Non-linear c-f exchange interaction effect and magnetic properties of rare earth metals

Abstract

Various anomalous behaviors of magnon dispersions in heavy rare earth metals are explained on the standpoint of non-linear c-f exchange interaction by calculating magnon energy. Various kinds of magnon instabilities occur on the second-order magnetic phase boundaries. In the ferromagnetic phase, there are two kinds of instabilities. On the ferro-helix boundary, the ferromagnetic magnon shows nearly flat dispersion with a vanishing spin wave constant. On the ferro-cone boundary, the softening of Q_f mode appears, where Q_f is the nesting wavenumber of the model Fermi surface without interaction. In the helix phase, there are two kinds of instabilities. On the helix-cone boundary, the magnon velocities at q = 0 and q = Q, where Q is the helical wavenumber, vanish, while near the helix-ferro boundary the whole region of 0 < q < Q shows softening in which Q decreases continuously and vanishes at the boundary, where the softening extends to the whole region of 0 < q < Q_f to be consistent with the ferromagnetic magnon softening. Softening of the cone magnon is consistent with these of the above two cases. By replacing the expected value ⟨S⟩ for S, the phase diagram and the magnon dispersion at finite temperature or for diluted materials are discussed. Anomalous magnon dispersions of Gd, Ho and Tb-Y alloy are explained consistently.