Paramagnetic Spin Waves and Correlation Functions in NiF2

The temperature dependence of one- and two-magnon excitations in Ni${\mathrm{F}}_2$ has been studied by the technique of inelastic light scattering. Above the Néel temperature of 73°K, the one-magnon scattering disappears in accordance with the vanishing of long-range magnetic order. The two-magnon peak persists and remains underdamped in the paramagnetic phase at least to a temperature of $1.5T_N$. Some paramagnetic scattering is evident even at $4T_N$. Since the two-magnon excitations observed consist of pairs of very-short-wavelength spin waves, these observations confirm the existence of underdamped spin waves well into the paramagnetic phase. It is emphasized that the two-magnon scattering of light is sensitive to a four-spin correlation function, in contrast to the two-spin correlation function which determines neutron scattering from individual spin waves of comparably short wavelength. These experiments constitute the first measurement of a four-spin correlation function in the paramagnetic phase.