Microscopic theory of spin transport K. Hosono, A. Takeuchi, Y. Takezoe, N. Nakabayashi Gen Tatara...

Microscopic theory of spin transport

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

Tokyo Metropolitan University

Spin current

E, T

S

FerromagnetSpin Seebeck

E

Spin-orbit

js

Spin Hall Spin pumping

s js

Spin diffusion

Uchida 08

Hirsch 99Murakami 03

Silsbee 79Tserkovnyak 02

Son 87Valet 93

Spin current

E, T

S

FerromagnetSpin Seebeck

E

Spin-orbit

js

Spin Hall Spin pumping

s js

Spin diffusion

Uchida 08

Hirsch 99Murakami 03

Silsbee 79Tserkovnyak 02

Son 87Valet 93

Pure spin current

Spin current : Questions

•These spin currents behave the same?•Thermally and electrically induced

•Local and diffusive

•What is s ? As function of applied field•Spin relaxation torque ?

•Thermally induced spin currents

•Discrete model (ferromagnetic metal)

•Electron hopping

•Local equilibriumTn temperature n chemical potentialnn magnetization

•Takezoe et al.

•Uniform magnetization •Charge current

•Driving force

•Spin current

,T

•Continuum limit

, T/T << 1/d•Charge current

•Spin current

S=

Aschcroft Mermin

•Non uniform magnetization •Gauge fieldAnm

•Spin current

js,i= b(nin) + (in) [c2T+c’ E]equilibrium driven

+ n(EiiT) homogeneous

T=EeffFor spin current

Spin current : Questions

•These spin currents behave the same?•Thermally and electrically induced

•Local and diffusive

•What is s ? As function of applied field•Spin relaxation torque ?

The same

•Spin pumping + Inverse spin Hall

•Local and diffusive spin current

Spin pumping effect

•Spin dynamics

Silsbee 79Tserkovnyak 02

•Silsbee 79

s js

Spin precession Spin accumulation Diffusive spin current

•Ferro-Normal junction

Boltzmann equation

•Tserkovnyak 02

Spin precession Spin current

•Spin continuity equation

Spin current

Detection of spin current

j js

B E, j

…?Spin-orbit •Hirsche 99

•Saitoh, App. Phys. Lett. 06 •Inverse spin Hall effect

Analogy with Ampere’s law

jB

Magnetization dynamics

Spin currentjs

Charge currentj or E

Spin-orbit

Seems O.K. phenomenologically

•Saitoh, App. Phys. Lett. 06 Inverse spin Hall effect

Spin pumping

•Spin current transmission through FN interface

•sd exchange interaction

Spin pumping•Takeuchi Hosono GT, PRB2010

• weak sd interaction perturvation

• disordered metal vertex correction

Spin pumping

•Spin current

Electron diffusion

Spin accumulation due to spin dynamics

s

•Takeuchi Hosono GT, PRB2010

Without spin-orbit

Spin pumping

(as interface effect (within mean free path))

•Spin current

No effective field

s

O(q0) O(q0)

•Charge current (general)

•o(q1) contribution may exist

•Takeuchi Hosono GT, PRB2010

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

•Charge current •Impurity spin-orbit interaction

•Hosono Takeuchi GT, JPSJ 2010•Takeuchi Hosono GT, PRB 2010

Small contribution to js

O(q) Dominant contribution

Charge accumulation by spin pumping

Inverse spin Hall

Spin pumping + Inverse spin Hall

•Impurity spin-orbit

•Hosono Takeuchi GT, JPSJ 2010•Takeuchi Hosono GT, PRB 2010

Inverse spin Hall (Saitoh 06)

Large diffusive current

Not useful ?Experiment ?

Spin pumping + Inverse spin Hall

•Impurity spin-orbit•Rashba spin-orbit

•Strong Rashba at interface

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

•Depends much on the spin-orbit interaction

Large inverse spin Hall current

Spin currents: Questions

•These spin currents behave the same?•Thermally and electrically induced

•Local and diffusive

•What is s ? As function of applied field•Spin relaxation torque ?

The sameDifferent in spin-charge conversion

Spin chemical potential ?

Son 87, Valet&Fert 93

•Calculated from vertex correction to js

•Applied electric field

•Nakabayashi, cond-mat 2010

Represents spin accumulation

Linear response theory

Spin chemical potential ?

•Arises from discontinuity

F N

E

e-r/ls

s

ls

•Agrees with phenomenology•Spin injection

•Nakabayashi, cond-mat 2010

No spin injectionSpin injection

Spin chemical potential ?

•Spin injection

•Nakabayashi, cond-mat 2010

Spin relaxation torque?

•Spin continuity equation

•Electrically and thermally induced

Arises from discontinuity

T=EeffFor spin relaxation

•Nakabayashi, cond-mat 2010

Summary

•Direct and diffusive spin currents

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

•Thermally and electrically induced spin currents

Spin current, spin relxation

Inverse spin Hall effect

Equivalent

Different roles

T=Eeff

•Spin chemical potential•Spin relaxation torque

Arises from E, 2T

Spin pumping and Inverse spin Hall effects

-Microscopic study-

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

Tokyo Metropolitan University

Tokyo

Mt. Fuji富士山

Narita

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