Magnetic ordering and effects of crystal electric field anisotropy in the hexagonal compounds $R$PtIn $(R=\mathrm{Y},\mathrm{Gd}\text{–}\mathrm{Lu})$

Single crystals of RPtIn $R=\mathrm{Y}$, 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 $P\overline{6}2m$). The $R=\mathrm{Tb}$ and Tm members of the series appear to order antiferromagnetically ($T_N=46.0$ and 3.0 K, respectively), whereas the $R=\mathrm{Gd}$, 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, 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 $R$PtIn series, a three-dimensional model of the magnetic moments in ${\mathrm{Fe}}_2\mathrm{P}$-type systems was developed, using the three coplanar 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 nonplanar easy axes, whose in-plane projections are rotated by 60° with respect to each other. Such a model is consistent with the reduced high-field magnetization values observed for the $R$PtIn compounds $R=\mathrm{Tb}\text{–}\mathrm{Tm}$, and qualitatively reproduces the features of the angular dependent magnetization of ${\mathrm{Ho}}_x{\mathrm{Y}}_{1-x}\mathrm{PtIn}$ at $H=55\mathrm{kG}$.

Figure 1

Powder x-ray diffraction pattern for TbPtIn. All peaks are indexed using a hexagonal $P\overline{6}2m$ structure, with $a=7.56\mathrm{\AA }$ and $c=3.87\mathrm{\AA }$.

Figure 2

Unit cell volumes and lattice parameters for $R$PtIn, $R=\mathrm{Gd}\text{–}\mathrm{Lu}$, as a function of $R^{3+}$ ionic radius. Dotted line: a guide for the eye, indicating the Lanthanide contraction.

Figure 3

Heat capacity for YPtIn and LuPtIn, with low-temperature $C_P∕T\mathrm{vs}{T}^2$ shown in lower inset (linear fits of the low-$T$ data give $\gamma$ in units of $\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^2$); upper inset: entropy difference $\Delta S$ (see text).

Figure 4

Anisotropic $H∕M$ data of GdPtIn and calculated average (line) at $H=1\mathrm{kG}$, with the anisotropic ZFC-FC low-temperature $M∕H$ data for $H=0.1\mathrm{kG}$ shown in the inset.

Figure 5

Anisotropic field-dependent magnetization loops for GdPtIn, at $T=2\mathrm{K}$.

Figure 6

Specific heat $C_P\left(T\right)$ of GdPtIn; small arrow indicates $T_C$ determined from the onset (see text).

Figure 7

Anisotropic $H∕M$ data of TbPtIn and calculated average (line) at $H=1\mathrm{kG}$; inset: low-temperature anisotropic $M∕H$ data.

Figure 8

(a) $C_P\left(T\right)$ and (b) low-temperature $d(M_{\mathrm{ave}}∕HT)∕dT$ for TbPtIn; dotted lines mark the peak positions, corresponding to the magnetic transitions.

Figure 9

Anisotropic field-dependent magnetization data for TbPtIn, at $T=2\mathrm{K}$, for increasing and decreasing field values (as indicated by arrows).

Figure 10

Anisotropic $H∕M$ data for DyPtIn and the calculated average (line) at $H=1\mathrm{kG}$; inset: ZFC-FC low-temperature anisotropic $M∕H$ data for $H=0.1\mathrm{kG}$.

Figure 11

Specific heat $C_P\left(T\right)$ of DyPtIn; small arrow indicates $T_C$ determined from the onset (see text).

Figure 12

Anisotropic field-dependent magnetization loops for DyPtIn, at $T=2\mathrm{K}$.

Figure 13

Anisotropic $H∕M$ data for HoPtIn and the calculated average (line) at $H=1\mathrm{kG}$; inset: low-temperature anisotropic $M∕H$ data.

Figure 14

Specific-heat $C_P\left(T\right)$ of HoPtIn; small arrow indicates $T_C$ determined from the onset (see text).

Figure 15

Anisotropic field-dependent magnetization curves for HoPtIn (symbols), and ${\mathrm{Ho}}_x{\mathrm{Y}}_{1-x}\mathrm{Pt}\mathrm{In},x\sim 0.04$ (lines), at $T=2\mathrm{K}$.

Figure 16

Anisotropic $H∕M$ data for ErPtIn and the calculated average (line) at $H=1\mathrm{kG}$; inset: low-temperature anisotropic $M∕H$ data.

Figure 17

Specific-heat ${\mathrm{C}}_P\left(T\right)$ of ErPtIn; small arrow indicates $T_C$ determined from the onset (see text).

Figure 18

Anisotropic field-dependent magnetization curves for ErPtIn, at $T=2\mathrm{K}$.

Figure 19

Anisotropic $H∕M$ data for TmPtIn and the calculated average (line) at $H=1\mathrm{kG}$; inset: low-temperature anisotropic $M∕H$ data.

Figure 20

(a) $C_P\left(T\right)$ and (b) low-temperature $d(M_{\mathrm{ave}}∕HT)∕dT$ for TmPtIn; dotted line marks the peak position, corresponding to $T_N$.

Figure 21

Anisotropic field-dependent magnetization curves for TmPtIn, at $T=2\mathrm{K}$.

Figure 22

Anisotropic $H∕M$ data for YbPtIn and the calculated average (line) at $H=1\mathrm{kG}$; inset: low-temperature anisotropic $M∕H$ data.

Figure 23

Specific-heat $C_P\left(T\right)$ of YbPtIn; small arrow indicates $T_m$.

Figure 24

Changes of the magnetic ordering temperatures $T_m$ for $R$PtIn $(R=\mathrm{Gd}\text{–}\mathrm{Tm})$ with the deGennes scaling factor (dG) (the dotted line represents the expected linear dependence). Open symbol (for $R=\mathrm{Tb}$) represents the low-temperature transition from the higher-$T$ to lower-$T$ antiferromagnetic state.

Figure 25

Schematic representation of the three coplanar Ising-like systems model in (a) the antiferromagnetic and (b) the CL-SPM state. Solid arrows: “up” and dotted arrows: “down” orientations of the magnetic moments along the easy axes.

Figure 26

The three-dimensional model for three magnetic moments at unique orthorhombic point symmetry sites: thin arrows (solid; up and dotted: down) represent the nonzero components of the magnetic moments along the [001] or the easy in-plane directions (as shown, the [120]-equivalent directions). Thick arrows: full magnetic moments in the CL-SPM state.

Figure 27

Angular-dependent magnetization for ${\mathrm{Ho}}_x{\mathrm{Y}}_{1-x}\mathrm{Pt}\mathrm{In}(x\sim 0.04)$ (full circles) at $H=55\mathrm{kG}$ and $T=2\mathrm{K}$. The solid lines represent the easy and hard plane calculated magnetizations as a function of $\theta$ (see text), for fixed angle $\alpha$.