Microscopic study on the angular dependence of coercivity at zero and finite temperatures

The angular dependence of coercivity in permanent magnets is an unsettled issue in magnetism. We investigate the angular dependences of threshold fields for magnetization reversal in a single-grain and hard-soft-hard magnet model at zero and finite temperatures. We study thermal fluctuation effects on magnetization reversal, which is a stochastic process for barrier crossing at finite temperatures. We show that the mechanism of magnetization reversal in the single grain is different between zero and finite temperatures, although the normalized threshold field at finite temperatures exhibits a similar angular dependence to that of the Stoner-Wohlfarth field. We examine the angular dependences of nucleation and pinning fields for different magnetic parameters in the soft and hard magnet phases. We find that the angular dependences of the nucleation and pinning fields differ from that of the single grain, in which an exchange field resistant to reversal plays an important role, and that the thermal fluctuation reduces the threshold fields, varies the angular dependences, and makes the difference between nucleation and pinning fields smaller. We also analyze the effect of the grain alignment distribution on the threshold fields and find that the distribution changes the angular dependences of the threshold fields in different ways. We discuss the detailed features of these phenomena and the mechanisms behind them.