Concomitant enhancement of spin susceptibility and pairing interaction in the reduced carrier-density regime of Li$_x$ZrNCl superconductor

Li-intercalated layered nitrides Li$_x$ZrNCl are novel superconductors, in which superconductivity emerges at relatively high transition temperature $T_c\sim12$ - 15~K with very low carrier density $\sim10^{21}$~cm$^{-3}$. The pristine $\beta$-ZrNCl is a simple band insulator, and electron doping is achieved by Li intercalation. Insulator-to-superconductor (IS) transition takes place at $x\sim0.05$ with maximum $T_c$ value of $\sim15$~K and $T_c$ decreases with further doping, which is opposite trend to the other superconductors in doped band insulators. Here we show the results of magnetic susceptibility measurements on Li$_x$ZrNCl with systematically controlled $x$. Estimated spin susceptibility $\chi_s$ is almost temperature-independent without substantial anisotropy. With decreasing $x$, $\chi_s$ evolves strongly, same as $T_c$. On the other hand, specific heat study revealed that the density of states is reduced but the pairing interaction is enhanced on the verge of IS transition. Therefore, our results may indicate that magnetic fluctuations are enhanced toward a band-insulator and that they are possibly responsible to superconductivity even in the present small carrier-density system.