Nanostructures on a Cu(111) surface:Spin excitations from first-principles

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Nanostructures on a Cu(111) surface:

Spin excitations from first-principles

Benedikt Schweflinghaus

Manuel dos Santos Dias, Samir Lounis

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)

Dynamical transverse magnetic susceptibility

 What we want (Linear Response Theory):

Adiabatic LDA:

 How to connect (via Dyson-like Eq.):

with

 What we get (TD-DFT, Kohn-Sham formalism):

Damping Damping Precession

Precession

Landau-Lifshitz-Gilbert model

 Empirical ansatz:

 LLG equation (Eq. of motion):

 Linear response:

Fe dimer / Cu(111): Excitational modes

 LLG model ( ):

(a) (b)

 TD- DFT:

 Eigenvalues and Eigenstates:

Trimers

vs.

(a)

(c) (b)

Fe trimer (chain): Excitational modes

 Eigenstates:

(a)

(c) (b)

1 2 3

1 2 3

(a) (b) = (c)

Fe trimer: chain vs. triangle

(a)

(c) (b)

vs.

6 Fe atoms: chain vs. ring

(a)

(f) (b)

(c)

(d) (e)

(a) (b) = (c)

(d) = (e) (f)

Building up the Fe chain

(a) (b)

1 2

1 2

Building up the Fe chain

(a)

(c) 1 2 3 (b)

1 2 3

Building up the Fe chain

(a)

(c) (b)

(d) 1 2 3 4

1 2 3 4

Building up the Fe chain

(a)

(c)

(b) (d)

(e) 1 2 3 4 5

1 2 3 4 5

Building up the Fe chain

1 2 3 4 5 6

(a) (c) (b)

(e) (f) (d)

1 2 3 4 5 6

Summary

 Spin excitation spectra from first-principles

 Spectra can get very different (every atom counts):

 Electron self-energy

Work supported by the HGF-YIG Programme VH-NG-717

FunSiLab – Functional Nanoscale Structure Probe and Simulation Laboratory

• What is the structure?

• Where do I probe?

Outlook

 Renormalized DOS spectra via Dyson Equation

(degenerate modes)

Appendix

KKR Green function method within DFT

 Green function of reference system:

 Connection to regarded system via Dyson equation:

 Key quantity in DFT:

No periodic supercell needed

Takes into account the infinite system

Inelastic spectrum: Fe adatom / Cu(111)

 Resonance

 Increased B-field

Electron-magnon interaction: Self-Energy

G _{vac , vac}

G _{vac ,adatom}

S _adatom

V

G = G ⁰ + G ⁰ SG

s - s s

-Doniach, Engelsberg, PRL 17, 750 (1966) -Hertz, Edwards, J. Phys. F:

Metal Phys. 3, 2174 (1973)

Labels ij missing

Inelastic spectrum: Fe adatom / Cu(111)

vacuum vacuum

majority

minority

Adatom (d- orbitals) Adatom (d-

orbitals)

majority

minority

vacuum adatom

   G = (1 − G ⁰ Σ) ⁻¹ G ⁰

Khajetoorians et al., PRL (2011)

Self-energy: 3 Fe Atoms on Cu(111)

Self-energy: 6 Fe Atoms on Cu(111)