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 NiF2. 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(±0.14) cm-1, E=1.66(±0.03) cm-1, J1(coupling ions along the caxis)=-0.22(±0.50) cm-1, J2(coupling corner to body center ions) =13.87(±0.36) cm-1, and J3(coupling ions along the aorbaxes)=0.79(±0.40) cm-1. From these parameters, we have calculated the density of magnon states and find that it shows one sharp peak near 108 cm-1. 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 cm-1. 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 NiF2, and, in addition, it has supplied the first detailed comparison of neutron and Raman data for an S=1 ion.