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Utilizing X-ray for Local Excitations Study: Spectral Weights & Dispersions

Investigating low-energy local excitations using X-ray short wavelength for NiO and CoO with nodal directions and angular dependence analysis. Applying LDA+U for accurate gap and line shape determination.

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Utilizing X-ray for Local Excitations Study: Spectral Weights & Dispersions

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  1. Utilizing the short wavelength of X-ray to study low-energy local excitationsq-dependence of the spectral weights and dispersions Wei Ku (BNL & SUNY Stony Brook)

  2. Acknowledgement • Ben Larson & Jon Tischler (ORNL) • Chi-Cheng Lee & Hung-Chung Hsueh (BNL & Tamkang U. Taiwan) • Ken Finkelstein (CHESS, Cornell) • Paul Zschack (UNICAT-APS & UIUC) • Oscar Restrepo & Adolfo Eguiluz (UT-Knoxville & ORNL) • Peter Abbamonte, James P. Reed & Serban Smadici (UIUC) • Chen-Lin Yeh (BNL & Tamkang U. Taiwan) • Tim Graber (U. of Chicago) • Abhay Shukla (Universit ´e Pierre et Marie Curie) • Jean-Pascal Rueff (Synchrotron SOLIEL)

  3. Spherically Bent Analyzer Crystal 110 100 100 111 UNI-CAT ID-33 7.59 keV DE ~ 1.1 eV Io ~ 5•1012 Hz [hkl] 110 Detector q 110 IXS Measurement Directions 100 sample UNI-CAT ID-33 CHESS C-Line DE ~ 0.3 eV Io ~ 1011 Hz Non-Resonant Inelastic X-Ray Scattering (NIXS) Absolute IXS Measurements Absolute Response Calculations

  4. 25 25 CoO (1.1 eV Res.) NiO (1.1 eV Res.) (111) (100) (111) (100) 20 20 -1 -1 2.0 A 2.0 A -1 -1 7.0 A 7.0 A ) ) -3 -3 15 15 nm nm -1 -1 ) (eV ) (eV 10 10 w w s(q, s(q, 5 5 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 ²E (eV) ²E (eV) Strong Within-Mott-Gap Excitations at Large q NiO CoO q = 7/A q = 7/A q = 2/Å q = 2/Å • New in-gap features at large q! What are these excitation? • Strong angular dependence? (100) != (111) • Difference between NiO & CoO?

  5. Charge Excitations in NoO and CoOSmall momentum transfer cases NiO, q ~ 0.7 /Å • Linear response within time-dependent density functional theory • LDA+U approximation greatly improves the gap and line shape • Work well at small q in absolute unit

  6. Charge Excitations in NoO at Large q B. Larson et. al, Phys. Rev. Lett. 99, 026401 (2007) • Large q excitations  local d-d excitation (dipole forbidden) • Strong angular dependence and nodal directions ?

  7. 25 25 CoO (1.1 eV Res.) NiO (1.1 eV Res.) (111) (100) (111) (100) 20 20 -1 -1 2.0 A 2.0 A -1 -1 7.0 A 7.0 A ) ) -3 -3 15 15 nm nm -1 -1 ) (eV ) (eV 10 10 w w s(q, s(q, 5 5 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 ²E (eV) ²E (eV) 25 25 CoO LSDA+U = 8 eV NiO LSDA+U = 8 eV -1 -1 2.0 A (111) 2.0 A (111) -1 -1 1.9 A (100) 2.0 A (100) 20 20 -1 -1 7.0 A (111) 7.0 A (111) -1 -1 7.0 A (100) ) 7.1 A (100) ) -3 -3 15 15 nm nm -1 -1 ) (eV ) (eV 10 10 w w s(q, s(q, 5 5 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 ²E (eV) ²E (eV) • Large-q only excitations  local d-d excitation (dipole forbidden) • Strong local interaction needed for correct energy • How about the strong angular dependence and nodal directions ?

