Advertisement

Cooperative Jahn-Teller effect in a 2D mesoscopic C 60 n− system with D5d symmetry adsorbed on buffer layers using Ising EFT model

  • M. Abou GhantousEmail author
  • E. A. Moujaes
  • J. L. Dunn
  • A. Khater
Regular Article

Abstract

Fullerene molecules adsorbed on surfaces often show macroscopic average distortions. As charged ions C 60 n− are known to be Jahn-Teller (JT) active, it is suggested that these distortions could be a manifestation of cooperative JT effects (CJTE) due to interactions between neighbouring fullerene ions. In order to understand the distortion properties it is necessary to take correlations between different distortions into account. However, this can’t easily be done in the mean field approximation usually used to describe the CJTE. We therefore propose an alternative procedure to describe 2D mesoscopic islands of C60 ions in which a pseudo vector spin \(\vec S\) is evoked to represent degenerate JT-distorted states when the quadratic JT coupling is considered. This approach is analogous to methods used for 2D magnetic systems. We then use the differential operator technique in effective field theory within the Ising approach. We include the effects of weak surface interactions and dynamic motion between equivalent distortions via terms equivalent to anisotropy and a transverse field in magnetism respectively. For distortions to D 5d symmetry, we determine single site correlations as a function of temperature, the macroscopic average distortion describing a structural phase transition, and the isothermal response function. Phase diagrams are presented for relevant cases of the system parameters.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    C.C. Chancey, M.C.M. O’Brien, in The Jahn-Teller effect in C60 and other icosahedral complexes (Princeton University Press, Princeton, NJ, 1997)Google Scholar
  2. 2.
    I.B. Bersuker, in The Jahn-Teller Effect (Cambridge University Press, Cambridge, UK, 2006), Chap. 8Google Scholar
  3. 3.
    I.B. Bersuker, V.Z. Polinger, in Vibronic interactions in molecules and crystals (Springer-Verlag, Berlin, Heidelberg, NY, 1989), Chap. 6Google Scholar
  4. 4.
    M.D. Kaplan, B.G. Vekhter, in Cooperative Phenomena in Jahn-Teller Crystals (Plenum Press, NY, 1995)Google Scholar
  5. 5.
    G.A. Gehring, K.A. Gehring, Rep. Prog. Phys. 38, 1 (1975)ADSCrossRefGoogle Scholar
  6. 6.
    J.L. Dunn, C.A. Bates, Phys. Rev. B 52, 5996 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    L.M. Sindi, I.D. Hands, J.L. Dunn, C.A. Bates, J. Mol. Struct. 838, 78 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    A.J. Lakin, I.D. Hands, C.A. Bates, J.L. Dunn, Vibronic Interactions and the Jahn-Teller effect, edited by M. Atanasov, C. Daul (Springer, Dordrecht, 2011), Vol. 23, p. 231Google Scholar
  9. 9.
    S. Tomita, J.U. Andersen, E. Bonderup, P. Hvelplund, B. Liu, S.B. Nielsen, U.V. Pedersen, J. Rangama, K. Hansen, O. Echt, Phys. Rev. Lett. 94, 053002 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    I.D. Hands, J.L. Dunn, C.A. Bates, M.J. Hope, S.R. Meech, D.L. Andrews, Phys. Rev. B 77, 115445 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    A. Wachowiak, R. Yamachika, K.H. Khoo, Y. Wang, M. Grobis, D.-H. Lee, S.G. Louie, M.F. Crommie, Science 310, 468 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    J.L. Dunn, A.J. Lakin, I.D. Hands, New J. Phys., to be submittedGoogle Scholar
