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Microscopic theory of spin transport

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Microscopic theory of spin transport

K. Hosono, A. Takeuchi, Y. Takezoe, N. Nakabayashi

Gen Tatara

Tokyo Metropolitan University

Spin current

rs

js

E, T

js

E

S

Spin-orbit

Ferromagnet

Spin Seebeck

Spin Hall

Spin pumping

Spin diffusion

Hirsch 99

Murakami 03

Son 87

Valet 93

Silsbee 79

Tserkovnyak 02

Uchida 08

Spin current

rs

js

E, T

js

E

S

Spin-orbit

Ferromagnet

Spin Seebeck

Spin Hall

Spin pumping

Spin diffusion

Hirsch 99

Murakami 03

Son 87

Valet 93

Silsbee 79

Tserkovnyak 02

Uchida 08

Pure spin current

Spin current : Questions

- These spin currents behave the same?

- Thermally and electrically induced

- Local and diffusive

- What is ms ?

As function of applied field

- Spin relaxation torque ?

- Thermally induced spin currents

- Takezoe et al.

- Discrete model (ferromagnetic metal)

- Local equilibrium

Tn temperature

mn chemical potential

nn magnetization

- Electron hopping

- Uniform magnetization

- Charge current

- Spin current

- Driving force

m,T

- Continuum limit

m/m, T/T << 1/d

- Charge current

S= sT /sB

Aschcroft Mermin

- Spin current

- Non uniform magnetization

- Gauge field

Anm

- Spin current

js,i= b(nin) + (in) [c2T+c’ E]

equilibrium

driven

+ n(sBEi+sT iT)

homogeneous

T=Eeff

For spin current

Spin current : Questions

- These spin currents behave the same?

- Thermally and electrically induced

The same

- Local and diffusive

- What is ms ?

As function of applied field

- Spin relaxation torque ?

- Local and diffusive spin current

- Spin pumping + Inverse spin Hall

Spin pumping effect

Silsbee 79

Tserkovnyak 02

- Ferro-Normal junction

- Spin dynamics

Spin current

rs

- Silsbee 79

Boltzmann equation

Spin precession

js

Spin accumulation

Diffusive spin current

- Spin continuity equation

Spin precession

Spin current

- Tserkovnyak 02

Detection of spin current

- Inverse spin Hall effect

- Saitoh, App. Phys. Lett. 06

Analogy with Ampere’s law

js

j

B

E, j

…?

jB

Spin-orbit

- Hirsche 99

Inverse spin Hall effect

- Saitoh, App. Phys. Lett. 06

Spin-orbit

Charge current

j or E

Spin current

js

Magnetization

dynamics

Spin pumping

Seems O.K. phenomenologically

Spin pumping

- Takeuchi Hosono GT, PRB2010

- Spin current transmission through FN interface

- sd exchange interaction

- weak sd interaction perturvation

- disordered metal vertex correction

Spin pumping

- Takeuchi Hosono GT, PRB2010

- Spin current

Without spin-orbit

rs

Spin accumulation due to spin dynamics

Electron diffusion

Spin pumping

- Takeuchi Hosono GT, PRB2010

- Spin current

rs

No effective field

- o(q1) contribution may exist

(as interface effect (within mean free path))

- Charge current (general)

O(q0)

O(q0)

Spin pumping + Inverse spin Hall

- Hosono Takeuchi GT, JPSJ 2010
- Takeuchi Hosono GT, PRB 2010

Spin-orbit interaction

- Charge current

Spin pumping + Inverse spin Hall

- Hosono Takeuchi GT, JPSJ 2010
- Takeuchi Hosono GT, PRB 2010

- Charge current

- Impurity spin-orbit interaction

Charge accumulation

by spin pumping

Inverse spin Hall

Small contribution to js

O(q)

Dominant contribution

Spin pumping + Inverse spin Hall

- Hosono Takeuchi GT, JPSJ 2010
- Takeuchi Hosono GT, PRB 2010

- Impurity spin-orbit

r

Large diffusive current

Not useful ?

Experiment ?

j

S

j

Inverse spin Hall (Saitoh 06)

Spin pumping + Inverse spin Hall

- Depends much on the spin-orbit interaction

- Impurity spin-orbit

- Rashba spin-orbit

Large inverse spin Hall current

- Strong Rashba at interface

Beff=1T for Pt/Co/AlO Miron 2010

Spin currents: Questions

- These spin currents behave the same?

- Thermally and electrically induced

The same

- Local and diffusive

Different in spin-charge conversion

- What is ms ?

As function of applied field

- Spin relaxation torque ?

Spin chemical potential ?

- Nakabayashi, cond-mat 2010

Represents spin accumulation

Son 87, Valet&Fert 93

- Calculated from vertex correction to js

- Applied electric field

Linear response theory

Spin chemical potential ?

- Nakabayashi, cond-mat 2010

c e-r/ls

- Arises from discontinuity

F N

- Agrees with phenomenology

ms

- Spin injection

E

ls

Spin chemical potential ?

- Nakabayashi, cond-mat 2010

- Spin injection

Spin injection

No spin injection

Spin relaxation torque?

- Nakabayashi, cond-mat 2010

- Spin continuity equation

- Electrically and thermally induced

+gT2T

Arises from discontinuity

T=Eeff

For spin relaxation

- Hosono Takeuchi GT, JPSJ 79(2010)
- Takeuchi Hosono GT, PRB (2010)
- Nakabayashi, arXiv:1002.0207
- Takezoe

Summary

- Thermally and electrically induced spin currents

Equivalent

Spin current, spin relxation

T=Eeff

- Direct and diffusive spin currents

Inverse spin Hall effect

Different roles

- Spin chemical potential

Arises from E,2T

- Spin relaxation torque

Spin pumping and

Inverse spin Hall effects

-Microscopic study-

Narita

Tokyo

K. Hosono, A. Takeuchi, Y. Takezoe, N. Nakabayashi

Gen Tatara

Mt. Fuji

富士山

Tokyo Metropolitan University

Post doc position : tatara@phys.metro-u.ac.jp