  8. L L L I I c Linear Response & LDA+U Approximation Time dependent density functional theory with LDA+U approximation: Hartree long-range screening local Hartree local Fock p-h attraction d.c. C.-C. Lee, H.-C. Hsueh, and Wei Ku, to be published

  9. Real-Space Picture of Local Excitons eg x 2 eg x 2 EF of NiO d x 5 a1g x 1 t2g x 3 EF of CoO e’g x 2 L c particle Energy-resolvedWannier orbitals hole  X-ray sees this

  10. Local Excitations in NoO and CoOPoint group symmetry and new selection rules eg EF e’g • Local point group symmetry  nodal directions •  new selection rules

  11. Anisotropy of Local Excitations • Nodal direction  point group symmetry • Lack of [100] node in CoO  weak symmetry breaking B. Larson et. al, Phys. Rev. Lett. 99, 026401 (2007)

  12. Local Excitations in NoO and CoOSensitive probe of weak symmetry breaking NiO CoO NiO CoO NiO CoO • Lost of nodal directions : extremely sensitive to weak symmetry breaking • Visualization of symmetry breaking via Wannier functions

  13. Formation of Frenkel Excitons in Local Picture p1 h1 p1 h1 + p1 h1 p1 h1 same pair p-h attraction

  14. Hybridization of Frenkel Excitons in Wannier basis + p2 h2 p1 h1 local Fock + p1 h1 p1 h1 local Hartree

  15. Tightly-Bound Excitons in Charge Transfer Insulators:case study of LiF • Tightly bound exciton • Charge transfer insulator p-h in different atoms • Frenkel or Wannier exciton ? • Inelastic X-ray scattering • Structured spectral weight • Clear dispersion at large q ! • observe fs dynamics P. Abbamonte et. al., to be published

  16. x 20 ½ ½ 15 10 z y 5 0 x ½ -5 z y -10 Excitons in LiF as a Frenkel Exciton in a “Super Atom”

  17. x ½ z y 16 14 x 12 3 5 3 10 0 1 2 3 4 q = 0~1.5 Intensity divided by 2.6 z y Matrix Element and Structure in q-space real-space q-space

  18. L L L L T T local local Effective Two-Particle Hopping Define effective two particle kinetic kernel T via local local Propagation of exciton T gives hopping of p-h pair in real space  dispersion in q-space C-L Yeh, H.-C. Hsueh, and Wei Ku, to be published

  19. Effective Two-Particle Hopping in LiF • T(w) is complex and strongly w-dependent to fully account for • Landau continuum • Lower mobility with stronger p-h binding (0,0,1) (0,0,1) (0,.5,.5) (0,.5,.5) Re{T(w)} Im{T(w)} • within the continuum  fast decay • NN hopping dominant  cos() like dispersion C-L Yeh, H.-C. Hsueh, and Wei Ku, to be published

  20. Lph,hp ( q , w) (0, 0, 0) * 22 w (eV) q (reciprocal lattice unit) Time Evaluation of Charge Fluctuation in LiF Lph,hp ( R, t ) * 4 at the source of perturbation  well defined averaged frequency  steady decay in time t ( fs )

  21. Propagation of Frenkel Excitons (0, 0.5, 0.5) * 0.72 (0, 1, 1) * 1.42 (0, 1.5, 1.5) * 2.12 Lph,hp ( R, t ) (scaled by R2) • along the (011) “direct” path •  efficient propagation • steady group velocity t ( fs )

  22. Propagation of Frenkel Excitons (0, 0, 1) * 12 (0, 0, 2) * 22 Lph,hp ( R, t ) (scaled by R2) • along the (001) “indirect” path •  velocity decreases • interference due to multiple scattering t ( fs )

  23. Conclusion • Non-resonant IXS measurement vs. theory in absolute unit • Non-resonant inelastic scattering at large q sub-atomic spatial resolution  beyond dipole selection • Strong anisotropy & nodal directions of spectral weight at large q direct access to spatial distribution of underlying orbital  local point group symmetry new selection rules • Clearer signature of dispersion at large q propagation of excitations in space and time  good (space, time) resolution: ( a0, fs ) • Theory of local dynamics based on 1st-principles Wannier function real-space picture of local excitons and their propagation  visualization of particle holes pairs and their nodal directions  suitable for charge-transfer & more itinerant systems  applicable for exciton decay near surfaces and in nano-systems • Potential applications in correlated materials (orbiton, polaron, phason …)

  24. REXS IXS ~1.3 eV IXS ~1.4 eV Butorin et al., PRB 54, 4405 (1996) IXS Peak Positions The Correspondence is Less Direct With Resonant Emission X-ray Spectroscopy (REXS) And Cluster Calculations REXS Observes A Range of Gap Excitations In NiO and CoO

  25. C-SPEELS IXS NiO ~1.3 eV IXS ~1.4 eV Fromme et al., PRB 75, 693 (1995) The Non-Resonant X-Ray Scattering Observations Are Similar to Spin-Polarized Resonant-Exchange Electron Scattering In NiO and CoO

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