Phys. Rev. B 76 035323 (2007).
Extrinsic anisotropic magnetoresistance contribution to measured domain wall
resistances of in-plane magnetized (Ga,Mn)As
H.G. Roberts, S. Crampin, and S.J. Bending
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
We demonstrate the presence of an important extrinsic anisotropic
magnetoresistance
contribution to the domain wall resistance recently measured
in thin-film (Ga,Mn)As with in-plane magnetic anisotropy. Analytic results
for simple domain wall orientations supplemented by numerical results for
more general cases show that this previously omitted contribution can largely
explain the observed negative resistance.
Full text:[
arxiv]
Appl. Phys. A 88 555 (2007).
Lifetimes of electrons in the Schockley surface state band of Ag(111)
M. Becker
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
Abstract
We present a theoretical many-body analysis of the electron-electron
(e-e) inelastic damping rate Γ of electron-like excitations
in the Shockley surface state band of Ag(111). It takes into account
ab-initio band structures for both bulk and surface
states. Γ is found to increase more rapidly as a function of surface stat
e energy E than previously reported, thus leading to an
improved agreement with experimental data.
Prog. Surf. Sci. 82 293 (2007).
Dynamics of surface-localised electronic excitations studied with the
scanning tunnelling microscope
J. Kröger, M. Becker, H. Jensen, Th. von Hofe, N. Neel, L. Limot, J. Kliewer, R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
E. Pehlke
Institut für Theoretische Physik und Astrophysik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
C. Corriol, V. M. Silkin
Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal, 4,
E-20018 San Sebastian, Spain
D. Sanchez-Portal
Departamento de Física de Materiales, Centro Mixto CSIC-UPV/EHU,
Apartado 1072, E-20080 San Sebastián, Spain
A. Arnau, E. V. Chulkov, P.M.Echenique
Departamento de Física de Materiales,
Facultad de Ciencias Químicas, Universidad del País Vasco UPV/EHU,
Apartado 1072, E-20080 San Sebastián, Spain
Abstract
The decay rates of electron-like and hole-like excitations at metal surfaces
as determined by a scanning tunnelling microscope are
presented and discussed. Surface-localised electron states as diverse as
Shockley-type
surface states and quantum well states confined to ultrathin alkali
metal adsorption layers are covered. Recent developments in the
analysis of the experimental procedures that are used to
determine decay rates with the scanning tunnelling microscope,
namely the analysis of line shapes and the spatial decay of standing wave
patterns, are discussed.
Phys. Rev. Lett. 97 206602 (2006).
Angular dependence of domain wall resistivity in artificial magnetic
domain structures
A. Aziz, S.J. Bending, H.G. Roberts, S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
P.J. Heard
Interface Analysis Centre, University of Bristol, Bristol
BS2 8BS, United Kingdom
C.H. Marrows
School of Physics and Astronomy, University of Leeds, Leeds
LS2 9JT, United Kingdom
We exploit the ability to precisely control the magnetic domain structure
of perpendicularly magnetized Pt/Co/Pt trilayers to fabricate artificial
domain wall arrays and study their transport properties. The scaling
behaviour of this model system confirms the intrinsic domain wall origin
of the magnetoresistance, and systematic studies using domains patterned
at various angles to the current flow are excellently described by an
angular-dependent resistivity tensor containing perpendicular and parallel
domain wall resistivities. We find that the latter are fully consistent
with Levy-Zhang theory, which allows us to estimate the ratio of minority
to majority spin carrier resistivities,
ρ↓/ρ↑~5.5,
in good agreement with thin film band structure calculations.
Surf. Sci. 600 4280 (2006).
Influence of the tip of the STM on surface electron lifetimes
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
The results of
many-body GW calculations are reported which
quantify the influence of the electric field that exists between the
surface and the tip of a scanning tunneling microscope (STM) on the
inelastic lifetimes of image state electrons.
The tip-induced field causes a significant increase in inelastic scattering,
reducing the lifetimes of $n=1$ image state electrons at Cu(001) and Ag(001)
by over 50% under typical tunneling conditions used in the STM,
and even more for higher members of the image state series.
The reduced lifetimes result from changes in the image state
wave functions, which exhibit greater penetration of the metal surface,
and an increase in the number of inelastic scattering channels that are
available for decay.
