Effective $J\mathbf{=}1/2$ Insulating State in Ruddlesden-Popper Iridates: An $\mathrm{LDA}\mathbf{+}\mathrm{DMFT}$ Study

Using ab initio methods for correlated electrons in solids, we investigate the metal-insulator transition across the Ruddlesden-Popper (RP) series of iridates and explore the robustness of the $J_{\mathrm{eff}}=1/2$ state against band effects due to itineracy, tetragonal distortion, octahedral rotation, and Coulomb interaction. We predict the effects of epitaxial strain on the optical conductivity, magnetic moments, and $J_{\mathrm{eff}}=1/2$ ground-state wave functions in the RP series. To describe the solution of the many-body problem in an intuitive picture, we introduce a concept of energy-dependent atomic states, which strongly resemble the atomic $J_{\mathrm{eff}}=1/2$ states but with coefficients that are energy or time dependent. We demonstrate that the deviation from the ideal $J_{\mathrm{eff}}=1/2$ state is negligible at short time scales for both single- and double-layer iridates, while it becomes quite significant for ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ at long times and low energy. Interestingly, ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ is positioned very close to the $SU(2)$ limit, with only $\sim 3\%$ deviation from the ideal $J_{\mathrm{eff}}=1/2$ situation.

Figure 1

Spectral functions and orbital-resolved DOS obtained by the DMFT method for the RP series of iridates. Arrows indicate optical transitions corresponding to the peaks in the optical conductivities shown in Fig. 2. Dotted lines denote the band structures obtained by $\mathrm{GGA}+\mathrm{U}$ calculations. For 214 and 327, the $\mathrm{GGA}+\mathrm{U}$ band structures and the DMFT spectral functions are aligned by fixing the position of the topmost valence state at $X$. Orbitals ($1/2$, $\pm 1/2$) correspond to ${\psi }_{\pm 1/2}$, and “total(3/2)” stands for the sum over the remaining $t_{2g}$ states, i.e., $J_{\mathrm{eff}}=3/2$ states.

Figure 2

(a) Computed optical conductivities ${\sigma }_1$ for three iridates at their experimental lattice constants. For clarity, ${\sigma }_1$ is shifted up by $500(\Omega \mathrm{cm}{)}^{-1}$ for ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ and ${\mathrm{SrIrO}}_3$; $\alpha$ and $\beta$ indicate peak positions corresponding to the vertical transitions marked in Fig. 1. (b) Dependence of ${\sigma }_1$ on epitaxial strain (0% and $\pm 2\%$) in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

Figure 3

Dependence of computed properties of the 214 (a)–(c) and 327 (d)–(f) compounds on epitaxial strain in the range of $\pm 3\%$. (a),(d) Orbital-to-spin moment ratio ${\mu }_{\mathrm{L}}/{\mu }_{\mathrm{S}}$. (b),(e) Staggered rotation angle $\theta$ of ${\mathrm{IrO}}_6$ octahedra. (c),(f) Ratio of Ir-O bond lengths along $z$ and in-plane $c/a$, and inverse of parameter $\gamma$ describing the generalized $J_{\mathrm{eff}}=1/2$ wave function (see main text). Filled symbols with dashed (solid black) lines denote the results obtained by DMFT ($\mathrm{GGA}+\mathrm{U}$) calculations. Red triangles indicate $\mathrm{GGA}+\mathrm{U}$ results computed with unrelaxed experimental lattice parameters.