Theory of Magnetic Ordering in the Heavy Rare Earths: Ab Initio Electronic Origin of Pair- and Four-Spin Interactions.

We describe a disordered local moment theory for long-period magnetic phases and investigate the temperature and magnetic field dependence of the magnetic states in the heavy rare earth elements (HREs), namely, paramagnetic, conical and helical antiferromagnetic (HAFM), fan, and ferromagnetic (FM) states. We obtain a generic HRE magnetic phase diagram which is consequent on the response of the common HRE valence electronic structure to f-electron magnetic moment ordering. The theory directly links the first-order HAFM-FM transition to the loss of Fermi surface nesting, induced by this magnetic ordering, as well as provides a template for analyzing the other phases and exposing where f-electron correlation effects are particularly intricate. Gadolinium, for a range of hexagonal, close-packed lattice constants c and a, is the prototype, described ab initio, and applications to other HREs are made straightforwardly by scaling the effective pair and quartic local moment interactions that emerge naturally from the theory with de Gennes factors and choosing appropriate lanthanide-contracted c and a values.