Inertial and bias effects in magnetization relaxation in uniaxial nanomagnets with thermal noise
Phys. Rev. B 113, 184439 – Published 11 May, 2026
DOI: https://doi.org/10.1103/jg1c-vgfb
Abstract
Inertial effects in the stochastic motion of the magnetization of nanomagnets in a uniaxial potential biased by an external field are treated via the corresponding Fokker-Planck equation. This equation can be transformed to a simpler partial differential equation by applying an integral transformation and change of variables. The longitudinal magnetization relaxation function, obtained by solving this equation, simultaneously describes various relaxation modes, namely, a slow interwell mode associated with the reorientation of the magnetization vector through potential barriers, a set of almost degenerate intrawell modes arising due to the motion of the magnetization inside potential wells, as well as a fast relaxation mode caused by the inertia (magnetization nutation). These relaxation modes clearly manifest as three separate bands in the spectrum of the longitudinal component of the magnetic susceptibility tensor. The turnover formula of Mel'nikov and Meshkov is shown to provide a good approximation to the longest relaxation time of the magnetization. Moreover, for small values of the bias field the integral relaxation time has Arrhenius behavior (exponential increase with increasing barrier height), which disappears when the bias field exceeds a critical value.
