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 Pure spin current 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 S= sT /sB Charge current Aschcroft Mermin Spin current

T=Eeff 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 Spin dynamics js Ferro-Normal junction Silsbee 79 Tserkovnyak 02 Ferro-Normal junction Spin dynamics  Spin current Silsbee 79 Boltzmann equation rs 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 j js B E, j jB Saitoh, App. Phys. Lett. 06 Analogy with Ampere’s law j js B E, j …? jB Spin-orbit Hirsche 99

Inverse spin Hall effect Saitoh, App. Phys. Lett. 06 Spin-orbit Magnetization dynamics Spin current js Charge current j or E Spin pumping Seems O.K. phenomenologically

Spin pumping Spin current transmission through FN interface Takeuchi Hosono GT, PRB2010 Spin current transmission through FN interface sd exchange interaction weak sd interaction perturvation disordered metal vertex correction

Spin pumping Spin current rs Spin accumulation due to spin dynamics Takeuchi Hosono GT, PRB2010 Spin current Without spin-orbit rs Spin accumulation due to spin dynamics Electron diffusion

Spin pumping Spin current rs No effective field 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 S j r Large diffusive current Not useful ? Experiment ? 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

c  e-r/ls ls Spin chemical potential ? Arises from discontinuity F N 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

+gT2T T=Eeff Spin relaxation torque? Spin continuity equation Nakabayashi, cond-mat 2010 Spin continuity equation Electrically and thermally induced +gT2T Arises from discontinuity T=Eeff For spin relaxation

Summary T=Eeff Thermally and electrically induced spin currents 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 Different roles Inverse spin Hall effect Spin chemical potential Arises from E, 2T Spin relaxation torque

Inverse spin Hall effects -Microscopic study- 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