Precession Axis Modification to a Semi-analytical Landau-Lifshitz Solution Technique

A recent article [1] presents a semi-analytical method to solve the Landau-Lifshitz (LL) equation. Spin motion is computed analytically as precession about the effective field H, where H is assumed fixed over the time step. However, the exchange field dominates at short range and varies at the time scale of neighbor spin precessions, undermining the fixed field assumption. We present an axis corrected version of this algorithm. We add a scalar multiple of m to H (preserving torque and hence the LL solution) to produce a more stable precession axis parallel to the cross product of the torques m × H at two closely spaced time steps. We build a predictor-corrector solver on this foundation. The second order convergence of the solver enables calculation of adjustable time steps to meet a desired error magnitude.