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 Friedel 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 nontrivially the sign of the magnetic anisotropy energy. This behavior is general, and for illustration we address the transition-metal adatoms, Cr, Mn, Fe, and Co deposited on a 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 a 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 a Rh(111) surface [P. Blonski et al., Phys. Rev. B 81, 104426 (2010)].

• Received 1 November 2015
• Revised 9 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.125402