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

References in corpus (1)

• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors

Cited by in corpus (7)

• Microscopic approach to current-driven domain wall dynamics
• Spin pumping by a field-driven domain wall
• Effective temperature and Gilbert damping of a current-driven localized spin
• Calculation of current-induced torque from spin continuity equation
• Domain walls in (Ga,Mn)As diluted magnetic semiconductor
• Non-equilibrium thermodynamic study of magnetization dynamics in the presence of spin-transfer torque
• Gilbert and Landau-Lifshitz damping in the presense of spin-torque