${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$: A High-Kondo-Temperature Transition-Metal Oxide

We present a comprehensive study of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ using bulk sensitive hard and soft x-ray spectroscopy combined with local-density $\text{approximation}+\text{dynamical}$ mean-field theory (DMFT) calculations. Correlation effects on both the Cu and Ru ions can be observed. From the Cu $2p$ core-level spectra, we deduce the presence of magnetic ${\mathrm{Cu}}^{2+}$ ions hybridized with a reservoir of itinerant electrons. The strong photon energy dependence of the valence band allows us to disentangle the Ru, Cu, and O contributions and, thus, to optimize the DMFT calculations. The calculated spin and charge susceptibilities show that the transition metal oxide ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ must be classified as a Kondo system and that the Kondo temperature is in the range of 500–1000 K.

Popular Summary

Transition-metal oxides host a surprisingly rich variety of physical properties such as high-temperature superconductivity or colossal sensitivity of electrical resistance to magnetic fields. These behaviors originate from a delicate balance between the kinetic and Coulomb interaction energies of constituent electrons. However, a hallmark of the interacting electron physics—the Kondo effect—is rarely observed in transition-metal oxides. Here, we demonstrate that Kondo physics appears in the transition-metal oxide ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$.

The Kondo effect describes the scattering of electrons in a material due to magnetic impurities. It shows itself as a characteristic change in resistivity with temperature. To search for this effect in ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$, we combine calculations with x-ray photoemission experiments to study valence and core-level photoemission spectra. This allows us to eliminate ambiguities in describing the magnetic and electronic properties.

We find that spins in the copper ions exhibit Kondo behavior, with a high onset in the range of 500–1000 K. Therefore, ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ must be classified as a Kondo system. The high Kondo temperature is the key to reconcile contradictory conclusions of existing studies (conducted at moderate temperatures) on this material.

Over half a century after its discovery, the study of Kondo physics and related phenomena is largely limited to rare-earth compounds. Our work brings these investigations to transition-metal oxides. In particular, the perovskite material class studied here provides a new platform for integrating competing quantum phenomena in strongly correlated electron systems.

Figure 1

Magnetic susceptibility of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ reproduced from Refs. [11, 12, 21, 22] and of ${\mathrm{CaCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ from Ref. [23]. The black dashed line shows the Curie paramagnetic behavior for a $S=1/2$ ${\mathrm{Cu}}^{2+}$ ion scaled by a factor of 3. Inset: crystal structure of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ visualized by vesta [24]. The blue, red, gray, and indigo blue spheres represent Cu, O, Ru, and Ca atoms, respectively.

Figure 2

Valence band resonant photoemission of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$, with the experimental spectra taken at the Cu $2p$ ($L_3$) resonance ($h\nu =931.2\mathrm{eV}$) and at 10 eV below the resonance ($h\nu =921.2\mathrm{eV}$). The inset displays the experimental Cu-$L_{2,3}$ x-ray absorption spectrum.

Figure 3

(a) Experimental Cu $2p$ core-level x-ray photoemission spectrum of ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ reproduced from Ref. [49]. (b) Theoretical spectrum from the ${\mathrm{CuO}}_4$ cluster model. (c) Experimental Cu $2p$ core-level HAXPES spectrum of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$. (d) Theoretical spectrum from the $\mathrm{LDA}+\mathrm{DMFT}$ method.

Figure 4

Valence band spectra of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$: (a) experimental results measured at different photon energies and (b) $\mathrm{LDA}+\mathrm{DMFT}$ spectral intensities for the Cu $3d$, Ru $4d$, and O $2p$ states. The spectral broadening is taken into account using a 200-meV Gaussian to simulate the experimental resolution. (c) $\mathrm{LDA}+\mathrm{DMFT}$ spectral intensities of the Cu $3d$ orbitals in ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$. The Cu orbitals are defined in the local axis of the ${\mathrm{CuO}}_4$ plane, as shown in the inset.

Figure 5

Top: close-up of the Fermi-level region of the ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ spectrum together with the gold spectrum. Bottom: division of the ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ spectra by the gold spectrum.

Figure 6

(a) Temperature dependence of the Cu $xy$ spectral intensities in the $\mathrm{LDA}+\mathrm{DMFT}$ method. The inset shows the imaginary part of the self-energy of the Cu $xy$ orbital. (b) $\mathrm{LDA}+\mathrm{DMFT}$ hybridization densities $-1/\pi \mathrm{Im}\mathrm{\Delta }(\omega )$ of the Cu $xy$ orbital. The inset shows the hybridization densities in a wide energy range for selected temperatures (300, 900, and 2000 K).

