Relativistic dynamical spin excitations of magnetic adatoms

We present a first-principles theory of dynamical spin excitations in the presence of spin-orbit coupling. The broken global spin rotational invariance leads to a new sum rule. We explore the competition between the magnetic anisotropy energy and the external magnetic field, as well as the role of electron-hole excitations, through calculations for 3$d$-metal adatoms on the Cu(111) surface. The spin excitation resonance energy and lifetime display non-trivial behavior, establishing the strong impact of relativistic effects. We legitimate the use of the Landau-Lifshitz-Gilbert equation down to the atomic limit, but with parameters that differ from a stationary theory.Comment: 8 pages, 3 figures, accepted in PR

Role of Dzyaloshinskii-Moriya interaction for magnetism in transition-metal chains at Pt step-edges

We explore the emergence of chiral magnetism in one-dimensional monatomic Mn, Fe, and Co chains deposited at the Pt(664) step-edge carrying out an ab-initio study based on density functional theory (DFT). The results are analyzed employing several models: (i) a micromagnetic model, which takes into account the Dzyaloshinskii-Moriya interaction (DMI) besides the spin stiffness and the magnetic anisotropy energy, and (ii) the Fert-Levy model of the DMI for diluted magnetic impurities in metals. Due to the step-edge geometry, the direction of the Dzyaloshinskii vector (D-vector) is not predetermined by symmetry and points in an off-symmetry direction. For the Mn chain we predict a long-period cycloidal spin-spiral ground state of unique rotational sense on top of an otherwise atomic-scale antiferromagnetic phase. The spins rotate in a plane that is tilted relative to the Pt surface by $62^\circ$ towards the upper step of the surface. The Fe and Co chains show a ferromagnetic ground state since the DMI is too weak to overcome their respective magnetic anisotropy barriers. Beyond the discussion of the monatomic chains we provide general expressions relating ab-initio results to realistic model parameters that occur in a spin-lattice or in a micromagnetic model. We prove that a planar homogeneous spiral of classical spins with a given wave vector rotating in a plane whose normal is parallel to the D-vector is an exact stationary state solution of a spin-lattice model for a periodic solid that includes Heisenberg exchange and DMI. The validity of the Fert-Levy model for the evaluation of micromagnetic DMI parameters and for the analysis of ab-initio calculations is explored for chains. The results suggest that some care has to be taken when applying the model to infinite periodic one-dimensional systems.Comment: 21 pages, 9 figure

Renormalization of electron self-energies via their interaction with spin excitations: A first-principles investigation

Access to magnetic excitation spectra of single atoms deposited on surfaces is nowadays possible by means of low-temperature inelastic scanning tunneling spectroscopy. We present a first-principles method for the calculation of inelastic tunneling spectra utilizing the Korringa-Kohn-Rostoker Green function method combined with time-dependent density functional theory and many-body perturbation theory. The key quantity is the electron self-energy describing the coupling of the electrons to the spin excitation within the adsorbate. By investigating Cr, Mn, Fe and Co adatoms on a Cu(111) substrate, we spin-characterize the spectra and demonstrate that their shapes are altered by the magnetization of the adatoms, of the tip and the orbital decay into vacuum. Our method also predicts spectral features more complex than the steps obtained by simpler models for the adsorbate (e.g., localized spin models)

Engineering elliptical spin-excitations by complex anisotropy fields in Fe adatoms and dimers on Cu(111)

