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 intradimer magnetic exchange coupling from a comparison to cluster calculations.

Figure 1

RIXS spectra at $T=300\mathrm{K}$ (light red) and $T=36\mathrm{K}$ (dark blue) ($h\nu =454.2\mathrm{eV}$, $\sigma$ polarization, $ac$ scattering; see text). Black solid curves are Gaussian fits to the low-$T$ data. Also, the orbital character of the CF excitations is indicated. Insets: Experimental RIXS geometry. Left: $\varphi =90°$ geometry to define $\sigma$ (out-of-plane) and $\pi$ (in-plane) polarizations. Right: Definition of $\mathit{q}$ (brown arrow) and $q_{||}$ (red arrow). $\mathit{q}$ was fixed by the constant $\varphi =50°$ in our experiments, and $q_{||}$ was varied by rotating the sample around the polar axis, i.e., changing $\theta$.

Figure 2

(a) Excitation-energy dependence of RIXS spectra at $T=300\mathrm{K}$ in $\sigma$ polarization and $ac$ scattering. Corresponding excitation energies are indicated. (b) Ti $L$ edge XAS spectra with main polarizations along the different crystal axes both measured (solid curves) and calculated (dashed curves) for the geometry of panel (a). Photon energies from (a) are marked by vertical lines. (c),(d) $\sigma$- and $\pi$-polarized RIXS spectra for different photon energies in $ac$ (c) and $bc$ (d) scattering from experiments (solid curves) and multiplet calculations (broken curves).

Figure 3

(a) RIXS spectra taken at $h\nu =456.8\mathrm{eV}$ in $\pi$ polarization and $bc$ scattering ($T=15\mathrm{K}$), for $q_{||}$ corresponding to (from top to bottom) 36%, 31%, 25%, 19%, 11%, 0%, and -11% of the $\Gamma Y$ path in the BZ. The LEE is highlighted by the shaded area. (b) Two-spinon dynamical spin structure factor for a 28 site dimerized Heisenberg model. The dispersion of the LEE is indicated, obtained from fitting the data in panel (a) (blue square markers). At $q_{||}=0$ the spin gap extracted from NMR [16] is indicated. Inset: LEE spectral weight (i.e., experimental peak areas).