Excitations in Jahn-Teller coupled systems with complicated electronic level schemes

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Abstract
The method of Buyers and Holden (1975) for calculating excitation frequencies in singlet ground state ferromagnets is extended to systems undergoing cooperative Jahn-Teller transitions. The electron-lattice interaction is treated by the displaced operator technique. It is shown that the full response of the system always diverges at the molecular field transition temperature, as expected, provided account is taken of the zero-frequency transitions. Difficulties previously encountered in applying the displaced operator method to situations where there is coupling to non-commuting electron operators are avoided by using an exact result for the phonon equation of motion. Damping is added in a phenomenological way and estimates are made of the relaxation times in the theory. The excitation frequencies are calculated for a simple model of PrAlO3.