Theory of anisotropic magnetoresistance in atomic-sized ferromagnetic metal contacts
نویسندگان
چکیده
M. Häfner,1,2 J. K. Viljas,1,3 and J. C. Cuevas2 1Institut für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures, Universität Karlsruhe, D-76128 Karlsruhe, Germany 2Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain 3Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 5100, FIN-02015 TKK, Finland Received 24 November 2008; revised manuscript received 27 December 2008; published 29 April 2009
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Supplementary material for “ Anisotropic magnetoresistance in ferromagnetic atomic - sized metal contacts ”
The elements h iα,iα;σ are the spin-dependent on-site energies, h (0) iα,jβ;σ for i 6= j are the hopping elements, while h (0) iα,iβ;σ = 0 for α 6= β. For a nonorthogonal basis |iασ〉 we additionally need the spin-independent overlap integrals between different orbitals: Siασ,jβσ′ = 〈iασ|jβσ′〉 = siα,jβδσσ′ . The creation and annihilation operators then satisfy {ĉiασ, ĉjβσ′} = [s−1]iα,jβδσσ′ . In...
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