S. Maekawa(IMR, Tohoku University)

Spin Current vs. Charge Current Spin Current vs. Charge Current

in Magnetic Nanostructuresin Magnetic Nanostructures

Contents:(i) Spin current,(ii) Spin accumulation,(iii) Spin Hall effect,(iv) Spin current pumping.

(Charge current Spin Current)

YKIS2007 (November 20 ,2007)

FM current

normal metalsuperconductorhybrid device

charge current : cJ J J↑ ↓= +

sJ J J↑ ↓= −spin current :

Contents:(i) Spin accumulation,(ii) Spin current,(iii) Spin Hall effect,(iv) Spin current pumping.

What is a ferromagnet ?

Cu Fe,Co,Ni La1-xSrxMnO3CrO2

( )μ ↓ ↑= −BM N N

N N↑ ↓= N N↓ ↑> 0N N↓ ↑> =Electron number :

Atomic energy : i iε ε↑ ↓= i iε ε↓ ↑< i iε ε↓ ↑=

E

E E

EF

(half-metal)

Electric current :charge current :

cJ J J↑ ↓= + sJ J J↑ ↓= −spin current :J J↑ ↓≠ Magnetization :

Spin diffusion length（λN）

10 nm ～ 1 μm

λN

Ferromagnet MetalSemicond.Supercond.

λN

Spin Electronics Device !

Device size <

(Charge current usual electronics)

Tunnel magnetoresistance (TMR)

Parallel alignment Antiparallel alignment

(S. Maekawa and U. Gafvert: IEEE Mag. 18, 707 (1982))

Spin accumulation :

( ):

↑↓

Antiparallel alignment

( ):

↑↑

Parallel alignment

Antiparallel alignment

“Spin accumulation” “Spin current”

Parallel alignment

Spin accumulation in High-Tc superconductors :

(Z.W. Dong et al.: APL 71, 1718 (1997))

Critical current

Injection current

injI

injI

I I

V

Zeeman Effect Spin Accumulation

BHμ

BHμ

δμδμ

02 PeVΔ ≈

Magnetization( )BM n nμ ↑ ↓= −

Pair breaking :02 BHμΔ ≈

For Al,0 ~ 0.4 meVAlΔ

-3~ (10 V) ( ~ 1)bV O P~ (1 T)H O

Al AlB S(0) 4 (1Oe)M N PeV B M Oμ π→ =: :

For YBCO,0 0100 YBCO AlΔ Δ:

-1(10 V)bV O:

2(10 T)H O:

4(10 Oe)YBCOSB O:

2(0) 10 (0)YBCO AlN N⎡ ⎤⎣ ⎦:

Spin accumulation >> Zeeman effect

theory

Au

(S. Takahashi, H. Imamura, S.M., PRL. 82, 3911 (1999)

Spin accumulation signal:Spin accumulation signal:

P AP( ) /SR V V I= −

PP

APAP

650 nm10 mS

LR

== Ω

Non-Local Spin Accumulation Device, F. J. Jedema et. al., Nature 416, 713 (2002)

PP

Co-Al-Co

APAP

( )N xδμ μ μ↓↑

= −

spin

j j jj j j

↑ ↓

↑ ↓

= +⎧⎨ = −⎩

Spin accumulation:

Charge and Spin currents:

Non-local geometryfor measurement

NP AP

2 2 2 /S

V V eRI I

δμ−= =

2PeV+

AP2eV−

Spin accumulation signal:

xL0

x

Top view

Side view

F1 F2N

( )

( ) ( )

2

22s

0

1

σ μ σ μ

μ μ μ μλ

↑ ↑ ↓ ↓

↑ ↓ ↑ ↓

∇ + =

∇ − = −

Basic equations for Electro-chemical potential:

Charge conservation

Spin diffusion

, e e

σ σμ μ↑ ↓

↑ ↑ ↓ ↓= − ∇ = − ∇j j

Spin-dependent currents:

F FF

F F

p σ σσ σ

↓↑

↓↑

−=

+

N N N

F F F F F

12

,

( )

N :

F :

σ σ σ

σ σ σ σ σ

↓↑

↓ ↓↑ ↑

= =

≠ = +

s : spin diffusion lengthλ

8 μΩcm5 nm*Py14 μΩcm

6 μΩcm1.4 μΩcm

ρ

50 nm*

650 nm1000 nm

λS

Co

CuAl

( ) s/ exp xμ μ λ↑ ↓− ∝ −

(Py: Ni80Fe20)

Jedema et al.

