A simple model for the magnetoelectric interaction in multiferroics

Abstract

The (anti)ferromagnetic and ferroelectric transitions in some multiferroic compounds seem to be strongly correlated. Even for systems that do not show spontaneous ferroelectricity such as the LiMPO4 (M = Mn, Fe, Co, Ni) compounds, the coupling between magnetic and electric degrees of freedom is evident experimentally. Here, we present a simple numerical calculation to simulate this coupling that leads to the two transitions. We assume a magnetic sublattice consisting of classical magnetic moments coupled to a separated nonmagnetic sublattice consisting of classical electric dipoles. The coupling between them is realized through a phenomenological spin-lattice Hamiltonian, and the solution is obtained using the Monte Carlo technique. In the simplest version, the magnetic system is 2D Ising (anti)ferromagnetic lattice, with nearest neighbors interactions only, and the electric moments are permanent moments, coupled electrically. Within this approximation, the second order magnetic transition induces ferroelectricity in the electric dipoles. We show that these calculations can be extended to other magnetic systems, (x-y model and 3D Heisenberg) and to systems where the electric moments are created by strains, generated via spin-lattice coupling, so the model can be applied to model realistic systems such as the olivines mentioned above.