Statistical mechanics of nonuniform magnetization reversal

Thermally activated magnetization reversal in elongated particles is studied within a model that allows for spatially nonuniform magnetization configurations along the particle. An external field antiparallel to the existing magnetization is shown to given rise to an energy barrier which represents a spatially localized deviation from the initial uniform magnetization configuration. For sufficiently elongated particles, thermal fluctuations thus substantially lower the coercivity compared to the previous theories by N\'eel and Brown which assume a spatially uniform magnetization. The magnetization reversal rate is calculated using a functional Fokker-Planck description of the stochastic magnetization dynamics. Analytical results are obtained in the limits of small fields and fields close to the anisotropy field. In the former case the hard-axis anisotropy becomes effectively strong and the magnetization reversal rate is shown to reduce to the nucleation rate of kink-antikink pairs in the overdamped sine-Gordon model. The present theory therefore includes the nucleation theory of the double sine-Gordon chain as a special case.