A. T. Costa

Entanglement of Two Impurities through Electron Scattering

We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electrons state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. We find conditions for the impurity spins to be maximally entangled with a significant success probability. We then consider a more realistic description which includes both the forward and backscattering amplitudes. In this scenario, we obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling. We find that our scheme allows us to entangle the impurities maximally with a significant probability.

Impurity scattering induced entanglement of ballistic electrons.

We show how entanglement between two conduction electrons is generated in the presence of a localized magnetic impurity embedded in an otherwise ballistic conductor of special geometry. This process is a generalization of beam-splitter mediated entanglement generation schemes with a localized spin placed at the site of the beam splitter. Our entangling scheme is unconditional and robust to randomness of the initial state of the impurity. The entangled state generated manifests itself in noise reduction of spin-dependent currents.

Indirect exchange coupling between magnetic adatoms in carbon nanotubes

The long-range character of the exchange coupling between localized magnetic moments indirectly mediated by the conduction electrons of metallic hosts can play a significant role in determining the magnetic order of low-dimensional structures. Here we consider how this indirect coupling influences the magnetic alignment of adatoms attached to the walls of carbon nanotubes. A general expression for the indirect coupling in terms of single-particle Green functions is presented. Contrary to the general property that magnetic moments embedded in a metal display Friedel-like oscillations in their magnetic response, calculated values for the coupling across metallic zigzag nanotubes show monotonic behavior as a function of the adatom separation. Rather than an intrinsic property, the monotonicity is shown to reflect a commensurability effect in which the coupling oscillates with periods that coincide with the lattice parameter of the nanotube host. Such a commensurability effect does not dominate the coupling across semiconducting zigzag or metallic armchair nanotubes. We argue that such a long-range character in the magnetic interaction can be used in future spintronic devices.

Spin-orbit coupling and spin waves in ultrathin ferromagnets: The spin-wave Rashba effect

We present theoretical studies of the influence of spin-orbit coupling on the spin-wave excitations of the Fe monolayer and bilayer on the W110 surface. The Dzyaloshinskii-Moriya interaction is active in such films by virtue of the absence of reflection symmetry in the plane of the film. When the magnetization is in plane, this leads to a linear term in the spin-wave dispersion relation for propagation perpendicular to the magnetization, to produce a dispersion curve similar in nature to that found for electrons on semiconducting surfaces when the Rashba coupling is active. We also show spin-polarized electron-loss spectroscopy response functions that illustrate the role of spin-orbit coupling in such measurements. In addition to the modifications of the dispersion relations for spin waves, the presence of spin-orbit coupling in the W substrate leads to a substantial increase in the linewidth of the spin-wave modes. The formalism we have developed applies to a wide range of systems, and the particular system explored in the numerical calculations provides us with an illustration of phenomena which will be present in other ultrathin ferromagnet/substrate combinations.

Emergence of local magnetic moments in doped graphene-related materials

Motivated by recent studies reporting the formation of localized magnetic moments in doped graphene, we investigate the energetic cost for spin polarizing isolated impurities embedded in this material. When a well-known criterion for the formation of local magnetic moments in metals is applied to graphene we are able to predict the existence of magnetic moments in cases that are in clear contrast to previously reported density-functional theory (DFT) results. When generalized to periodically repeated impurities, a geometry so commonly used in most DFT calculations, this criterion shows that the energy balance involved in such calculations contains unavoidable contributions from the long-ranged pairwise magnetic interactions between all impurities. This proves the fundamental inadequacy of the DFT assumption of independent unit cells in the case of magnetically doped low-dimensional graphene-based materials. We show that this can be circumvented if more than one impurity per unit cell is considered, in which case the DFT results agree perfectly well with the criterion-based predictions for the onset of localized magnetic moments in graphene. Furthermore, the existence of such a criterion determining whether or not a magnetic moment is likely to arise within graphene will be instrumental for predicting the ideal materials for future carbon-based spintronic applications.

Dynamic RKKY interaction in graphene

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, based on which the energetically favourable alignment between magnetic moments embedded in this material can be calculated. The general consensus is that the strength of the RKKY interaction in undoped graphene decays as 1/D 3 or faster, where D is the separation between magnetic moments. Such an unusually fast decay for a 2-dimensional system suggests that the RKKY interaction may be too short ranged to be experimentally observed in graphene. Here we show in a mathematically transparent form that a far more long ranged interaction arises when the magnetic moments are taken out of their equilibrium positions and set in motion. We not only show that this dynamic version of the RKKY interaction in graphene decays far more slowly but also propose how it can be observed with currently available experimental methods. PACS numbers:

Theory of local dynamical magnetic susceptibilities from the Korringa-Kohn-Rostoker Green function method

Within the framework of time-dependent density functional theory combined with the Korringa-Kohn-Rostoker Green function formalism, we present a real space methodology to investigate dynamical magnetic excitations from first-principles. We set forth a scheme which enables one to deduce the correct effective Coulomb potential needed to preserve the spin-invariance signature in the dynamical susceptibilities, i.e. the Goldstone mode. We use our approach to explore the spin dynamics of 3d adatoms and different dimers deposited on a Cu(001) with emphasis on their decay to particle-hole pairs.

Dynamical magnetic excitations of nanostructures from first principles.

Within time-dependent density functional theory, combined with the Korringa-Kohn-Rostoker Green functions, we devise a real space method to investigate spin dynamics. Our scheme enables one to deduce the Coulomb potential which assures a proper Goldstone mode is present. We illustrate with application to 3d adatoms and dimers on Cu(100).

Spin waves in zigzag graphene nanoribbons and the stability of edge ferromagnetism

We studied the low-energy spin excitations of zigzag graphene nanoribbons of varying width. We found their energy dispersion at small wave vectors to be dominated by antiferromagnetic correlations between the ribbons edges, in accordance with previous calculations. We point out that spin wave lifetimes are very long owing to the semi-conducting nature of electrically neutral nanoribbons. However, the application of very modest gate voltages causes a discontinuous transition to a regime of finite spin wave lifetimes. On further increasing doping, the ferromagnetic alignments along the edge become unstable against transverse spin fluctuations. This makes the experimental detection of ferromagnetism in this class of systems very delicate and poses a difficult challenge to the possible use of these nanoribbons as the basis for spintronic devices.

Microscopic theory of spin waves in ultrathin ferromagnetic films: Fe on W(110)

We present theoretical studies of the spin wave excitations in ultrathin Fe films adsorbed on the W(110) surface, within the framework of itinerant electron theory, and with use of a realistic electronic structure. The electronic structure of the films and the substrate, taken as semi-infinite, is described by the empirical tight-binding scheme with ferromagnetism in the film driven by intra-atomic Coulomb interactions within the d shell. We calculate the exchange stiffness directly, then explore spin wave dispersion relations and Landau damping throughout the surface Brillouin zone through use of the random phase approximation. We also compare dispersion relations so generated with results based on the adiabatic description of spin motions; the latter approach overlooks Landau damping, of course, which we find appreciable at the shorter wavelengths. We comment also on apparent hybridization gaps and optical spin waves which have appeared in earlier theoretical studies of spin waves in the bulk transition metal ferromagnets.