We investigate the dynamics of Fe adatoms and dimers deposited on the Cu(111) metallic surface in the presence of spin-orbit coupling, within time-dependent density functional theory. The \textit{ab initio} results provide material-dependent parameters that can be used in semiclassical approaches, which are used for insightful interpretations of the excitation modes. By manipulating the surroundings of the magnetic elements, we show that elliptical precessional motion may be induced through the modification of the magnetic anisotropy energy. We also demonstrate how different kinds of spin precession are realized, considering the symmetry of the magnetic anisotropy energy, the ferro- or antiferromagnetic nature of the exchange coupling between the impurities, and the strength of the magnetic damping. In particular, the normal modes of a dimer depend on the initial magnetic configuration, changing drastically by going from a ferromagnetic metastable state to the antiferromagnetic ground state. By taking into account the effect of the damping into their resonant frequencies, we reveal that an important contribution arises for strongly biaxial systems and specially for the antiferromagnetic dimers with large exchange couplings. Counter intuitively, our results indicate that the magnetic damping influences the quantum fluctuations by decreasing the zero-point energy of the system

Transverse dynamical magnetic susceptibilities from regular static density functional theory: Evaluation of damping and g-shifts of spin-excitations

The dynamical transverse magnetic Kohn-Sham susceptibility calculated within time-dependent density functional theory shows a fairly linear behavior for a finite energy window. This observation is used to propose a scheme where the computation of this quantity is greatly simplified. Regular simulations based on static density functional theory can be used to extract the dynamical behavior of the magnetic response function. Besides the ability to calculate elegantly damping of magnetic excitations, we derive along the way useful equations giving the main characteristics of these excitations: effective $g$-factors and the resonance frequencies that can be accessed experimentally using inelastic scanning tunneling spectroscopy or spin-polarized electron energy loss spectroscopy.Comment: 7 pages, 1 figur

Perpendicular Reading of Single Confined Magnetic Skyrmions

Thin-film sub-5 nm magnetic skyrmions constitute an ultimate scaling alternative for future digital data storage. Skyrmions are robust non-collinear spin-textures that can be moved and manipulated by small electrical currents. We show here an innovative technique to detect isolated nanoskyrmions with a current-perpendicular-to-plane geometry, which has immediate implications for device concepts. We explore the physics behind such a mechanism by studying the atomistic electronic structure of the magnetic quasiparticles. We investigate how the isolated skyrmion local-density-of-states which tunnels into the vacuum, when compared to the ferromagnetic background, is modified by the site-dependent spin-mixing of electronic states with different relative canting angles. Local transport properties are sensitive to this effect, as we report an atomistic conductance anisotropy of over 20% for magnetic skyrmions in Pd/Fe/Ir(111) thin-films. In single skyrmions, engineering this spin-mixing magnetoresistance possibly could be incorporated in future magnetic storage technologies

Theoretical probing of inelastic spin-excitations in adatoms on surfaces

We review our recent work on the simulation, description and prediction of spin-excitations in adatoms and dimers deposited on metallic surfaces. This work done together with Douglas L. Mills, is an extension of his seminal contribution (with Pascal Lederer) published 50 years ago on the spin-dynamics of transition metal impurities embedded in transition metal hosts [P. Lederer, D.L. Mills, Phys. Rev. {\bf 160}, 590 (1967)]. The main predictions of his model were verified experimentally with state of the art inelastic scanning tunneling spectroscopy on adatoms. Our formalism, presented in this review, is based on time-dependent density functional theory, combined with the Korringa-Kohn-Rostoker Green function method. Comparison to experiments is shown and discussed in detail. Our scheme enables the description and prediction of the main characteristics of these excitations, \emph{i.e.} their resonance frequency, their lifetime and their behavior upon application of external perturbations such as a magnetic field.Comment: 24 pages, invited review to the special issue "Spins at Surfaces" in Surface Scienc

Spin excitations of individual Fe atoms on Pt(111): impact of the site-dependent giant substrate polarization

We demonstrate using inelastic scanning tunneling spectroscopy (ISTS) and simulations based on density functional theory that the amplitude and sign of the magnetic anisotropy energy for a single Fe atom adsorbed onto the Pt(111) surface can be manipulated by modifying the adatom binding site. Since the magnitude of the measured anisotropy is remarkably small, up to an order of magnitude smaller than previously reported, electron-hole excitations are weak and thus the spin-excitation exhibits long lived precessional lifetimes compared to the values found for the same adatom on noble metal surfaces