Rare-Earth-Iron Exchange Interaction in the Garnets. II. Exchange Potential for Ytterbium

Abstract

To determine the magnitude of the anisotropy of the ytterbium-iron (Yb-Fe) exchange interaction we have evaluated the exchange splittings of the lowest ${}_{}{}^2{}_{}{}^{}F_{\frac{5}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}F_{\frac{7}{2}}^{}{}_{}{}^{}$ doublets of ytterbium (${\mathrm{Yb}}^{3+}$) in ytterbium iron garnet (YbIG). By using the wave functions of ${\mathrm{Yb}}^{3+}$ in yttrium gallium garnet (those for YbIG are not known) we are able to express these splittings in terms of ten parameters which characterize the anisotropy of the exchange interaction. As there are only six experimental splittings it is necessary to reduce the number of unknowns by assuming: (1) that the rare-earth-iron (RE-Fe) exchange interaction takes place through the neighboring eight oxygen ions, and (2) (somewhat more uncertainly) that the rare-earth-oxygen (RE-O) exchange interaction is axial about the RE-O axis. This leads us to express the exchange splittings in two sets of four exchange constants. We find a good four-parameter fit of the experimental exchange splittings by adopting essentially zero values for the rare-earth-ferric ion exchange interactions that take place through the four nearest oxygen ions. This result corroborates qualitative conjectures on the RE-Fe exchange based on superexchange bonding angles. The validity of the extrapolation of the anisotropy of the Yb-Fe exchange interaction to other rare earths is discussed.