Spin-Wave Analysis of the Quadratic-Layer Antiferromagnets ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$, ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$, and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$

In this and the following two papers, low-temperature spin-wave properties of quadratic-layer antiferromagnets having the ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ structure are reported and analyzed in detail. Here we present the results of a least-squares adjustment of spin-wave theory to the temperature variation of the sublattice magnetization in the compounds ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$, ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$, and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$, as reflected by ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ NMR frequency measurements in zero field. Lowest-order temperature-dependent and temperature-independent corrections to simple spin-wave theory, as formulated by Oguchi, are included in the analysis. The free parameters of the fits are taken to be the exchange coupling, the zero-temperature spin-wave gap energy, and the zero-temperature ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ NMR frequency. Our conclusions are as follows. Spin-wave theory accounts for the sublattice magnetization of these compounds up to somewhat less than one-half the Néel temperature, with the temperature-dependent corrections yielding less than 20% improvement in the range of fit for the ${\mathrm{Mn}}^{2+}$ compounds and a negligible improvement for ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$. The breakdown of spin-wave theory is clearly not ascribable to spin-wave interaction effects and is apparently caused by excitations of a fundamentally different nature. Exchange values obtained are in excellent agreement with data from neutron and susceptibility measurements. The "effective" spin-wave-energy-gap values obtained give some evidence for interplanar exchange coupling between second-neighbor planes, yielding upper limits for such coupling of a few parts in 1$0^4$ of the primary exchange. Earlier conclusions regarding the large zero-point spin reduction in ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ are refined here, giving a result slightly larger than but within error limits of the spin-wave-theory value (17.7%).