Skyrmions in a frustrated model of multiferroic superlattices

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.