Mitglied der HelmholtzGemeinschaft Firstprinciples investigation of selfenergies and
- Slides: 16
Mitglied der Helmholtz-Gemeinschaft First-principles investigation of self-energies and theoretical magnetic excitation spectra Benedikt Schweflinghaus 1, Manuel dos Santos Dias 1, Antonio T. Costa 2, Samir Lounis 1 Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, Germany 2 Department Instituto de Fisica, Universidade Federal Fluminense, Rio de Janeiro, Brazil 1 12 th of March 2013 | DPG 2013 Regensburg | PGI-1 and IAS-1
Introduction: Today state of the art I Stipe et al. , Science (1998) Fe adatoms on Cu(111) Spin excitations Khajetoorians et al. , PRL (2011) Characteristics: • Position • Linewidth / lifetime • Shape • Need for theory based on first-principles! • Here: KKR Green function method 18 September 2020 Benedikt Schweflinghaus
Dynamical transverse magnetic susceptibility § What we want (Linear Response Theory): Z § What we get (TD-DFT, Kohn-Sham formalism): with § How to connect (via Dyson Eq. ): Adiabatic LDA: Details on the method: Lounis, Costa, Muniz, Mills, PRL (2010) and PRB (2011) 18 September 2020 Benedikt Schweflinghaus
Beyond present state-of-the-art: Self-Energy V -Doniach, Engelsberg, PRL 17, 750 (1966) -Hertz, Edwards, J. Phys. F: Metal Phys. 3, 2174 (1973) -Hong, Mills, PRB 59, 13840 (1999) -Zhukov, Chulkov, Echenique, PRL 93, 096401 (2004) -Müller, Master 18 September 2020 Thesis, RWTH-Aachen (2011) Benedikt Schweflinghaus
Imag. part of Self-Energy: Fe adatom/Cu(111) “weight” “resonance” § Step for both spins of § integration over resonance in § step height determined by density of opposite spin § Fe adatom: § Compare to experiment? 18 September 2020 Benedikt Schweflinghaus
Inelastic spectrum: Fe adatom / Cu(111) § Resonance Khajetoorians et al. , PRL (2011) 18 September 2020 § Increased ΔB = B-B 0 increased damping shorter lifetime of spin excitation Benedikt Schweflinghaus
Inelastic spectrum: Fe adatom / Cu(111) Adatom (d-orbitals) vacuum minority majority § Is this unique for Fe? vacuum adatom Khajetoorians et al. , PRL (2011) 18 September 2020 Benedikt Schweflinghaus
Other TM adatoms on Cu(111) Co Mn majority minority § Step in Cr minority Step in inelastic spectrum? No! § Steps, peaks, satellites, . . . , extinction of features Δz § Not shown: Shape also depends on Δz 18 September 2020 Benedikt Schweflinghaus
Summary § Roadmap to magnetic inelastic spectrum from first-principles: § Theoretical spectra for different TM adatoms / Cu(111) • • : steps in and , but height may differ : now step height comparable, but all kinds of features (steps, peaks, satellites, . . . ) Work supported by the match to experiment? HGF-YIG Programme § Outlook: • Include electronic structure of tip • Include spin-orbit coupling • Different substrates, clusters VH-NG-717 Fun. Si. Lab – Functional Nanoscale Structure Probe and Simulation Laboratory Thank you for your attention! 18 September 2020 Benedikt Schweflinghaus
Appendix 18 September 2020 Benedikt Schweflinghaus
DOS 18 September 2020 Benedikt Schweflinghaus
Self-energy: TM adatoms / Cu(111) 18 September 2020 Benedikt Schweflinghaus
Simple Model (1 atom, 1 orbital) Now: Symmetric (e. g. Mn) vs. asymmetric (e. g. Fe) case (Bext = 0. 2 me. V, ): vs. 18 September 2020 Benedikt Schweflinghaus
Beyond actual approach: Self Energy V 18 September 2020 Benedikt Schweflinghaus
KKR Green function method within DFT § Green function of reference system: § Connection to regarded system via Dyson equation: No periodic supercell needed Takes into account the infinite system § Key quantity in DFT: 18 September 2020 Clean crystal surface Cluster on surface Benedikt Schweflinghaus
KKR Green-function method within density-functional theory Dyson eq. : Reference system → New system No periodic supercell needed Takes into account the infinite system KKR Representation of Green function: G 0 Im E G “Single-site” (within the atom) EF 30~40 energy pointssurface are Crystal needed 18 September 2020 “Back-scattering” (contribution of all other atoms) Re E Cluster on surface Benedikt Schweflinghaus
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