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Novel magnetic moments with yet-to-be-explored interactions can be realised in cluster Mott insulators. In this new class of materials, charge carriers occupy quasimolecular orbitals and are delocalised over a cluster, e.g., a dimer, while intercluster charge fluctuations are suppressed by Coulomb repulsion. Ba3InIr2O9 hosts Ir dimers with three holes (Figure 92a). Showing persistent spin dynamics down to 20 mK, it is viewed as a promising candidate for spin-liquid behaviour. To address magnetism in Ba3InIr2O9, one has to understand the character of the magnetic moments. This is achieved by RIXS interferometry at the Ir L3 edge, studying the interference pattern in the q-dependent RIXS intensity.
RIXS data of Ba3InIr2O9 measured at beamline ID20 show a rich excitation spectrum (Figure 93a). They differ strongly from results for Mott-insulating iridates with holes localised in single-site orbitals. Remarkably, the spectra fall on top of each other for constant qc, the q component parallel to the dimer axis. The peak energies do not depend considerably on q, suggesting a local character, while the qc-dependence of the RIXS intensity I(qc) is a first signature of the quasimolecular nature. The formation of quasimolecular orbitals can be rationalised by the strong intradimer hopping t ~ 0.5 eV that results from the intradimer Ir-Ir distance being smaller than in Ir metal. The quasimolecular character is firmly established by RIXS interferometry, which measures the dynamical structure factor S(q,w) via q-dependent interference patterns. These reveal the symmetry and character of excited states in the same way as elastic scattering does for the ground state. RIXS on dimers is an inelastic twist of Young s double-slit experiment, and hence yields a sinusoidal interference pattern . L-edge RIXS proceeds via an intermediate state with a strongly localised core hole, which takes over the role of a nearly ideal (point-like) slit . The interference arises since the RIXS amplitude is a coherent sum over scattering processes on all Ir sites over which a given excited state is delocalised. Figure 93b shows the integrated RIXS intensity over a broad range of qc, covering many Brillouin zones. For two sites connected by the vector d, a dominant sin2(q d/2) modulation of the RIXS intensity I(q) pinpoints that the excitations are delocalised over the dimer. The period yields an Ir-Ir distance |d| = 2.601(9) A in good agreement with elastic scattering.
The classic elastic double-slit experiment shows cos2(q d/2) behaviour. In RIXS, the interference carries information on the symmetry of the excitations. With inversion symmetry, a cos2(q d/2) modulation is expected if ground state and excited state show the same parity. In contrast, sin2(q d/2) behaviour reflects opposite parity, e.g., the excitation from a bonding to an antibonding orbital.
For quasimolecular orbitals, a central question is whether intradimer hopping is large enough to counteract the effects of spin-orbit coupling. Comparing the RIXS spectra with exact diagonalisation results yields a microscopic description that highlights the importance of spin-orbit coupling. It supports an intuitive picture that considers (anti-) bonding orbitals built from spin- orbit-entangled j=1/2 and 3/2 states on sites 1 and 2, |j±m> = 1/√2 (|j, m>1 ± |j, m>2), where m denotes linear combinations of states with different jz. In the ground state, two of the three holes occupy the bonding j=1/2 orbital (Figure 92b). However, the third hole occupies the antibonding j=1/2 orbital for small hopping but the bonding j=3/2 orbital for large hopping, i.e., large bonding- antibonding splitting (Figure 92b). The observation of RIXS excitations below 0.3 eV indicates that Ba3InIr2O9 is close to the phase transition between these two cases. The RIXS interference strongly depends on the bonding/antibonding
Fig. 92: a) Crystal structure of Ba3InIr2O9 with Ir2O9 dimers (green). b) Sketch of quasimolecular dimer orbitals occupied by three holes.
Fig. 93: a) RIXS spectra of Ba3InIr2O9. b) Integrated RIXS intensity showing sin2(q d/2) modulation. The arrow in (a) marks the fixed energy range for integration.