Charge partitioning and anomalous hole doping in Rh-doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

The simultaneous presence of sizable spin-orbit interactions and electron correlations in iridium oxides has led to predictions of novel ground states including Dirac semimetals, Kitaev spin liquids, and superconductivity. Electron and hole doping studies of spin-orbit assisted Mott insulator ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ are being intensively pursued due to extensive parallels with the ${\mathrm{La}}_2{\mathrm{CuO}}_4$ parent compound of cuprate superconductors. In particular, the mechanism of charge doping associated with replacement of Ir with Rh ions remains controversial with profound consequences for the interpretation of electronic structure and transport data. Using x-ray absorption near edge structure measurements at the Rh L, K, and Ir $L$ edges we observe anomalous evolution of charge partitioning between Rh and Ir with Rh doping. The partitioning of charge between Rh and Ir sites progresses in a way that holes are initially doped into the $J_{\mathrm{eff}}=1/2$ band at low $x$ only to be removed from it at higher $x$ values. This anomalous hole doping naturally explains the reentrant insulating phase in the phase diagram of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ and ought to be considered when searching for superconductivity and other emergent phenomena in iridates doped with $4d$ elements.

Figure 1

(a) Edge-jump normalized Rh $K$-edge XANES data for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ and ${\mathrm{Rh}}_2{\mathrm{O}}_3$ reference, all measured at room temperature. (b) XANES measurements at the Rh ${\mathit{L}}_3$ edge for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ with ${\mathrm{Rh}}^{3+}$ and ${\mathrm{Rh}}^{4+}$ reference samples. All plots are shifted in the vertical direction for clarity. (c) Derived Rh oxidation state based on energy shifts of leading Rh $K$ and $L$ absorption edges.

Figure 2

(a) Calculated probability ${\mathrm{P}[\mathrm{Rh}}^{3+}]$ for emergence of ${\mathrm{Rh}}^{3+}$ state when the number of Ir neighbors exceeds a critical number $n_c$ in the 1–4 range. On the right axis is the experimentally derived ${\mathrm{P}[\mathrm{Rh}}^{3+}]$. (b) shows ${\mathrm{P}[\mathrm{Rh}}^{4+}]$ when the number of nearest-neighbor Ir is below $n_c$. Right axis is the Rh valence from Fig. 1. Experimental results imply that Rh is 3+ when the number of Ir neighbors exceeds a critical number between 3 and 4 (and Rh is 4+ when below this critical number).

Figure 3

(a) Ir ${\mathit{L}}_3$ and (b) ${\mathit{L}}_2$ XANES measurements for $x=0.05, x=0.15$, and $x=0.45$ samples together with Ir 4+ and 5+ standards. Data have been shifted in the vertical scale for clarity. The inset in (b) shows the $\%\left({\mathrm{Ir}}^{5+}\right)$ as a function of Rh, $x$ on the left axis. The right axis shows the Ir ${\mathit{L}}_{3,2}$ peak shifts for $x=0.05, x=0.15$, and $x=0.45$

Figure 4

Number of $5d$ Ir holes calculated empirically using Rh valence values derived from Rh $K$-edge data in Fig. 1 are shown superimposed on the low temperature phase diagram adapted from Qi et al. [22].