  We developed numerical calculations to simulate the magnetoelectric coupling
in multiferroic compounds, using the Monte Carlo technique. Two simple models
were used to simulate the compounds. In the first one, the magnetic ions are
represented by a spin 1/2 2D Ising lattice of ions, and the electric lattice by
classical moments, coupled one to one with the magnetic moments. The coupling
between both lattices allows to the leading lattice, that is, the magnetic one,
to change the orientation of the electrical dipoles in one direction
perpendicular to the magnetic dipoles. This direction was chosen to accomplish
the symmetry requirements of the magnetoelectric effect. In the second case,
the magnetic lattice is also a 2D Ising lattice, but the electric momenta are
in a lattice that also behaves as an Ising lattice, perpendicular to the
magnetic moments. In this case, the one-to-one coupling of the electric and
magnetic momenta is represented by a two-valued energy parameter, allowing the
possibility of independent transition temperatures for both lattices. Both
models contain three independent parameters. We studied the physical properties
obtained with both models, as functions of the ratio of the three parameters.
The results in both cases allowed us to compare changes in the physics of the
models, and with the physics of compounds measured experimentally.
