Effects of magnetic frequency and the coupled magnetic-mechanical loading on a ferromagnetic shape memory alloy

In the present work, the microstructure evolution and macro-response of a ferromagnetic shape memory alloy under stimuli of magnetic fields with different frequency and coupled magnetic-mechanical loading are investigated via a real-space phase field simulation. It is found that the coercive field is reduced from 0.724 to 0.423 with the magnetic frequency f decrease from 2.5 × 10-5 Hz to 0.833×10-5 Hz, wherein the concomitant domain wall motion and magnetization rotation are captured as well. Moreover, simulation results demonstrate that, under the coupled magnetic-mechanical loading, the coercive field of the magnetic hysteresis loop could be reduced by applying a compressive strain perpendicular to the magnetic field direction. The domain evolution is mainly divided into three types during the coupled magnetic-mechanical loading, namely (a) domain wall motion with the magnetization rotation, (b) pure magnetization rotation, and (c) 180. domain coordinated domain switching. To better understand the domain evolution, we propose an index S = |mavg 1 |+| mavg 2| , with |mavg 1| and |mavg 2| indicating the absolute value of the averaged magnetization component m1 and m2 over the whole studied system, to characterize the magnetization change during the microstructure evolution.