Quadrupole and octupole excitations in the magnetoelectric akermanites

We study the magnetoelectric multiferroic compounds, A₂CoGe₂O₇ (A=Ba, Sr), in which the coexistence of ferroelectric and magnetic order enables a strong cross-coupling and the mutual control of magnetization by electric and polarization by magnetic fields. The magnetoelectric response is not limited to the static properties but is revealed in spin excitations too, characterized by mixed magnetic and electric dipole components.

Electron spin resonance and far-infrared absorption spectra exhibit several spin excitations beyond the conventional magnon modes expected in two-sublattice antiferromagnets. We compute the experimentally measured spectra including the full multi-component local Hilbert space of the S=3/2 cobalt ions.

Depending on the size of the single-ion anisotropy, we find that the THz modes correspond to either spin-stretching electro-magnons or pure spin-quadrupolar excitations manifested by two-magnon bound states. We discuss the selection rules for the various unconventional excitations, which are in full agreement with the experiments, as well as the non-reciprocal directional dichroism and its electric field control. We also discuss the observed octupole excitations in the sister compound, Sr₂CoSi₂O₇.