Micromagnetic Solutions for Ferromagnetic Spheres

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Abstract
Computer solutions are described for micromagnetic equilibrium conditions (Brown's equations). Computations relate to spherical particles and are made possible by assuming a constraint on the magnetization. Magnetic moment vectors are constrained to rotate horizontally with their angle of rotation varying in a vertical direction. This produces micromagnetic solutions of domains separated by Bloch walls. The study demonstrates that domains exist as equilibrium solutions and that the magnetization in each domain is not constant. Although these solutions do not produce uniformly magnetized regions, domains are identifiable because of their separation by sharp magnetization reversals. These transitions can be identified unambiguously as Block walls. Solutions exist for particles of different size, and the energies for double and triple domain states are calculated. The results of the computer study show the existence of critical radii. All computer solutions are checked for stability with a special stability matrix computed for this purpose.