A study of spin-Hamiltonian parameters for Hf3+ ions in orthophosphate MPO4 (M=Sc, Lu, Y) crystals

The spin-Hamiltonian (SH) parameters ( g factors g ∥ , g ⊥ and hyperfine structure constants A ∥ 177 , A ∥ 179 , A ⊥ 177 , A ⊥ 179 ) of 5d1 ion Hf3+ in zircon-type orthophosphate MPO4 (M=Sc, Lu, Y) crystals are calculated from two microscopic SH theory methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM). The calculated results show that when the high-order (i.e., the third-order rather than the conventional second-order) perturbation formulas in PTM are used, the calculated values from both PTM and CDM methods are not only close to each other, but also in good agreement with the experimental values. This suggests that the two microscopic SH theory methods based on crystal-field theory are effective to the explanations of SH parameters for 5dn ions in crystals. The covalence effect, the signs of constants A i ( i = ∥ or ⊥ ) and the core polarization constants κ obtained from the calculations are also discussed.