Selection of an optimal numerical scheme for simulation system of the Landau–Lifshitz equations considering temperature fluctuations

To create a variety of devices based on magnetic materials it is often necessary to conduct a large-scale simulation of different magnetic phenomena. The most appropriate is the so-called micromagnetic modeling based on a system of Landau–Lifshitz equations in which the evolution of the magnetic moments of individual particles is studied. Although this topic has been widely discussed, the question of taking into account the temperature fluctuations, which plays a key role in the description of phase transitions and the transition of the system from a state of unstable equilibrium during magnetization reversal, remains open. Accounting for temperature fluctuations imposes strong constraints on the intensity of the parasitic energy source generated by numerical scheme which in turn leads to substantial restrictions on the time step and reduce the count rate. In the paper two explicit numerical schemes have been proposed which are based on the analytic solution of the simplified problem of the evolution of magnetic moments of infinite sample with a body-centered cubic lattice in the spatially homogeneous case. New-constructed numerical schemes have been compared with classical Runge-Kutta methods for the initial conditions of the form of the Bloch domain wall, Neel domain wall and random initial conditions for a finite cylindrical sample. It is shown that one of the schemes is optimal in terms of maximizing the counting rate having fixed intensity of the source or drain of.