In this work we study phase transitions and surface properties of multiferroic superlattice by Monte-Carlo simulation. 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 dimension L × L. The magnetic film we consider as a film with a body-centered cubic lattice, the ferroelectric film as a film with body-centered cubic lattice. We have studied a new model for the interface coupling between a ferromagnetic film and a ferroelectric film in a superlattice of multiferroic. This interaction has the form of a Dzyaloshinskii-Moriya (DM) interaction between the order parameters of ferroelectric films and the spins of ferromagnetic layers at the interface. We have taken into account the frustration due to the NNN interactions in both magnetic and ferroelectric layers. The ground state shows uniform non collinear spin configurations in zero field and skyrmions in an applied magnetic field. Monte Carlo simulation has been used to study the phase transition occurring in the superlattice with and without applied field. Skyrmions have been shown to be stable at finite temperatures and up to finite values of the NNN exchange interactions. We have also shown that the nature of the phase transition can be of second or first order, depending on the value of magnetoelectric interaction. As expected, the magnetic frustration enhances creation of skyrmions. The existence of skyrmions confined at the ferromagnetic-ferroelectric interface is very interesting. For MC simulations, we use the Metropolis algorithm for a system with linear dimensions L × L × L z .

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 m z ferromagnetic layers and L f z ferroelectric layers sandwiched in the z-direction. Each xy plane has the dimension L × 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 × L × 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 |J mf | on the interface. The secondorder 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.

The formation and conditions of stability of a skyrmions at the interface between a ferroelectric layer and antiferromagnetic layer with triangilar lattice and its phase transition are studied. All interactions between spins and polarizations are limited to nearest neighbors (NN). The antiferromagnetic exchange interaction among the spins inside antiferromagnetic layer will compete with the perpendicular interface interaction between adjacent layers. The ground state spin configuration at zero temperature is calculated by using the numerical high performance steepest descent method. The resulting configuration is non-collinear. Small values of external field yields small values of angles between spins in the plane so that the ground state configurations have antiferromagnetic and non collinear domains. We observe the creation of single spin vortices. We noted that for zero applied magnetic field the skyrmions in the antiferromagnetic/ferroelectric bilayers with triangular lattice can be created in the region of interface magnetoelectric interaction value between 0.85 and 1.95. The strong external magnetic field applied perpendicular to the interface with non-collinear Dzyaloshinskiy-Morya-like magnetoelectric interaction at the interface leads to remove the skyrmion phase and magnetic phase transitions. With increasing the interface magnetoelectric coupling, the skyrmion lattice disappear. We found the formation perfect skyrmion structure at non-zero external magnetic field and moderate values of magnetoelectric interaction. The skyrmions structure is stable in a large region of the interface magnetoelectric interaction between antiferromagnetic and ferroelectric films. The results of Monte Carlo simulations that we carried out confirm that observed skyrmions are stable up to a finite temperature.