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Effects of spinorbit coupling on the electronic structure of surfaces

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Lifting of degeneracies -depends on the magnetization direction ... MD = Change of the photocurrent upon reversal of the magnetization. MLD in normal. emission ... – PowerPoint PPT presentation

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Title: Effects of spinorbit coupling on the electronic structure of surfaces


1
Effects of spin-orbit coupling on the electronic
structure of surfaces
  • Jürgen Henk
  • Theory Department
  • Max Planck Institute of Microstructure Physics
  • Halle (Saale), Germany

2
Outline
  • Spin-orbit coupling (SOC)
  • Effects of SOC on the electronic structure
  • Band structure and magnetic dichroism of Fe
  • Ab-initio theory
  • Electronic structure calculations
  • Photoemission calculations
  • SOC at surfaces
  • Rashba-Bychkov effect in 2DEGs
  • Au(111)
  • Bi/Ag(111)
  • Summary and outlook

3
Spin-orbit coupling
Electron in a magnetic field
Relativistic motion ? spin precession
Magnetic moment
Hamiltonian
Why spin-orbit coupling? Central potential
Angular momentum (orbital motion)
Spin
4
Effect of SOC on the band structure
Fe, 110 direction
Without SOC
With SOC
Lifting of degeneracies -depends on the
magnetization direction
Exchange splitting
Origin of the magneto-crystalline anisotropy (MCA)
Pure spin states
Spin mixing
Tiny changes ? very accurate computations
5
Effect of SOC on the band structure
Without SOC
With SOC
6
Magnetic linear dichroism
Probing hybridization by angle-resolved
photoemission MD Change of the photocurrent
upon reversal of the magnetization
MLD in normal emission
Fe(110)
  • Rampe, G. Güntherodt, D. Hartmann, JH, T.
    Scheunemann, R. Feder
  • Phys. Rev. B 57 (1998) 14370

7
Magnetic linear dichroism
Hot spots in Fe(110) Hybridization
and
D
B
D
B
C
A
Change of the character SOC
Valence-band structure
8
Magnetic linear dichroism
Energy dependence _at_ Eb 0.5 eV
PE spectra
Theory
Experiment
B
B
Photon energy
Identification of SOC-induced hybridization (hot
spots)
9
Summary Spin-orbit coupling
  • Electronic structure
  • Band gaps
  • Hybridization of both orbital and spin
    components
  • ? Magneto-crystalline anisotropy
  • Electron spectroscopies
  • Spin-polarized low-energy electron diffraction
    (SPLEED)
  • Mott scattering
  • Photoemission
  • Spin polarization of photoelectrons
  • Magnetic dichroism

What about SOC at surfaces? Are there special
effects being not present in the bulk?
10
Electronic-structure calculations
  • Description of the electronic structure
  • Solution of the many-body problem
  • Density-functional theory (DFT)
  • Local spin-density approximation (LSDA)
  • Parameter-free (ab initio)
  • Reduction to a single-particle problem
  • Effective potential contains many-particle
    effects
  • Kohn-Sham equations (self-consistent)
  • Correlation better described than in Hartree-Fock
    approximation
  • Quantities ground state
  • Total energy
  • Electron density
  • Magnetization density

Walter Kohn Nobel prize 1998
11
Spin-orbit coupling
  • Relativistic calculations
  • Dirac equation instead of the Schrödinger
    equation
  • SOC and magnetism treated on equal footing
  • Basis for the photoemission calculations

12
Multiple-scattering theory
  • Successive computation of the scattering
    properties
  • Free electrons - atom - layer stack of layers -
    solid
  • Flexible low-dimensional systems
  • Surfaces, thin films, adatoms,
  • Numerical realization layer Korringa-Kohn-Rostoke
    r method
  • Computer program package omni2k for electron
    spectroscopies

13
Photoemission theory
  • One-step model Excitation and transport are
    coherent processes
  • Spin-density matrix
  • ?? time-reversed SPLEED state (electron
    diffraction)
  • Photocurrent and spin
    polarization
  • Golden rule
  • Sudden approximation Interaction of the
    photoelectron with the remaining system is
    neglected

Feynman diagram
14
Summary Ab-initio theory
  • Electronic structure calculations
  • Density-functional theory (DFT)
  • Local spin-density approximation (LSDA)
  • Spin-polarized relativistic layer KKR method
  • ? SOC and magnetism treated on equal footing
  • Photoemisison calculations
  • Spin- and angle-resolved photoelectron
    spectroscopy (SPARPES)
  • One-step model
  • Input from the DFTLSDA calculations

Application to Au(111) and Bi/Ag(111)
15
Rashba-Bychkov effect in a 2DEG
Rashba-Bychkov effect spin splitting due to
spin-orbit coupling (SOC) in a two-dimensional
electron gas (2DEG)
  • Interface
  • Band bending
  • Asymmetric confinement of the 2DEG
  • Spin splitting due to SOC

Interface in a semiconductor heterostructure
2DEG
  • Structural inversion asymmetry (SIA)
  • Non-centrosymmetric solids
  • Interfaces

Asymmetric confinement
Rashba-Bychkov effect at a metal surface?
16
Rashba-Bychkov effect at a surface
Structural inversion asymmetry
  • Surface
  • Band gap surface barrier
  • Asymmetric confinement of the surface state
  • Spin splitting due to SOC

Metal surface
Surface state
Band gap
  • Ingredients
  • Asymmetric confinement (SIA)
  • Strong atomic SOC
  • Free-electron like surface state

