Contributions to zero-field splitting from spin triplets of 3d4and 3d6ions in tetragonal symmetry

In this paper, the perturbation formulas for the zero-field splitting (ZFS) parameters of 3${\mathit{d}}^4$ and 3${\mathit{d}}^6$ ions in tetragonal symmetry are derived taking into account all the excited spin-triplet states ${}_{}{}^3{}_{}{}^{}$L (L=P,D,F,G,H), in the strong-field scheme. The contribution of the spin triplets to the ZFS and the validity of the ${}_{}{}^5{}_{}{}^{}$D approximation for 3${\mathit{d}}^4$ ions at tetragonal sites are investigated. The results show that the spin-triplet contribution to the ZFS is not negligible, and the validity of ${}_{}{}^5{}_{}{}^{}$D approxmation is highly limited in general, although a great deal of early studies of the ZFS for 3${\mathit{d}}^4$ and 3${\mathit{d}}^6$ ions in crystals were based on the ${}_{}{}^5{}_{}{}^{}$D approximation. Applications are made to ${\mathrm{Fe}}^{4+}$ ions in ${\mathrm{CdSiP}}_4$ and ${\mathrm{Cr}}^{2+}$ ions in ${\mathrm{Rb}}_2$ ${\mathrm{CrCl}}_{\mathit{r}}$, and the obtained results are in good agreement with the experimental data. The contribution of spin triplets is found to be either comparable to or larger than that of ${}_{}{}^5{}_{}{}^{}$D state in these crystals.