Theory of the zero-field splitting of 6S(3d5)-state ions in cubic crystals

A study is made of the zero-field splitting (ZFS) of 6S(3d5) ions in cubic crystals, based on an extended crystal-field (CF) model which assumes two constants ζte and ζtt in the description of the spin-orbit (SO) interaction. In addition to the recognized origin for the ZFS, namely, the combined effect of the CF and the SO couplings, a second source is found to arise from the SO interaction alone through a difference between ζte and ζtt caused by covalency. To understand this second effect, we have investigated the SO coupling processes which contribute to the ZFS, using the Macfarlane-Zdansky perturbation procedure. Processes in which the couplings are all between states of different configurations t2me5-m are found to make a positive contribution proportional to ζte4. Other processes contribute negatively through a term in ζte2ζtt2. The ZFS is thus determined by the relative magnitudes of these two parts, and a small difference between ζte and ζtt will cause a great change in its value. Application of this new theory is successfully made to Mn2+ ions in tetrahedral II-VI compounds and in fluoroperovskites