Free Charge Carriers in Mixed Valency Oxides as Possible Mediators of Magnetoelectric Effect

We show, that in a substance with mixed-valence ions, which can supply free carriers and have electric dipole and spin moments, three types of long-range order (ferromagnetic, ferroelectric and magnetoelectric (ME)) can occur at low temperatures. The origin of the effect is that free charge carriers can mediate the multiferroic behavior via spin - spin (RKKY), dipole-dipole and dipole - spin interactions. We show that there is an optimal carrier concentration, at which the strength of ME interaction is maximal and comparable to that of RKKY interaction. Our analysis shows that disorder and finite conductivity in the above substances does not suppress multiferroic effects.