An octupole angular momentum in octahedra that exhibit the E⊗ε Jahn-Teller effect

The vibronic angular momentum operator-which commutes with the Hamiltonian for the linear coupling case of the E(X) epsilon Jahn-Teller effect for transition-metal ions and rare-earth ions in regular octahedra-is shown to have an octupole angular momentum in both its electronic part and its vibrational part. The Hamiltonian and the angular momentum are invariant under the operations of the magnetic point group O h (T h ) (or m3m). A three-dimensional model is presented to aid the reader in visualising this group. The significance of this angular momentum is also discussed for the non-linear coupling regime.