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Powder diffraction in the 21 st century?

Ordering phenomena on the perovskite and spinel lattices: synchrotron and neutron studies Paolo G. Radaelli ISIS Facility, Rutherford Appleton Laboratory and Dept of Physics & Astronomy, University College London. Powder diffraction in the 21 st century?.

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Powder diffraction in the 21 st century?

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  1. Ordering phenomena on the perovskite and spinel lattices: synchrotron and neutron studiesPaolo G. RadaelliISIS Facility, Rutherford Appleton Laboratory and Dept of Physics & Astronomy, University College London

  2. Powder diffraction in the 21st century? • In many systems single crystal diffraction is the tool of choice to study ordering phenomena. There are many classic and recent examples, esp. in low-dimensional systems. [1] J. L. de Boer, A. Meetsma, J. Baas, and T. T. M. Palstra, PRL 84 (2000) 3962. NaV2O5 [1] • Yet, powder diffraction still gives a significant contribution, esp. in systems where the high-temperature phase is highly symmetric, (perovskites, spinels, pyrochlores, etc.) Paolo G. Radaelli, Oxford, Sept 2003

  3. Outline • Charge ordering in manganites: methodology. • Frustrated systems. • Fe3O4 revisited. • Dimer formation on the pyrochlore lattice: • ½-filled system: CuIr2S4 • 1-filled system: MgTi2O4 • Data quality issues. • Summary. Paolo G. Radaelli, Oxford, Sept 2003

  4. Mn+3 Mn+3 Mn+4 Mn+3 Mn+3 Mn+4 Mn+3 Mn+3 Charge and Orbital Ordering in La0.5Ca0.5 MnO3 1E.O. Wollan and W.C. Koehler, Phys. Rev. 100 (1), 545-563 (1955).

  5. NPD: average structure

  6. û û c û û û û û û û û û û a Special position: 4b [ ] 0,0, ½ Charge Ordering: symmetry analysis Pnma (Pbnm) y=0 y= ½

  7. Special position: 4b [ ] 0,0, ½ Charge Ordering: symmetry analysis P21/m c a y=0 y= ½

  8. û û û û û û Orbital Ordering: symmetry analysis P21/m (2a) c a

  9. Charge and Orbital Ordering in La0.5Ca0.5 MnO3 Mn+3 Mn+3 Mn+4 Mn+3 Mn+3 Mn+4 Mn+3 Mn+3 PGR et al., PRB

  10. SX results A. Daoud-Aladine et al., PRL 89 (2002) 097205

  11. “Wigner crystal” model “Stripe” model c axis a) b) a axis frustrated spin up Mn+3 FM spin down Mn+4 AFM La0.333Ca0.667MnO3Charge, Orbital and Magnetic Ordering

  12. Neutron Powder Diffraction Data

  13. c axis a axis La0.333Ca0.667MnO3Canted Magnetic Structure

  14. “Wigner crystal” model “Stripe” model 0.60 0.20 0.10 0.40 0.00 0.20 -0.10 0.00 -0.20 -0.20 -0.30 -0.40 -0.40 -0.60 -0.50 -3w -2w -w 0 w 2w 3w -3w -2w -w 0 w 2w 3w Frequency Frequency Displacement Patterns for the“Wigner crystal” and “Stripe” models a) b)

  15. Comparison with x-ray data a) Average structureb) “Stripe” modelc) “Wigner Crystal” model

  16. La0.333Ca0.667MnO3Superstructure Neutron Powder Diffraction Data

  17. Magnetic structure NPD Symmetry and mode analysis A priori knowledge Mode screening SXPD Full structural refinement NPD, SXPD Charge and Orbital Ordering : Flow Chart ADP magnitude/direction NPD Propagation vectors SXPD, ED Neutrons X-rays/el. Theory N&X

  18. Bernal-Fowler (Pauling) rules

  19. The Anderson Condition Anderson, P. W. Ordering and Antiferromagnetism in Ferrites. Physical Review102, 1008-1013 (1956). U=2e2/d Charge U=2J Magnetic E=2nTU E=6U E=3U

  20. In 1939, Verwey discovered a sharp increase of the resistivity of Fe3O4 around 120K, accompanied by a structural distortion1. • He then proposed to write the chemical formula of magnetite as Fe3+Fe2.5+2O4, all the tetrahedral Fe being 3+. At the M-I transition, charges on the B-site would order onto an orthorhombic superstructure. 1E.J.W. Verwey, Nature 144 (1939) pp. 327-328. 2E.J.W. Verwey and P.W. Haayman, Physica 9 (1941) pp. 979-987 The Verwey transition

