Effect of spin excitations with simultaneous magnetic- and electric-dipole character on the static magnetoelectric properties of multiferroic materials

Abstract

We derive a sum rule to demonstrate that the static magnetoelectric (ME) effect is governed by optical transitions that are simultaneously excited by the electric and magnetic components of light. The ME sum rule is applicable to a broad class of materials lacking the spatial inversion and the time-reversal symmetries, including multiferroic compounds. Due to the dynamical ME effect, the optical excitations in these materials can exhibit directional dichroism, i.e., the absorption coefficient can be different for counter-propagating light beams. According to the ME sum rule, the magnitude of the linear ME effect of a material is mainly determined by the directional dichroism of its low-energy optical excitations. An application of the sum rule to the multiferroic ${\mathrm{Ba}}_{2}$${\mathrm{CoGe}}_{2}$${\mathrm{O}}_{7}$, ${\mathrm{Sr}}_{2}$${\mathrm{CoSi}}_{2}$${\mathrm{O}}_{7}$, and ${\mathrm{Ca}}_{2}$${\mathrm{CoSi}}_{2}$${\mathrm{O}}_{7}$ shows that in these compounds the static ME effect is mostly governed by the directional dichroism of the spin-wave excitations in the giga-terahertz spectral range. On this basis, we argue that the studies of directional dichroism and the application of the ME sum rule promote the synthesis of new materials with large static ME effect.