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Microscopic theory of spin transport

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

  2. 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

  3. 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

  4. 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 ?

  5. Thermally induced spin currents • Takezoe et al. • Discrete model (ferromagnetic metal) • Local equilibrium Tn temperature mn chemical potential nn magnetization • Electron hopping

  6. Uniform magnetization • Charge current • Spin current • Driving force m,T

  7. Continuum limit m/m, T/T << 1/d • Charge current S= sT /sB Aschcroft Mermin • Spin current

  8. 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

  9. 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 ?

  10. Local and diffusive spin current • Spin pumping + Inverse spin Hall

  11. 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

  12. 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

  13. 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

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

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

  16. 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)

  17. Spin pumping + Inverse spin Hall • Hosono Takeuchi GT, JPSJ 2010 • Takeuchi Hosono GT, PRB 2010 Spin-orbit interaction • Charge current

  18. 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

  19. 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)

  20. 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

  21. 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 ?

  22. 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

  23. Spin chemical potential ? • Nakabayashi, cond-mat 2010 c e-r/ls • Arises from discontinuity F N • Agrees with phenomenology ms • Spin injection E ls

  24. Spin chemical potential ? • Nakabayashi, cond-mat 2010 • Spin injection Spin injection No spin injection

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

  26. 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

  27. 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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