Electronic correlations and crystal-field effects in R Cu 3 Ru 4 O 12 ( R = La , Pr , Nd )

Among the large class of $A$-site ordered perovskites of stoichiometry $A{C}_{3}{B}_{4}{\mathrm{O}}_{12}$, the rare-earth $(R)$ ruthenates $R{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ $(R=\mathrm{La}, \mathrm{Pr}, \mathrm{Nd})$ are interesting compounds due both to $\mathrm{Ru}\text{\ensuremath{-}}4d$-derived electronic correlations and to unconventional crystal-electric-field effects of the $R$ ions. Here we report on detailed investigations of these compounds utilizing x-ray diffraction, neutron scattering, magnetic susceptibility, and electrical resistivity measurements as well as heat capacity and nuclear resonance experiments. A broad range of external parameters is scanned and depending on the specific technique, temperatures range from 100 mK to 730 K in external magnetic fields up to 14 T. In this work ${\mathrm{LaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ serves as reference compound with a nonmagnetic $A$ site, characterized in detail recently [S. Riegg et al., Phys. Rev. B 93, 115149 (2016)]. All compounds investigated reveal heavy-fermion behavior with a ${T}^{2}$ dependence of the low-temperature electrical resistivity and significantly enhanced Sommerfeld coefficients. Toward low temperatures, the compounds with $R=\mathrm{Pr}$ and Nd are dominated by the magnetic moments of the $R$ ions, which occupy crystallographic positions with point-group symmetry ${T}_{h}$. The crystal-electric-field effects are clearly visible especially in heat capacity and inelastic neutron scattering data from which the crystal-electric-field parameters are derived. The ground state of the ${\mathrm{Pr}}^{3+}$ ion is identified as a triplet $({\mathrm{\ensuremath{\Gamma}}}_{4}^{(1)})$, whereas for ${\mathrm{Nd}}^{3+}$ it is a quartet $({\mathrm{\ensuremath{\Gamma}}}_{67})$. Evidence for lowering of the ${T}_{h}$ symmetry is observed at the Pr site at temperatures below 10 K, suggesting the formation of orbital order. Moreover, the spin-lattice relaxation derived from $^{63}\mathrm{Cu}$ nuclear quadrupole resonance indicates characteristic temperatures close to 7 K and 350 mK, probably related to orbital and magnetic order, respectively.