Comparative Studies of Magnetism in KNi${\mathrm{F}}_3$ and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$

Bulk magnetic properties of the related antiferromagnets KNi${\mathrm{F}}_3$ and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ are analyzed by use of both high- and low-temperature theoretical methods. A crystal-field theory for the ${\mathrm{Ni}}^{2+}$ ion is outlined, using the strong-field coupling scheme, and is used to construct relevant spin Hamiltonians for the two systems. KNi${\mathrm{F}}_3$ is found to be a simple-cubic antiferromagnet for which all except nearest-neighbor interactions are negligible. Writing an exchange interaction $J{\mathbf{S}}_i·{\mathbf{S}}_j$ between nearest-neighbor spins ${\mathbf{S}}_i$ and ${\mathbf{S}}_j$, the experimental observations are quantitatively fitted for $J=89\mathrm{}\pm 4$ °K with a suggestion of a small temperature dependence of $J$. Reasons are put forward to suggest that ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ is, to a very good approximation, a two-dimensional quadratic-layer antiferromagnet with a magnetic state which, over a large temperature region, shows a long-range order in two dimensions but not in the third. A good theoretical interpretation of most of the published experimental data can be obtained using such a picture. ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ is made up of Ni${\mathrm{F}}_2$ magnetic planes, which are essentially the same as those found in KNi${\mathrm{F}}_3$, but with these magnetic layers separated in the third dimension by two nonmagnetic KF layers. We find an intraplane exchange $J\sim 125$ °K and an interplane exchange $J^{\prime }$ which is at least an order of magnitude smaller and probably ferromagnetic in sign. A number of major differences between typical two- and three-dimensional magnetic structures are discussed, and some experiments are outlined for which the use of two- dimensional systems like ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ could provide new and interesting information concerning magnetic cooperative phenomena. Finally, the possible origins of the difference in exchange values $J$ between KNi${\mathrm{F}}_3$ and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ are discussed, and the relevance of our findings in connection with the supposedly anomalous properties of another series containing two-dimensional antiferromagnets, namely, the calcium manganites, is assessed.