Functional Keldysh Theory of Spin Torques

Abstract

We present a microscopic treatment of current-induced torques and thermal fluctuations in itinerant ferromagnets based on a functional formulation of the Keldysh formalism. We find that the nonequilibrium magnetization dynamics is governed by a stochastic Landau-Lifschitz-Gilbert equation with spin transfer torques. We calculate the Gilbert damping parameter $\alpha$ and the non-adiabatic spin transfer torque parameter $\beta$ for a model ferromagnet. We find that $\beta \ne \alpha$, in agreement with the results obtained using imaginary-time methods of Kohno, Tatara and Shibata [J. Phys. Soc. Japan 75, 113706 (2006)]. We comment on the relationship between $s-d$ and isotropic-Stoner toy models of ferromagnetism and more realistic density-functional-theory models, and on the implications of these relationships for predictions of the $\beta /\alpha$ ratio which plays a central role in domain wall motion. Only for a single-parabolic-band isotropic-Stoner model with an exchange splitting that is small compared to the Fermi energy does $\beta /\alpha$ approach one. In addition, our microscopic formalism incorporates naturally the fluctuations needed in a nonzero-temperature description of the magnetization. We find that to first order in the applied electric field, the usual form of thermal fluctuations via a phenomenological stochastic magnetic field holds.

14 pages, 3 figures

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• Hydrodynamic theory of coupled current and magnetization dynamics in spin-textured ferromagnets
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• Current driven quantum criticality in itinerant electron ferromagnets
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• Theory of spin magnetohydrodynamics
• Effective temperature and Gilbert damping of a current-driven localized spin
• Calculation of current-induced torque from spin continuity equation
• Gilbert Damping in Conducting Ferromagnets I: Kohn-Sham Theory and Atomic-Scale Inhomogeneity
• Spin and charge transport induced by gauge fields in a ferromagnet
• Proposal of a robust measurement scheme for the non-adiabatic spin torque using the displacement of magnetic vortices
• Domain walls in (Ga,Mn)As diluted magnetic semiconductor
• A spin dynamics approach to solitonics
• Influence of magnetic viscosity on domain wall dynamics under spin-polarized currents
• Transient spin dynamics in a single-molecule magnet
• Stochastic dynamics of magnetization in a ferromagnetic nanoparticle out of equilibrium
• Current-induced non-adiabatic spin torques and domain wall motion with spin relaxation in a ferromagnetic metallic wire
• Multiscale approach to spin transport in magnetic multilayers
• Current-induced spin torques in III-V ferromagnetic semiconductors
• Intrinsic Spin Torque Without Spin-Orbit Coupling
• Microscopic calculation of thermally-induced spin-transfer torques
• Measurement of Gilbert damping parameters in nanoscale CPP-GMR spin-valves
• A generalized Stoner criterion and versatile spin ordering in two-dimensional spin-orbit coupled electron systems
• Spin transfer torques due to the bulk states of topological insulators
• Microscopic theory of magnon-drag electron flow in ferromagnetic metals
• Quantum Brownian Motion of a Magnetic Skyrmion
• Numerical Computation of Spin-Transfer Torques for Antiferromagnetic Domain walls
• Anisotropy of spin-transfer torques and Gilbert damping induced by Rashba coupling
• The fractional Landau-Lifshitz-Gilbert equation
• Quantum Scattering Theory of Spin Transfer Torque, Spin Pumping and Fluctuations
• Non-equilibrium thermodynamic study of magnetization dynamics in the presence of spin-transfer torque
• The quantum-mechanical basis of an extended Landau-Lifshitz-Gilbert equation for a current-carrying ferromagnetic wire
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• Tensor damping in metallic magnetic multilayers
• AC- and DC-driven noise and I-V characteristics of magnetic nanostructures
• Spin-wave-induced spin torque in Rashba spin-orbit coupling system
• Spin torque due to diffusive spin current in magnetic texture
• Laser-induced torques in spin spirals
• Thermal fluctuation field for current-induced domain wall motion
• A microscopic model for current-induced switching of magnetization for half-metallic leads
• Possible charge analogues of spin transfer torques in bulk superconductors
• Alternating Current-induced Interfacial Spin-transfer Torque
• Quantum noise in the spin transfer torque effect
• Current driven defect unbinding transition in an XY ferromagnet
• Dynamically stable negative-energy states induced by spin-transfer torques
• Quantum Theory of Spin-Transfer and Spin-Pumping in Collinear Antiferromagnets and Ferrimagnets
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• Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics
• Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas
• Nonequilibrium interacting electrons in a ferromagnet