Magnetic field dependence of the Schottky anomaly in filled skutterudites ${\mathrm{Pr}}_{1-x}{\mathrm{Eu}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$

By performing a series of thermodynamic measurements in an applied magnetic field $H_{\mathrm{ext}}$, we investigated the effects of Eu substitution on the Pr sites in the filled skutterudite compound ${\mathrm{Pr}}_{1-x}{\mathrm{Eu}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ ($0\le x\le 1$). A heat capacity Schottky anomaly is present over the whole doping range. For the samples with $x>0.5$, the temperature of the maximum, $T_{max}$, shifts to lower temperature with increasing $H_{\mathrm{ext}}$. We argue that this behavior reflects the antiferromagnetic (AFM) ordering of the Eu moments, as the AFM transition is suppressed by $H_{\mathrm{ext}}$. The Schottky anomaly in the samples with $x\le 0.5$ shifts to higher temperatures with increasing magnetic field, signaling the presence of an internal magnetic field due to short-range AFM correlations induced by magnetic moments of neighboring Eu sites. In low $H_{\mathrm{ext}}$, the Schottky gaps show a nonlinear relationship with $H_{\mathrm{ext}}$ as the magnetic moments become weakly magnetized. In high $H_{\mathrm{ext}}$, the magnetic moments of Eu sites become completely aligned with $H_{\mathrm{ext}}$. Thus, increasing $H_{\mathrm{ext}}$ does not further increase the magnetization; hence the Schottky gaps increase linearly with $H_{\mathrm{ext}}$.

Figure 1

Specific heat $C-C_{\text{ph}}$ vs temperature $T$ of ${\mathrm{Pr}}_{1-x}{\mathrm{Eu}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ measured in different magnetic fields $H$ for the (a) $x=0.05$, (b) $x=0.50$, and (c) $x=0.80$ samples. The solid curves are fits of the data using the sum of Schottky and superconducting contributions for (a) and (b), and Schottky and normal-state contributions for (c), as described in the text.

Figure 2

(a) Splitting of the ground state ${}^{8}S_{7/2}$ of Eu into eight equally spaced energy levels by both internal and external magnetic fields. (b) Schematic representation of the net magnetic moment $\mathbf{m}$ and external magnetic field pointing in different directions.

Figure 3

Plots of the Schottky gap $\mathrm{\Delta }$ vs $H_{\mathrm{ext}}$, for relatively small applied magnetic fields. The solid curves are fits of the data as discussed in the text. Inset: Fitting parameters $A$ (left vertical axis) and $H_{\mathrm{int}}$ (right vertical axis) plotted as a function of Eu substitution $x$.

Figure 4

Plots of $\mathrm{\Delta }$ vs $H$ data for high applied magnetic fields. The straight lines are guides to the eye and show that all the $\mathrm{\Delta }$ vs $H$ plots have the same slope of ($1.4\pm 0.04$) K/T.