Magnetic-field driven domain wall evolution in rhombohedral magnetostrictive single crystals: a phase-field simulation

Single crystal of Tb_0.3Dy_0.7 Fe₂ (Terfenol-D) with a composition close to the pre-transitional rhombohedral side of the ferromagnetic morphotropic phase boundary has demonstrated remarkable magnetostrictive properties, stimulating intensive research interest in the field of magneto-mechanical transducers and actuators. The enhanced magnetoelastic response of (Tb-Dy)Fe₂ single crystals has been extensively linked to the structural phase transition and magnetic domain evolution. This research utilized the micromagnetic microelastic phase-field technique to examine the evolution of domain walls in rhombohedral ferromagnetic single crystals of (Tb-Dy)Fe₂, which is essential for understanding the magnetostriction “jump” effect. The study involved simulating the creation and development of domains and domain boundaries under a periodic boundary condition that allows for non-zero strain. It was found that the two typical distinct types of domain walls (i.e., 71° and 109°) exhibited disparate responses to the applied magnetic fields. At magnetic field magnitudes below the coercive field, a domain wall broadening mechanism was detected within the 71° domain wall. However, upon surpassing the coercive field, a process of homogeneous magnetization switching ensued, devoid of evident displacement of the 71° domain walls. The magnetization switching effectively elucidated the magnetostriction “jump” effect of the rhombohedral single crystals. The act of sweeping the 109° domain walls resulted in the occurrence of heterogeneous magnetization switching. This study elucidates the evolutionary mechanism of two typical rhombohedral domain walls in response to applied magnetic fields, potentially offering valuable insights into the future design of excellent magnetostrictive materials through domain engineering.