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    Optical study of orbital excitations in transition-metal oxides
    (Milton Park : Taylor & Francis, 2005) Rückamp, R.; Benckiser, E.; Haverkort, M.W.; Roth, H.; Lorenz, T.; Freimuth, A.; Jongen, L.; Möller, A.; Meyer, G.; Reutler, P.; Büchner, B.; Revcolevschi, A.; Cheong, S.-W.; Sekar, C.; Krabbes, G.; Grüninger, M.
    The orbital excitations of a series of transition-metal compounds are studied by means of optical spectroscopy. Our aim was to identify signatures of collective orbital excitations by comparison with experimental and theoretical results for predominantly local crystal-field excitations. To this end, we have studied TiOCl, RTiO3 (R = La, Sm and Y), LaMnO3, Y2BaNiO5, CaCu2O3 and K4Cu4OCl10, ranging from early to late transition-metal ions, from t2g to eg systems, and including systems in which the exchange coupling is predominantly three-dimensional, one-dimensional or zero-dimensional. With the exception of LaMnO3, we find orbital excitations in all compounds. We discuss the competition between orbital fluctuations (for dominant exchange coupling) and crystal-field splitting (for dominant coupling to the lattice). Comparison of our experimental results with configuration-interaction cluster calculations in general yields good agreement, demonstrating that the coupling to the lattice is important for a quantitative description of the orbital excitations in these compounds. However, detailed theoretical predictions for the contribution of collective orbital modes to the optical conductivity (e.g. the line shape or the polarization dependence) are required to decide on a possible contribution of orbital fluctuations at low energies, in particular, in case of the orbital excitations at ≈0.25 eV in RTiO3. Further calculations are called for which take into account the exchange interactions between the orbitals and the coupling to the lattice on an equal footing.
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    RIXS interferometry and the role of disorder in the quantum magnet Ba3 Ti3-x Irx O9
    (College Park, MD : APS, 2023) Magnaterra, M.; Moretti Sala, M.; Monaco, G.; Becker, P.; Hermanns, M.; Warzanowski, P.; Lorenz, T.; Khomskii, D. I.; van Loosdrecht, P. H. M.; van den Brink, J.; Grüninger, M.
    Motivated by several claims of spin-orbit-driven spin-liquid physics in hexagonal Ba3Ti3-xIrxO9 hosting Ir2O9 dimers, we report on resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge for different x. We demonstrate that magnetism in Ba3Ti3-xIrxO9 is governed by an unconventional realization of strong disorder, where cation disorder affects the character of the local moments. RIXS interferometry, studying the RIXS intensity over a broad range of transferred momentum q, is ideally suited to assign different excitations to different Ir sites. We find pronounced Ir-Ti site mixing. Both ions are distributed over two crystallographically inequivalent sites, giving rise to a coexistence of quasimolecular singlet states on Ir2O9 dimers and spin-orbit-entangled j=1/2 moments of 5d5Ir4+ ions. RIXS reveals different kinds of strong magnetic couplings for different bonding geometries, highlighting the role of cation disorder for the suppression of long-range magnetic order in this family of compounds.
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    Resonant inelastic x-ray incarnation of Young’s double-slit experiment
    (Washington : American Association for the Advancement of Science (A A A S), 2019) Revelli, A.; Moretti, Sala, M.; Monaco, G.; Becker, P.; Bohatý, L.; Hermanns, M.; Koethe, T.C.; Fröhlich, T.; Warzanowski, P.; Lorenz, T.; Streltsov, S.V.; van Loosdrecht, P.H.M.; Khomskii, D.I.; van den Brink, J.; Grüninger, M.
    Young’s archetypal double-slit experiment forms the basis for modern diffraction techniques: The elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young’s experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns, which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba 3 CeIr 2 O 9 with structural Ir dimers and strong spin-orbit coupling. The double “slits” in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.