Electronic, magnetic, and electric transport properties of Ce${}_3$Rh${}_4$Sn${}_{13}$ and Ce${}_3$Co${}_4$Sn${}_{13}$: A comparative study

We present an investigation of the magnetic, thermodynamic, and electric transport properties and the electronic structure of the strongly correlated compounds Ce${}_3$Rh${}_4$Sn${}_{13}$ and Ce${}_3$Co${}_4$Sn${}_{13}$. The main goal of this report is to compare the physical properties of both compounds and to explain the abnormal electrical resistivity behavior in Ce${}_3$Co${}_4$Sn${}_{13}$ above $\sim 160$ K, which has not been observed in Ce${}_3$Rh${}_4$Sn${}_{13}$. We suggest that a possible local distortion of the trigonal Sn2 prisms around Co occurs in Ce${}_3$Co${}_4$Sn${}_{13}$ below $\sim 160$ K, which could change the electronic structure near the Fermi level and, as a consequence, explain the metallic behavior visible in the resistivity above this temperature. We determined experimentally the hybridization energy $\Delta$ between the $f$-electron and conduction-electron states for both compounds and its influence on the different $\rho \left(T\right)$ behaviors under pressure. The complimentary experimental data allowed us to explain the semimetallic properties of both compounds and the transition between semimetallic and metallic behavior in Ce${}_3$Co${}_4$Sn${}_{13}$, which is not observed for Ce${}_3$Rh${}_4$Sn${}_{13}$.

Figure 1

dc magnetic susceptibility, $\chi$, measured in a magnetic field of 500 Gs and $1/\chi$ vs temperature for Ce${}_3$Rh${}_4$Sn${}_{13}$ samples (#1 and #2) and for Ce${}_3$Co${}_4$Sn${}_{13}$. The line represents the approximation of the $\chi \left(T\right)$ data by the modified Curie-Weiss law $\chi ={\chi }_0+C/(T-{\theta }_{\mathrm{CW}})$ between 2 K and 300 K; the fit is not enough good. The $\chi \left(T\right)$ data are well described by this expression in the temperature region $T>15$ K. The inset displays the low-temperature $\chi \left(T\right)$ data in a log-log scale.

Figure 2

X-ray diffraction (XRD) of Ce${}_3$Co${}_4$Sn${}_{13}$ with Cu$K$${}_{\alpha }$ radiation and at different temperatures. The upper inset displays the temperature change of the (532) XRD line between 12 K and 300 K. The lower left panel displays the temperature dependence of the parameter ${\Delta }_2$, which is proportional to the half-width of the $K_{\alpha 2}$ diffraction peak. The lower right panel shows the temperature dependence of the intensity of the (320) diffraction line

Figure 3

The structure of Ce${}_3$Co${}_4$Sn${}_{13}$ at the room temperature and at $T=120$ K highlighting the arrangement of the Sn1(Sn2)${}_{12}$ icosahedra, with Sn atoms at $T=293$ K (yellow) and at $T=120$ K (blue). Ce (green circles) and Co (black circles) are represented as isolated atoms. The lattice parameters measured at two different temperatures are normalized in the figure to a value obtained at $T=293$ K. The drawing of the figure is produced by vesta.[24]

Figure 4

Magnetization $M$ vs magnetic field $B$ measured at different temperatures for Ce${}_3$Rh${}_4$Sn${}_{13}$ (sample #2). The solid lines are fits of the Langevin function to the magnetization data at $T=2,4$, and 6 K. The saturated value of $M$, obtained at $T=1.9$ K from an extrapolation of $M$ vs $1/B$ to $1/B=0$, is 0.75 ${\mu }_B$ for Ce${}_3$Rh${}_4$Sn${}_{13}$ (sample #1), 0.98 ${\mu }_B$ for Ce${}_3$Rh${}_4$Sn${}_{13}$ (sample #2), and 0.96 ${\mu }_B$ for Ce${}_3$Co${}_4$Sn${}_{13}$.

Figure 5

(a) Magnetization $M$ per formula unit vs magnetic field $B$ measured at different temperatures for La${}_3$Rh${}_4$Sn${}_{13}$. The inset shows a symmetric hysteresis loop at $T=1.9$ K (in the superconducting state). Panel (b) displays the magnetic susceptibility for La${}_3$Rh${}_4$Sn${}_{13}$ at the magnetic field $B=1000$ Gs.

Figure 6

Ce${}_3$Rh${}_4$Sn${}_{13}$ (#2): $C\left(T\right)/T$ [in panel (a)] as a function of applied magnetic fields. The inset exhibits $C/T$ low-$T$ data for the reference compound La${}_3$Rh${}_4$Sn${}_{13}$ near the critical temperature $T_c$. Panel (b) shows the specific heat $C$ at different magnetic fields. The $C/T$ and $C$ data for La${}_3$Rh${}_4$Sn${}_{13}$ is measured for $B=0$.

Figure 7

Ce${}_3$Rh${}_4$Sn${}_{13}$ (#1): $C\left(T\right)/T$ as a function of applied magnetic fields. The arrow signals atypical behavior which could result from the magnetic transition.

Figure 8

Ce${}_3$Co${}_4$Sn${}_{13}$: $C\left(T\right)/T$ [panel (a)] as a function of temperature at various applied magnetic fields. Panel (b) shows the specific heat data, $C$, vs $T$ in the magnetic fields specified in panel (a).

Figure 9

The entropy $S$ of the samples Ce${}_3$Rh${}_4$Sn${}_{13}$ and Ce${}_3$Co${}_4$Sn${}_{13}$ vs temperature at different magnetic fields.

Figure 10

The Ce $3d$ XPS spectra of Ce${}_3{M}_4$Sn${}_{13}$ and La${}_3{M}_4$Sn${}_{13}$, where $M=\mathrm{Rh}$ and Co with evidence for the 3$d^{9}4f^n$ components ($n=1,2$) for Ce${}_3{M}_4$Sn${}_{13}$, while $n=0,1$ in case of La${}_3{M}_4$Sn${}_{13}$.

Figure 11

The Ce 4$d$ XPS spectra obtained for Ce${}_3{M}_4$Sn${}_{13}$, $M=\mathrm{Rh}$ or Co.

Figure 12

The valence band XPS spectra measured for Ce${}_3{M}_4$Sn${}_{13}$ and La${}_3{M}_4$Sn${}_{13}$, where $M=\mathrm{Rh}$ or Co.

Figure 13

Electrical resistivity at different magnetic fields for Ce${}_3$Rh${}_4$Sn${}_{13}$; samples #1 and #2 are shown in panels (a) and (b), respectively.

Figure 14

Electrical resistivity at different magnetic fields for Ce${}_3$Co${}_4$Sn${}_{13}$. The inset shows the resistivity of La${}_3$Rh${}_4$Sn${}_{13}$ and La${}_3$Co${}_4$Sn${}_{13}$.

Figure 15

Electrical resistivity for Ce${}_3$Rh${}_4$Sn${}_{13}$ (#2) under applied pressure and normalized by the resistivity at $T=300$ K [in panel (a)]. The inset shows the $\rho$ data vs $\log T$. Panel (b) shows $\Delta \rho$ vs $\log T$, where $\Delta \rho =\rho \left({\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}\right)-\rho \left({\mathrm{La}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}\right)$.

Figure 16

Electrical resistivity for Ce${}_3$Co${}_4$Sn${}_{13}$ under applied pressure. The inset shows the $\Delta \rho$ data vs $\log T$, where $\Delta \rho =\rho \left({\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}\right)-\rho \left({\mathrm{La}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}\right)$.