Ordered magnetic state in $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ single crystals

The filled skutterudite compound ${\mathrm{Pr}}_{0.87}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ was prepared in single-crystal form and characterized via x-ray-diffraction, neutron-diffraction, specific-heat, electrical-resistivity, and magnetization measurements. Long-range magnetic ordering occurs at $T_c\approx 4.1\mathrm{K}$, with the bulk magnetization described by the critical exponents $\beta =0.57,\gamma =0.884$, and $\delta =2.55$. The magnetic structure consists of ordered moments on both Pr and Fe sites and may involve a ferrimagnetic arrangement. The electrical resistivity exhibits a very weak dependence on both applied magnetic field and pressure at most temperatures, but at low temperatures, its power-law temperature-dependence varies with magnetic field. Specific-heat measurements indicate an enhanced effective mass.

Figure 1

(a) ac magnetic susceptibility ${\chi }_{\mathrm{ac}}\left(T\right)$ at amplitudes of 0.5 (open) and 0.1 Oe (filled), indicating the onset of magnetic ordering between 4 and 5 K. (b) Inverse dc magnetic susceptibility $H∕M$ up to 300 K, indicating Curie-Weiss $T$-dependence. The inset shows low-$T$ dc magnetic susceptibility $M∕H$ in various applied fields.

Figure 2

Inverse dc magnetic susceptibility $H∕M$ at low $T$, showing deviation from Curie-Weiss behavior at $\sim 20\mathrm{K}$. The inset emphasizes the agreement between the Curie-Weiss fit and the scaled Arrott analysis discussed in the text.

Figure 3

Magnetization $M\left(H\right)$ isotherms for several temperatures above and below the magnetic ordering transition. Below 4.2 K, the $M\left(H\right)$ curves coalesce at an applied field $H_{\mathrm{X}}\approx 0.5\mathrm{T}$. The inset shows a hysteresis loop at temperature $T=2\mathrm{K}$, demonstrating the small coercivity and remanence of ${\mathrm{Pr}}_{0.87}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$.

Figure 4

Scaled Arrott plot demonstrating linear magnetization $M^{1∕\beta }$ isotherms evenly spaced in temperature. The lines were fit to $M^{1∕\beta }$ corresponding to intermediate values of the field $H$, as discussed in the text.

Figure 5

(a) Collapse of magnetization isotherms onto two curves, for $T$ above and below the magnetic ordering temperature $T_{\mathrm{c}}$, indicating the chosen scaling exponents. (b) $M^{1∕\beta }$ intercepts from the scaled Arrott plot (Fig. 4) demonstrate linear spacing in $T$, with $T_c=4.08\mathrm{K}$. A linear extrapolation to $T=0\mathrm{K}$ yields a value $M_0=0.60{\mu }_B∕\mathrm{f}.\mathrm{u}.$

Figure 6

Neutron-diffraction intensity of the (110) peak, indicating the onset of magnetic ordering around 4 K. The curve is a power-law fit to the data.

Figure 7

(Color online). Solid blue circles are the observed integrated magnetic intensities. The black vertical lines represent a magnetic model that involves an AFM alignment of Fe spins and a FM alignment of Pr spins. The solid green curve and the dashed red curve are the square of the Pr and Fe magnetic form factors, respectively, for comparison purposes.

Figure 8

The specific heat divided by temperature vs $T$. The magnetic transition is associated with the broad peak centered at $\sim 4\mathrm{K}$.

Figure 9

Electrical resistivity $\rho \left(T\right)$ at field $H=0$ T and pressure $P=1\mathrm{atm}$. ${\mathrm{Pr}}_{0.87}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ exhibits little $H$ or $P$ dependence over most of this temperature range. The inset shows $\rho (T,P)$ at low $T$. There is a change in $\partial \rho ∕\partial T$ at $\sim 10\mathrm{K}$ for all measured $P$.

Figure 10

(a) Electrical resistivity $\rho (T,H)$ at low $T$. There is a change in sign of $\partial \rho ∕\partial H$ as $T$ sweeps through the magnetic ordering transition. (b) Exponents and $\rho$ intercepts from power-law fits to low $T\rho \left(T\right)$ (Fig. 11). The exponent goes through a minimum as $H$ increases to 18 T, while ${\rho }_0$ saturates above 8 K.

Figure 11

(a),(b) Power-law fits to low-temperature electrical resistivity $\rho \left(T\right)$ for various fields $H$ up to 18 T, separated for clarity. Fit parameters are plotted in Fig. 10b.

Figure 12

(a) A representative CEF fit to the inverse magnetic susceptibility, after subtraction of the ${\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ contribution and correction for partial filling. (b) A representative CEF fit to the electrical resistivity, which includes lattice, impurity, and magnetic contributions.