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
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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
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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.)
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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)
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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
0º
-3.6º
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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

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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
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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
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Spin-orbit coupling at Bi/Ag(111)
Experiment
Free-electron model
DFT calculations
1st band
2nd band
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Spin-orbit coupling at Bi/Ag(111)
2nd band
1st band
2nd band
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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

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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