Research on the Spin-Hamiltonian Parameters and Local Structure for the Tetragonal $Mo^{5+}$ Centers in $CaWO_{4}$ Crystal

The spin-Hamiltonian parameters (g factors $g_{∥}$, $g_{⊥}$ and hyperfine structure constants $A_{∥}(A)$, $A_{⊥}(A)$, $A_{∥}(B)$ and $A_{⊥}(B)$, A(A) and A(B) belonging to isotopes $\text{}^{95}Mo^{5+}$ and $\text{}^{97}Mo^{5+})$ of $Mo^{5+}$ ion at the tetragonally-compressed tetrahedral $W^{6+}$ site in $CaWO_4$ crystal are calculated from the high-order perturbation formulae based on the two-mechanism model, where besides the contributions to spin-Hamiltonian parameters due to the crystal-field mechanism concerning the crystal-field excited states in the extensively-applied crystal-field theory, those due to charge-transfer mechanism concerning charge-transfer excited states (which are omitted in crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. The calculations show that for the high-valence state $d^{n}$ ions (e. g., $Mo^{5+}$ considered) in crystals, the contributions due to charge-transfer mechanism should be taken into account in the studies of spin-Hamiltonian parameters. The local structure of $Mo^{5+}$ center in $CaWO_4$ crystal due to the impurity-induced local lattice relaxation is estimated from the calculations. The results are discussed.