Determination of a Quantum Spin Liquid Ground State from Model Independent Evidence of Fractionalization

Fractional magnetic excitations, spinons, are the most prominent emergent excitations in a quantum spin liquid (QSL) [1], and they are well understood within the Tomonaga-Luttinger liquid phase realized in one-dimensional (1D) Heisenberg antiferromagnetic (HAFM) spin chain [2]. Fractionalization reveals itself as a continuum of dynamical structure factor S(q, ω) captured via inelastic neutron scattering (INS) [2]. However, its interpretation requires a material-specific dynamical structure factor S’(q, ω) that also explicitly depends on the unwanted interactions originating from anisotropy, disorders, and inhomogeneities in the bulk samples [3,4]. This challenge has triggered a desperate search for more robust emergent excitations, better materials, and model-independent experimental observables to diagnose a QSL. Here by employing high-resolution soft X-ray RIXS at Cu <i>L₃</i>-edge on a prototypical 1D-HAF chain Sr₂CuO₃, we demonstrate a model-independent determination of the RIXS spectra into two and multi-spinons excitations, hence the fractionalization. Firstly, we identify distinct resonances for the two-spinon and the multi-spinon excitations, e.g. four-spinon, with an energy separation dictated only by <i>J</i>. Secondly, we find that the multi-spinon resonance is narrower than two-spinon, giving the opportunity to enhance the pure two-spinon response (suppress the multi-magnon response) by properly detuning the incident photon energy. Our 1D <i>t-J</i> Hamiltonian-based <i>exact</i> calculations fully capture the low energy spin dynamics probed by RIXS and show that relative spectral weight enhancement/suppression is intrinsic to the symmetry of fractional excitations, i.e. it does not depend on the material-specific details. We further show that detuning-dependent spectral weight control can be employed to disentangle two-spinon excitations from multi-spinon, crucial for identifying fractionalization and thus, a quantum spin liquid ground state.<br/><br/>1. J . Knolle et. al., Ann. Rev. Condens. Matter Phys. <b>10</b>, 451 (2019). C. Broholm, et al., Science 376, 6475 (2020).<br/>2. M. Mourigal et. al., Nat. Phys. <b>9</b>, 435 (2013).<br/>3. J. A. Paddison et. al., Nature Physics <b>13</b>, 117 (2017).<br/>4. Y. Shen et. al., Nature <b>540,</b> 559 (2016).<br/><br/><br/>Acknowledgements<br/>This work was supported by the US Department of Energy (DOE) Office of Science, Early Career Research Program. This research used beamline 2-ID of NSLS-II, a US DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under contract no. DE-SC0012704.