  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.
