Spin Wave Excitations in the Multiferroic Ba$_2$CoGe$_2$O$_7$

Ba$_2$CoGe$_2$O$_7$ is a multiferroic material where spin waves exhibit giant directional dichroism and natural optical activity at THz frequencies due to the large ac magnetoelectric effect [S. Bordacs et al., Nature Physics {\bf 8}, 734 (2012)]. We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba$_2$CoGe$_2$O$_7$ in high magnetic fields up to 33 T [Penc et al., Phys. Rev. Lett. {\bf 108}, 257203 (2012)]. In the ESR and THz absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. A multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active.