Inertial dynamics and equilibrium correlation functions of magnetization at short times

TL;DR

This paper develops a method based on Taylor series expansion to analyze equilibrium correlation functions of magnetization in ferromagnetic nanoparticles with inertial dynamics, simplifying the analysis and providing analytical expressions.

Contribution

It introduces a Taylor series-based method to analyze correlation functions in inertial magnetization dynamics, deriving analytical coefficients and approximations.

Findings

Analytical expressions for correlation function coefficients are derived.

Finite series approximations effectively compute short-time correlation functions.

The method simplifies the analysis of inertial magnetization dynamics.

Abstract

The method of moments is developed and employed to analyze the equilibrium correlation functions of the magnetization of ferromagnetic nanoparticles in the case of inertial magnetization dynamics. The method is based on the Taylor series expansion of the correlation functions and the estimation of the expansion coefficients. This method significantly reduces the complexity of analysis of equilibrium correlation functions. Analytical expressions are derived for the first three coefficients for the longitudinal and transverse correlation functions for the uniaxial magnetocrystalline anisotropy of ferromagnetic nanoparticles with a longitudinal magnetic field. The limiting cases of very strong and negligibly weak external longitudinal fields are considered. The Gordon sum rule for inertial magnetization dynamics is discussed. In addition, we show that finite analytic series can be used as a simple and satisfactory approximation for the numerical calculation of correlation functions at short times.