On dissipation mechanisms in micromagnetics

Within the framework of a dynamic version of micromagnetics [1,2], the space-time evolution of magnetization in a rigid, saturated ferromagnet is governed by the following equation: γ^-1 = ×( + + div ), where the interaction couple × and the couple stress are to be constitutively specified. Under constitutive assumptions for , , and the free energy ψ, that allow for equilibrium response and viscosity out of equilibrium and agree with the dissipation principle - ^. + ^. ∇ - ≥ 0, the above evolution equation yields a broad generalization of the standard Gilbert equation. In particular, while the standard Gilbert equation only incorporates relativistic dissipation, it is shown that the dissipation mechanisms compatible with the generalized Gilbert equation include exchange dissipation [2], dry-friction dissipation [3], and others. It is also shown that the additional term proposed in [4] to account for exchange dissipation, rather than having a genuine dissipative nature, modifies instead the nature of possible equilibria; and that such a modification is an automatic side effect when dry-friction dissipation is incorporated in the manner of [3]. Received 31 October 2000