Thermal fluctuation field for current-induced domain wall motion

TL;DR

This paper investigates how thermal fluctuations influence current-induced domain wall motion in magnetic nanowires, using a quantum mechanical approach to extend the fluctuation-dissipation theorem to non-equilibrium conditions.

Contribution

It introduces a quantum effective Hamiltonian for domain wall motion under current, generalizing the Caldeira-Leggett model, and clarifies the conditions under which the fluctuation-dissipation theorem applies.

Findings

Thermal noise follows the fluctuation-dissipation theorem at low current densities.

The Gilbert damping alpha relates to coupling with the thermal environment.

The nonadiabaticity parameter beta relates to spin current coupling with thermal fluctuations.

Abstract

Current-induced domain wall motion in magnetic nanowires is affected by thermal fluctuation. In order to account for this effect, the Landau-Lifshitz-Gilbert equation includes a thermal fluctuation field and literature often utilizes the fluctuation-dissipation theorem to characterize statistical properties of the thermal fluctuation field. However, the theorem is not applicable to the system under finite current since it is not in equilibrium. To examine the effect of finite current on the thermal fluctuation, we adopt the influence functional formalism developed by Feynman and Vernon, which is known to be a useful tool to analyze effects of dissipation and thermal fluctuation. For this purpose, we construct a quantum mechanical effective Hamiltonian describing current-induced domain wall motion by generalizing the Caldeira-Leggett description of quantum dissipation. We find that even for the current-induced domain wall motion, the statistical properties of the thermal noise is still described by the fluctuation-dissipation theorem if the current density is sufficiently lower than the intrinsic critical current density and thus the domain wall tilting angle is sufficiently lower than pi/4. The relation between our result and a recent result, which also addresses the thermal fluctuation, is discussed. We also find interesting physical meanings of the Gilbert damping alpha and the nonadiabaticy parameter beta; while alpha characterizes the coupling strength between the magnetization dynamics (the domain wall motion in this paper) and the thermal reservoir (or environment), beta characterizes the coupling strength between the spin current and the thermal reservoir.