Mitglied der HelmholtzGemeinschaft Nanostructures on a Cu111 surface

Mitglied der Helmholtz-Gemeinschaft Nanostructures on a Cu(111) surface: Spin excitations from first-principles Benedikt Schweflinghaus Manuel dos Santos Dias, Samir Lounis Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, Germany 3 rd of April 2014 | DPG 2014 Dresden | PGI-1 and IAS-1

Introduction: Today state of the art B. C. Stipe et al. , Science (1998) Fe adatoms on Cu(111) Aim: Spin-characterize spectra from first-principles (KKR Green function method) A. A. Khajetoorians et al. , PRL (2011) 25 September 2020 • Position • Lifetime (linewidth) • Shape, Asymmetries Benedikt Schweflinghaus

Dynamical transverse magnetic susceptibility § What we want (Linear Response Theory): § What we get (TD-DFT, Kohn-Sham formalism): with § How to connect (via Dyson-like Eq. ): Adiabatic LDA: Details on the method: Lounis, Costa, Muniz, Mills, PRL (2010) and PRB (2011) 25 September 2020 Benedikt Schweflinghaus

Landau-Lifshitz-Gilbert model § Empirical ansatz: § LLG equation (Eq. of motion): Precession Damping § Linear response: 25 September 2020 Benedikt Schweflinghaus

Fe dimer / Cu(111): Excitational modes § LLG model ( § Eigenvalues and Eigenstates: ): § TD-DFT: (a) 25 September 2020 (b) Benedikt Schweflinghaus

Trimers vs. 25 September 2020 Benedikt Schweflinghaus

Fe trimer (chain): Excitational modes § Eigenstates: (a) (c) (a) 1 2 3 (b) (c) 25 September 2020 Benedikt Schweflinghaus

Fe trimer: chain vs. triangle (a) (b) = (c) (b) vs. 25 September 2020 Benedikt Schweflinghaus

6 Fe atoms: chain vs. ring (a) (b) (c) 25 September 2020 (a) (d) (e) (b) = (c) (d) = (e) (f) Benedikt Schweflinghaus (f)

Building up the Fe chain (a) 1 (b) 2 1 25 September 2020 2 Benedikt Schweflinghaus

Building up the Fe chain (a) (c) 1 2 3 (b) 1 25 September 2020 2 3 Benedikt Schweflinghaus

Building up the Fe chain (a) (b) (c) 1 2 3 4 1 25 September 2020 (d) 2 3 4 Benedikt Schweflinghaus

Building up the Fe chain (a) (b) (d) (e) 1 2 3 4 5 (c) 1 25 September 2020 2 3 4 5 Benedikt Schweflinghaus

Building up the Fe chain (a) (b) (c) 1 2 3 4 5 (f) 6 1 25 September 2020 (e) (d) 2 3 4 5 6 Benedikt Schweflinghaus

Summary § Spin excitation spectra from first-principles § Spectra can get very different (every atom counts): • What is the structure? • Where do I probe? (degenerate modes) Outlook § Electron self-energy § Renormalized DOS spectra via Dyson Equation Work supported by the HGF-YIG Programme VH-NG-717 Fun. Si. Lab – Functional Nanoscale Structure Probe and Simulation Laboratory 25 September 2020 Thank you for your attention! Benedikt Schweflinghaus

Appendix 25 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: 25 September 2020 Clean crystal surface Cluster on surface Benedikt Schweflinghaus

Inelastic spectrum: Fe adatom / Cu(111) § Resonance Khajetoorians et al. , PRL (2011) 25 September 2020 § Increased B-field increased damping shorter lifetime of spin excitation Benedikt Schweflinghaus

Electron-magnon interaction: Self-Energy Labels ij missing 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 25 September 2020 Thesis, RWTH-Aachen (2011) Benedikt Schweflinghaus

Inelastic spectrum: Fe adatom / Cu(111) vacuum Adatom (d-orbitals) minority majority vacuum adatom Khajetoorians et al. , PRL (2011) 25 September 2020 Benedikt Schweflinghaus

Self-energy: 3 Fe Atoms on Cu(111) 25 September 2020 Benedikt Schweflinghaus

Self-energy: 6 Fe Atoms on Cu(111) 25 September 2020 Benedikt Schweflinghaus