RKKY-like contributions to the magnetic anisotropy energy: 3d adatoms on Pt(111) surface

The magnetic anisotropy energy defines the energy barrier that stabilizes a magnetic moment. Utilizing density functional theory based simulations and analytical formulations, we establish that this barrier is strongly modified by long-range contributions very similar to Frieden oscillations and Rudermann-Kittel-Kasuya-Yosida interactions. Thus, oscillations are expected and observed, with different decaying factors and highly anisotropic in realistic materials, which can switch non-trivially the sign of the magnetic anisotropy energy. This behavior is general and for illustration we address transition metals adatoms, Cr, Mn, Fe and Co deposited on Pt(111) surface. We explain in particular the mechanisms leading to the strong site-dependence of the magnetic anisotropy energy observed for Fe adatoms on Pt(111) surface as revealed previously via first-principles based simulations and inelastic scanning tunneling spectroscopy (A. A. Khajetoorians et al. Phys. Rev. Lett. 111, 157204 (2013)). The same mechanisms are probably active for the site-dependence of the magnetic anisotropy energy obtained for Fe adatoms on Pd or Rh(111) surfaces and for Co adatoms on Rh(111) surface (P. Blonski et al. Phys. Rev. B 81, 104426 (2010)).