Effect of Ga and Cd substitutions on the first-order antiferromagnetic transition in ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$

The cubic neodymium-based compound ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ exhibits a first-order antiferromagnetic (AFM) transition at $T_{\text{N}}=0.53$ K. Strong magnetic fluctuations at temperatures up to 5 K were suggested by the downward curvature of the electrical resistivity $\rho \left(T\right)$ and the reduced magnetic entropy $S_{\text{m}}$ of $0.5R\ln 2$ at $T_{\text{N}}$. In this study, we measured $\rho \left(T\right)$, the isothermal magnetization $M\left(B\right)$, magnetic susceptibility $\chi \left(T\right)$, and specific heat $C\left(T\right)$ of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x=1$ and ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y=1$ and 2. The sharp peak of the magnetic specific heat $C_{\text{m}}\left(T\right)$ at $T_{\text{N}}$ for $x$ = 0 is changed to a weak and broad maximum at 0.55 K for $x$ = 1. This drastic change in $C_{\text{m}}\left(T\right)$ suggests that the isovalent Cd substitution for Zn disorders the exchange interactions between the Nd moments to hinder the first-order AFM transition. On the other hand, $C_{\text{m}}\left(T\right)$ for $y=1$ and 2 exhibits a lambda-shaped anomaly, which is a characteristic of a second-order AFM transition, at elevated temperatures of 0.78 and 1.5 K, respectively. The stabilization of the AFM order by the Ga substitution indicates that $4p$ electron doping strengthens the AFM interaction. We therefore propose that the first-order transition in ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ is maintained by competitive magnetic interactions inherent in the Nd diamond sublattice.

Figure 1

Electrical resistivity $\rho$ versus temperature of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ [22], ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x=1$ and ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y=1$ and 2. The inset shows the difference of $\rho \left(T\right)$ from the value at 4 K, $\mathrm{\Delta }\rho \left(T\right)=\rho \left(T\right)-\rho \left(4\text{K}\right)$. The data of $x=$ 1, $y=$ 1 and 2 are offset for clarity. A magnetic field of $B=0.1$ T was applied to kill extrinsic superconductivity of impurity phases.

Figure 2

Temperature dependence of the inverse magnetic susceptibility ${\chi }^{-1}$ of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ [22], ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x$ = 1, and ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y$ = 1 and 2 measured at $B$ = 0.1 T. The upper inset shows the magnetic specific heat divided by temperature, $C_{\text{m}}/T$, versus $T$. The solid line represents the CEF calculation using the parameters of $W$ = 0.85 K and $X$ = $-0.285$ determined for ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ [22]. The CEF level scheme of the Nd ion is depicted. The lower inset shows the ${\chi }^{-1}\left(T\right)$ data for $T\le$ 20 K.

Figure 3

Isothermal magnetization $M\left(B\right)$ at 1.8 K of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ [22], ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x$ = 1, and ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y$ = 1 and 2. The dashed line is the calculation using the CEF parameters of $W$ = 0.85 K and $X$ = $-0.285$, which describes the ${\mathrm{\Gamma }}_6$ doublet ground state, without intersite magnetic interaction, $K$ = 0. The solid lines are the calculations including the intersite magnetic interactions of $K$ = $+0.25$ K for $x$ = 1, $-0.10$ K for $y$ = 1, and $-0.40$ K for $y=$ 2.

Figure 4

Temperature dependence of the magnetic specific heat divided by temperature, $C_{\text{m}}/T$, of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}, {\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x$ = 1 and ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y$ = 1 and 2. The arrows denote the AFM transition temperatures $T_{\text{N}}$. Inset: Magnetic entropy $S_{\text{m}}$ estimated by integrating the $C_{\text{m}}/T$ data with respect to the temperature. The $S_{\text{m}}$ data are vertically lifted to reach the value of $R\ln 2$ at 5 K. The $C_{\text{m}}$ and $S_{\text{m}}$ data for $x,y=$ 0 are cited from [22].

Figure 5

(a) Magnetic specific heat $C_{\text{m}}$ versus temperature of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x$ = 1. The solid curves for the data in $B=$ 0.5, 1, and 2 T are the fits using a two-level model, see text for details. The inset shows the temperature dependence of the magnetization divided by magnetic field, $M\left(T\right)/B$, at $B=$ 0.02, 0.05, 0.1, 0.3, and 0.5 T. (b,c) $C_{\text{m}}\left(T\right)$ of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y$ = 1 and 2, respectively, in magnetic fields. (d) Specific heat evaluated by the mean-field calculation with the CEF parameters of $W=0.85$ K and $X=-0.285$ [22], and the AFM interaction of $K=-0.40$ K.

Figure 6

Magnetic field versus temperature ($B$–$T$) phase diagrams of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ [22] and the Cd and Ga substituted samples. The (green) dashed line indicates the magnetic field variation of $T_{\mathrm{N}}$ for $y=2$ obtained from the mean-field calculation with the intersite AFM interaction of $K=-0.40$ K.