Abstract: By means of the irreducible tensor method, a theoretical approach to the spin Hamiltonian of transition metal complexes involving the spin-orbit interaction, spin-other orbit interaction, Fermi interaction, magnetic spin-spin interaction and external magentic interaction is proposed. The parameter of the spin Hamiltonian, expressed in the molecular parameters is obtained. Under approximation of atomic orbital, the g-factor of ruby is calculated and the result is in good agreement with the experiments.

Key words: Spin Hamiltonian, Magnetic spin-spin interaction, Fermi interaction, Lande-factor, Quasi-spin