A detailed account is given of the calculation of the generalized susceptibility functions of Gd, Dy, Er, and Lu using realistic energy bands. These susceptibilities clearly show the influence of the Fermi-surface geometry in determining the helical ordering arrangements of the heavy rare earths, and the ferromagnetic ordering of Gd. A microscopic discussion of the magneto-elastic effect for a general ordered spin state is also presented. The first-order transition from the helical state to the ferromagnetic or conical ferromagnetic state in Tb, Dy, Ho, and Er is explained by this effect. Dy is used as an example of the application of the formalism, and a fundamental understanding is obtained of the transition between the helical and the ferromagnetic state and of the anomalous thermal expansion in both ordered states.

• Received 12 September 1968

DOI:https://doi.org/10.1103/PhysRev.178.783