Thermally Activated Transitions Between Micromagnetic States

We review work by the authors on thermal activation in nanoscopic magnetic systems. These systems present unique difficulties in analyzing noise-induced escape over a barrier, including the presence of nonlocal interactions, nongradient terms in the energy functional, and dynamical textures as initial or saddle states. We begin with a discussion of magnetic reversal between single-domain configurations of the magnetization. Here the transition (saddle) state can be either a single-domain or a spatially varying (instanton-like) configuration, and depending on the system parameters can exhibit either Arrhenius or non-Arrhenius reversal rates. We then turn to a discussion of transitions between magnetic textures, which can be either static and topologically protected or dynamic and not topologically protected. An example of the latter case is the droplet soliton, a rotating nontopologically-protected configuration, which we find can occur either as a metastable or transition state in a nanoscopic magnetic system. After discussing various issues in calculating transition rates, we present results for the activation barriers for creation and annihilation of these magnetic textures. We conclude with a discussion of activated transitions between topologically protected skyrmion textures and other configurations, on which work is ongoing.