Mapping the magnetic exchange interactions from first principles: Anisotropy anomaly and application to Fe, Ni, and Co

Mapping the magnetic exchange interactions from model Hamiltonian to density functional theory is a crucial step in multi-scale modeling calculations. Considering the usual magnetic force theorem but with arbitrary rotational angles of the spin moments, a spurious anisotropy in the standard mapping procedure is shown to occur provided by bilinear-like contributions of high order spin interactions. The evaluation of this anisotropy gives a hint on the strength of non-bilinear terms characterizing the system under investigation.Comment: 11 pages, 1 figur

Surface state scattering by adatoms on noble metals

When surface state electrons scatter at perturbations, such as magnetic or nonmagnetic adatoms or clusters on surfaces, an electronic resonance, localized at the adatom site, can develop below the bottom of the surface state band for both spin channels. In the case of adatoms, these states have been found very recently in scanning tunneling spectroscopy experiments\cite{limot,olsson} for the Cu(111) and Ag(111) surfaces. Motivated by these experiments, we carried out a systematic theoretical investigation of the electronic structure of these surface states in the presence of magnetic and non-magnetic atoms on Cu(111). We found that Ca and all 3$d$ adatoms lead to a split-off state at the bottom of the surface band which is, however, not seen for the $sp$ elements Ga and Ge. The situation is completely reversed if the impurities are embedded in the surface: Ga and Ge are able to produce a split-off state whereas the 3$d$ impurities do not. The resonance arises from the s-state of the impurities and is explained in terms of strength and interaction nature (attraction or repulsion) of the perturbing potential.Comment: 6 pages, 5 figure

Anatomy of magnetic anisotropy induced by Rashba spin-orbit interactions

Magnetic anisotropy controls the orientational stability and switching properties of magnetic states, and therefore plays a central role in spintronics. First-principles density-functional-theory calculations are able, in most cases, to provide a satisfactory description of bulk and interface contributions to the magnetic anisotropy of particular film/substrate combinations. In this paper we focus on achieving a simplified understanding of some trends in interfacial magnetic anisotropy based on a simple tight-binding model for quasiparticle states in a heavy-metal/ferromagnetic-metal bilayer film. We explain how to calculate the magnetic anisotropy energy of this model from the quasiparticle spin-susceptibility, compare with more conventional approaches using either a perturbative treatment of spin-orbit interactions or a direct calculation of the dependence of the energy on the orientation of the magnetization, and show that the magnetic anisotropy can be interpreted as a competition between a Fermi-sea term favoring perpendicular anisotropy and a Fermi-surface term favoring in-plane anisotropy. Based on this finding, we conclude that perpendicular magnetic anisotropy should be expected in an itinerant electron thin film when the spin magnetization density is larger than the product of the band exchange splitting and the Fermi level density-of-states of the magnetic state

Non-collinear Korringa-Kohn-Rostoker Green function method: Application to 3d nanostructures on Ni(001)

Magnetic nanostructures on non-magnetic or magnetic substrates have attracted strong attention due to the development of new experimental methods with atomic resolution. Motivated by this progress we have extended the full-potential Korringa-Kohn-Rostoker (KKR) Green function method to treat non-collinear magnetic nanostructures on surfaces. We focus on magnetic 3d impurity nanoclusters, sitting as adatoms on or in the first surface layer on Ni(001), and investigate the size and orientation of the local moments and moreover the stabilization of non-collinear magnetic solutions. While clusters of Fe, Co, Ni atoms are magnetically collinear, non-collinear magnetic coupling is expected for Cr and Mn clusters on surfaces of elemental ferromagnets. The origin of frustration is the competition of the antiferromagnetic exchange coupling among the Cr or Mn atoms with the antiferromagnetic (for Cr) or ferromagnetic (for Mn) exchange coupling between the impurities and the substrate. We find that Cr and Mn first-neighbouring dimers and a Mn trimer on Ni(001) show non-collinear behavior nearly degenerate with the most stable collinear configuration. Increasing the distance between the dimer atoms leads to a collinear behavior, similar to the one of the single impurities. Finally, we compare some of the non-collinear {\it ab-initio} results to those obtained within a classical Heisenberg model, where the exchange constants are fitted to total energies of the collinear states; the agreement is surprisingly good.Comment: 11 page

Theory of real space imaging of Fermi surfaces

A scanning tunneling microscope can be used to visualize in real space Fermi surfaces with buried impurities far below substrates acting as local probes. A theory describing this feature is developed based on the stationary phase approximation. It is demonstrated how a Fermi surface of a material acts as a mirror focusing electrons that scatter at hidden impurities.Comment: 10 pages, 4 figure

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)).Comment: published manuscript with additional figures and comment

Quantum well states and amplified spin-dependent Friedel oscillations in thin films

Electrons mediate many of the interactions between atoms in a solid. Their propagation in a material determines its thermal, electrical, optical, magnetic and transport properties. Therefore, the constant energy contours characterizing the electrons, in particular the Fermi surface, have a prime impact on the behavior of materials. If anisotropic, the contours induce strong directional dependence at the nanoscale in the Friedel oscillations surrounding impurities. Here we report on giant anisotropic charge density oscillations focused along specific directions with strong spin-filtering after scattering at an oxygen impurity embedded in the surface of a ferromagnetic thin film of Fe grown on W(001). Utilizing density functional theory, we demonstrate that by changing the thickness of the Fe films, we control quantum well states confined to two dimensions that manifest as multiple flat energy contours, impinging and tuning the strength of the induced charge oscillations which allow to detect the oxygen impurity at large distances ($\approx$ 50nm).Comment: This paper has an explanatory supplemen

Spin-polarization of platinum (111) induced by the proximity to cobalt nanostripes

We measured a spin polarization above a Pt (111) surface in the vicinity of a Co nanostripe by spin-polarized scanning tunneling spectroscopy. The spin polarization is exponentially decaying away from the Pt/Co interface and is detectable at distances larger than 1 nm. By performing self-consistent ab-initio calculations of the electronic-structure for a related model system we reveal the interplay between the induced magnetic moments within the Pt surface and the spin-resolved electronic density of states above the surface.Comment: 19 pages, 6 figure

Changing the Magnetic Configurations of Nanoclusters Atom-by-Atom

The Korringa-Kohn-Rostoker Green (KKR) function method for non-collinear magnetic structures was applied on Mn and Cr ad-clusters deposited on the Ni(111) surface. By considering various dimers, trimers and tetramers, a large amount of collinear and non-collinear magnetic structures is obtained. Typically all compact clusters have very small total moments, while the more open structures exhibit sizeable total moments, which is a result of the complex frustration mechanism in these systems. Thus, as the motion of a single adatom changes the cluster structure from compact to open and vice versa, this can be considered as a magnetic switch, which via the local exchange field of the adatom allows to switch the cluster moment on and off, and which might be useful for future nanosize information storage.Comment: 7 page