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Physical Review Letters

Configuration Interaction in Jahn-Teller Systems: Homogeneous Broadening of Zero-Phonon Lines Due to Nonradiative Transitions

M. Montagna, Oreste Pilla, G. Viliani

Published Sep 22, 1980• 13 citations
Publisher

Abstract

Fano's theory of configuration interaction has been extended to Jahn-Teller systems. Homogeneous broadening and shift of the zero-phonon lines are directly connected with interlevel spin-orbit interaction and with the density of states of the interacting continuum. Application to MgO: ${\mathrm{V}}^{2+}$ and ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$: ${\mathrm{Cr}}^{3+}$ gives excellent agreement between theory and experiment.

DOI
10.1103/physrevlett.45.1008

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Fano's theory of configuration interaction has been extended to Jahn-Teller systems. Homogeneous broadening and shift of the zero-phonon lines are directly connected with interlevel spin-orbit interaction and with the density of states of the interacting continuum. Application to MgO: V2+{\mathrm{V}}^{2+}V2+ and {\mathrm{Al}}_{2}$${\mathrm{O}}_{3}: Cr3+{\mathrm{Cr}}^{3+}Cr3+ gives excellent agreement between theory and experiment.
The optical dephasing, caused by a quadratic interaction with acoustic phonons, is studied on the basis of the nonperturbative theory. The effect of a strong weakening of the elastic springs on the electronic transition is studied. It is found that, if the weakening brings the system close to the dynamical instability, then the usual ∝ T7 dependence of the homogeneous width of a zero-phonon line (ZPL) is replaced by the ∝ T3 dependence in a broad temperature interval. An equation is derived which describes the additional broadening of a ZPL caused by the dynamical instability of the final state. The model explains the temperature broadening and shift of the zero-phonon lines of some nitrogen-containing centers in diamond crystals.
The electron-phonon coupling for Cr 3+ in different oxide host lattices (MgO, α-Al 2 O 3 and LaAlO 3 ) was probed by performing temperature dependent line broadening measurements for zero-phonon emission lines of single ions and exchange coupled pairs. No differences in electron-phonon coupling were found comparing the results for pairs and single ions in α-Al 2 O 3 (3NN and 4NN pairs) and LaAlO 3 (NN pairs). In Cr 3+ doped MgO (Cr 3+ -V Mg -Cr 3+ pairs), it was found that the electron-phonon coupling strength parameter is larger for the pairs than for the isolated Cr 3+ ions. This is probably due to changes in the surroundings of Cr 3+ by local charge compensation by a magnesium vacancy, and not to interaction between the Cr 3+ ions.
A recursive method is developed to treat electrons coupled to phonons. It is applied to small systems with $E\ensuremath{\bigotimes}\ensuremath{\beta}$ Jahn-Teller coupling. Two cases are considered, a model with one electron and two orbitals on a single site (related to the Rabi Hamiltonian) and a model with two electrons on two sites. The corresponding Green's functions are represented by rational functions. It is found that the spectra change substantially when one phonon couples to the electron but are relatively robust under an increasing number of phonons.