Energy Levels for Rare Earth Ions Subject Both to Exchange and Crystalline Fields

The term splitting has been calculated for the lowest lying J state of the rare earth ions samarium through through ytterbium for the case in which the ions are simultaneously subjected to exchange and crystalline fields of arbitrary relative magnitude. The crystalline field is taken to be cubic and as representing the potential of eight negative ions situated at the corners of a cube. The calculation is carried out for the magnetic axis in the two major (local) crystalline directions, [100] and [111]. The relevance of these calculations to the rare earth iron garnets is discussed.