High-energy spin waves in the spin-1 square-lattice antiferromagnet La${}_2$NiO${}_4$

Inelastic neutron scattering is used to study the magnetic excitations of the $S=1$ square-lattice antiferromagnet La${}_2$NiO${}_4$. We find that the spin waves cannot be described by a simple classical (harmonic) Heisenberg model with only nearest-neighbor interactions. The spin-wave dispersion measured along the antiferromagnetic Brillouin-zone boundary shows a minimum energy at the $(1\mathrm{/}2,0)$ position as is observed in some $S=1\mathrm{/}2$ square-lattice antiferromagnets. Thus, our results suggest that the quantum dispersion renormalization effects or longer-range exchange interactions observed in cuprates and other $S=1\mathrm{/}2$ square-lattice antiferromagnets are also present in La${}_2$NiO${}_4$. We also find that the overall intensity of the spin-wave excitations is suppressed relative to linear spin-wave theory indicating that covalency is important. Two-magnon scattering is also observed.