We consider the square-lattice antiferromagnetic Heisenberg Hamiltonian extended with a single-ion axial anisotropy term as a minimal model for the multiferroic Ba${}_2$CoGe${}_2$O${}_7$. Developing a multiboson spin-wave theory, we investigate the dispersion of the spin excitations in this spin-3/2 system. As a consequence of a strong single-ion anisotropy, a stretching (longitudinal) spin mode appears in the spectrum. The inelastic neutron scattering spectra of Zheludev et al. [Phys. Rev. B 68, 024428 (2003)] are successfully reproduced by the low energy modes in the multiboson spin-wave theory, and we anticipate the appearance of the spin stretching modes at $\approx$4 meV that can be identified using the calculated dynamical spin structure factors. We expect the appearance of spin stretching modes for any $S>1/2$ compound where the single-ion anisotropy is significant.

• Received 10 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.174428