Two-Spinon and Orbital Excitations of the Spin-Peierls System TiOCl

We combine high-resolution resonant inelastic x-ray scattering with cluster calculations utilizing a recently derived effective magnetic scattering operator to analyze the polarization, excitation energy, and momentum dependent excitation spectrum of the low-dimensional quantum magnet TiOCl in the range expected for orbital and magnetic excitations (0 - 2.5 eV). Ti 3d orbital excitations yield complete information on the temperature-dependent crystal-field splitting. In the spin-Peierls phase we observe a dispersive two-spinon excitation and estimate the inter- and intra-dimer magnetic exchange coupling from a comparison to cluster calculations.