Microscopic mechanism of the zero-field splitting parameters for 6 S(3d5) state ions at trigonal symmetry crystal filed

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The microscopic mechanism of the zero-field splitting parameters (ZFS) including D and (a-F) for 6 S(3d5) state ion in trigonal-symmetry crystal field have been investigated using the complete diagonaliztion method (CDM) by taking into account the spin-spin (SS), the spin-other-orbit (SOO) and the orbit-orbit (OO) magnetic interactions besides the well-known spin-orbit (SO) magnetic interaction. It was found that the contribution to the ZFS parameters D and (a-F) arising from the spin-orbit (SO) magnetic interaction is the most important in most of the crystal field (CF) ranges,but the contribution to the zero-field splitting (ZFS) parameter D and (a-F) from the other three mechanisms, including the SS mechanism, SOO mechanism and OO mechanism, cant be ignored. The ZFS parameters D and (a-F) arise from the net spin quartet states as well as the combined effects of the spin doublet states and the spin quartets states, and the contribution to the ZFS parameters from the net spin doublet states are zero. Our investigation shows that the rank-2 ZFS parameter D primarily results from the net spin quartet states whereas the rank-4 ZFS parameter (a-F) primarily results from the combined effect of the spin doublet states and the spin quartet states. An illustrative evaluation is performed for the typical crystal material Fe3+: Al2O3. Good agreement between the theoretical values and the experimental finding are obtained.