Resonant x-ray scattering study of magnetic and orbital order in ${\mathrm{KCuF}}_3$

We present the results of resonant x-ray scattering experiments on ${\mathrm{KCuF}}_3.$ Structurally forbidden reflections, corresponding to magnetic and $3d$-orbital long-range order, have been observed. Integrated intensities have been measured as a function of incident energy, polarization, azimuthal angle, and temperature. By means of ab initio local spin density approximation (LSDA) and local spin density approximation with on-site Coulomb interaction (LSDA+U) calculations we determine the electronic structure of ${\mathrm{KCuF}}_3$ and obtain the resonant x-ray scattering spectrum at the Cu K edge, which shows good agreement with the experimental data. Orbital and spin degrees of freedom are strongly coupled, and the temperature dependence of the intensity of orbital Bragg peaks reveals a correlation between magnetic and orbital order parameters.