Zero-field splitting and g-factor studies for 3d5 ions in tetragonal and trigonal symmetry

In this paper, the rigorous analytical expressions for the zero field splittings D, a, F and g-factors of a 3d5 ion in tetragonal and trigonal crystal fields are derived. In the derivations, the energy levels equivalence between microscopic Zeeman interaction and phenomenological spin-Hamiltonian was used. The deduced expressions do not depend on any interaction model and are universal expressions. As some examples, we studied the specific examples of MnCO3,Rb2CdF4:Mn2+ and KZnF3:Mn2+. Good agreement between calculation and experiments shows that the formulas are reasonable.