Non-equilibrium thermodynamic study of magnetization dynamics in the presence of spin-transfer torque

TL;DR

This paper develops a non-equilibrium thermodynamic framework to analyze magnetization dynamics under spin-transfer torque, revealing how relaxation time influences damping and switching behavior in magnetic multilayers.

Contribution

It introduces a thermodynamic model linking relaxation time to damping and torque ratios, providing new insights into magnetization reversal mechanisms.

Findings

The ratio of damping to non-adiabatic torque depends on the relaxation time.

Equal damping and torque coefficients occur when relaxation time is very short.

Switching time decreases as the relaxation time increases.

Abstract

The dynamics of magnetization in the presence of spin-transfer torque was studied. We derived the equation for the motion of magnetization in the presence of a spin current by using the local equilibrium assumption in non-equilibrium thermodynamics. We show that, in the resultant equation, the ratio of the Gilbert damping constant, $\alpha$, and the coefficient, $\beta$, of the current-induced torque, called non-adiabatic torque, depends on the relaxation time of the fluctuating field $\tau_{c}$. The equality $\alpha=\beta$ holds when $\tau_c$ is very short compared to the time scale of magnetization dynamics. We apply our theory to current-induced magnetization reversal in magnetic multilayers and show that the switching time is a decreasing function of $\tau_{c}$.