Multiferroic Ba$_2$CoGe$_2$O$_7$ is well known for having an unconventional metal-ligand d-p hybridization mechanism responsible for the magnetically induced ferroelectricity [1,2]. It exhibits many exotic quantum phenomena, and among them anisotropic spin excitations and self-tunable single ion anisotropy under external applied magnetic field have been observed recently, using inelastic neutron scattering (INS) technique . A spin gap of about 0.1 meV has been observed under zero magnetic field and interpreted as an effect of spin-nematic interaction . However, we have predicted such gap via linear spin wave theory by introducing the Dzyaloshinskii–Moriya interaction in the spin Hamiltonian. We have observed a spin gap of 0.105 meV in energy at 2 K under zero magnetic field and the gap energy decreases with increasing temperature. We enlighten the discussion on understanding the origin of the zero-field spin gap in details.
 H. Murakawa, et al., “Comprehensive study of the ferroelectricity induced by the spindependent d-p hybridization mechanism in Ba$_2$XGe$_2$O$_7$ (X = Mn, Co, and Cu),” Phys. Rev. B 85, 174106, 2012.
 H. Murakawa, et al., “Ferroelectricity induced by spin-dependent metal-ligand hybridization in Ba$_2$CoGe$_2$O$_7$,” Phys. Rev. Lett. 105, 137202, 2010.
 R. Dutta, et al., “Spin dynamics study and experimental realization of tunable single-ion anisotropy in multiferroic Ba$_2$CoGe$_2$O$_7$ under external magnetic fields,” Phys. Rev. B, 104, L020403, 2021.
 M. Soda, et al., “Spin-nematic interaction in the multiferroic compound Ba$_2$CoGe$_2$O$_7$,” Phys. Rev. Lett., 112, 127205, 2014.