Phase-field simulations on the frequency-dependent evolution of nano-magnetic domains and hysteresis loops of ferromagnetic Terfenol-D

Abstract

Ferromagnetic materials are intelligent materials that exhibit large magnetic-field-induced strains and stress-induced magnetization upon application of magnetic fields and/or mechanical stress. Their hysteresis behavior also exhibits frequency dependence which is closely related to the evolution of nano magnetic domains. In this paper, a phase-field model of nano-domain evolution in two-dimensional ferromagnetic nanostructures is established based on the time-dependent Ginzburg-Landau kinetic theory. The model is applied to study the domain evolution and hysteresis loops of Terfenol-D at different frequencies. The obtained results are consistent with the trend of existing experiments. In addition, the effect of lattice size of the nano-structure on the hysteresis loops of Terfenol-D is also demonstrated. It shows that the larger the lattice area, the more there are nano vortices and magnetic energy loss. The effect of temperature on the spontaneous magnetization is also investigated. It is found that, as temperature increases, the stability of nano-domain walls weakens and the degree of vortices decreases. This phase-field simulation establishes the direct connection between the nano-scale domain phenomena and the macroscopic hysteresis loops. It clearly demonstrates that the nano-vortex structure is the main cause of energy loss, and that this phase-field method is an effective approach to uncover the underlying mechanisms of hysteresis behavior in ferromagnetic Terfenol-D.