Intermediate-valence behavior of the transition-metal oxide ${\text{CaCu}}_3{\text{Ru}}_4{\text{O}}_{12}$

The transition-metal oxide ${\text{CaCu}}_3{\text{Ru}}_4{\text{O}}_{12}$ with perovskite-type structure shows characteristic properties of an intermediate-valence system. The temperature-dependent susceptibility exhibits a broad maximum around 150–160 K. At this temperature, neutron powder diffraction reveals a small but significant volume change whereby the crystal structure is preserved. Moreover, the temperature-dependent resistivity changes its slope. NMR Knight shift measurements of Ru reveal a cross-over from high temperature paramagnetic behavior of localized moments to itinerant band states at low temperatures. Additional density-functional theory calculations can relate the structural anomaly with the $d$-electron number. The different experimental and calculational methods result in a mutually consistent description of ${\text{CaCu}}_3{\text{Ru}}_4{\text{O}}_{12}$ as an intermediate-valent system in the classical sense of having low-energy charge fluctuations.

Figure 1

(Color online) Temperature dependence of the lattice constant $a$ of ${\text{CaCu}}_3{\text{Ru}}_4{\text{O}}_{12}$ as resulting from the Rietveld refinements of the neutron powder-diffraction measurements. The solid line is a fit according to a usual anharmonic behavior described in the text.

Figure 2

(Color online) Heat capacity $C/T$ versus $T$ of ${\text{CaCu}}_3{\text{Ru}}_4{\text{O}}_{12}$. A small but significant peak is observed in the temperature range $135<T<160\text{K}$. To account for the phonon contributions, the data were fitted by a Debye term and four Einstein modes (solid red line). The right-hand inset shows the heat-capacity anomaly on an expanded scale for heating (open blue squares) and cooling (open green circles) evidencing the absence of hysteresis. The left hand inset shows the associated entropy change of about $70\text{mJ}/\left(\text{f}\text{.u}\text{.}\text{mol}\text{K}\right)$.

Figure 3

(Color online) The top frame shows the Knight shift $K$ of Cu (blue circles, left scale) and Ru (red triangles, right scale), respectively. Please note the different sign of the two scales. The bottom frame shows the spin-lattice relaxation rate $1/T_1$ of ${\text{CaCu}}_3{\text{Ru}}_4{\text{O}}_{12}$ for ${}^{63}\text{C}\text{u}$ and ${}^{101}\text{R}\text{u}$, respectively. The full lines represent fits to the data according to a Korringa law. For comparison, the relaxation rates of pure Cu and Ru metal are also shown.