Enhancing superconductivity of Y5Rh6Sn18 by atomic disorder

We investigate the effect of enhancement of superconducting transition temperature ${T}_c$ by nonmagnetic atom disorder in the filled skutterudite-related tetragonal ${\mathrm{Y}}₅{\mathrm{Rh}}₆{\mathrm{Sn}}₁₈$ compound doped with Ca. We documented experimentally that ${\mathrm{Y}}₅{\mathrm{Rh}}₆{\mathrm{Sn}}₁₈$ and its Ca-doped alloys are electronically inhomogeneous at the nanoscale, when Ca content is smaller than $\ensuremath{\sim}1.5$ in the ${\mathrm{Y}}_{5\ensuremath{-}x}{\mathrm{Ca}}_x{\mathrm{Rh}}₆{\mathrm{Sn}}₁₈$ system, while for $x\ensuremath{\ge}1.5$ much stronger chemical phase inhomogeneity is observed with an about 20% volume fraction of the second 3:4:13 cubic phase, which we interpret as a fluctuation of stoichiometry within the bulk sample. Then the enhancement of ${T}_c$ vs $x$ could be modeled by a mechanism proposed in recent theoretical reports for increasing the mean-field transition temperature ${T}_c$ in the presence of nonmagnetic disorder. The increase in disorder with doping increases the sample inhomogeneity and causes a systematic increase in ${T}_c$, while for two-phase $x\ensuremath{\ge}1.5$ samples the critical temperature ${T}_c^★\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{T}_c$ rapidly increases. Based on band structure calculations performed under pressure, we demonstrate how the change in density of states would affect ${T}_c$ of ${\mathrm{Y}}₅{\mathrm{Rh}}₆{\mathrm{Sn}}₁₈$. We obtained the Gr\"uneisen parameter ${\ensuremath{\gamma}}_G$ larger for the inhomogeneous phase with respect to ${\ensuremath{\gamma}}_G$ of the bulk ${T}_c$ phase and attribute the enhancement of ${T}_c$ to larger stiffening of the high-temperature ${T}_c^★$ phase.