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ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-28207-w a Data, qc = 0 b Data, qc = 0.5 c Calculation, qc = 0 d Calculation, qc = 0.5 200 100 10 200 10 100 11 00 200 6 200 6 100 100 11 00 111 111 111 111 (–, 0) (–, –) (0, 0) (–, 0) (–, –) (–, 0) (–, –) (0, 0) (–, 0) (–, –) 222 244 222 244 e (1/2, 1/2) f (3/8, 3/8) 30 18 15 g (5/16, 5/16) qc = 0 qc = 0.5 qc = 0 qc = 0.5 qc = 0 qc = 0.5 20 10 5 000 20 10 8 10 5 4 000 0 100 200 300 0 100 200 300 h (1/4, 1/4) i (1/8, 1/8) 10 10 10 555 000 422 211 000 0 100 200 300 0 100 200 300 Energy (meV) Energy (meV) 9 10 0 100 200 300 j (1/16, 1/16) qc = 0 qc = 0.5 qc = 0 qc = 0.5 qc = 0 qc = 0.5 Fig. 3 Magnetic dispersion and excitonic longitudinal mode decay. a, b In-plane momentum dependence of the magnetic excitations measured at qc = 0 and 0.5. The black and green symbols correspond to the energy of the magnetic modes and the vertical bars to their peak widths. Both quantities were extracted from the energy spectra at different points in reciprocal space (such as shown in panels e–j and Fig. 2c–e). c and d Theoretical calculations of the magnetic dispersion relation, overplotted with the experimentally determined excitation energies and line widths. The presence of the mode at qc = 0.5 that is absent at qc = 0 evinces that this is an excitonic longitudinal mode. e–j RIXS spectra at reciprocal space as highlighted by color-matching arrows in panel a. Circles represent the data and dotted lines outline the different components of the spectrum, which are summed to produce the solid line representing the total spectrum. Error bars are determined via Poissonian statistics. The isolation of the longitudinal mode (highlighted with red shading) from other contributions was possible by simultaneously analyzing qc = 0.5 and qc = 0 for each in-plane reciprocal-lattice wavevector (see Methods section for details). because this effective parameterization reflects the difference between on-site and longer-range interactions in the real material. The model identifies the quasiparticle dispersion at qc = 0 as the transverse mode with a persistent well-defined nature even at high energies. Above the transverse mode, the spin response is funda- mentally influenced by the finite charge gap. A broad continuum involving electron-hole spin transitions across the charge gap is present for all qc values covering a broad energy-momentum range. A new mode emerges around (0, 0) and (0.5, 0.5) for qc = 0.5, which we identify as the excitonic longitudinal mode. To understand the excitonic longitudinal mode discussed, we first note that the tight-binding band structure analysis of 4 NATURE COMMUNICATIONS | (2022)13:913 | https://doi.org/10.1038/s41467-022-28207-w | www.nature.com/naturecommunications 0 100 200 300 Energy (meV) Intensity (arb. units) Intensity (arb. units) Intensity (arb. units) Intensity (arb. units) Intensity (arb. units) Intensity (arb. units) Energy (meV) Energy (meV)PDF Image | Antiferromagnetic excitonic insulator state in Sr3Ir2O7
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