Fig. 4: Additional mode in high-energy-resolution RIXS spectra.

a Comparison of spectra for Sr₅Ir₃O₁₁ and Sr₂IrO₄ near the zone center (π, π). Low energy data for Sr₅Ir₃O₁₁ (Sr₂IrO₄) are fitted using two (one) pseudo-Voigt peaks, shown as solid red and blue (black) lines. DL single magnons are fitted by the peaks in gray dashed lines. Error bars denote square roots of the absolute intensities. b 2D color plot of the high-energy-resolution RIXS spectra of Sr₅Ir₃O₁₁ near the zone center, overlaid with peak positions extracted from the fits in a. `Peak 1' (red circles) and `Peak 2' (blue circles) are used to follow the excitations of Sr₅Ir₃O₁₁. The single magnon dispersion of Sr₂IrO₄ is marked by black circles. A magnetic mode around 90 meV corresponds to DL single magnon in Sr₅Ir₃O₁₁, which mirrors the single magnon mode of Sr₃Ir₂O₇^24,27. Solid lines are linear fits to the peak positions. Error bars represent the standard error of the estimated parameters obtained from the fitting. c Ratio of coherent single-magnons to the total magnetic spectral weight throughout the Brillouin zone for Sr₂IrO₄ (left panel) and Sr₅Ir₃O₁₁ (right panel), as estimated from the RIXS measurements in Fig. 3. Data points are marked as blue dots on the surfaces generated by interpolating them. d Schematic of magnon dispersion and low energy edge of spinon continua for Sr₂IrO₄ (left panel) and Sr₅Ir₃O₁₁ (right panel). Two-spinon continuum is marked by the pink shaded area and the red line represents the lower bound of the continuum, as given by Eq. (2). The blue line represents the single-magnon dispersion extracted by fitting the data shown in Supplementary Fig. 7 using the J-Q model. The dashed part of blue lines indicates the decay of single magnons due to strong magnon-spinon couplings.