A generalized effective spin Hamiltonian

A generalized effective spin Hamiltonian H SG describing the electron paramagnetic resonance of transition group ions in a crystal is proposed on the basis of group theory. In this method the spin Hamiltonian is considered strictly by the space-time symmetry. In the first order perturbation, the irreducible spin tensors T LM ( L = 0, 1,..., 2 S ) describe completely the electron paramagnetic resonance of paramagnetic ions with ground state having 2 S + 1 energy levels. Some irreducible tensors in several point-group symmetry are presented for convenience of obtaining H SG explicitly. Such a H SG is equivalent to the KS (Koster-Statz) matrix.