Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation

TL;DR

This paper investigates how stochastic forces with finite correlation time affect spin wave dynamics in the Landau-Lifshitz-Gilbert equation, revealing conditions for damping, stability, and undamped spin waves.

Contribution

It introduces a detailed analysis of correlation effects in the stochastic LLG equation, including phase diagrams and conditions for undamped spin waves.

Findings

Spin-wave dispersion and damping are influenced by stochastic force strength and correlation time.

A phase diagram in the b1-D plane shows stability regions for damped spin waves.

Finite lifetime of magnons exists even without deterministic damping.

Abstract

We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of the magnetic moments is additionally subjected to an uniaxial anisotropy and is driven by a multiplicative coupled stochastic field with a finite correlation time $\tau$. The mean value for the spin wave components offers that the spin-wave dispersion relation and its damping is strongly influenced by the deterministic Gilbert damping parameter $\alpha$, the strength of the stochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlation function can be calculated in the low correlation time limit by deriving an evolution equation for the joint probability function. The stability analysis enables us to find the phase diagram within the $\alpha-D$ plane for different values of $\tau$ where damped spin wave solutions are stable. Even for zero deterministic Gilbert damping the magnons offer a finite lifetime. We detect a parameter range where the deterministic and the stochastic damping mechanism are able to compensate each other leading to undamped spin-waves. The onset is characterized by a critical value of the correlation time. An enhancement of $\tau$ leads to an increase of the oscillations of the correlation function.