Nonequilibrium effects in spin-torque oscillators

TL;DR

This paper investigates how nonequilibrium effects influence the behavior of spin-torque oscillators, revealing that spin relaxation mechanisms critically affect magnetization dynamics and the conditions for persistent precession.

Contribution

It introduces a nonequilibrium Keldysh framework to analyze spin relaxation effects, showing their impact on magnetization precession in spin-torque oscillators.

Findings

Spin relaxation enables persistent precessions without magnetic anisotropy.

Absence of spin relaxation prevents steady precession in isotropic systems.

Spin relaxation alters the power-voltage relationship in oscillators.

Abstract

One of the cornerstones of spintronics is the application of a spin-transfer torque to a nanomagnet, driving the magnetization of the nanomagnet into a steady-state precession and realizing a spin-torque oscillator. Such a steady state, sustained by a balance between driving and dissipation, could be a textbook example for a nonequilibrium situation. Nevertheless, most theoretical descriptions of spin-torque oscillators simply assume local equilibrium. Here, based on a simple model, we investigate the relevance of nonequilibrium effects in spin-torque oscillators. We use a nonequilibrium Keldysh description, which allows us to treat the effects of spin relaxation, and find that, in the absence of spin relaxation, persistent precessions of the magnetization are not allowed, if magnetic anisotropies are absent. However, introducing spin relaxation enables persistent precessions, where the strength of the spin relaxation has quantitative and qualitative effects on the magnetization dynamics. In the presence of magnetic anisotropy, we find that persistent precessions are allowed even if spin relaxation is absent, but spin relaxation causes a nonlinear relation between the oscillator power and the applied voltage bias. Finally, we consider an alternative spin relaxation mechanism and study the resulting magnetization precessions, highlighting the importance of understanding the exact nature of the relaxation in nanomagnets.