Monte Carlo simulation on the magnetization rotation near magnetic morphotropic phase boundary

For several decades, morphotropic phase boundary (MPB) in ferroelectric materials has attracted constant interest due to its great enhancement of piezoelectric properties. However, such a MPB has been studied merely in ferroelectric system, not in ferromagnetic system. Recently, we reported the magnetic MPB in a ferromagnetic system of TbCo2-DyCo2 and correspondingly a larger magnetostriction (i.e. a piezoelectricity-like phenomenon in ferromagnets) occurs near MPB. Very surprisingly, such a MPB in TbCo2-DyCo2 system has been ever regarded as a spin reorientation transition (SRT) where the spontaneous magnetization (Ms) gradually rotates from <111> in TbCo2-rich phase to <001> of DyCo2-rich phase and vice versa. But, our experiment of synchrotron x-ray diffractometry demonstrates the MPB region is the coexistence of TbCo2 and DyCo2 phases and hence the Ms cannot rotate gradually from <111> to <001>1. Thus, the process of magnetization rotation near MPB in a ferromagnetic system of TbCo2-DyCo2 remains obscure due to a lack of in-situ observation of magnetic moment rotation. In the present work, by using a method of Monte Carlo simulation, we successfully reproduce the observed effects and furthermore clarify the magnetization rotation process near the magnetic MPB of TbCo2-DyCo2 systems. Namely, the direction of magnetization changes discontinuously from <111> to <001> near the MPB via the phase transition process from TbCo2-rich phase to DyCo2-rich phase. Our simulation provides an effective way to understand the origin of the magnetic MPB.