Neutron Scattering Investigation of Phase Transitions and Magnetic Correlations in the Two-Dimensional Antiferromagnets ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$, ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$, ${\mathrm{Rb}}_2$Fe${\mathrm{F}}_4$

The quasi-elastic magnetic scattering from the planar antiferromagnets ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$, ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$, ${\mathrm{Rb}}_2$Fe${\mathrm{F}}_4$ has been studied over a wide range of temperatures both above and below the phase transition. In all three compounds the diffuse scattering above the phase transition takes the form of a ridge rather than a peak, thus giving the first concrete evidence for the two-dimensional nature of the magnetism. At $T_N$ (97.1, 38.4, 56.3°K, respectively), the crystals undergo sharp phase transitions to long-range order (LRO) in three dimensions. For $0.002\le 1-\frac{T}{T_N}\le 0.1$, the sublattice magnetizations in ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$ follow a ${(T_N-T)}^{\beta }$ law with $\beta =0.14\mathrm{} \mathrm{and} 0.16$, respectively. ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$ is found to have two distinct magnetic phases, both with identical ordering within the planes but with different stacking arrangements of the spins between planes; both phases are found to have identical $T_N\text{'}\mathrm{s}$ and $\beta \text{'}\mathrm{s}$ to within the experimental accuracy of 0.1°K. The sublattice magnetization in ${\mathrm{Rb}}_2$Fe${\mathrm{F}}_4$ has a rather more complicated behavior, apparently due to magnetostrictive effects. Finally, in the ordered phase in each compound, the three-dimensional magnetic Bragg peaks are accompanied by "diffuse" scattering which is completely two-dimensional in form. These results are discussed in terms of a model in which the phase transition is viewed as being essentially two-dimensional in character, the three-dimensional ordering simply following as a necessary consequence of the onset of LRO with the planes. The systems therefore should have distinct two- and three-dimensional critical regions. The three-dimensional region apparently was not experimentally accessible with 0.1°K temperature control in ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$, indicating that in these compounds ${|\frac{T}{T_N}-1|}_3\le 2\times {10}^{-3\mathrm{}}$.