  13. 13.
    N. Koga, K. Morokuma, Phys. Lett. 196, 191 (1992)Google Scholar
  14. 14.
    L.F. Feiner, J. Phys. C Solid State Phys. 15, 1495 (1982)ADSCrossRefGoogle Scholar
  15. 15.
    J.L. Dunn, Phys. Rev. B 69, 064303 (2004)ADSCrossRefGoogle Scholar
  16. 16.
    E.A. Moujaes, J.L. Dunn, J. Phys.: Condens. Matter 22, 085007 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    M. Capone, M. Fabrizio, P. Giannozzi, E. Tosatti, Phys. Rev. B 62, 7619 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    S.-K. Ma, in Modern Theory of Critical Phenomena (Perseus Pub., Mass., Cambridge, 2000)Google Scholar
  19. 19.
    R. Honmura, T. Kaneyoshi, Prog. Theor. Phys. 60, 635 (1978)ADSCrossRefGoogle Scholar
  20. 20.
    E.F. Sarmento, C. Tsallis, Phys. Rev. B 27, 5784 (1983)ADSCrossRefGoogle Scholar
  21. 21.
    T. Kaneyoshi, M. Jaščur, I.P. Fittipaldi, Phys. Rev. B 48, 250 (1993)ADSCrossRefGoogle Scholar
  22. 22.
    R. Honmura, T. Kaneyoshi, J. Phys. C Solid State Phys. 12, 3979 (1979)ADSCrossRefGoogle Scholar
  23. 23.
    M.C. Passeggi, K.W.H. Stevens, J. Phys. C: Condens. Matter 6, 98 (1973)Google Scholar
  24. 24.
    H.B. Callen, Phys. Rev. 130, 890 (1963)ADSzbMATHCrossRefGoogle Scholar
  25. 25.
    A. Khater, M. Abou Ghantous, to be submittedGoogle Scholar
  26. 26.
    M.D. Kuz’min, A.S. Chernyshov, V.K. Pecharsky, K.A. Gschneidner Jr., A.M. Tishin, Phys. Rev. B 73, 132403 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    J.G. Hou, J.L. Yang, H.Q. Wang, X.Q. Li, C.G. Zeng, L.F. Yuan, B. Wang, D.M. Chen, Q.S. Zhu, Nature 409, 304 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    L.F. Yuan, J.L. Yang, H.Q. Wang, C.G. Zeng, X.Q. Li, B. Wang, J.G. Hou, Q.S. Zhu, D.M. Chen, J. Am. Chem. Soc. 125, 169 (2003)CrossRefGoogle Scholar
  29. 29.
    K.J. Franke, G. Schulze, N. Henningsen, I. Fernandez-Torrente, J.I. Pascual, S. Zarwell, K. Ruck-Braun, M. Cobian, N. Lorente, Phys. Rev. Lett. 100, 036807 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    S.I. Bozhko, S.A. Krasnikov, O. Lübben, B.E. Murphy, K. Radican, V.N. Semenov, H.C. Wu, B. Bulfin, I.V. Shvets, Phys. Rev. B 84, 195412 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    I.D. Hands, J.L. Dunn, C.A. Bates, Phys. Rev. B 82, 155425 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    P.J. Moriarty, Surf. Sci. Rep. 65, 175 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    D.V. Gruznev, A.V. Matetskiy, I.V. Gvozd, A.V. Zotov, A.A. Saranin, Surf. Sci. 605, 1951 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    S.J. Mitchell, D.P. Landau, Phys. Rev. Lett. 97, 025701 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    U. Wol, Phys. Rev. Lett. 62, 361 (1989)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Wang, R. Yamachika, A. Wachowiak, M. Grobis, M.F. Crommie, Nature Mater. 7, 194 (2008)ADSCrossRefGoogle Scholar
  37. 37.
