Mean-field theory of the electromagnon resonance

We present the analytical theory of the electromagnon resonance for the multiferroics of spin origin. We consider the spin density evolution under the influence of magnetoelectric coupling in the presence of the electromagnetic wave. The dielectric permeability is found for the eigen-wave perturbations accompanied by perturbations of the electric field. The imaginary part of the dielectric permeability is found as the function of the applied electric field frequency, while the frequency of the eigen-waves is found from the dispersion equation as the function of the wave vector and parameters of the system. The result shows the existence of two peaks. One sharp peak is associated with the magnon resonance, while the second wide peak at the approximately four times smaller frequency is interpreted as the electromagnon resonance in accordance with existing experimental data.