Advertisement

Molecules with two electronic energy levels: coupling between the molecules in the solid state via the optical and acoustic phonon branches

  • Jamil A. Nasser
Regular Article
  • 10 Downloads

Abstract

In the adiabatic approximation the values of the spring constants of the springs contained in a molecule depend on its electronic state. We consider molecules with two electronic energy levels separated by Δ. For a crystal of such molecules, the phonon branches depend therefore on the electronic states of the molecules. One can ask if that dependence does not introduce a coupling between the molecules via the optical and the acoustic branches.

It is known that for a one-dimensional chain of N identical diatomic molecules there are two phonon branches, an optical branch and an acoustic one. In this study we introduce in the hamiltonian of the chain two assumptions: (i) each molecule has two electronic energy levels separated by Δ and the spring constant of the spring contained in the molecule has a value which depends on its electronic state; (ii) the spring constant of the spring which links two molecules nearest neighbours has a value which depends on the electronic states of both molecules linked.

One can show that phonons create on each molecule a field-like which favours the excited level and create between two molecules nearest neighbours an exchange-like interaction which can be ferro-like, antiferro-like and which can be equal to zero. For some values of T and Δ, the chain can display a first-order phase transition with the presence of a thermal hysteresis loop. The phase transition takes place between the phase where all the molecules are in the fundamental level and that where they are in the excited one. The parameters of the model can be expressed in function of the applied pressure and of the volume of the crystal.

Keywords

Solid State and Materials 

References

  1. 1.
    A. Messiah, Mécanique Quantique (Dunod, Paris, 2003) Google Scholar
  2. 2.
    J. Owen, J.H. Thomley, Rep. Prog. Phys. 29, 675 (1966) ADSCrossRefGoogle Scholar
  3. 3.
    K.L. Ronayne, H. Paulsen, A. Höfer, A.C. Dennis, J.A. Wolny, A.I. Chumakov, V. Schünemann, H. Winkler, H. Spiering, A. Bousseksou, P. Gütlich, A.X. Trautwein, J.J. McGarney, Phys. Chem. Chem. Phys. 8, 4685 (2006) CrossRefGoogle Scholar
  4. 4.
    M. Sorai, S. Seki, J. Phys. Chem. Solids. 35, 555 (1974) ADSCrossRefGoogle Scholar
  5. 5.
    J.A. Nasser, Eur. Phys. J. B 21, 3 (2001) ADSCrossRefGoogle Scholar
  6. 6.
    J.A. Nasser, K. Boukheddaden, J. Linares, Eur. Phys. J. B 39, 219 (2004) ADSCrossRefGoogle Scholar
  7. 7.
    J.A. Nasser, Eur. Phys. J. B 48, 19 (2005) ADSCrossRefGoogle Scholar
  8. 8.
    J.A. Nasser, S. Topçu, L. Chassagne, M. Wakim, B. Bennali, J. Linares, Y. Alayli, Eur. Phys. J. B 83, 115 (2011) ADSCrossRefGoogle Scholar
  9. 9.
    J.A. Nasser, L. Chassagne, Y. Alayli, S.E. Allal, F. de Zela, J. Linares, Eur. J. Inorg. Chem. 2018, 493 (2018) CrossRefGoogle Scholar
  10. 10.
    R. Balian, From  Microphysics  to  Macrophysics. Methods   and   Applications   of   Statistical   Physics (Springer-Verlag, Berlin, 1991) Google Scholar
  11. 11.
    J.-P. Martin, Mécanisme  des  Transitions  de  Spin  dans les  Composés  Moléculaires  à  l’Etat  Solide,  Ph.D.  thesis, Université de Paris-Sud, Centre d’Orsay, 1994 Google Scholar
  12. 12.
    Y. Garcia, V. Ksenofontov, G. Levchenko, P. Gütlich, J. Mater. Chem. 10, 2274 (2000) CrossRefGoogle Scholar
  13. 13.
    E. König, G. Ritter, S.K. Kulshreshtha, Chem. Rev. 85, 219 (1985) CrossRefGoogle Scholar
  14. 14.
    J. Wajnflasz, Phys. Stat. Solidi 40, 537 (1970) ADSCrossRefGoogle Scholar
  15. 15.
    R. Zimmermann, E. König, JPCS 38, 779 (1977) ADSGoogle Scholar
  16. 16.
    H. Spiering, E. Meissner, H. Köppen, E.W. Müller, P. Gütlich, Chem. Phys. 68, 65 (1982) CrossRefGoogle Scholar
  17. 17.
    P. Gütlich, in Structure and Bonding (Springer-Verlag, Berlin, 1981), Vol. 44 Google Scholar
  18. 18.
    A. Bousseksou, J. Nasser, J. Linares, K. Boukheddaden, F. Varret, J. Phys. I 2, 1381 (1992) Google Scholar
  19. 19.
    A. Bousseksou, M. Verelst, H. Constant-Machado, G. Lemercier, J.-P. Tuchagues, F. Varret, Inorg. Chem. 35, 110 (1996) CrossRefGoogle Scholar
  20. 20.
    A. Bousseksou, J.J. McGarvey, F. Varret, J.A. Real, J.-P. Tuchagues, A.C. Dennis, M.L. Boillot, Chem. Phys. Lett. 318, 409 (2000) ADSCrossRefGoogle Scholar
  21. 21.
    V.K. Palfi, T. Guillon, H. Paulsen, G. Molnãr, A. Bousseksou, C.R. Chim. 8, 1317 (2005) CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire d’Ingénierie des Systèmes de Versailles (LISV), EA 4048, CNRS, Université de Versailles Saint QuentinVersaillesFrance

Personalised recommendations