The temperature- and field-dependent specific heat $C(T,H)$ measurement on the noncentrosymmetric superconductors ${\mathrm{Li}}_2{\mathrm{Pd}}_3\mathrm{B}$, ${\mathrm{Li}}_2{\mathrm{Pt}}_3\mathrm{B}$, and ${\mathrm{Li}}_2{\left({\mathrm{Pd}}_{0.5}{\mathrm{Pt}}_{0.5}\right)}_3\mathrm{B}$ were carried out over a wide range of $T$ and $H$. $C(T,H)$ of the limit compounds is found to be distinctly different: within the superconducting phase, the electronic specific heat of the Pd-based compound follows $C_e^S(T<T_c=6.95\mathrm{K},0\mathrm{T})=3\exp [-16.4∕T]\mathrm{J}∕\mathrm{mol}\mathrm{K}$ while for the Pt-based compound $C_e^S(T<T_c=2.56\mathrm{K},0\mathrm{T})=\alpha T^2\mathrm{mJ}∕\mathrm{mol}\mathrm{K}$, where $\alpha =7.3\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^3$. An increase in $H$ tends to reduce weakly the exponential argument and the coefficient of the quadratic term. The above-mentioned findings are in agreement with the description that, due to the difference in the strength of the spin-orbit coupling, the pairing symmetry in the Pd- (Pt-) based compound is predominately a spin-singlet (spin-triplet) state. Within the very low-temperature range, the field-induced normal-state of the Pd-based limit manifests $C^N(T,7T>H_{c2})=9.3T+1.1T^3\mathrm{mJ}∕\mathrm{mol}\mathrm{K}$ while that of the Pt-based isomorph shows $C^N(T,7T>H_{c2})=9.3T+0.92T^3\mathrm{mJ}∕\mathrm{mol}\mathrm{K}$. For the intermediate alloy ${\mathrm{Li}}_2{\left({\mathrm{Pt}}_{0.5}{\mathrm{Pd}}_{0.5}\right)}_3\mathrm{B}$, $C(T,H)$ mimics that of the Pt-based compound; specifically, $C_e^S(T<T_c=3.9\mathrm{K},0\mathrm{T})=\alpha T^2\mathrm{mJ}∕\mathrm{mol}\mathrm{K}$ where $\alpha =4.6\left(2\right)\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^3$. The ratio of the coefficients of the quadratic terms in ${\mathrm{Li}}_2{\left({\mathrm{Pt}}_{0.5}{\mathrm{Pd}}_{0.5}\right)}_3\mathrm{B}$ and ${\mathrm{Li}}_2{\mathrm{Pt}}_3\mathrm{B}$, ${\alpha }_{{\mathrm{Pt}}_{0.5}{\mathrm{Pd}}_{0.5}}∕{\alpha }_{\mathrm{Pt}}$, is equal to $Z_{{\mathrm{Pt}}_{0.5}{\mathrm{Pd}}_{0.5}}^2∕Z_{\mathrm{Pt}}^2$, confirming that the line nodes are driven by the spin-orbit interaction. The finding that these nodes can survive even in a 50% Pd-diluted material gives extra support to the reported claim that the $x$-dependent evolution of $T_c$, $H_{c1}$, $H_{c2}$, and ${(\partial H_{c2}∕\partial T)}_{T_c}$ is almost linear.

• Received 11 April 2007

DOI:https://doi.org/10.1103/PhysRevB.76.104506