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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 : [email protected]