Determination of precession and dissipation parameters in micromagnetism

The precession β and the dissipation parameter α of a ferromagnetic material can be considered microscopically space dependent. Their space distribution is difficult to obtain by direct measurements. In this article we consider an inverse problem, where we aim at recovering α and β from space measurements of the magnetization. The evolution of the magnetization in micromagnetism is governed by the Landau-Lifshitz (LL) equation. We first study the sensitivity of the LL equation. We derive the existence, uniqueness and stability results for the LL equation and the corresponding sensitivity equations. On the basis of the results we analyze the inverse problem. We employ the energy method and we minimize the underlying cost functional by means of the steepest descent method. We derive a convergence result for the proposed algorithm. The presented numerical examples support the theoretical results.