Quantitative determination of the atomic scattering tensor in orbitally orderedYTiO3by using a resonant x-ray scattering technique

Abstract

The orbitally ordered state of ${\mathrm{YTiO}}_{3}$ has been investigated utilizing resonant x-ray scattering (RXS) near the Ti K-edge. The RXS intensities have been observed at the $1\stackrel{\ensuremath{\rightarrow}}{s}4p$ dipole transition energy (the main edge). The atomic scattering tensor of the Ti ion has quantitatively been determined by measurements of the azimuthal angle and polarization dependence of the signal at several scattering vectors. On the basis of the tensor, we discuss not only the scattering mechanism but also the wave function of the orbitally ordered state, finding it to be a linear combination of two ${t}_{2g}$ orbitals. In addition, RXS at the $1\stackrel{\ensuremath{\rightarrow}}{s}3d$ transition energy (the pre-edge) was also observed. This signal was found to have the same azimuthal angle and polarization dependence as that at the main edge.