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Effects of spin-orbit coupling on the electronic

structure of surfaces

- Jürgen Henk
- Theory Department
- Max Planck Institute of Microstructure Physics
- Halle (Saale), Germany

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

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

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

Effect of SOC on the band structure

Without SOC

With SOC

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

Magnetic linear dichroism

Hot spots in Fe(110) Hybridization

and

D

B

D

B

C

A

Change of the character SOC

Valence-band structure

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)

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?

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

Spin-orbit coupling

- Relativistic calculations
- Dirac equation instead of the Schrödinger

equation - SOC and magnetism treated on equal footing
- Basis for the photoemission calculations

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

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

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)

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?

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

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

Analytical calculation - dispersion

Dispersion without SOC

Inner ()

Dispersion with SOC

Outer (-)

splitting

SOC ? effective B-field in the electrons

restframe

Time-reversal symmetry

Analytical calculation spin polarization

Time-reversal symmetry System remains nonmagnetic

- Spin polarization
- Complete (100)
- Within the surface plane
- Perpendicular to the wave vector

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.)

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

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)

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

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

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

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?

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

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

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

Spin-orbit coupling at Bi/Ag(111)

Experiment

Free-electron model

DFT calculations

1st band

2nd band

Spin-orbit coupling at Bi/Ag(111)

2nd band

1st band

2nd band

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

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)

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