Mitglied der HelmholtzGemeinschaft Firstprinciples investigation of selfenergies and

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Mitglied der Helmholtz-Gemeinschaft First-principles investigation of self-energies and theoretical magnetic excitation spectra Benedikt Schweflinghaus

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

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

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.

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

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)

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

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

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

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

Appendix 18 September 2020 Benedikt Schweflinghaus

DOS 18 September 2020 Benedikt Schweflinghaus

DOS 18 September 2020 Benedikt Schweflinghaus

Self-energy: TM adatoms / Cu(111) 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.

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

Beyond actual approach: Self Energy V 18 September 2020 Benedikt Schweflinghaus

KKR Green function method within DFT § Green function of reference system: § Connection

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

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