Multiferroics, which exhibit both ferroelectricity and ferromagnetism, are currently under intensive investigation. Their spontaneous polarization and saturation magnetization are very low in comparison to many standard ferroelectrics and ferromagnets. In order to explain the experimentally observed enhanced polarization and magnetization in multiferroic nanoparticles, we investigate the influence of surface and particle size on ferromagnetic and ferroelectric properties. The studies are based on two microscopic models: the modified Heisenberg and the transverse Ising model and a multiferroic coupling term. A Green's function technique beyond the random phase approximation allows the calculation of static and dynamic properties in dependence of temperature, particle size, and different model parameters. It is demonstrated that magnetization, polarization, phase transition temperatures, spin-wave energies, and their damping are very sensitive to the exchange interaction constants on the surface and to the electromagnetic coupling constant. We obtain that the magnetization and the polarization are enhanced in BiFeO_3 nanoparticles due to surface and size effects. The results compare very well with the experimental data.
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