Doping effect on the electronic structure and thermodynamic properties in ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$

A comprehensive study of heat and electric transport, magnetic, and electronic structure (experiment and calculations) properties is reported for a skutterudite-related ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ heavy fermion system with the respective substitution of Co and Sb into Ru and Sn sites. ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ is obtained as a heavy fermion system with high electronic contribution to the specific heat $C\left(T\right)/T$ of $\sim 3\text{J}/{\mathrm{K}}^2{\text{mol}}_{\text{Ce}}$, and a significant Schottky anomaly below about 10 K. The complex study gives a consistent interpretation of the impact of doping on the crystal electric-field effect and Kondo temperature. For ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ we report a field-induced phase transition between the magnetically correlated heavy fermion phase and the single-ion Kondo impurity state, which does not depend on the type of dopant. We also demonstrate that doping does not improve the poor thermoelectric properties of ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$.

Figure 1

XRD patterns with Mo $K_{\alpha }$ radiation for ${\mathrm{Ce}}_3{\mathrm{Co}}_{0.5}{\mathrm{Ru}}_{3.5}{\mathrm{Sn}}_{13}$ (black line) and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$ (blue line) with Rietveld refinement (red line). Inset displays the lattice parameter $a$ vs $x$ for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}{\mathrm{Sb}}_x$ (blue points) and ${\mathrm{Ce}}_3{\mathrm{Ru}}_x{\mathrm{Co}}_{4-x}{\mathrm{Sn}}_{13}$ (black points).

Figure 2

Valence-band XPS spectra for the samples labeled at the top of the figure. Also are shown the total DOS calculated for ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ (a), and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$ (g).

Figure 3

Atomic partial DOS for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$.

Figure 4

Effect of Sb doping in ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}{\mathrm{Sb}}_x$ (a) and of Ru doping in ${\mathrm{Ce}}_3{\mathrm{Ru}}_x{\mathrm{Co}}_{4-x}{\mathrm{Sn}}_{13}$ (c) on the total DOS. Panels (b) and (c) exhibit total DOSs near the Fermi level in detail.

Figure 5

The Fermi-surface sheets of ${\mathrm{Ce}}_3{\mathrm{Co}}_{4-x}{\mathrm{Ru}}_x{\mathrm{Sn}}_{13}$ in the first Brillouin zone. Left column corresponds to the spin down; right column corresponds to spin up. The $\mathrm{\Gamma }$ point is at the center of the cubic Brillouin zone. The calculations were carried out for the high-temperature structure $Pm\overline{3}n$.

Figure 6

The Ce $3d$ XPS spectra at room temperature for ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ (a), ${\mathrm{Ce}}_3{\mathrm{RuCo}}_3{\mathrm{Sn}}_{13}$ (b), ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13}$ (c), and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.7}{\mathrm{Sb}}_{1.3}$ (d), and as an example, a deconvoluted spectrum for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.7}{\mathrm{Sb}}_{1.3}$ on the basis of the Gunnarsson-Schönhammer theoretical model, with spin-orbit components $3d^{9}4f^1$ (blue line) and $3d^{9}4f^2$ (red line). The brown dotted line represents the background; the thick red line shows the fit after deconvolution to the lowest XPS spectrum. From the deconvolution procedure, the Sn $3s$ line contribution at 885 eV (green line) provides about 15% of the total peak intensity due to $3d_{5/2}^{9}4f^1$ final states.

Figure 7

The Ce $4d$ XPS spectra for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$ (a) and ${\mathrm{Ce}}_3{\mathrm{Ru}}_3{\mathrm{CoSn}}_{13}$ (b) with no evidence of the $4d^{9}4f^0$ components.

Figure 8

The Sn $4d$ XPS spectra for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}{\mathrm{Sb}}_x$ (a) and for ${\mathrm{Ce}}_3{\mathrm{Ru}}_{4-x}{\mathrm{Co}}_x{\mathrm{Sn}}_{13}$ (b). The inset shows the calculated Sn $4d$ DOS. Note, the intensity of the Sb $4d$ line increases with increasing amount of Sb, as expected.

Figure 9

(a) Magnetic susceptibility $\chi$ of ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}{\mathrm{Sb}}_x$ in external field of 1000 Gs. The solid red line represents the CEF fit to $1/\chi$ data for the two excited doublets separated from the ground-state doublet by energy ${\mathrm{\Delta }}_1=12$ K for $x=0.65$ and 11 K for $x=1.3$, and ${\mathrm{\Delta }}_2=117$ K $\left(x=0.65\right)$ and 110 K $\left(x=1.3\right)$, respectively. The deviation of $1/\chi$ from the fit observed above $\sim 200$ K is due to structural deformation (see [15]). In panel (b) the Van Vleck formula is fitted to $\chi$ and $1/\chi$ data measured at magnetic field of 1000 Gs for the ${\mathrm{Ce}}_3{\mathrm{Ru}}_x{\mathrm{Co}}_{4-x}{\mathrm{Sn}}_{13}$ samples. The total CEF splitting of two doublets is about 245 K for sample $x=1$, 470 K for sample $x=3$, and 500 K for sample $x=3.5$. Panel (c) displays magnetization $M$ per Ce atom vs magnetic field $B$ measured at different temperatures for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.7}{\mathrm{Sb}}_{1.3}$. The solid lines are fits of the Langevin function to the magnetization data. Very similar $M$ vs $B$ isoterms are obtained for remaining compounds.

Figure 10

$C\left(T\right)/T$ vs $T$ for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{12.35}{\mathrm{Sb}}_{0.65}$. The inset shows $C\left(T\right)$ data and the fit of the resonance level model to the experimental data.

Figure 11

${\mathrm{Ce}}_3{\mathrm{Co}}_3{\mathrm{RuSn}}_{13}$; $C\left(T\right)/T$ vs $T$ for ${\mathrm{Ce}}_3{\mathrm{Co}}_3{\mathrm{RuSn}}_{13}$ at different magnetic fields $B$. The inset shows $C\left(T\right)$ for different $B$ [open points, plotted with the same colors as $C\left(T\right)/T$, respectively] and the fit of the resonance level model to the experimental data.

Figure 12

$C\left(T\right)/T$ vs $T$ $\left(B=0\right)$ for different ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}{\mathrm{Sb}}_x$ and ${\mathrm{Ce}}_3{\mathrm{Co}}_{4-x}{\mathrm{Ru}}_x{\mathrm{Sn}}_{13}$ samples.

Figure 13

Kondo temperature $T_K\equiv {\mathrm{\Delta }}_K/k_B$ vs magnetic field for ${\mathrm{Ce}}_3{\mathrm{Co}}_3{\mathrm{RuSn}}_{13}$ determined on the basis of the Kondo resonant-level model.

Figure 14

Temperature-dependent thermopower $S$ of ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13},{\mathrm{Ce}}_3{\mathrm{Co}}_3{\mathrm{RuSn}}_{13}$, and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$.

Figure 15

Thermal resistivity $W$ and thermal conductivity $\kappa$ (inset) for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13},{\mathrm{La}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13},{\mathrm{Ce}}_3{\mathrm{Co}}_3{\mathrm{RuSn}}_{13}$, and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$ in temperature range 2 and 300 K. The calculated electron thermal conductivity is represented by the dotted lines.

Figure 16

The figure of merit for ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{13},{\mathrm{Ce}}_3{\mathrm{Co}}_3{\mathrm{RuSn}}_{13}$, and ${\mathrm{Ce}}_3{\mathrm{Ru}}_4{\mathrm{Sn}}_{11.05}{\mathrm{Sb}}_{1.95}$.