Directional dichroism of THz radiation in Sr$_2$CoSi$_2$O$_7$*

The microscopic mechanism of magnetoelectric coupling in akermanite-like Co-oxide multiferroics is unique because the local electric polarization mainly arises from the hybridization of Co ion and its ligands orbitals and is less affected by the details of the actual magnetic order of Co spins. As a consequence of this magnetoelectric effect, the spin waves located in the THz range exhibit giant directional dichroism in Ba$_2$CoGe$_2$O$_7$ [S. Bordacs et al., Nature Physics {\bf 8}, 734 (2012)]. Here we studied spin excitations in a sister compound Sr$_2$CoSi$_2$O$_7$ in magnetic fields up to 17 T. We found that the giant directional dichroism at THz frequencies is present below the Neel temperature (T$_N$) where the spins are ordered antiferromagnetically and persists as well above T$_N$ due to the large uniform magnetization and electric polarization induced by the external magnetic field. The relation of the observed ac magnetoelectric effect to the dc magnetoelectric effect studied by Akaki et al. [Phys. Rev. B {\bf 86}, 060413(R) (2012)] is also discussed.