←

←

Τ = 4.2Κ

*Bass and Pratt

Bulk spin polarizationof F:

F 50 70%*p = :

1 2

N

N N N

600 , 1200 , 100 A6 cm

250nm 50nm

R R I

A w d

μρ μ

= Ω = Ω =⎧⎪ = Ω⎨⎪ = = ×⎩

Co-Al-Co tunnel device

P AP N/2T N L

SV V

IR P R e λ−−

= =

N 650nmλ =

N 350nmλ =

N NN

N

3 RA

ρ λ= = Ω

NN

/N

12

( ) xx e eP R I λδμ −= ⋅

SR

L

15 eV

μ14 2 43

N Fitting parameter: , P λ

T 0.1P =

(F. J. Jedema et al., Nature 416, 713 (2002)S. Takahashi and S.M., PRB 67, 052409 (2003))

Hall effect

current

magneticfield

Spin Hall effect

Spin current ( )J J↑ ↓−

current

(Anomalous Hall effect)

J↓

J↑

spin current

spin current:

current:IInjection current:

J J↑ ↓−

J J↑ ↓+

Ferromagnet

Normal metal / semiconductor

Spin Hall effect ：

Intrinsic Spin Hall Effect:Spin-Orbit Coupling in the Band Structure

Ballistic transport

Extrinsic Spin Hall Effect:Spin-Orbit Scattering of Electrons

Diffusive transport

Experiments:Valenzuela & Tinkham, Nature 442, 176 (2006).Saitoh et al., APL 88, 182509 (2006)Kimura et al., PRL 98,156601(2007),

metallic systems

Anomalous Hall effect in ferromagnets

side jump

Boltzman equation for AHE (Anomalous Hall Effect):

Hamiltonian:† †

, , k k k kk k k

k k ka a U a aσσ

σ σ σ σσ σ σ

ξ ′′ ′ ′

′ ′

= +∑ ∑ ∑H

( ) ( )ˆ ˆimp so ji k k r

kkj

U u i k k eσσσσ σσδ λ σ ′− ⋅′

′ ′ ′⎡ ⎤′= + ⋅ ×⎣ ⎦∑

Impurity potential:

Current density with spin σ :

spin-orbit scatt. 1 4 4 2 4 43

†ˆ k kk

kkj e a amσ σ σ

σ

σω⎡ ⎤= +⎢ ⎥⎣ ⎦∑ h

Anomalous velocity: ˆF imp

sok kk σσσ λ

ω τ σ⎡ ⎤= ×⎣ ⎦

Fermi distribution function:

0 0 0imp SS imp k k k k k

kf f v f fmσ σ σ σσ στ α τ σ⎡ ⎤= − ⋅∇ + × ⋅∇⎢ ⎥⎣ ⎦h

(2 ) (0)SS impso/3 N uα π λ=

skew scattering

q,x xN SH

s,y ySH N

J EJ eN

/δμ

σ σσ σ

−⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥ −∇⎣ ⎦⎣ ⎦ ⎣ ⎦

Spin Hall conductivity:

s,x xN SH

q,y ySH N

J eJ E

N/

δμσ σσ σ

−∇−⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦

SH SH SHSS SJ σ σ σ= +

( )N

/q N

s N

j Ej e

σσ δμ

=⎧⎨ = − ∇⎩

spin // x[ ]⎧ = + ×⎪⎨ ⎡ ⎤= + ×⎪ ⎣ ⎦⎩

q q H

s s H q

sJ j x j

J j x j

α

α

σ αyq y

zj E x jN H spin⎡ ⎤= + ×⎣ ⎦

x

σ δμ αNzs

IJ xe z AN H

Pt

⎡ ⎤∂= − + ×⎢ ⎥∂ ⎣ ⎦

z

y

Spin current

Charge current

Charge current

Spin current

Room Temperature Spin Hall EffectT. Kimura (ISSP, RIKEN), Y. Otani (ISSP, RIKEN), T. Sato (ISSP)S. Takahashi (IMR, CREST), S. Maekawa (IMR, CREST)

( Phys. Rev. Lett. 98, 156601(2007))

Nonlocal Spin Hall device

``Conversion between charge-current and spin-current’’

スピン流

スピン流電荷蓄積

Py

Pt

Cu

IV

[ ]H =S Q

VRI

Δ→

Spin-current induced Spin Hall effect

PyPt

Cu

1 2 3

(Kimura et al.)

