Crystal field effect and microscopic origins of the g-factors for 6S(3d 5)-state ions at tetragonal symmetry crystal filed

Abstract

The crystal field effect and microscopic origins of the Zeeman g-factors g // and g ⊥ for 6S(3d 5) 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 Δ g //(=2.0023 − g //) and Δ g ⊥(=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 Δ g //(±5/2) and Δ g ⊥(±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 Δ g //(±1/2) and Δ g ⊥(±1/2) primarily result from the spin quartet states, whereas Δ g //(±5/2) and Δ g ⊥(±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.