Magnetic anisotropy of a transition metal monolayer and bilayer

Abstract

The magnetic anisotropy of a free-standing transition metal monolayer and bilayer versus the band filling is systematically studied by using the recursion method. We show rigourously that the magnetic anisotropy energy must present a minimum number of nodes as a function of the band filling which enables us to suggest a “canonical” picture. We relate the origin of irregular oscillations spoiling this picture to energy-band crossings and employ the Wigner-von Neumann theory to discuss it. Particularly, we show in the framework of a rudimentary model that the irregular contribution is suppressed by the substrate. Our results are consistent with the available data. For Fe and Co isolated (001) monolayers, a very small magnetic anisotropy is found. Moreover, the shape of the anisotropy energy curve might explain the controversial situation for Fe. Some other problems known from the recent literature are also considered.