Ultramicroscopy 106 614 (2006).
Magnetisation reversal in epitaxial Fe(100) disks studied by high resolution
scanning Hall probe microscopy
J. Neal, H.G. Roberts, M.R. Connolly, S Crampin, S.J. Bending
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
G. Westlbauer, J.A.C. Bland
Department of Physics,
University of Cambridge,
Cambridge CB3 0HE,
United Kingdom
Abstract
Magnetisation reversal has been investigated in 2μm diameter epitaxial
Fe(100) disks using scanning Hall probe microscopy. The high spatial
resolution (~200 nm) and non-invasiveness of our Hall sensors has allowed the
domain structure, which is governed by biaxial in-plane anisotropy, to be
resolved in the disks. We find that most disks appear to exhibit a double
vortex magnetisation reversal mechanism, in agreement with the results of
micromagnetic simulations with the OOMMF code. Although the switching dynamics
tend to be influenced by domain wall pinning sites within our Fe samples, we
find a strong correlation between most of our measured images and the results
of simulations. Additional confirmation for the double vortex reversal
mechanism is drawn from local measurements of out-of-plane magnetic induction
loops.
J. Appl. Phys. 99 08C504 (2006).
Investigation of artificial domains realized by local gallium focused ion-beam
modification of Pt/Co/Pt trilayer structures
A. Aziz, S.J. Bending, H.G. Roberts, S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
P.J. Heard
Interface Analysis Centre, University of Bristol, Bristol
BS2 8BS, United Kingdom
C.H. Marrows
School of Physics and Astronomy, University of Leeds, Leeds
LS2 9JT, United Kingdom
We present the results of experimental investigations of magnetic switching
and magnetotransport in a generation of magnetic devices containing
artificially patterned domains. Our devices are realized by locally reducing
the coercive field of a perpendicularly magnetized
Pt(3.5 nm)/Co(0.5 nm)/Pt(1.6 nm) trilayer structure using a gallium focused
ion beam. Artificial domain walls are created at the interfaces between dosed
and undosed regions when an external magnetic field switches the former but
not the latter. We have exploited this property to create stripelike domains
with widths down to submicron length scales, separated by undosed regions.
Using the extraordinary Hall effect to monitor the local magnetization we have
investigated the reversal dynamics of these artificial domains by measuring
major and minor hysteresis loops. The coercive field of regions irradiated
with identical doses systematically increases as their size decreases. In the
lower branch of minor loops, reversal is seen to occur via a few large
Barkhausen events. Preliminary measurements of transport across domain walls
reveal a positive domain-wall resistance, that does not change sign from
4.2 to 300 K.
Phys. Rev. B 73 081402R (2006).
Theoretical analysis of STM-derived lifetimes of excitations in the
Shockley surface state band of Ag(111)
M. Becker
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
Abstract
We present a quantitative many-body analysis using
the GW approximation
of the decay rate Γ due to electron-electron scattering
of excitations in the Shockley surface state band of Ag(111),
as measured using the scanning tunnelling microscope (STM).
The calculations include the perturbing influence of the STM, which
causes a Stark-shift of
the surface state energy E and concomitant increase in Γ.
We find Γ varies more rapidly with E than recently found
for image potential states, where the STM has been shown to significantly
affect measured lifetimes.
For the Shockley states, the Stark-shifts
that occur under normal tunnelling conditions are relatively small
and previous STM-derived lifetimes need not be corrected.
Prog. Surf. Sci. 80 26 (2005).
Surface state electron dynamics of clean and adsorbate-covered metal
surfaces studied with the scanning tunnelling microscope
J. Kröger, L. Limot, H. Jensen, R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
E. Pehlke
Institut für Theoretische Physik und Astrophysik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
Abstract
Using low-temperature scanning tunnelling microscopy and spectroscopy we
have studied the dynamics of surface state electrons confined to
vacancy islands on Ag(111) and localised at single magnetic and
non-magnetic atoms adsorbed on Ag(111) and Cu(111).
The line width of confined electronic states is found to be only weakly
affected by the actual geometry of the vacancy island. A corresponding
model shows that lossy boundary scattering is the dominant
lifetime-limiting process in the vacancies studied. We present a
corrected analysis of the spatial decay of electron interference patterns,
leading to a more consistent description of the Ag(111) surface state
lifetime than was previously the case. A scanning tunnelling spectroscopy
study of single
adsorbed atoms is presented. By means of an extended Newns-Anderson model
an observed resonance is interpreted in terms of an adsorbate-induced
bound state split off from the bottom of the surface-state band.
