Uniaxial ferromagnetism in NiZrF6·6H2O

NiZr${\mathrm{F}}_6$·6${\mathrm{H}}_2$O crystallizes in the trigonal NiSn${\mathrm{Cl}}_6$·6${\mathrm{H}}_2$O structure with one trigonally distorted ${\left[\mathrm{N}\mathrm{i}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$ complex per unit cell. We have measured ${\chi }_{\parallel }$ and ${\chi }_{\perp }$ for this salt between 0.05 and 4.2 K and $C_p$ in zero field and in $H_{\parallel }=2000\mathrm{}$ Oe between 0.09 and 4.2 K. The susceptibilities are those of a uniaxial ferromagnet with the easy axis along the trigonal direction and $T_C\approx 0.16$ K. $C_p\mathrm{}(H=0\mathrm{})\mathrm{}$ exhibits a sharp cooperative peak at $T_C=0.164\mathrm{}\pm 0.002$ K and a Schottky anomaly with $\frac{C_{max}}{R}\approx 0.24$ and $T_{max}\approx 1.5$ K. Thus, the ${}_{}{}^3{}_{}{}^{}A_{2g}^{}{}_{}{}^{}$ ground state of ${\left[\mathrm{N}\mathrm{i}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$ is split into a lower doublet and an upper singlet separated by $\sim 3k$ and the ionic moments are Ising-like near $T_C$. $C_p(H_{\parallel }=2\mathrm{} \mathrm{kOe})$ shows two overlapping rounded anomalies. The data are well described by an Oguchi model in which pairs of spins are treated exactly and their interaction with the rest of the crystal is represented by a mean field. The pair Hamiltonian is