Studies of the EPR Parameters gi and Ai for Co2+ in the Octahedral Sites of Y3Al5O12 and Y3Ga5O12 Crystals

Abstract

The perturbation formulas of EPR g factors g || , g ? and hyperfine structure constants A || , A ? for the trigonal octahedral 3d 7 cluster are derived considering not only the configuration interaction effect due to the admixture among ground and excited states, but also the covalency effect due to the admixture between the d electrons of the 3d 7 ion and the p electrons of ligands. In these formulas, the parameters related to both effects and the trigonal field parameters are estimated from the optical spectra and the structural parameters of the studied system. According to these formulas, the EPR parameters g || , g ? , A || and A ? for Co 2þ in the octahedral sites of Y 3 Al 5 O 12 and Y 3 Ga 5 O 12 garnets are satisfactorily explained from the optical spectra and the structure data. The role of the covalency effect is discussed.

Theoretical Investigations of the Spin Hamiltonian Parameters and the Local Structure of a Trigonal Co2+ Center in Bi4Ge3O12

“…Based on the cluster approach, the orbital reduction factors k and k , the spin-orbit coupling coefficients ζ and ζ , and the dipolar hyperfine structure parameters P and P can be determined by using the expressions [11] …”

“…For a Co 2+ (3d 7 ) ion in trigonally distorted octahedra, the second-order perturbation formulas of the spin Hamiltonian parameters g , g ⊥ , A and A ⊥ , based on the cluster approach, can be expressed as [11] …”

“…x can be determined from the energy splitting ∆ [= E( 4 A 2 ) − E( 4 E)] of the ground orbital state 4 T 1 in trigonal crystal-fields by using the relationship ∆ = ζ α 2 3α [11]. The splitting ∆ can be obtained from the d-d transition energy matrices for a 3d 7 ion in trigonal symmetry.…”

“…The parameters α, α , ν i and W i j in (1) are related to the admixture among the ground and excited states via crystal-field and electrostatic interactions (note: their detailed expressions can be found in [11]. Since the trigonal field parameters V and V occur in these expressions and the energy matrices, the anisotropies ∆g(= g − g ⊥ ) and ∆A(= A − A ⊥ ) for the g and A factors are related to the trigonal field parameters and hence to the trigonal distortion (or local structure) of the studied Co 2+ impurity center.…”

“…N γ (γ = e g or t 2g ) is the normalization factor and λ γ is the orbital mixing coefficient. By the semiempirical LCAO method [11,12], these parameters can be obtained from the normalization condition a Calculations based on the impurity Co 2+ at the ideal Bi 3+ site, i. e., ∆Z = 0. b Calculations based on the local structural parameters in (9) due to the displacement ∆Z. c The signs of A and A ⊥ were not given in [10].…”