First-principles effective Hamiltonian modeling of multiferroic materials

Because of the strong coupling between the spin, orbital, and lattice degrees of freedom, multiferroic materials display very rich and novel physics. However, first-principles methods so far still cannot be applied directly to study the finite temperature properties of multiferroic materials. The first-principles effective Hamiltonian methods, on the contrary, can be used. In this review we introduce these methods and their applications in studying the phase diagrams of magneto-ferroelectrics RMn₂O₅ and CuO, and the electromagnon in RMn₂O₅.