Dynamic magnetoelectric phenomena with electromagnons in rare-earth borate multiferroics

Electroactive spin excitations (electromagnons), an analog of the low-frequency quasiferromagnetic antiferromagnetic resonance (AFMR) mode in Fe subsystem, are observed in multiferroic rare-earth ferroborates [specifically in SmFe$_3$(BO$_3$)$_4$] in the frequency range of 40–150 GHz, which are shown to contribute dominantly to the giant static (quasistatic) magnetodielectric effect and which produce two types of dynamic magnetoelectric effects: (a) giant optical activity, which occurs for the wave vector k parallel to the crystallographic $c$-axis, $\mathbf{k} \parallel c$, in a transverse magnetic field $\mathbf{H}\parallel a$ and is accompanied by polarization-plane rotation by more than 70 deg mm$^{-1}$ in the resonance, and (b) directional birefringence and dichroism in a transverse magnetic field $\mathbf{H}\parallel b$-axis, which show up in transmission asymmetry between the forward ($\mathbf{k}\parallel c$) and backward ($\mathbf{k} \parallel -c$) directions, being equivalent to the sign change of the magnetic field, $H_b \to -H_b$. A theory is developed which explains the observed dynamic magnetoelectric phenomena quantitatively by taking into consideration different symmetries of the tensors of magnetic, magnetoelectric and dielectric susceptibilities for $\mathbf{H}\parallel a$ and $\mathbf{H} \parallel b$.