AN EFFECTIVE HAMILTONIAN FOR JAHN-TELLER COUPLING OF T1G AND T2G IONS

An investigation is made of the properties of paramagnetic ions which have orbital triplets interacting with lattice vibrations. The linear coupling between the orbital levels and local distortions which have Eg symmetry are eliminated by a sequence of transformations on the Hamiltonian. These lead to an equivalent Hamiltonian in which the Jahn-Teller energy appears explicitly and most of the other operators have modified forms. The Hamiltonian of the lattice is discussed in more detail than usual by the introduction of symmetry adapted coordinates and momenta. Explicit formulae are obtained for the Jahn-Teller energy in terms of elastic constants and coupling coefficients, and for the displacements of lattice points, which are a consequence of the Jahn-Teller effect. It is also shown how a continuum model of the lattice can be introduced, and used to derive a cosθ/R2 dependence for the distortion associated with the Jahn-Teller effect. The analysis throws a good deal of light on the reason why the cluster model works so well.