Thermal fluctuation field for current-induced domain wall motion

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.

16 page, no figure

References in corpus (13)

• Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations
• Current-induced domain wall motion in a nanowire with perpendicular magnetic anisotropy
• Microscopic Calculation of Spin Torques in Disordered Ferromagnets
• Functional Keldysh Theory of Spin Torques
• Threshold Current of Domain Wall Motion under Extrinsic Pinning, $\beta$-Term and Non-Adiabaticity
• Thermally-Assisted Current-Driven Domain Wall Motion
• Spin torque and force due to current for general spin textures
• Adiabatic Domain Wall Motion and Landau-Lifshitz Damping
• Template nanowires for spintronics applications: nanomagnet microwave resonators functioning in zero applied magnetic field
• Experimental Test of Analytic Theory of Spin Torque Oscillator Dynamics
• Current-induced noise and damping in non-uniform ferromagnets
• Theory of Domain Wall Dynamics under Current
• Creep of current-driven domain-wall lines: intrinsic versus extrinsic pinning