Extensions of the geometric solution of the two dimensional coherent magnetization rotation model

Abstract

The problem of the determination of the orientation of a (classical) magnetic moment submitted to an applied field in the presence of an arbitrary anisotropy energy function is investigated theoretically, in two dimensions. The framework is the geometrical method introduced by Slonczewski. After rederiving Slonczewski's results in general terms (i.e. not only in the uniaxial case), extensions and additional properties of the geometric solution are described. An orientation of the critical curve is proposed, a geometrical evaluation of the energy demonstrated, the determination of the anisotropy function by means of switching field angular measurements is discussed and finally, the critical curves are completely characterized. This geometrical solution has several applications. First, it visualizes directly the dependence of the particle switching field on field orientation. Second, it gives simple analytical formulae for the energy barrier close to switching. This quantity is relevant in the study of the reversal of single-domain particles.