Spin-orbit coupled systems in the "atomic" limit: rhenates, osmates, iridates

Abstract

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized $t_{2g}$ orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses "single-particle" and "multi-particle" excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated $5d$ oxides. We present new higher resolution RIXS data at the Re-L${}_3$ edge in Ba${}_2$YReO${}_6$ which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba${}_2$$\mathcal{M}$ReO${}_6$ (with $\mathcal{M}$=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as $t_{2g}$-$e_g$ interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the osmates, the exchange is one or two orders of magnitude weaker in the rhenates and iridates, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the $\mathcal{M}$O${}_6$ cluster. This suggests a possible role for non-dispersive intra-cluster excitons in Ba${}_2$YIrO${}_6$ which may lead to a weak breakdown of the atomic $J_{\mathrm{eff}}=0$ picture and to small magnetic moments.

arXiv comment11 pages, 6 figs, added experimental coauthors, revised following referee comments, published in PRB

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• EDRIXS: An open source toolkit for simulating spectra of resonant inelastic x-ray scattering
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• Antiferromagnetic Skyrmions and Skyrmion Density Wave in Rashba Hund's Insulator
• The interplay between structural, magnetic and electronic states in the pyrochlore iridate Eu2Ir2O7
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• Spin-orbit coupling driven insulating state in hexagonal iridates Sr3MIrO6 (M = Sr, Na and Li)
• Evidences for the random singlet phase in a new honeycomb iridate SrIr${}_2$O${}_{6-\delta }$
• Multipolar magnetism in $5d^2$ vacancy-ordered halide double perovskites
• Electronic excitations in $5d^4$ J=0 Os${}^{4+}$ halides studied by RIXS and optical spectroscopy
• Small moments without long-range magnetic ordering in the zero-temperature ground state of the double-perovskite iridate Ba${}_2$YIrO${}_6$
• Spin-orbit coupling in a half-filled $t_{2g}$ shell: the case of $5d^3$ K${}_2$ReCl${}_6$
• Dynamic Jahn-Teller Phenomena in Heavy Transition Metal Compounds
• Electronic origin of ferroic quadrupole moment under antiferroic quadrupole orders and finite magnetic moment in $J_{\mathrm{eff}}=3/2$ systems
• Jahn-Teller states mixed by spin-orbit coupling in an electromagnetic field
• Varying magnetism in the lattice distorted Y2NiIrO6 and La2NiIrO6
• Resonant inelastic X-ray scattering investigation of Hund's and spin-orbit coupling in $5d^2$ double perovskites
• In-gap states and strain-tuned band convergence in layered structure trivalent iridate K0.75Na0.25IrO2
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