Almost pure $J_{\text{eff}}=\frac{1}{2}$ Mott state of $\mathrm{In}{}_2\mathrm{Ir}{}_2\mathrm{O}{}_7$ in the limit of reduced intersite hopping

The pyrochlore iridate ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ is a $J_{\mathrm{eff}}=\frac{1}{2}$ Mott insulator with frustrated magnetism. Despite the large trigonal distortion, only a small admixture of $J_{\mathrm{eff}}=\frac{3}{2}$ component in the $J_{\mathrm{eff}}=\frac{1}{2}$ bands is observed as compared with other pyrochlore iridates $A_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($A$ = trivalent cation). We argue that the reduced intersite hopping between the $J_{\mathrm{eff}}=\frac{1}{2}$ and the $J_{\mathrm{eff}}=\frac{3}{2}$ manifold, due to the large trigonal distortion and the covalent character of In-O bonds, plays a predominant role in the distinct behavior of ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. Such effect of the intersite hopping should not be dismissed in the local physics of $J_{\mathrm{eff}}=\frac{1}{2}$ Mott insulators.

Figure 1

(a) Crystal structure of ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. (b) Local structure of two corner-sharing ${\mathrm{IrO}}_6$ octahedra. The blue arrows indicate the direction of trigonal compression. (c) Ir $L_3$ edge RIXS spectrum of the ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ polycrystalline sample at $T=7\mathrm{K}$ with incident energy $E_i=11215\mathrm{eV}$. The Gaussian fits of the peaks are represented by a dashed blue line. The excitations labeled as $E_1$ and $E_2$ correspond to the ones depicted in (d). (d) Splittings of $J_{\mathrm{eff}}=\frac{1}{2}$ and $\frac{3}{2}$ states into three Kramers doublets (${\varphi }_0$, ${\varphi }_1$, and ${\varphi }_2$) under a trigonal crystal field in a single-ion description. (e) The energy split $\mathrm{\Delta }E=E_2-E_1$ against $\mathrm{\Delta }x$ for $A_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $A$ = Pr [28], Y [17], and In.

Figure 2

Temperature-dependent (a) resistivity $\rho \left(T\right)$, (b) magnetic susceptibility $M/H\left(T\right)$, and (c) specific heat $C\left(T\right)$ of the ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ polycrystalline sample. The inset of (a) shows the Arrhenius plot of $\rho \left(T\right)$ and the black line indicates the fit at high temperatures. In (b), the black arrows denote the zero-field-cooling ($\to$) and field-cooling ($\leftarrow$) curves. The inset shows the temperature dependence of inverse magnetic susceptibility, and the black line indicates the Curie-Weiss fit. The inset of (c) shows specific heat divided by temperature around the anomaly at 55 K.

Figure 3

$J_{3/2}$ and $J_{5/2}$ resolved DOS for Ir $t_{2g}$ bands in $A_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ for $A$ = Y, Lu, and In. The area beneath the curve of $J_{3/2}$-derived DOS is filled for clarity. The Fermi level $E_{\mathrm{F}}$ is indicated by dashed black lines. The ratio of the area under the $J_{5/2}$- and $J_{3/2}$-derived DOS curves within $\pm 0.5\mathrm{eV}$ of $E_{\mathrm{F}}$ $(\pm 0.4\mathrm{eV}$ for $A$ = In) is shown.

Figure 4

$J_{3/2}$ and $J_{5/2}$ resolved DOS for Ir $t_{2g}$ bands for model $A_2{\left({\mathrm{Ir}}_{1/16}{\mathrm{Hf}}_{15/16}\right)}_2{\mathrm{O}}_7$ for $A$ = In and Y for undistorted ($\mathrm{\Delta }x=0$) ${\mathrm{IrO}}_6$ and the experimentally observed distortion of ${\mathrm{IrO}}_6$. The area beneath the curve of $J_{3/2}$-derived DOS is filled for clarity. The ratio of the area under the $J_{5/2}$- and $J_{3/2}$-derived DOS curves within $\pm 0.3\mathrm{eV}$ of $E_{\mathrm{F}}$ is shown.