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. r s. j s. E, T. j s. E. S. Spin-orbit. Ferromagnet Spin Seebeck. Spin Hall. Spin pumping. Spin diffusion. Hirsch 99 Murakami 03.

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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(nin) + (in) [c2T+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

…?

jB

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

+gT2T

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


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