Superconductivity and non-Fermi-liquid behavior of La${}_3$Pd${}_4$Si${}_4$ and Ce${}_3$Pd${}_4$Si${}_4$

Measurements of temperature and field dependent bulk properties have been carried out on ${\{\mathrm{Ce},\mathrm{La}\}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$. Rietveld refinements of x-ray powder intensity data confirm the orthorhombic ${\mathrm{U}}_3{\mathrm{Ni}}_4{\mathrm{Si}}_4$-type structure for both compounds. While ${\mathrm{La}}_3{\mathrm{Pd}}_3{\mathrm{Si}}_4$ exhibits superconductivity below 2 K together with some indications of a two gap scenario, the former can be characterized as a Kondo lattice system in presence of crystalline electric field splitting. Due to the closeness of a quantum critical point, distinct non-Fermi-liquid features dominate the low temperature physics of ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$.

Figure 1

X-ray powder pattern and Rietveld refinement of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$. The inset is a sketch of the crystal structure in projection along [100].

Figure 2

Temperature dependent electrical resistivity $\rho$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$. The solid line is a least-squares fit as explained in the text. The inset shows $\rho \left(T\right)$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ at various externally applied magnetic fields.

Figure 3

Temperature dependent heat capacity $C_p$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ plotted as $C_p/T$ vs $T$ for various externally applied magnetic fields. The dashed line represents an ideal superconducting transition with $T_c=1.98$ K.

Figure 4

(a) Low temperature specific heat $C_p$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ plotted in a normalized representation $C_p/\left({\gamma }_n{T}_c\right)$ vs $T/T_c$. ${\gamma }_n$ is the Sommerfeld constant in the normal state region of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$. The solid line is the heat capacity of a fully gapped BCS superconductor, whereas the dashed line represents a model with two different superconducting gaps. For details see the text. The dashed–double-dotted line is a power law $C_p\propto T^3$. (b) Temperature dependent difference $\delta$ of experimental and theoretical heat capacity data $C_p/\left({\gamma }_n{T}_c\right)$ below $T_c$. The colors refer to (a). (c) Upper critical magnetic field ${\mu }_0{H}_{c2}$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ as derived from resistivity (50% criterion) and specific heat data (thermodynamic mean value of the transition). The dashed line is a least-squares fit employing Eq. (1) and the solid line is a fit based on the WHH model (see text). The dashed-dotted line is the thermodynamic critical field.

Figure 5

Temperature dependent resistivity $\rho$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ and ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ plotted on a logarithmic temperature scale. The magnetic contribution ${\rho }_{\text{mag}}\left(T\right)$ of ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ is also shown in this plot, where the dashed line should emphasize Kondo interaction; ${\rho }_{\text{mag}}\approx \rho \left({\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4\right)-\rho \left({\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4\right)$. The solid line is a least-squares fit as explained in Fig. 2.

Figure 6

Low temperature electrical resistivity $\rho$ measured at various externally applied magnetic fields. The inset shows resistivity details together with power law fits for the zero and 12 T run.

Figure 7

Temperature dependent magnetic susceptibility $\chi$ of ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ plotted as $1/\chi$ vs $T$. The solid line is a fit employing a modified Curie-Weiss law. The inset displays the isothermal magnetization ($T=2$ K) of ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$; the solid line is the magnetization of an effective spin 1/2 system with a Landè factor $g_{\text{eff}}=0.775$.

Figure 8

Temperature dependent specific heat $C_p$ of ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ plotted as $C_p/T$ vs $\ln T$. For purpose of comparison, $C_p/T$ of ${\mathrm{La}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$ is added, too. The solid line represents the heat capacity of a spin fluctuation model according to Eq. (2) near to the quantum critical point and the dashed-dotted line is a smooth extrapolation of heat capacity data using the Debye model with ${\theta }_D=280$ K. The dashed line is the calculated magnetic entropy $S_{\text{mag}}$ of ${\mathrm{Ce}}_3{\mathrm{Pd}}_4{\mathrm{Si}}_4$, referring to the right axis.