  We use a Green's function method with Random Phase Approximation to show how
magnetic correlations may affect electric polarization in multiferroic
materials with magnetic-exchange-type magnetoelectric coupling. We use a model
spin 1/2 ferromagnetic ferroelectric system but our results are expected to
apply to multiferroic materials with more complex magnetic structures. In
particular, we find that transverse magnetic correlations result in a change in
the free energy of the ferroelectric solutions leading to the possibility for
thermal hysteresis of the electric polarization above the magnetic Curie
temperature. Although we are motivated by multiferroic materials, this problem
represents a more general calculation of the effect of fluctuations on coupled
order parameters.
