Single crystals of RPtIn, $R~=$ Y, Gd - Lu were grown out of In-rich ternary solution. Powder X-ray diffraction data on all of these compounds were consistent with the hexagonal ZrNiAl-type structure (space group P $bar{6}$ 2 m). The $R~=$ Tb and Tm members of the series appear to order antiferromagnetically ($T_N~=$ 46.0 K, and 3.0 K respectively), whereas the $R~=$ Gd, Dy - Er compounds have at least a ferromagnetic component of the magnetization along the c-axis. The magnetic ordering temperatures of all of these systems seem to scale well with the de Gennes factor dG, whereas the curious switching from ferromagnetic to antiferromagnetic ordering across the series is correlated with a change in anisotropy, such that, in the low temperature paramagnetic state, $chi_{ab} > chi_c$ for the antiferromagnetic compounds, and $chi_c > chi_{ab}$ for the rest. In order to characterize the magnetic ordering across the RPtIn series, a three-dimensional model of the magnetic moments in Fe$_2$P-type systems was developed, using the textit{three co-planar Ising-like systems model} previously introduced for the extremely planar TbPtIn compound: given the orthorhombic point symmetry of the R sites, we assumed the magnetic moments to be confined to six non-planar easy axes, whose in-plane projections are rotate by $60^0$ with respect to each other. Such a model is consistent with the reduced high-field magnetization values observed for the RPtIn compounds, R$~=$ Tb - Tm, and qualitatively reproduces the features of the angular dependent magnetization of Ho$_x$Y$_{1-x}$PtIn at $H~=$ 55 kG.
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