Collapse Of The Simple Localized 3d(1) Orbital Picture In Mott Insulator

The orbital degree of freedom of electrons greatly influences the physical properties of materials such as magnetic order and unconventional superconductivity. An orbital is a minimal unit of "shape," and the orbital state can be unraveled by observing the spatial anisotropic distribution of electrons. However, it is difficult to experimentally extract the orbital information in a crystal because of various technical problems. Here, the Ti-3d orbital state in perovskite-type oxides RTiO3 (R = Y, Sm, and La) is directly determined by a core differential Fourier synthesis (CDFS) method using synchrotron x-ray diffraction. The valence electron-density distribution, including information on the anisotropy and the hybridization between atomic orbitals, can be extracted from the CDFS analysis. Our study not only demonstrates the relationship between the magnetic- and orbital-ordered states called the Kugel-Khomskii model, but also provides a nontrivial picture of the orbital state reconstructed by the orbital hybridization.