Magnetoelectric interaction at the interface in the superlattices of multiferroic: Monte Carlo study of the phase transitions

In this work, we study the phase transitions and surface properties of a multiferroic superlattice by Monte-Carlo simulation. The superlattice is formed by alternating magnetic and ferroelectric layers. We consider a multilayer film of a multiferroic consisting of L-z(m) ferromagnetic layers and L-z(f) ferroelectric layers sandwiched in the z-direction. Each xy plane has the dimension L x L. We consider the magnetic film as a film with a body-centered cubic lattice, the ferroelectric film as a film with a simple cubic lattice. For MC simulations, we use the Metropolis algorithm for a system with linear dimensions L x L x L-z. We varied L in the range L= 40, 60, 80,100 to determine size effects. In numerical simulations, the thickness of the superlattice was chosen with L-z = 8, 16, 12, 24. The effect of temperature, external magnetic and electric fields, and the magnetoelectric coupling at the interface in the region of phase transitions was investigated. The phase diagram shows that the transition temperature increases with an increase in the magnetoelectric interaction parameter vertical bar J(mf)vertical bar on the interface. The second-order phase transition in the superlattice occurs in the region of values from J(mf) = 0 to J(mf) = -3.3. When J(mf) = -2 5 and above, phase transitions occur at the same temperature. After J(mf) =-3.5 in both subsystems the first-order phase transition occurs. The transition temperatures, the magnetization of the layer, the polarization of the layer, the susceptibility, the internal energy, the magnetization and the polarization of the interface are determined. The dependences of the magnetization and polarization of surface layers on temperature are studied for various parameters of the magnetoelectric interaction and the values of external fields. The obtained results show that in the temperature dependence of energy and other physical quantities at low temperatures there are no regions of metastability.