Abstract: The magnetic interactions as well as the microscopic origins of the spin_Hamilto nian (SH) parameters including b02, g∥, g⊥,Δg for 4B 1(3d3) state ion in a tetragonal crystal field have been investigated usin g the complete diagonalization method (CDM). It is found that the contribution t o the spin_Hamiltonian parameters arising from the spin_orbit (SO) magnetic inte raction is the most important for most part of the crystal field (CF) ranges. H owever, the contributions to the zero_field split (ZFS) parameter b02 fr om the other three mechanisms including the SS mechanism and SOO mechanism as we ll as SO_SS_SOO combined coupling mechanism exceed 20% for most part of the CF ranges, especially for some CF ranges, in which the contributions to the ZFS pa rameter b02 from the other three mechanisms exceed tha t from the SO mech anism. It is shown in present studies that the approximate expression of ZFS par ameter b02 developed by Macfarlane is not convergent f or most part of t he CF ranges. The microscopic origins of the splitting in the lowest existing st ate 2Eg are studied. Different mechanisms of the splitting 2 Eg state for C4v and C3v crystal fiel ds are explained using group theory.

Keywords: 
• 4B1(3d3) state ion /
• magnet ic interaction /
• spin_Hamilt onian parameters /
• complete diagonalization method /
• perturbation theory method