Crystal field effect and microscopic origins of the g-factors for 6S(3d5)-state ions at tetragonal symmetry crystal filed

The crystal field effect and microscopic origins of the Zeeman g-factors g// and g⊥ for 6S(3d5) state ions at tetragonal symmetry crystal filed, taking into account the spin–spin (SS), the spin–other–orbit (SOO), and the orbit–orbit (OO) magnetic interactions besides the well-known spin–orbit (SO) magnetic interaction, have been investigated using the microscopic spin Hamiltonian theory and the complete diagonalization method (CDM). It is found that the g//(±1/2) ≠ g//(±5/2) and g⊥(±1/2) ≠ g⊥(±5/2), where the g-factors g//(±1/2) and g⊥(±1/2) express the g  -factors of the ground state |M˜s=±1/2〉, whereas the g-factors g//(±5/2) and g⊥(±5/2) express the g  -factors of the ground state |M˜s=±5/2〉. It is shown that although the SO magnetic interaction is the most important one, the contributions to the shifts of g-factors Δg//(=2.0023 − g//) and Δg⊥(=2.0023 − g⊥) from other three magnetic interactions including the SS, SOO, and OO magnetic interactions are appreciable and should not be omitted, especially for the shifts of g-factors Δg//(±5/2) and Δg⊥(±5/2). The individual contributions to the shifts of g-factors arising from the spin quartet states and spin doublet states have been studied. The investigations show that the Δg//(±1/2) and Δg⊥(±1/2) primarily result from the spin quartet states, whereas Δg//(±5/2) and Δg⊥(±5/2) from the spin quartet states as well as the combined effects between the spin quartet states and the spin doublet states. The contribution to the shifts of g-factors from the net spin doublet states is zero.