Comparison of magnetostatic field calculation methods on two-dimensional square grids as applied to a micromagnetic standard problem

Magnetization reversal modes and coercivities were calculated for a magnetic particle with thickness : width : length aspect ratios 0.1 : 1 : 5 as a function of the reduced particle width d/lex, where d is the particle width and lex is the intrinsic magnetostatic exchange length. With only exchange energy and magnetostatic energy included, the particle corresponds to μMAG standard problem No. 2. The problem is modeled with two-dimensional grids of three-dimensional spins, and the results are compared for two methods of calculating magnetostatic energies, the “constant magnetization” method and the “constant charge” method. For both magnetostatic computational methods, the coercivity decreases from Hc/Ms=0.06±0.003 to 0.014±0.003 over the range 3<d/lex<80, where the uncertainties reflect the field step size. Also over this interval, as d/lex increases, the magnetization exhibits three modes of reversal: nearly uniform rotation, transverse switching of end domains followed by propagation of head-to-head domain walls from the ends to the center of the particle, and nucleation and propagation of vortices accompanied by more complex domain structures.