Calculation of Integral Coefficients for Correlation Magnetodynamics and Verification of the Theory

Abstract

There are several ways to describe magnetic systems. The most precise is the atomistic approach, which describes the evolution of magnetization of every single atom. For practical applications, a micromagnetic approach is used. In the micromagnetic approach, the equation describes the evolution of the distribution of an average magnetization in a continuous material.Because of the intense exchange interaction and temperature fluctuations, a correct transition from atomistic model to a micromagnetic model is a difficult problem in statistical physics. We have derived equations of correlation magnetodynamics (CMD) using the approximation of two-particles distribution function which accounts for correlations between closest magnetic moments. To estimate the level of two-particle correlations we introduce an extra equation, similar to the energy balance equation in the fluid dynamics.To develop new theory numerical modeling was used widely. CMD equations include several coefficients, which may be obtained using numerical integration of many-particles distribution functions in a wide range of parameters. To calculate such integrals we developed specific numerical methods and parallel codes.To verify CMD equations, a big amount of calculations in atomistic approach was processed. System of ordinary stochastic differential Landau-Lifshitz equations was solved with aid of Runge-Kutta fourth-order method with the special stochastic source of temperature fluctuations. New parallel program code was developed to model magnetic systems with various crystal lattices.The developed system of CMD equations shows results similar to the atomistic model in a wide range of parameters for ferromagnetic with different crystal lattices.