    O. Gunnarsson, H. Handschuh, P.S. Bechthold, B. Kessler, G. Gantefor, W. Eberhardt, Phys. Rev. Lett. 74, 1875 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    V.L. Aksenov, V.V. Kabanov, Phys. Rev. B 57, 608 (1998)ADSCrossRefGoogle Scholar
  39. 39.
    N. Manini, P. Gattari, E. Tosatti, Phys. Rev. Lett. 91, 196402 (2003)ADSCrossRefGoogle Scholar
  40. 40.
    T. Frederiksen, K.J. Franke, A. Arnau, G. Schulze, J.I. Pascual, N. Lorente, Phys. Rev. B 78, 233401 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    P.G. de Gennes, Solid State Commun. 1, 132 (1963)ADSCrossRefGoogle Scholar
  42. 42.
    M. Abou Ghantous, A. Khater, to be submitted (2012)Google Scholar
  43. 43.
    S. Rusponi, T. Cren, N. Weiss, M. Epple, P. Buluschek, L. Claude, H. Brune, Nature Mater. 2, 546 (2003)ADSCrossRefGoogle Scholar
  44. 44.
    M.A. Moore, H.C. Williams, J. Phys. C Solid State Phys. 5, 3168 (1972)ADSCrossRefGoogle Scholar
  45. 45.
    R.B. Stinchcombe, J. Phys. C Solid State Phys. 6, 2459 (1973)ADSCrossRefGoogle Scholar
  46. 46.
    J.W. Tucker, J. Phys. A 27, 659 (1994)ADSzbMATHCrossRefMathSciNetGoogle Scholar
  47. 47.
    F.C.S.Á Barretto, I.P. Fittipaldi, Physica A 129, 360 (1985)ADSCrossRefGoogle Scholar
  48. 48.
    P. Gambardella, S. Rusponi, M. Veronese, S.S. Dhesi, C. Grazioli, A. Dallmeyer, I. Cabria, R. Zeller, P.H. Dederichs, K. Kern, C. Carbone, H. Brune, Science 300, 1130 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    P. Gambardella, S. Rusponi, T. Cren, N. Weiss, H. Brune, C. R., Phys. 6, 75 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    A. Khater, M. Abou Ghantous, J. Magn. Magn. Mater. 323, 2711 (2011)ADSCrossRefGoogle Scholar
  51. 51.
    M. Abou Ghantous, A. Khater, J. Magn. Magn. Mater. 323, 2504 (2011)ADSCrossRefGoogle Scholar
  52. 52.
    N. Read, S. Sachdev, J. Ye, Phys. Rev. B 52, 384 (1995)ADSCrossRefGoogle Scholar
  53. 53.
    S. Sachdev, in Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 2001)Google Scholar
  54. 54.
    M. Votja, Rep. Prog. Phys. 66, 2069 (2003)ADSCrossRefGoogle Scholar
  55. 55.
    L. Berger, Y. Labaye, M. Tamine, Phys. Rev. B 77, 104431 (2008)ADSCrossRefGoogle Scholar
  56. 56.
    T. Kaneyoshi, J.W. Tucker, M. Jaščur, Physica A 186, 495 (1992)ADSCrossRefGoogle Scholar
  57. 57.
    S. Rohart, V. Repain, A. Tejeda, P. Ohresser, F. Scheurer, P. Bencok, J. Ferré, S. Rousset, Phys. Rev. B 73, 165412 (2006)ADSCrossRefGoogle Scholar
  58. 58.
    A. Khater, M. Abou Ghantous, M. Fresneau, J. Phys. D 35, 951 (2002)ADSCrossRefGoogle Scholar
  59. 59.
    A. Khater, M. Abou Ghantous, M. Fresneau, J. Magn. Magn. Mater. 247, 305 (2002)ADSCrossRefGoogle Scholar
  60. 60.
    H. Wang, C. Zeng, B. Wang, J.G. Hou, Q. Li, J. Yang, Phys. Rev. B 63, 085417 (2001)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. Abou Ghantous
    • 1
    Email author
  • E. A. Moujaes
    • 2
  • J. L. Dunn
    • 3
  • A. Khater
    • 4
  1. 1.Department of PhysicsTexas A and M University at Qatar, Education CityDohaQatar
  2. 2.Departamento de FísicaUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  3. 3.School of Physics and AstronomyUniversity of NottinghamNottinghamUK
  4. 4.Laboratoire de Physique de L’État Condensé, UMR 6087Université du MaineLe MansFrance

Personalised recommendations