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We use a Green's function method with Random Phase Approximation to show howmagnetic correlations may affect electric polarization in multiferroicmaterials with magnetic-exchange-type magnetoelectric coupling. We use a modelspin 1/2 ferromagnetic ferroelectric system but our results are expected toapply to multiferroic materials with more complex magnetic structures. Inparticular, we find that transverse magnetic correlations result in a change inthe free energy of the ferroelectric solutions leading to the possibility forthermal hysteresis of the electric polarization above the magnetic Curietemperature. Although we are motivated by multiferroic materials, this problemrepresents a more general calculation of the effect of fluctuations on coupledorder parameters.

The effect of transverse magnetic correlations on a coupled order parameter: shifted transition temperatures and thermal hysteresis