Quantum theory of magnetoelectricity in rare-earth multiferroics: Nd, Sm, and Eu ferroborates

The quantum theory of magnetoelectricity in rare-earth ferroborates is developed. It is shown that the electric polarization in the materials is induced by means of two single-ion mechanisms: effective magnetic and crystal fields produce the electric dipole moment directly in the electronic 4f shells of rare-earth ions (the electronic contribution) and also through displacement of oppositely charged ion sublattices (the ionic one). The magnetoelectrical properties are described in detail for the neodymium, samarium, and europium ferroborates. In particular, the field and temperature dependencies of polarization are obtained.