Rate of magnetization reversal due to nucleation of soliton-antisoliton pairs at point-like defects

The rate of magnetization reversal due to the nucleation of soliton-antisoliton pairs at point-like defects is found for a uniaxial ferromagnet in an applied magnetic field. Point-like defects are considered as local variations in the magnetic anisotropy over a length scale smaller than the domain-wall width. A weak magnetic field applied along the easy axis causes the magnetization to become metastable, and the lowest activation barrier for reversal involves the nucleation of a soliton-antisoliton pair pinned to a point-like defect. Formulas are derived for the activation energy and field of reversal, and the reversal-rate prefactor is calculated using Langer's theory for the decay of a metastable state. As the applied field tends to zero, the lowest activation energy is found to be exactly half that of an unpinned soliton-antisoliton pair, and results from the formation of a spatially nonuniform metastable state when the defect strength become large. The smallest field of reversal is exactly half of the anisotropy field. The reversal-rate prefactor is found to increase with the number of point-like defects but decreases with increase in the defect strength due to a decrease in the activation entropy when translational symmetry is broken by the point-like defects, and soliton-antisoliton pairs become more strongly localized to the pinning sites.