Thermostatted models for hysteresis in magnetic nanoparticles
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The modeling of hysteresis in magnetic nanoparticles is interesting theoretically as an example of a driven, non-equilibrium system, and also important practically due to the use of the particles in magnetic storage devices. Here two new models for hysteresis in nanoparticles are presented, in which blocks of atoms in the particle are represented by spherical rotors with attached magnetic moments, and where the effects of temperature are included using the techniques of Nos´e and Gaussian thermostatting. For both the Nos´e and Gaussian models, the equations of motion with thermostatting are developed and put into dimensionless form. The effectiveness of the thermostats is then verified by comparing the kinetic and potential energy distributions of the lattices with calculated thermal distributions, and by examining the behavior of the models at low temperature. The maximum vi of the heat capacity of the Nos´e model is determined, and interpreted as the blocking temperature of a superparamagnetic system. Hysteresis loops are then observed with the application of a changing magnetic field, and the changes in the loops with temperature and field frequency are discussed. It is found that the coercive field of both models is in reasonable agreement with the coercive field of a cobalt nanoparticle in a recent experiment by Wernsdorfer. Finally, the movement of both models to equilibrium in the process of magnetization reversal is found to agree approximately with the N´eel-Brown model for reversal in single domain particles, and a time scale for the models is established by comparison to the experiment.