High-temperature series analysis of spin-one uniaxial ferromagnets:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Ni</mml:mi><mml:mi>M</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>·6<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>O compounds

For the first time high-temperature series for the susceptibility and heat capacity have been employed to analyze data on ferromagnetic systems with single-ion anisotropy comparable with or greater than the pair interactions between ions. The salts $\mathrm{Ni}M{\mathrm{F}}_{6}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O with $M=\mathrm{S}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{n},\phantom{\rule{0ex}{0ex}}\mathrm{Z}\mathrm{r}$ are spin-one ferromagnetic systems. Each has an easy-axis single-ion anisotropy and long-range dipole-dipole interaction in addition to the more commonly discussed short-range exchange interactions. We show that the same set of interaction parameters can fit simultaneously and quantitatively both susceptibility and heat-capacity data. We also discuss the unusually small deviations of the data from the mean-field predictions for the three large single-ion anisotropy systems ($M=\mathrm{Z}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{n}$).

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