Quaternion-based algorithm for micromagnetics

Abstract

We describe an algorithm for the integration of the Landau-Lifshitz equation for the precession of a magnetic moment in the presence of dissipation. The algorithm describes the rotation of the magnetization vector in terms of rotation matrices (implemented using quaternions). Its major advantage is that it separates precessional and dissipational rotations, which allows the former to be computed analytically over long time intervals. This allows the use of a much longer time increment $\ensuremath{\Delta}t$ than is possible with conventional algorithms, especially for problems with low anisotropy and weak exchange coupling. The spirit of the method is similar to that of the exact solution of the single-particle problem by Kikuchi [J. Appl. Phys. 27, 1352 (1956)], who also separated the precessional and dissipational motions.