Dynamical Simulation for Long-Time Relaxation From Metastable States: Quantitative Estimation of Coercive Field and Relaxation Time

Abstract

The bistability of spin-transition materials is the origin of their multifunctional properties. It causes hysteresis phenomena, i. e., relaxation from a metastable state, of the spin (electronic) state, magnetization, etc. The collapse of a strong metastable state is a long-time relaxation phenomenon. To study such nonequilibrium dynamical phenomenon, time evolution dynamics analyses are important. However, it is difficult to estimate long-time relaxation phenomena by studying time evolution dynamics simulations due to the limitation of the simulation time. Furthermore, because the relaxation occurs in a stochastic process, a wide distribution of the relaxation time has to be considered in the analysis of the relaxation. To overcome these difficulties, we recently developed two methods for the quantitative estimation of the relaxation time from a metastable magnetic state and of the coercive field. In the first method, the relaxation time and coercive field are estimated using the survival (unrelaxed) probability of the ensemble of systems at each field, which extends the limitation of the simulation time. In the second method, they are estimated from the field-dependent free energy barrier obtained from the survival probability under a sweeping field. These methods are applicable to the estimation of the relaxation time and coercive field of any magnetic particles. In this paper, staring with the Stoner–Wohlfarth model, the difference in the characteristic features of the magnetization reversal dynamics between zero and finite temperatures is discussed. Then, the methods of quantitative estimation of the coercive field and relaxation time are presented. The estimation of them using a neodymium permanent magnet grain was demonstrated with the two methods, and the methodological features and the validity of the estimation were discussed. The present study has a common theme to general metastable states including spin transitions.