Zeeman and zero-field splitting of 3d 4 and 3d 6 ions with orbital singlet ground state at orthorhombic and tetragonal symmetry sites

Abstract

The spin Hamiltonian (SH) parameters for 3 d 4 and 3 d 6 ions with the spin S = 2 in the first- and second-kind orthorhombic crystal field (CF) are studied within the 5 D approximation. Four possible energy level schemes with a distinct orbital singlet ground state with S = 2 have been established due to our previous CF studies. For each scheme the microscopic spin Hamiltonian (MSH) formulas for the zero-field splitting (ZFS) parameters in the extended Stevens operator notation B q k as well as the electronic Zeeman parameters g i are derived by computer using the ALTRAN algebraic program. The microscopic approach enables one to express the parameters B q k and g i in terms of the spin-orbit (λ) and spin-spin (ρ) coupling parameters, the orthorhombic energy level splittings (Δ i) and mixing coefficients (q,s). The present perturbation calculations extend to higher orders of perturbation theory as well as being more comprehensive than the earlier ones, since two new energy level schemes not considered before are now dealt with. Due to the ascent in symmetry method, the MSH results are also applicable to tetragonal symmetry cases involving the real ZFS terms. Some inconsistencies in the previous MSH derivations carried out by hand are clarified. Conversion relations between the ZFS parameters B 0 2, B 2 2, B 0 4, B 2 4, B 4 4 and those expressed in several other notations used in the EPR literature are provided. Specific applications of the MSH formulas derived here provide guidelines for the millimeter/submillimeter and high magnetic field EPR studies of 3 d 4 and 3 d 6 ions at orthorhombic and tetragonal symmetry sites.