Relaxation time and critical slowing down of a spin-torque oscillator

TL;DR

This study investigates the relaxation dynamics of spin-torque oscillators, revealing exponential relaxation away from critical points and critical slowing down near them, with implications for their stability and response times.

Contribution

It provides a theoretical analysis of relaxation times and critical slowing down in spin-torque oscillators using analytical and numerical methods, extending to various oscillator types.

Findings

Relaxation to self-oscillation states occurs exponentially within nanoseconds.

Relaxation rate is proportional to the current.

Critical slowing down causes relaxation times to extend to hundreds of nanoseconds near critical points.

Abstract

The relaxation phenomena of spin-torque oscillators consisting of nanostructured ferromagnets are interesting research targets in magnetism. A theoretical study on the relaxation time of a spin-torque oscillator from one self-oscillation state to another is investigated. By solving the Landau-Lifshitz-Gilbert equation both analytically and numerically, it is shown that the oscillator relaxes to the self-oscillation state exponentially within a few nanoseconds, except when magnetization is close to a critical point. The relaxation rate, which is an inverse of relaxation time, is proportional to the current. On the other hand, a critical slowing down appears near the critical point, where relaxation is inversely proportional to time, and the relaxation time becomes on the order of hundreds of nanoseconds. These conclusions are primarily obtained for a spin-torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer, and are further developed for application to arbitrary types of spin-torque oscillators.