Frequency dependence of magnetoelectric phenomena in BaMnF4

Equations of motion of the Landau-Lifshitz type are used together with the free-energy expression of an earlier publication [D. L. Fox et al., Phys. Rev. B 21, 2926 (1980)] to derive expressions for dynamic phenomena in the low-temperature phase of BaMn${\mathrm{F}}_4$. The magnon frequency decreases and the optical-phonon frequency increases with the strength of the magnetoelectric coupling. Three susceptibilities, magnetic, magnetoelectric, and dielectric, are found; all three have poles at both the magnon and the phonon frequency.