Electrochemical Potential

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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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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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







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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


7/407/31/2015 Heusler Workshop, Minneapolis

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]



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).



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



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)



Outline







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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



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



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’



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

↑(↓) = ±↑ ↓



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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7/31/2015 Heusler Workshop, Minneapolis 21

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






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







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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 .

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