Figure 7

Local susceptibility ${\chi }_{\mathrm{loc}}(T)$ (blue) and the dynamical spin susceptibility ${\chi }_{\mathrm{loc}}(\omega =+0)$ (red), calculated by the $\mathrm{LDA}+\mathrm{DMFT}$ method.

Figure 8

Valence band PES (left) and Cu-$L_{2,3}$ XAS (right) of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ samples synthesized by the different groups used in this work.

Figure 9

Photoionization cross section values of Cu $3d$, Ru $4d$, and O $2p$ interpolated from the data tabulated in Refs. [56, 57, 58]. The vertical lines indicate the photon energies used for the photoemission data shown in Fig. 4.

Figure 10

Correlation function $\chi (\tau )$ of the spin and charge (inset) channel calculated by the $\mathrm{LDA}+\mathrm{DMFT}$ method, where $\beta =1/k_{B}T$ is the inverse temperature.

Figure 11

(a) The Cu $xy$ spectral intensities in $\mathrm{LDA}+\mathrm{DMFT}$ results for different double-counting ${\mu }_{\mathrm{dc}}^{\mathrm{Cu}}$ values. The positions of the low-energy peak in the experimental PES data are indicated by vertical dashed lines. The calculation is performed at 300 K. (b) Local susceptibility ${\chi }_{\mathrm{loc}}(T)$ and (c) dynamical spin susceptibility ${\chi }_{\mathrm{loc}}(\omega =+0)$ at the Cu site. Here, the model with all Ru $4d$ states is employed. The dashed lines in (a) and (b) show the results obtained with $U_{\mathrm{Ru}}=0.0\mathrm{eV}$. (d) Hybridization densities $-1/\pi \mathrm{Im}\mathrm{\Delta }(\omega )$ of the Cu $xy$ orbital in $\mathrm{LDA}+\mathrm{DMFT}$ with $U_{\mathrm{Ru}}=3.1\mathrm{eV}$ (solid line) and with $U_{\mathrm{Ru}}=0.0\mathrm{eV}$ (dashed line). The inset shows the hybridization densities near $E_F$.

Figure 12

(a) Experimental Ru $3d$ core-level photoemission spectrum of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ (black line) and theoretical spectra from the $\mathrm{LDA}+\mathrm{DMFT}$ calculation with $U_{\mathrm{Ru}}=3.1\mathrm{eV}$ (red line) and $U_{\mathrm{Ru}}=0.0\mathrm{eV}$ (blue line). (b) Top: local spin susceptibility and bottom: screened spin moment $M_{\mathrm{scr}}(T)=\sqrt{T{\chi }_{\mathrm{loc}}(T)}$ [63, 64] on the Ru site computed by the $\mathrm{LDA}+\mathrm{DMFT}$ method. The horizontal dashed line indicates the atomic value of the ${\mathrm{Ru}}^{4+}$ ion.

Figure 13

(a) Cu $2p_{3/2}$ core-level photoemission spectra calculated by the $\mathrm{LDA}+\mathrm{DMFT}$ method with selected ${\mu }_{\mathrm{dc}}^{\mathrm{Ru}}$ values (with ${\mu }_{\mathrm{dc}}^{\mathrm{Cu}}=70.1\mathrm{eV}$). (b) The spectra by $\mathrm{LDA}+\mathrm{DMFT}$ with selected ${\mu }_{\mathrm{dc}}^{\mathrm{Cu}}$ values (with ${\mu }_{\mathrm{dc}}^{\mathrm{Ru}}=16.2\mathrm{eV}$). The experimental spectrum is shown for comparison.

Figure 14

$\mathrm{LDA}+\mathrm{DMFT}$ results for the models (left) with and (right) without the Ru $4d$ $e_g$ states at selected temperatures. Top: Cu $xy$ spectral intensities; middle: the hybridization densities of the Cu $xy$ orbitals; bottom: local susceptibility ${\chi }_{\mathrm{loc}}(T)$ and the dynamical spin susceptibility ${\chi }_{\mathrm{loc}}(\omega =+0)$ at the Cu site. ${\mu }_{\mathrm{dc}}^{\mathrm{Cu}}=70.1\mathrm{eV}$ is employed in the two models, and ${\mu }_{\mathrm{dc}}^{\mathrm{Ru}}=16.2\mathrm{eV}$ (${\mu }_{\mathrm{dc}}^{\mathrm{Ru}}=13.4\mathrm{eV}$) for the model with (without) Ru $4d$ $e_g$ states.