1. Utilizing the short wavelength of X-ray to study low-energy local excitations q-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. Non-Resonant Inelastic X-Ray Scattering (NIXS) [hkl] sample Detector Spherically Bent Analyzer Crystal q UNI-CAT ID-33 7.59 keV  E ~ 1.1 eV I o ~ 510 12 Hz UNI-CAT ID-33 CHESS C-Line  E ~ 0.3 eV I o ~ 10 11 Hz 100 110 111 IXS Measurement Directions Absolute Response CalculationsAbsolute IXS Measurements

4. New in-gap features at large q! What are these excitation? Strong angular dependence? (100) != (111) Difference between NiO & CoO? 25 20 15 10 5 0 s(q,  ) (eV nm -3 ) 302520151050 ²E (eV) CoO (1.1 eV Res.) (111) (100) 2.0 A 7.0 A 25 20 15 10 5 0 s(q,  ) (eV nm -3 ) 302520151050 ²E (eV) NiO (1.1 eV Res.) (111) (100) 2.0 A 7.0 A Strong Within-Mott-Gap Excitations at Large q NiOCoO q = 2/Å q = 7/A

5. Charge Excitations in NoO and CoO Small momentum transfer cases 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 NiO, q ~ 0.7 /Å

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

7. 25 20 15 10 5 0 s(q,  ) (eV nm -3 ) 302520151050 ²E (eV) CoO (1.1 eV Res.) (111) (100) 2.0 A 7.0 A 25 20 15 10 5 0 s(q,  ) (eV nm -3 ) 302520151050 ²E (eV) NiO (1.1 eV Res.) (111) (100) 2.0 A 7.0 A 25 20 15 10 5 0 s(q,  ) (eV nm -3 ) 302520151050 ²E (eV) CoO LSDA+U = 8 eV 2.0 A (111) 1.9 A (100) 7.0 A (111) 7.0 A (100) 25 20 15 10 5 0 s(q,  ) (eV nm -3 ) 302520151050 ²E (eV) NiO LSDA+U = 8 eV 2.0 A (111) 2.0 A (100) 7.0 A (111) 7.1 A (100) 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. Linear Response & LDA+U Approximation  L L  L Time dependent density functional theory with LDA+U approximation:  local Fock p-h attraction local HartreeHartree long-range screening d.c. C.-C. Lee, H.-C. Hsueh, and Wei Ku, to be published

9. Real-Space Picture of Local Excitons d x 5 e g x 2 t 2g x 3 e g x 2 a 1g x 1 e’ g x 2  F of NiO  F of CoO  L Energy-resolved Wannier orbitals  X-ray sees this particle hole

10. EFEF e’ g egeg Local Excitations in NoO and CoO Point group symmetry and new selection rules 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 CoO Sensitive probe of weak symmetry breaking Lost of nodal directions : extremely sensitive to weak symmetry breaking Visualization of symmetry breaking via Wannier functions NiOCoO NiOCoO NiO

13. Formation of Frenkel Excitons in Local Picture p1h1 p1h1 same pair p-h attraction + p1h1 p1h1

14. Hybridization of Frenkel Excitons in Wannier basis local Fock + p1h1 p2h2 local Hartree + p1h1 p1h1

15. Tightly-Bound Excitons in Charge Transfer Insulators: case study of LiF P. Abbamonte et. al., to be published 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

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

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

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

19. Effective Two-Particle Hopping in LiF C-L Yeh, H.-C. Hsueh, and Wei Ku, to be published T(  ) is complex and strongly  -dependent to fully account for 1.Landau continuum 2.Lower mobility with stronger p-h binding Re{T(  )}Im{T(  )} (0,.5,.5) (0,0,1) within the continuum  fast decay NN hopping dominant  cos() like dispersion

20. Time Evaluation of Charge Fluctuation in LiF at the source of perturbation  well defined averaged frequency  steady decay in time t ( fs ) L ph,hp ( R, t ) * 4 (0, 0, 0) * 2 2 L ph,hp ( q,  )  (eV) q (reciprocal lattice unit)

21. Propagation of Frenkel Excitons (0, 0.5, 0.5) * 0.7 2 (0, 1, 1) * 1.4 2 (0, 1.5, 1.5) * 2.1 2 t ( fs ) L ph,hp ( R, t ) (scaled by R 2 ) along the (011) “direct” path  efficient propagation  steady group velocity

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

23. 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: ( a 0, 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 …) Conclusion

24. 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 ~1.3 eV IXS ~1.4 eV IXS IXS Peak Positions REXS Butorin et al., PRB 54, 4405 (1996)

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