Two-Magnon Raman Scattering and Exchange Interactions in Antiferromagnetic KNi${\mathrm{F}}_3$ and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ and Ferrimagnetic RbNi${\mathrm{F}}_3$

We have observed Raman scattering of 5145-Å argon-laser radiation by two-magnon excitations in the antiferromagnetic nickel fluorides KNi${\mathrm{F}}_3$ and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ and ferrimagnetic RbNi${\mathrm{F}}_3$. For both the cubic perovskite structure of KNi${\mathrm{F}}_3$ and the tetragonal structure of ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$, which behaves like a two-dimensional antiferromagnet, the experimental results are in excellent agreement with the theoretical spectra computed by a Green's-function technique. This method is reviewed for the general case of a two-sublattice Néel ferrimagnet with antiparallel spins. From a comparison with this theory, we find values of $J=70.5\mathrm{}\pm 0.8 \mathrm{and} 77.0\pm 2.0$ ${\mathrm{cm}}^{-1\mathrm{}}$, respectively, for the Heisenberg exchange constants in these two materials. The experimentally observed temperature dependence of the two-magnon Raman spectra, which persists above the Néel temperature in both cases, is described. For hexagonal RbNi${\mathrm{F}}_3$, with the aid of magnon-assisted optical-absorption and magnetic-susceptibility data, we have calculated the magnon dispersion relations and estimated the dominant exchange constants. These values are 48 ${\mathrm{cm}}^{-1\mathrm{}}$ for the antiferromagnetic 180° ${\mathrm{Ni}}^{2+}$ - ${\mathrm{F}}^{-}$ - ${\mathrm{Ni}}^{2+}$ superexchange interaction and 113 ${\mathrm{cm}}^{-1\mathrm{}}$ for the 90° ferromagnetic interaction, with a small second-nearest ${\mathrm{Ni}}^{2+}$ interaction constant approximately 4 ${\mathrm{cm}}^{-1\mathrm{}}$. The identification of the low-temperature Raman line at 510 ${\mathrm{cm}}^{-1\mathrm{}}$ as arising from two different Brillouin-zone-edge magnons is consistent with our exchange constants when magnon-magnon binding effects are taken into account. A Bethe-Peierls-Weiss analysis using the present exchange parameters gives a Curie temperature close to the experimental value, 139 °K, and predicts high-temperature sublattice magnetizations in good agreement with the results of nuclear-magnetic-resonance measurements. Finally, comparisons are made among these nickel fluorides, and with results found from experiments in other magnetic insulators.