Criterion for Uniform Micromagnetization

Current theories of "single-domain" ferromagnetic particles compare the free energy in a state of uniform magnetization with that in an arbitrarily chosen state of nonuniform magnetization. In this paper, the comparison is made between an initial uniform state and all neighboring states, uniform or nonuniform, as an initially large applied field decreases. The initial state becomes unstable when, for some choice of the varied magnetization, the second variation of the free energy changes from positive to negative. This instability criterion leads to a boundary-value problem; the relative magnitudes of certain eigenvalues determine whether the deviation from the initial state occurs by uniform rotation or by development of nonuniform magnetization. Formulas for the critical radius are found in simple cases; they agree, except for a numerical factor, with formulas of Kondorskii.