Intermediate states

1. Theory of probing orbitons in YTiO3 with Resonant Inelastic X-ray Scattering L.J.P. Ament1, J. van den Brink1, G. Khaliullin2 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands2Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany 4. Cross Section: UCL expansion The sum over intermediate states n is hard to compute.For  > En we can trade the sum over intermediate states n fora perturbation expansion in 1/: the Ultrashort Core hole Lifetime(UCL) expansion: Synchrotron X-rays Momentum transfer q & Energy loss  Valence level wres (1-10 keV) Core level Ti O Y Ti Ti Ti O O 7. Conclusions 1. What is RIXS? RIXS = Resonant Inelastic X-ray Scattering 5. RIXS coupling mechanisms Interestingsample How does the core hole affect orbitons? Two mechanisms:1. Superexchange constant modified at core hole atom2. Core hole potential directly induces orbital flip Core hole potential effectively lowers U: 3d t2g 2p Core hole Core-hole couples to valence electrons via core-hole potential 2. What are orbitons and YTiO3? 3d t2g Oxygen ions have filled 2p-shell.Ti ions have 1 electron in 3d t2g levels.We assume t2g levels are degenerate: 2p Core hole Both mechanisms change H. The latter also works for local model. 5. Comparison to experiment Recently, Ulrich et al.1measured RIXS spectra of YTiO3 at the SLS: YTiO3 is a ferromagnetic Mott insulator at low T. Only orbital degree of freedom with superexchange interaction: Mechanism 1 2-orbitoncontinuum 1-orbitonshoulder Mechanism 2 Many hopping terms are zero by symmetry of overlap integrals. Note: direction-dependent superexchange interaction! For instance, sites i, j are neighbors in x-direction: Mechanism 2 gives very good agreement, only 1-orbiton ‘peak’ is too strong. For mechanism 1, we neglected polarization dependence.Agreement of local model with data is very much worse (2-peak structure, temperature dependence, dispersion, intensity trend): Superexchange Hamiltonian leadsto orbital ordered ground state withcollective excitations: orbitons! Big debate about existence of orbitons. Opposite picture: local model of YTiO3 where t2g orbitals are split by coupling to the lattice, and orbital excitations are local.3 3. RIXS Cross Section Comparing the two extreme models for YTiO3 (local Vs. collective excitations), the experimental RIXS spectra clearly favor the collective model over the local one. Raman scattering experiments reached exactly the same conclusion. New RIXS measurements with momentum transfer along the [110]-direction could verify the existence of the 1-orbiton peak. Kramers-Heisenberg relation: Intermediate states Dipole operator Core-hole existsa very short time: ≈ 0.5-3 eV 1C. Ulrich, G. Ghiringhelli, M. Moretti, N. Pezzotte, T. Schmitt, L. J.P. Ament, G. Khaliullin, J. van den Brink, H. Roth, T. Lorenz and B. Keimer, to be published2G. Khaliullin and S. Okamoto, Phys. Rev. B 68, 205109 (2003)3E. Pavarini et al., New J. Phys. 7, 188 (2005) with