  21. -1 +1 -1 +1 -1 +1 -1 +1 -1 The Verwey Model Z=2 Z=1 Z=0

  22. Neutron data (HRPD) Synchrotron data (BM16) J.P. Wright, J.P. Attfield and P.G. Radaelli, PRL 87 (2001) 266401 J.P. Wright, J.P. Attfield and P.G. Radaelli, PRB 66 (2002) 214422

  23. - - - - - - - - + + + + + + + + - - - - 2 2 2 3 4 3 1 1 1 3 4 3 2 2 2 4 3 4 1 1 1 4 3 4 2 2 2 B1 (2.4+) B2 (2.6+) B3 (2.6+) B4 (2.4+)

  24. “Bond” ordering on a pyrochlore lattice • Conventional charge ordering concept may fail in many systems (Fe3O4, Manganites, etc.). One never recovers integral valences. • Possibility of Peiers and spin-Peierls-like transition on the pyrochore lattice (spinels, pyrocholres, etc.) Paolo G. Radaelli, Oxford, Sept 2003

  25. Heitler-London Singlet Singlet (S=0) Triplet (S=1) Hund-Mulliken Singlet (Molecular orbital) } 1 2 2 1  Singlet (S=0) 1,2 1,2

  26. What if the “objects” dimerised? CuIr2S4½ holes/site“Octamers” MgTi2O41 electron/site“Helices” Paolo G. Radaelli, Oxford, Sept 2003

  27. CuIr2S4 • Y. Koyama ‡ • Yew-San Hor§ Sample synthesis, transport meas. • Valery Kiryukhin§ synchrotron data • Hiroki Ishibashi§|| • Sang-Wook Cheong§ • Y. Horibe†‡§ Electron Microscopy • C.H. Chen† • Matthias J. Gutmann* Neutron diffraction • Richard M. Ibberson* PDF analysis * ISIS Facility, Rutherford Appleton Laboratory † Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, USA ‡ Department of Materials Science and Engineering, Waseda University, Japan § Department of Physics and Astronomy, Rutgers University New Jersey, USA. || Department of Materials Science, Osaka Prefecture University, Osaka, Japan. Paolo G. Radaelli, Oxford, Sept 2003

  28. CuIr2S4: Charge Ordering and spin pairing. • The copper iridium thiospinel CuIr2S4 is a very young relative of magnetite, since it was synthesized for the first time in 19941. • It is reminiscent of Fe3O4 in that it is half-filled and has a coupled M-I and structural transition (at 230 K), but with one striking difference: it undergoes a Pauli paramagnet-to-diamagnet phase transition at the same time2. 1S. Nagata et al., Physica B 194-196 (1994) P. 1077. 2 T. Furubayashi et al., J.Phys.Soc.J 63 (1994) p. 3333. Paolo G. Radaelli, Oxford, Sept 2003

  29. Magneto-transport in CuIr2S4 T. Furubayashi et al., J.Phys.Soc.J 63 (1994) p. 3333

  30. N1+ modes +5 -2 -7 9,5 3,5 -7 -11 +1 +13 -8 -6 +3 15,3 +1 +6 +8 8,12 -3 6,10 8,2 +8 +12 +6 +10 6,4 -4 -16 c -2 -14 +7 2,14 4,16 -4 -5 +4 +2 11,7 -5 -9 1,7 +3 +15 13,1 -1 a Example of Mode analysis I41/amdP21/m

  31. HRPD Data

  32. PGR et al., Nature 416 (2002) p. 155.

  33. CuIr2S4: Irradiation effect1. 1H. Ishibashi et al., PRB 66 (2002) 144424.

  34. CuIr2S4: Conclusions. • The crystal structure of CuIr2S4 at low temperatures accounts well for the observed transport and magnetic properties. Band structure calculations indicate HM rather than HL singlets (a Peierls rather than a spin-Peierls transition). • The ‘Octamer-based’ description of the spinel crystal structure is simple and elegant. Yet, the underlying CO structure represents a step up in complexity with respect to all previously known arrangements. • X-ray irradiation destroys the octamers but preserves the dimers. Paolo G. Radaelli, Oxford, Sept 2003

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