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Transition metal oxides of the $4d$ and $5d$ block have recently become thetargets of materials discovery, largely due to their strong spin-orbit couplingthat can generate exotic magnetic and electronic states. Here we report thehigh pressure synthesis of Lu$_2$Rh$_2$O$_7$, a new cubic pyrochlore oxidebased on $4d^5$ Rh$^{4+}$ and characterizations via thermodynamic, electricaltransport, and muon spin relaxation measurements. Magnetic susceptibilitymeasurements reveal a large temperature-independent Pauli paramagneticcontribution, while heat capacity shows an enhanced Sommerfeld coefficient,$\gamma$ = 21.8(1) mJ/mol-Rh K$^2$. Muon spin relaxation measurements confirmthat Lu$_2$Rh$_2$O$_7$ remains paramagnetic down to 2 K. Taken in combination,these three measurements suggest that Lu$_2$Rh$_2$O$_7$ is a correlatedparamagnetic metal with a Wilson ratio of $R_W = 2.5$. However, electrictransport measurements present a striking contradiction as the resistivity ofLu$_2$Rh$_2$O$_7$ is observed to monotonically increase with decreasingtemperature, indicative of a nonmetallic state. Furthermore, although themagnitude of the resistivity is that of a semiconductor, the temperaturedependence does not obey any conventional form. Thus, we propose thatLu$_2$Rh$_2$O$_7$ may belong to the same novel class of non-Fermi liquids asthe nonmetallic metal FeCrAs.

Coexistence of metallic and nonmetallic properties in the pyrochlore Lu$_2$Rh$_2$O$_7$