Crystal field effects in the intermetallic $R{\mathrm{Ni}}_3{\mathrm{Ga}}_9$ ($R=\mathrm{Tb}$, Dy, Ho, and Er) compounds

In this paper, we report temperature-dependent magnetic susceptibility, electrical resistivity, and heat-capacity experiments in the family of intermetallic compounds $R{\mathrm{Ni}}_3{\mathrm{Ga}}_9$ ($R$ = Tb, Dy, Ho, and Er). Single-crystalline samples were grown using Ga self-flux method. These materials crystallize in a trigonal ${\mathrm{ErNi}}_3{\mathrm{Al}}_9$-type structure with space group $R32$. They all order antiferromagnetically with $T_N<20\mathrm{K}$. The anisotropic magnetic susceptibility presents large values of the ratio ${\chi }_{\text{easy}}/{\chi }_{\text{hard}}$ indicating strong crystalline electric-field (CEF) effects. The evolution of the crystal-field scheme for each $R$ was analyzed in detail by using a spin model including anisotropic nearest-neighbor Ruderman-Kittel-Kasuya-Yosida interaction and the trigonal CEF Hamiltonian. Our analysis allows one to understand the distinct direction of the ordered moments along the series—the Tb-, Dy-, and Ho-based compounds have the ordered magnetic moments in the easy $\mathit{ab}$ plane and the Er sample magnetization easy axis is along the $\widehat{c}$ direction.

Figure 1

Rietveld refinement of the x-ray powder-diffraction data (filled dot) for $R{\mathrm{Ni}}_3{\mathrm{Ga}}_9$ at room temperature. The solid lines are the calculated and the difference between experimental and calculated patterns, respectively. The bars in the bottom panels represent the Bragg indexation according to the structural model, taken from the COD code 96-210-0947. The inset represents the evolution of the unit-cell parameters with $R$ as extracted from the refinement. Error bars are smaller than the symbol sizes used.

Figure 2

Temperature dependence of the magnetic susceptibility for (a) ${\mathrm{TbNi}}_3{\mathrm{Ga}}_9$, (b) ${\mathrm{DyNi}}_3{\mathrm{Ga}}_9$, (c) ${\mathrm{HoNi}}_3{\mathrm{Ga}}_9$, and (d) ${\mathrm{ErNi}}_3{\mathrm{Ga}}_9$ measured for magnetic field of $H$ = 1 kOe applied parallel ${\chi }_{//}$ (open symbols) and perpendicular ${\chi }_{\perp }$ (filled symbols) to the trigonal $c$ axis. The solid lines are best fits to the data for both directions using our mean-field model (see below). The insets in (a) and (d) represent the inverse $1/{\chi }_{\text{poly}}\left(T\right)$ of polycrystalline susceptibility fitted with a linear Curie-Weiss law for $\mathit{T}>100\text{K}$. From this fitting we extracted the ${\mu }_{\text{eff}}$ and ${\mathrm{\Theta }}_{\text{CW}}$ magnitudes for all compounds (see Table 1). The insets in (b) and (c) show the low-$T$ region and the presence of more complex ground states.

Figure 3

Main panel: Magnetic contribution to the specific heat divided by temperature for ${\mathrm{TbNi}}_3{\mathrm{Ga}}_9, {\mathrm{DyNi}}_3{\mathrm{Ga}}_9, {\mathrm{HoNi}}_3{\mathrm{Ga}}_9$, and ${\mathrm{ErNi}}_3{\mathrm{Ga}}_9$. The inset shows the $C_{\text{mag}}/T$ data for Tb-, Dy-, Ho-, and Er-based samples together with the best fit to the data of the mean-field model [11, 12].

Figure 4

Evolution of the normalized Neel temperature ($T_N$) for $R{\mathrm{Ni}}_3{\mathrm{Ga}}_9$ ($R$ = Tb, Dy, Ho, and Er) and de Gennes factors $G={(g_J-1)}^{2}J(J+1)$ for $R$ atoms ($R$ = Tb, Dy, Ho, and Er). The inset shows the evolution of the normalized ${\mathrm{\Theta }}_{\text{CW}}$ together with $G$.

Figure 5

Temperature dependence of the electrical resistivity for the $R{\mathrm{Ni}}_3{\mathrm{Ga}}_9$ single crystal in the low-$T$ region showing the change in slope at $T_N$. The current ($I$) has been applied parallel to the $\mathit{ab}$ plane. The inset shows the full temperature range.

Figure 6

Magnetization for (a) ${\mathrm{TbNi}}_3{\mathrm{Ga}}_9$, (b) ${\mathrm{DyNi}}_3{\mathrm{Ga}}_9$, (c) ${\mathrm{HoNi}}_3{\mathrm{Ga}}_9$, and (d) ${\mathrm{ErNi}}_3{\mathrm{Ga}}_9$ under applied magnetic perpendicular (filled symbols) and field parallel (empty symbols) to the $c$ axis. All datasets were collected at $T$ = 2 K. The solid lines represent the results from the spin model fittings.

Figure 7

(a) Crystal structure of $R{\text{Ni}}_3{\mathrm{Ga}}_9$ ($R$ = rare earth). (b) Planes of $R$. Sublattices A and B are shown in red and blue. ${\mathrm{J}}_1$ and ${\mathrm{J}}_2$ are magnetic exchange interactions. Quadrupolar couplings ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ act on the same links as ${\mathrm{J}}_1$ and ${\mathrm{J}}_2$.

Figure 8

CEF splitting of the ground-state multiplet obtained from the simulations of Figs. 2, 3, and 6 for ${\mathrm{TbNi}}_3{\mathrm{Ga}}_9, {\mathrm{DyNi}}_3{\mathrm{Ga}}_9, {\mathrm{HoNi}}_3{\mathrm{Ga}}_9$, and ${\mathrm{ErNi}}_3{\mathrm{Ga}}_9$.