Pressure effect on the adiabatic potential in the crystals with D<sup>2</sup><sub>3d</sub> space symmetry and strong electron-phonon interaction
DOI:
https://doi.org/10.24144/2415-8038.2019.46.22-29Keywords:
Adiabatic potential, Electron-vibronic interaction, Phase transition of order-disoder type, Method of invariants, Deformation tensorAbstract
Purpose. The CuInP2S6 and CuInP2Se6 crystals are characterized by an order-disorder phase transition mechanism, which is caused by electron-phonon interaction and the Jan-Teller cooperative effect. Vibronic instability is related to the electronic configuration of copper d10 in octahedral symmetry, and the disorder in the paraelectric phases can be explained by the jumping movements of Cu ions. It is of interest to study the conditions of this instability at the pressure. The main aim of our paper is to carry out the investigation of the matrix of the vibronic potential energy and the adiabatic potentials at the pressure.
Methods. Adiabatic potentials concept based on the group -theoretical analysis and Pikus’ method of invariants.
Results. For the case of hydrostatic pressure for crystals with D3d symmetry, an adiabatic potential depending on the components of the strain tensor and the coordinates of normal vibrations active in the Jahn-Teller effect has been obtained. We carried out the numerical simulations of the pressure effect on the shape of the adiabatic potentials From our qualitative analysis follows that the changing of the adiabatic potential depth (EJT ) and the value of the minimum displacement ρ0 takes place. Especially the shape of the adiabatic potential energy is changed at the shift strain εxy.
Conclusions. Using the symmetry methods, we constructed the matrix of the vibronic potential energy and found the adiabatic potentials. It is shown that in a consequence of the phase transition the splitting of the equivalent minima (disorder) of the adiabatic potential on the group of the nonequivalent minima (order) is occurred. The shape of these adiabatic potentials shows that in their concept one can confirm about the order-disorder phase transition and also to consider the pressure influence on these potentials.
References
Maisonneuve, V. V., Cajipe, V.B., Simon, A., Von Der Muhll, R., Ravez, J. (1997), ”Ferrielectric ordering in lamellar CuInP2S6”, Phys. Rev. B., V. 56, pp. 10860-10863.
Vysochanskii, Yu.M., Stephanovich, V.A.; Molnar, A.A.; Cajipe, V.B.; Bourdon, X. (1998), ”Raman spectroscopy study of the ferroelectric - paraelectric transition in layered CuInP2S6”, Phys. Rev. B., V.58, pp. 9119-9124.
Babuka, T., Glukhov, K., Vysochanskii, Yu.M., Makowska-Janusik, M. (2019), ”Layered ferrielectric crystals CuInP2S(Se)6: a study from the first principles”, Phase Transitions, V.92, №5, pp. 440-450.
Grzechnik, A., Cajipe, V.B., Payenb, C., McMillanc, P.F. (1998), ”Pressure-induced phase transition in ferrielectric CuInP2S6” Solid State Communications, V. 108, No. 1, pp. 43-47.
Bercha, D.M.; Bercha, S.A., Glukhov, K.E., Sznajder, M. (2014), ”Electron-Phonon Interactionas a Mechanism of Phase Transition in a Layered CuInP2S6 Crystal” Acta Physica Polonica A., V. 126, №5, pp. 1143-1145.
Bercha, D.M., Bercha, S.A., Glukhov, K.E., Sznajder, M. (2015), ”Vibronic interaction in crystals with the Jahn-Teller centers in the elementary energy bands concept”, Condensed Matter Physics, V. 18, pp. 33705:1-17
Bir, G. L., Pikus, G. E. (1974), ”Symmetry and Strain-Induced Effects in Semiconductors”, J. Wiley, New York
Bercha, S.A., Rizak, V.M. (2014), ”Similarities and differences in the construction of dispersion laws for charge carriers in semiconductor crystals and adiabatic potentials in molecules”, Condensed Matter Physics, V. 17, No 2, pp. 23701
Polinger, V. (2015), ”Off-center instability of Nb+ in KNbO3 under ambient pressure”, Chemical Physics, V. 459, pp. 72-80
Bersuker, I.B., Polinger, V.Z. (1989), Vibronic Interactions in Molecules and Crystals, Springer-Verlag, Berlin
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