

spin transport in epitaxial heusler alloy/ iii-v...

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