Direct Solution of the Landau-Lifshitz-Gilbert Equation for Micromagnetics

A mathematical framework is presented for solving the Landau-Lifshitz-Gilbert equation expressed in Cartesian components of magnetization according to the backward difference method without conflicting with the constraint of constant magnetization. Test calculation shows that the method allows the use of a large time step almost independent of spatial mesh size and damping constant. The derived program is used to calculate the magnetization structure of a crosstie wall in a Permalloy film yielding calculated structures which closely resemble the electron-holography image of an actual cross-tie wall. It is also used to investigate magnetization reversal mechanisms in fine ferromagnetic particles by pursuing time dependent changes in magnetization structures. The paper gives detailed descriptions of the reversal mechanisms which differ depending on the size of the particle.