Paradigm Au(111)
Also W(110), Gd(0001),
Surface potential Additional SOC
Atomic potential Strong SOC
17
Analytical calculation - model
  • Hamiltonian
  • Hamiltonian for an isotropic 2DEG
  • Ansatz for the wave function
  • Relation
  • ? 2 wave functions, indexed by

SOC
Rashba terms
Pauli spinor
18
Analytical calculation - dispersion
Dispersion without SOC
Inner ()
Dispersion with SOC
Outer (-)
splitting
SOC ? effective B-field in the electrons
restframe
Time-reversal symmetry
19
Analytical calculation spin polarization
Time-reversal symmetry System remains nonmagnetic
  • Spin polarization
  • Complete (100)
  • Within the surface plane
  • Perpendicular to the wave vector

20
Isotropic 2DEG versus Au(111)
2DEG isotropic parabolic complete in-plane
Au(111) threefold parabolic? complete? in-plane?
Symmetry Dispersion Spin polarization
Three-fold rotational symmetry
Value and sign of a, ß and ??
Probes
Theory Electronic-structure calculations Photoemis
sion calculations
Experiment Spin-resolved photoemission
(Osterwalder et al.) Dichroism (Carbone, Rossi et
al.)
21
Au(111) - Dispersion
Experiment
Ab-initio theory
J. Osterwalder et al. (Zürich)
L
L
Momentum distribution at EF
Dispersion
Splitting
L
L
  • Parabolic dispersion
  • Circular momentum distribution

No significant signature of the threefold symmetry
22
Au(111) Normal-emission spectra
Determination of free parameters (optical
potential) ? unique parameter set
Ab-initio theory
Experiment
J. Osterwalder et al.
Intensity
Spin polarization
Spin polarization due to SOC
(Tamura-Henk-Feder)
23
Au(111) Off-normal-emission spectra
Linear dichroism in spin-integrated spectra
Ab-initio theory
Experiment
J. Osterwalder et al. (Zürich)
Dichroism due to surface symmetry
3.6º
Signature of the threefold symmetry

-3.6º
24
Au(111) - Choosing the right set-up
  • Goal
  • Determine the initial-state ESP from that of the
    photoelectrons
  • Good set-ups
  • Photoelectron spin polarization aligned with that
    of the initial state
  • Set-up for linearly polarized light
  • P-polarized light
  • ESP normal to the scattering plane
  • COmplete PHotoEmission Experiment
  • Used in Zürich/PSI (Zürich set-up)
  • Set-up for circularly polarized light
  • Strong dichroism?
  • Used in Trieste/ELETTRA (Trieste set-up)

due to SOC
25
Au(111) Spin polarization
Zürich set-up
Binding energy 0.17 eV
Pz
Prad
Ptan
6
60
4
-60
Ab-initio theory
-4
-6
Threefold symmetry
Experiment
40
L
-40
  • Sign
  • Order of magnitude
  • Threefold symmetry

26
Au(111) Dichroism
Is there a magnetic or spin-related circular
dichroism?
Spin asymmetry or left-right asymmetry?
Trieste set-up
s
s-
Spectral density _at_ EF
Intensity _at_ EF
Wave vector
Wave vector
Left-right asymmetry in experiment, too?
27
Au(111) Dichroism
Dichroism s - s-
K. Menon et al.
Experiment
Trieste set-up
Energy
  • Left-right asymmetry
  • No magnetic dichroism
  • Circular dichroism (CDAD)

Wave vector
28
Summary Spin-orbit coupling in Au(111)
  • Electronic structure
  • Parabolic dispersion, split into two bands
  • Spin polarization
  • Almost complete
  • In-plane
  • Normal to the wavevector
  • No significant effects of the threefold
    rotational symmetry
  • Photoemission
  • Energy- and momentum distributions
  • Good set-ups
  • Strong reduction of the photoelectron spin
    polarization
  • Dichroism
  • Signature of the surface symmetry

29
Spin-orbit coupling at Bi/Ag(111)
Surface alloy v3xv3R30-Bi/Ag(111)
Bi
Work in progress
Ag
Giant splitting
sp bands
Chr. Ast et al., cond-mat/0509509
30
Spin-orbit coupling at Bi/Ag(111)
Experiment
Free-electron model
DFT calculations
1st band
2nd band
31
Spin-orbit coupling at Bi/Ag(111)
2nd band
1st band
2nd band
32
Summary Spin-orbit coupling in Bi/AgAu(111)
  • Findings so far
  • Giant spin splitting of the Bi sp states
  • Agreement between experiment and ab initio
    theory
  • Open questions
  • Hybridization of the 1st and the 2nd band
  • Effect of the threefold-rotational symmetry (Ag
    sites surrounding Bi sites)
  • Degree and orientation of the spin polarization

33
Summary and outlook
  • Summary
  • Spin-orbit coupling
  • Effects of SOC on the electronic structure
  • Ab-initio theory
  • SOC at surfaces
  • Rashba-Bychkov effect in 2DEGs
  • Au(111)
  • Bi/Ag(111)
  • Work in progress
  • Effect of electronic correlations Gd(0001)
  • Effect of magnetization reversal at surfaces
    Ni(111)

34
Thanks
  • MPI-MSP Halle
  • Patrick Bruno, Arthur Ernst
  • University Zürich
  • Moritz Hoesch, Jürg Osterwalder
  • Elettra/TASC, Trieste
  • Carlo Carbone, Krishna Menon, Mattia Mulazzi,
    Giorgio Rossi
  • EFL Lausanne
  • Marco Grioni
  • MPI-FKF Stuttgart
  • Christian Ast, Klaus Kern
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