Direct evidence of the anisotropy of magnetization in rare-earth metals and rare-earth/Fe-2 alloys
Résumé
We report on the genuine origin of the anisotropy of the magnetization M in rare-earth (RE) metals and RE-based alloys. Taking Ho-based layered nanostructures as testing ground, we prove that the anisotropy of M is substantial despite that the sixfold magnetic anisotropy constant K-6(6) vanishes, which contradicts the established wisdom [E. R. Callen and H. B. Callen, J. Phys. Chem. Solids 16, 310 (1960)]. Furthermore, we show that the symmetric anisotropic contributions to M and K-6(6) vary with temperature distinctively from one another, which indicates that both anisotropic effects are unrelated and stem from dissimilar microscopic sources. Our findings are discussed according to the theory [R. J. Elliott and M. F. Thorpe, J. Appl. Phys. 39, 802 (1968)] that predicts the emergence of symmetric anisotropic indirect-exchange terms under the presence of orbital moments. We show evidence that the anisotropy of M is caused by the indirect-exchange coupling among localized 4f magnetic moments mediated by spin-orbit coupled conduction electrons, which ultimately generates a spatially nonuniform spin polarization that replicates the lattice symmetry.