Pentavalent iridium pyrochlore $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$: A prototype material system for competing crystalline field and spin-orbit coupling

A new pyrochlore oxide $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ with an $\mathrm{I}{\mathrm{r}}^{5+}$ charge state was prepared by high-pressure techniques. Although strong spin-orbit coupling (SOC) dominates the electronic states in most iridates so that a SOC-Mott state is proposed in $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$ in the assumption of an undistorted $\mathrm{Ir}{\mathrm{O}}_6$ octahedral crystalline field, the strongly distorted one in the current $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ exhibits a competing interaction with the SOC. Unexpected from a strong SOC limit, $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ deviates from a nonmagnetic and insulating $J=0$ ground state. It displays short-range ferromagnetic correlations and metallic electrical transport properties. First-principles calculations well reproduce the experimental observation, revealing the large mixture between the $j_{\mathrm{eff}}=1/2$ and $j_{\mathrm{eff}}=3/2$ bands near the Fermi surface due to the significant distortion of $\mathrm{Ir}{\mathrm{O}}_6$ octahedra. This work sheds light on the critical role of a noncubic crystalline field in electronic properties which has been ignored in past studies of $5d$-electron systems.

Figure 1

(a) Crystal structure of pyrochlore with chemical formula $A_2{B}_2{\mathrm{O}}_6{\mathrm{O}}^{\prime }$ in space group Fd-3m. The ${\mathrm{O}}^{\prime }{A}_4$ tetrahedra and corner-sharing $B{\mathrm{O}}_6$ octahedra are shown. (b) Powder x-ray diffraction pattern and Rietveld refinement results of $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$. Observed (black circle), calculated (red line), and difference (blue line) profiles are shown together with the allowed Bragg reflections (ticks). The inset shows the distorted O-Ir-Or bond angles in a single $\mathrm{Ir}{\mathrm{O}}_6$ octahedron.

Figure 2

X-ray absorption spectroscopy of the Ir-$L_3$ edges of $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ and the related references for comparison.

Figure 3

(a) Temperature dependence of magnetic susceptibility of $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ measured at 5 T in zero-field-cooling (ZFC) and field-cooling (FC) modes. The inset shows the Curie-Weiss fitting in 8–60 K. (b) Field-dependent magnetization at different temperatures. The inset shows the enlarged view for the magnetic hysteresis behavior at 2 K.

Figure 4

(a) Temperature dependence of resistivity measured at zero field and 9 T for $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$. The inset shows the enlarged view for field-induced upturn at lower temperatures. (b) Field-dependent magnetoresistance MR $(=100\%\times [\rho \left(H\right)-\rho \left(0\right)]/\rho (0\left)\right)$ at different temperatures. The inset shows the resistivity fitted using a Fermi liquid model below 25 K. (c) Specific heat as a function of temperature below 250 K measured at zero field. The inset shows the fitting below 20 K as described in the text.

Figure 5

(a), (b) First-principles numerical results for the band dispersion along several high-symmetry directions of $\mathrm{C}{\mathrm{d}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ based on LDA and $\mathrm{LDA}+\mathrm{SOC}$ methods, respectively. (c), (d) The calculated density of states near the Fermi surface using the LDA and $\mathrm{LDA}+\mathrm{SOC}$ methods, respectively. One can find strong mixture between the $j_{\mathrm{eff}}=1/2$ and 3/2 bands near the Fermi level in (d), indicating the competing $\mathrm{\Delta }$ and $\lambda$.