-200 -100 0 100 200

-0.1

-0.05

0

0.05

0.1

ΔΩ

V/I

C (

m)

ΔΩ

V/I

C (

m)

VC

IeM

H

ΔRSHE

a

b

-0.03

0

0.03

0.06

μ0H (mT)

RT

77 K

Nonlocal Spin Hall resistivity

スピン蓄積

Py

Pt

Cu

電流

IV

[ ] →Q S

VRISH = Δ

Charge-current induced Spin Hall effect

スピン蓄積

1 2 3

ΔΩ

V/I

S (

m)

ΔΩ

V/I

S (

m)

VS

IeM

H

a

b

-0.06

-0.03

0

0.03

0.06

-200 -100 0 100 200-0.2

-0.1

0

0.1

0.2

μ0H (mT)

RT

77 K

Nonlocal Spin Hall resistivity

IV I

V

[ ] →Q S

VRISH = Δ

Onsager Reciprocal Relation!!

[ ] →S Q

VRISH = Δ

Charge-current induced SHESpin-current induced SHE

Charge-current Spin-current

Valenzuela & Tinkham:

1.8 ×104

τsf / τ

Alb2 0.011λso

4.15 ×10−10 Ωcm2

ρNλN

5.88 μΩcm705 nm

ρNλN

◎ Side jump analysis:

kF=1. 5 ×108 cm−1 (Au)

41 10

0.011

SJSJ so

F imp

so

SHH

N k lσ λσ

λ

α −⎧= = ×⎪

⎨⎪⎩

:

:

( )110F imp imp so k l l λ: =

Spin-current induced Spin Hall effect:

(Nature 442, 176 (2006))

Spin pumping:

[ ] ∂⎛ ⎞∝ ×⎜ ⎟∂⎝ ⎠S j

SI St

α

α

x

z

IS

S

H

Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect E. Saitoh et al., APL88 (2006)

0.21502.2 ×10−11 Ωcm22.45 μΩcm90 nmAue

0.0111800041.5 ×10−11 Ωcm25.88 μΩcm705 nmAlc

0.074756.8 ×10−11 Ωcm23.50 μΩcm195 nmAgd

0.031230015.0 ×10−11 Ωcm21.00 μΩcm1500 nmCub

0.26331.8 ×10−11 Ωcm212.8 μΩcm14 nmPtf

2100

τsf / τ

0.03314.3 ×10−11 Ωcm21.43 μΩcm1000 nmCua

λsoρNλNρNλN

14 K2F N N

soRk

λρ λ

⎛ ⎞≈ ⎜ ⎟

⎝ ⎠24

9sfso

τ λτ

=

kF=1.5 ×108 cm−1T=4.2K

2

N sf

N

Dm

ne

λ τ

ρτ

⎫=⎪⎬

= ⎪⎭25.8K

2/ kR h e= ≈ Ω

2 2

32

sfN N

F

hk e

=τπρ λτ

a) Jedema et. al., b) Kimura et. al.(77K), c) Valenzuela&Tinkham, d) Godfrey&Johnsone) Seki et al..(RT), f) Kurt et. al.

Spin-orbit coupling : λso

Spin-orbit interaction strength in Pt and Auis about 30 times larger than that in Al.

( ) 30,( )

H

H

Pt Al

αα

=( ) 30,( )

so

so

PtAl

λλ

=

Pt, Au: Strong spin-orbit materialSpin absorberSpin generator

Takahashi, MaekawaPRL88, 116601 (2002)

S. Maekawa(IMR, Tohoku University)

Spin Current vs. Charge Current Spin Current vs. Charge Current

in Magnetic Nanostructuresin Magnetic Nanostructures

Contents:(i) Spin current,(ii) Spin accumulation,(iii) Spin Hall effect,(iv) Spin current pumping.

(Charge current Spin Current)

YKIS2007 (November 20 ,2007)