Monte Carlo approach to phase transitions in ferroelectromagnets

Abstract

A Monte Carlo algorithm based on the hybrid Ising-DIFFOUR model is proposed to investigate the phase transition in ferroelectromagnetic lattice in which the ferroelectric order and antiferromagnetic order coexist below a certain temperature. The Ising spin moment and ferroelectric displacement and their susceptibilities as well, as a function of temperature for systems of different magnetoelectric couplings, are simulated and compared with the mean-field approach. The typical antiferromagnetic transition at Néel point and the ferroelectric transition at Curie point are observed at zero coupling. It is demonstrated that a weak ferromagnetic order can be activated by introducing the magnetoelectric coupling or applying external magnetic field, while the external electric field has little effect on the ferromagnetic ordering behavior.

Study of magnetoelectric coupling effect in the hexagonal ferroelectromagnet

“…3, in which the ME coupling coefficient g is given as 0.022, 0.025, 0.028. We find that the average polarization experiences an anomaly at T N , indicating the contribution of ME coupling, which qualitatively agrees with the results of former researches [12,16]. From the figure, we can find that, when ME coupling is stronger, T N becomes higher.…”

“…The spin configuration of the nearest-neighbor Mn ions forms the triangular lattice structure in the basal plane with the nearest-neighbor Mn spins rotate 120 from each other. Given that the hexagonal phase of RMnO 3 may be transformed in condition of a high temperature and pressure to the orthorhombic perovskite-type structure, the ME properties related with the external electric (or magnetic) fields have been studied by the model of A-type antiferromagnet with the FM intraplane interaction and the AFM interplane one [15,16]. However, for the case of a real situation, we would better take the triangular magnetic structure in the basal plane into account.…”

Effects of magnetic correlation on the electric properties in multiferroic materials

“…The effect of magnetoelectric coupling is particularly strong when temperature is close to or just below magnetic phase transition temperature and may result in a change of electric properties [4][5][6]. In recent studies, it has been found that pair correlation between magnetic lattice sites, hereafter referred to as magnetic correlation for brevity, played an important role on the electric properties [7][8][9][10][11], and there have been theoretical works devoted to the investigations of this effect [11][12][13][14][15][16].…”

A study of the dielectric and magnetic properties of multiferroic materials using the Monte Carlo method

“…Then, several macroscopic approximations were put forward to explain magnetoelectricity, most of them based on Landau's phenomenological theory. X. S. Gao 9 and J. M. Liu 10 simulated the dielectric and magnetic properties of multiferroic materials based on a microscopic model proposed by Janssen in 1994 11 for the magnetoelectric coupling using the Monte Carlo (MC) method.…”

“…It will also be assumed that the magnetic and electric systems mutually interact between them. Following the models of Janssen 11 and Gao 9 the Hamiltonian for the system may be written as:…”