Origin of the different electronic structure of Rh- and Ru-doped ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$

One way to induce insulator-to-metal transitions in the spin-orbit Mott insulator ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ is to substitute iridium with transition metals (Ru, Rh). However, this creates intriguing inhomogeneous metallic states, which cannot be described by a simple doping effect. We detail the electronic structure of the Ru-doped case with angle-resolved photoemission and show that, in contrast to Rh, it cannot be connected to the undoped case by a rigid shift. We further identify bands below $E_F$ coexisting with the metallic ones that we assign to nonbonding Ir sites. We rationalize the differences between Rh and Ru by a different hybridization with oxygen, which mediates the coupling to Ir and sensitively affects the effective doping. We argue that the spin-orbit coupling does not control either the charge transfer or the transition threshold.

Figure 1

Sketch of the ionic $t_{2g}$ levels for Rh, Ir, and Ru. SOC splits them into one $J_{1/2}$ and two $J_{3/2}$ levels ($J_{3/2-m_J}$ with $m_J=\pm 1/2,3/2$), with a much larger value for Ir, being a $5d$ TM, than Rh and Ru (${\lambda }_{5d}\simeq 0.5\text{eV}$ vs ${\lambda }_{4d}\simeq 0.1\text{eV}$). We assume a shift $\varepsilon$ between Ir and the other TM (see Fig. 4 for a discussion of its origin). Electrons should be transferred to the lowest available energy level, unless the Coulomb repulsion $U$ forbids double occupation.

Figure 2

(a) Energy-momentum plot along ${\mathrm{\Gamma }}^{\prime }X$ in ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ ($k_y=3$; see Brillouin zone sketch below). The lines highlight the three main bands [19]. (b) Same for ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ doped with 45% Ru. (c) EDC at $X$ as a function of Ru doping (as indicated) fitted with a polynomial background (dashed line) and an asymmetric Gaussian (black line). (b) Same at ${\mathrm{\Gamma }}^{\prime }$ fitted with a fixed steplike background and a Gaussian. (e) Relative spectral weight of the $J_{1/2}$ and $J_{3/2-3/2}$ peaks compared to the pure, when spectra are normalized to the background intensity. More samples are included than those shown in panels (c) and (d).

Figure 3

Energy-momentum plot of ARPES intensity measured for $x=0.45$ at 20 K with 100 eV photon energy and linear horizontal polarization, along (a) $\mathrm{\Gamma }\mathrm{X}$ ($k_y=2)$ and (b) $\mathrm{\Gamma }\mathrm{M}$. To enhance the low features near $E_F$, the image is multiplied by a Fermi step along $y$, centered at $-0.27\mathrm{eV}$ with width 0.2 eV and amplitude 20. Markers sample the dispersions shown in panels (c) and (d) to ease identification of the different bands. (c) Comparison of the high binding energy bands (black markers) with the dispersion measured in pure ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ (lines). The dispersion are extracted either from MDC fits or from local maximum. (d) Comparison of the bands near $E_F$ (color markers) with the dispersion measured in 15% doped Rh [9]. The Rh dipsersions are shifted up to match the Ru data by the indicated amounts.

Figure 4

(a) Band structure calculated for an ordered structure ${\mathrm{Sr}}_2{\left(\mathrm{Ir}\mathrm{Rh}\right)}_{0.5}{\mathrm{O}}_4$ along $\mathrm{\Gamma }\mathrm{X}$, without SOC. The color is proportional to the atomic character (red-blue scale). (b) Same for Ru. [(c), (d)] Sketch of the energy levels of oxygen, Ir, and TM dopant and their relative hybridization, based on calculation presented in the Supplemental Material, but not to scale. The hybridized states have mixed atomic character, and their color indicates the dominant one. The circled part represents hybridization of N levels, from Ir and TM.