Stiffness analysis for the muMAG standard problem #4

V.D. Tsiantos, D. Suess, T. Schrefl and J. Fidler

JAP (2001), in press - Intermag/3M 2001 paper HF-10

In this paper solutions to micromagnetic standard problem #4, a 500 nm x 125 nm wide NiFe film, are presented. A 3D-finite element simulation based on the solution of the Gilbert equation has been used. The simulations show that two different reversal mechanisms occur for the two different applied fields. For a field at 170 degrees counterclockwise from the saturation direction there is a non-uniform rotation of magnetisation towards the direction of the applied field, with the magnetisation at the ends rotating faster than the magnetization in the centre. For a field at 190 degrees counterclockwise from the saturation direction the magnetisation at the ends and in the centre rotate in opposite directions leading to the formation of a 360 degree wall after 0.22&nbps;ns associated with a peak in the exchange energy. Moreover, the time for the magnetization component parallel to the long axis to cross the zero is 0.136 ns and 0.135 ns for field 1 and field 2, respectively. The stiffness of the problem has been investigated solving the system of ordinary differential equations with a non-stiff method (Adams) and a stiff one (backward differentiation formulae, BDF). For the measure of stiffness the ratio of the total number of time steps (nst) taken by the two solvers, that is nst(Adams)/nst(BDF), has been used. This ratio is 0.784 for field 1 and 0.593 for field 2, which means that the non-stiff method (Adams) uses larger time steps than the stiff method (BDF) and consequently the systems are not stiff. The average time step for the Adams method was 0.2 ps for both fields.

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