Energy barriers to magnetization reversal in perpendicularly magnetized thin film nanomagnets

Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The magnetization reversal rate depends primarily on the energy barrier the system needs to surmount in order for reversal to proceed. In this paper, we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially incoherent; that is, rather than all parts of the element switching simultaneously, reversal proceeds instead through a soliton-like domain wall sweeping through the system. We show that for square nanomagnetic elements, the energy barrier increases with element size up to a critical length scale, beyond which the energy barrier is constant. For circular elements, the energy barrier continues to increase indefinitely, albeit more slowly beyond a critical size. In both cases, the energy barriers are smaller than those expected for coherent magnetization reversal.