The analysis of spin Hamiltonian and crystal field tensors for Fe3+ in crystals of LiCaAlF6 and LiSrAlF6

In single crystals of LiCaAlF₆ and LiSrAlF₆ doped with Fe³⁺ the trigonal EPR spectra with multiplicityK _M = 1 were observed due to Fe³⁺ substituted for Al³⁺. The spin Hamiltonian parameters describing the fine structure and the superhyperfine structure were determined. It is argued that the tensorsB ₂ andB ₄ of the spin Hamiltonian for Fe³⁺ ions are essentially determined by the quadratic contributions of the crystal field at the substitution site. The signs and the relative values of the elements in the spin Hamiltonian tensorB ₄ of rankL = 4 for Fe³⁺ are determined by the irreducible tensor product V ₄ ?V ₄]₂ of the crystal field tensorV ₄ of rankL = 4 at the substitution sites. The ratio between the invariant sum of the spin Hamiltonian tensorB ₄ for Fe³⁺ in oxygen octahedra FeO₆] and that in fluorine octahedra FeF₆] is directly proportional to the fourth power of the ratio between the effective charges of surrounding ions. The sign of the spin Hamiltonian parameterB ₂₀ corresponds to the sign of the element V ₄ ?V ₄]₂₀ in the irreducible tensor product V ₄ ?V ₄]₂ of rankL = 2.