Magnetism of Rare-Earth Compounds with Non-Magnetic Crystal-Field Ground Levels

Among rare-earth compounds, there are many materials having non-magnetic crystal-field (CF) ground levels. To understand their magnetic behaviour at low temperatures, we study the effects of the CF levels and the Heisenberg-like coupling on the magnetic process of such a crystalline with mean-field and CF theory. It is found that the material can be magnetically ordered if the Heisenberg exchange is sufficiently strong. Additionally we obtain a condition for initial magnetic ordering, and derive a formula for estimating the Curie temperature if the ordering occurs.