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Microscopic theory of spin transport
K. Hosono, A. Takeuchi, Y. Takezoe, N. Nakabayashi Gen Tatara Tokyo Metropolitan University
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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
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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
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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 ?
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Thermally induced spin currents
Takezoe et al. Discrete model (ferromagnetic metal) Local equilibrium Tn temperature mn chemical potential nn magnetization Electron hopping
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Uniform magnetization
Charge current Spin current Driving force m,T
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Continuum limit m/m, T/T << 1/d S= sT /sB Charge current
Aschcroft Mermin Spin current
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T=Eeff Non uniform magnetization Gauge field Anm Spin current
js,i= b(nin) + (in) [c2T+c’ E] equilibrium driven + n(sBEi+sT iT) homogeneous T=Eeff For spin current
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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 ?
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Local and diffusive spin current
Spin pumping + Inverse spin Hall
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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
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…? Detection of spin current Inverse spin Hall effect j js B E, j jB
Saitoh, App. Phys. Lett. 06 Analogy with Ampere’s law j js B E, j …? jB Spin-orbit Hirsche 99
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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
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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
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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
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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)
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Spin pumping + Inverse spin Hall
Hosono Takeuchi GT, JPSJ 2010 Takeuchi Hosono GT, PRB 2010 Spin-orbit interaction Charge current
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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
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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)
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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
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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 ?
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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
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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
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Spin chemical potential ?
Nakabayashi, cond-mat 2010 Spin injection Spin injection No spin injection
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+gT2T T=Eeff Spin relaxation torque? Spin continuity equation
Nakabayashi, cond-mat 2010 Spin continuity equation Electrically and thermally induced +gT2T Arises from discontinuity T=Eeff For spin relaxation
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Summary T=Eeff Thermally and electrically induced spin currents
Hosono Takeuchi GT, JPSJ 79(2010) Takeuchi Hosono GT, PRB (2010) Nakabayashi, arXiv: 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
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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 :
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