Theory of Magnetic Ordering in the Heavy Rare Earths

Abstract

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.

Exploring the magnetic phase diagram of dysprosium with neutron diffraction

“…It is well-known that the interaction between the localized 4f electrons through conduction electrons contributed by the 5d and 6s shells, known as the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, is primarily responsible for such oscillatory arrangements [4][5][6] . However, the exact magnetic structure in rare-earth materials can be the effect of the RKKY interaction perturbed by the anisotropic crystal-field and magnetoelastic interactions 7,8 . Moreover, the competition between the interactions is temperature and field dependent, resulting in the complex magnetic phase diagram.…”

Microwave absorption in terbium, erbium and MnAu₂ at selected frequencies from 20-120 GHz

“…The driving force in the spiral-to-ferromagnetic transition in Tb is the negative magnetoelastic energy associated with the ferromagnetic state (there is no magnetoelastic energy associated with the spiral state at equilibrium) (3).…”

Probing the Fermi surface by positron annihilation and Compton scattering

“…The role of the so-called "webbing" Fermi surface 16 in driving the magnetic order in the heavy rare earths is, today, well established. 17 Positron annihilation was used right from the beginning of such investigations, with early calculations by Loucks including a calculation of the positron wavefunction.…”