Neutron and Optical Investigation of Magnons and Magnon-Magnon Interaction Effects in NiF2

Neutron inelastic scattering and Raman light scattering have been used to investigate spin-wave excitations in the canted antiferromagnet Ni${\mathrm{F}}_2$. All the zone-center Raman-active phonons have been observed as well. By neutron scattering, we have measured the dispersion of one-magnon excitations in the (010) plane of the crystal. These data have been analyzed, together with published values for the antiferromagnetic-resonance mode frequencies, to give values for the two anisotropy parameters and three exchange constants in the spin Hamiltonian for the crystal. We find $D=4.36\mathrm{} (\pm 0.14)$ ${\mathrm{cm}}^{-1\mathrm{}}$, $E=1.66\mathrm{} (\pm 0.03)$ ${\mathrm{cm}}^{-1\mathrm{}}$, $J_1 \left(\mathrm{coupling}\mathrm{ions}\mathrm{along}\mathrm{the} c \mathrm{axis}\right)=-0.22\mathrm{} (\pm 0.50)$ ${\mathrm{cm}}^{-1\mathrm{}}$, $J_2 \left(\mathrm{coupling}\mathrm{corner}\mathrm{to}\mathrm{body}\mathrm{center}\mathrm{ions}\right)=13.87\mathrm{} (\pm 0.36)$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $J_3 (\mathrm{coupling}\mathrm{ions}\mathrm{along}\mathrm{the} a or b \mathrm{axes})=0.79\mathrm{} (\pm 0.40)$ ${\mathrm{cm}}^{-1\mathrm{}}$. From these parameters, we have calculated the density of magnon states and find that it shows one sharp peak near 108 ${\mathrm{cm}}^{-1\mathrm{}}$. The one-magnon Raman scattering confirms the values of the antiferromagnetic-resonance frequencies, while the second-order (two-magnon) scattering gives a broad line corresponding to a weighted two-magnon density of states centered at 203 ${\mathrm{cm}}^{-1\mathrm{}}$. We have interpreted the two-magnon line shape in terms of the neutron data by a Green's-function theory which includes the effect of magnon-magnon interaction. In this theory of line shape, the density of states is approximated by a one-exchange-parameter model, corresponding to a weighted zone-boundary energy. Nevertheless, excellent agreement with experiments is obtained. This study, therefore, has served to characterize completely the interactions in Ni${\mathrm{F}}_2$, and, in addition, it has supplied the first detailed comparison of neutron and Raman data for an $S=1\mathrm{}$ ion.