Accuracy of the Backward-Difference Solution of the Landau–Lifshitz–Gilbert Equation

概要

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The reason for the low time-step accuracy of the previously developed approximate backward-difference solution of the Landau–Lifshitz–Gilbert (LLG) equation was found, and improved methods were developed. The improvement was carried out in two steps: correction of the expansion coefficients for the first-order backward-difference treatment of magnetization, and extension of the corrected scheme to a strict Crank–Nicolson scheme based on Newton's iteration. The time-step dependence of the velocity of a Bloch wall in planar- and perpendicular-magnetization films and the switching time of a fine iron–oxide particle were calculated to examine the time-step accuracy of the derived programs. The time-step dependence decreased considerably in the solutions obtained by the corrected program except for the Bloch wall motion in a perpendicular-magnetization film. However, it was removed almost entirely in the solutions obtained by the Crank–Nicolson method in which Newton's iteration was repeated twice per time step.
Published by the Japan Society of Applied Physics through the Institute of Pure and Applied Physicsの論文
2003-03-15