Generalization of the Heisenberg Hamiltonian for a crystal with allowance for orbital degrees of freedom

Generalised form of the Heisenberg Hamiltonian is proposed for crystals, the structure units of wrich include the group of the lowest states with different orbital as well as spin quantum numbers (the spin-orbital multiplet). The technique of irreducible tensor operators is used for constructing the Hamiltonian. Application of the Hamiltonian obtained to the study of orbital ordering in the model crystal with orbitally degenerated centres is considered.