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