Polarization, specific heat, band gap and phonon energy of multiferroic GaV4S8

The recently experimentally observed multiferroic properties of GaV4S8 are studied using a microscopic model and a Green's function technique. The polarization P in < 111 > direction is saturated at low temperatures. For higher temperatures P increases and goes through a maximum at T-N similar to 13 K, then decreases strongly approaching the phase transition temperature T-fe. The polarization decreases by increasing an external magnetic field h and at higher h values the maximum vanishes. The specific heat C-p shows two maxima, at T-N and T-JT. C-p(h) is also observed. We have discussed the electronic and phonon contributions to C-p in dependence on the temperature region. The phonon energy omega for the phonon mode at 440 cm(-1) and their damping gamma are also calculated in dependence on temperature T and magnetic field h. P(h) and omega(h) is an evidence for the multiferroic behavior. The temperature dependence of the band gap energy for GaV4S8 and GaNb4S8 is obtained.