A preliminary line shape analysis of the bound state indicates that
adsorbed atoms can modify the surface-state lifetime.
J. Appl. Phys. 98 124102 (2005).
Artificial domain structures realized by local gallium focused Ion-beam
modification of Pt/Co/Pt trilayer transport structure
A. Aziz, S.J. Bending, H.G. Roberts, S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
P.J. Heard
Interface Analysis Centre, University of Bristol, Bristol
BS2 8BS, United Kingdom
C.H. Marrows
School of Physics and Astronomy, University of Leeds, Leeds
LS2 9JT, United Kingdom
We demonstrate that a high-resolution Ga focused ion beam can be used to
introduce artificial domain structures in Pt(1.6 nm)/Co(0.5 nm)/Pt(3.5 nm)
trilayer transport structures. We have used thin SiO2 overlayers
to control the effective energy and dose of Ga ions at the Pt/Co interface.
The extraordinary Hall effect (EHE) was used to characterize the magnetic
properties of the patterned films. Using 30 keV Ga ions and SiO2
overlayer thicknesses in the range of 0-24 nm, we achieve complete control
of the coercive field of our Pt/Co/Pt trilayer structures. The magnetization
reversal mechanism for an artificial domain of size of
3x0.5 μm2 is investigated using EHE.
Phys. Rev. B. 72 193401 (2005).
Lifetimes of Shockley electrons and holes at the Cu(111) surface
M.G. Vergniory
Materia Kondentsatuaren Fisika Saila, Zientzi Fakultatea,
Euskal Herriko Unibertsitatea,
644 Posta kutxatila, E-48080 Bilbo, Basque Country, Spain
J.M. Pitarke
Materia Kondentsatuaren Fisika Saila, Zientzi Fakultatea,
Euskal Herriko Unibertsitatea,
644 Posta kutxatila, E-48080 Bilbo, Basque Country, Spain
and
Donostia International Physics Center (DIPC) and Unidad de Fisica
Materiales CSIC-UPV/EHU,
Manuel de Lardizabal Pasealekua, E-20018 Donostia, Basque Country,
Spain
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
A theoretical many-body analysis is presented of the electron-electron
inelastic lifetimes of Shockley electrons and holes at the (111)
surface of Cu. For a description of the decay of Shockley states both
below and above the Fermi level, single-particle wave functions have
been obtained by solving the Schrödinger equation with the use of
an approximate one-dimensional pseudopotential fitted to reproduce
the correct bulk energy bands and surface-state dispersion. A
comparison with previous calculations and experiment indicates that
inelastic lifetimes are very sensitive to the actual shape of the
surface-state single-particle orbitals beyond the G-bar
(k=0) point, which controls the coupling between the
Shockley electrons and holes.
Phys. Rev. B 72 035443 (2005).
Resonator design for use in scanning
tunneling spectroscopy studies of surface electron lifetimes
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
H. Jensen, J. Kröger, L. Limot, and R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
Abstract
We derive expressions for the lossy boundary-scattering
contribution to the linewidth of surface electronic states
confined with atomic corrals and island resonators. Correcting
experimentally measured linewidths for these contributions along with
thermal and intrumental broadening enables
intrinsic many-body lifetimes due to electron-electron and electron-phonon
scattering to be determined. In small resonators lossy-scattering dominates
linewidths whilst different scaling of widths and separations cause levels
to merge in large resonators. Our results enable the design of
resonators suitable for lifetime studies.
Full text:[
arxiv]
Phys. Rev. Lett. 95 046801 (2005).
Lifetimes of Stark-shifted image states
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
The inelastic lifetimes of electrons in image-potential states at Cu(100)
that are
Stark-shifted by the electrostatic tip-sample interaction in the scanning
tunneling microscope are calculated using the many-body GW approximation.
The results demonstrate that in typical tunneling conditions the image state
lifetimes are significantly reduced from their field-free values.
The Stark-shift to higher energies increases the number of inelastic scattering
channels that are available for decay, with field-induced changes in
the image state
wave function increasing the efficiency of the inelastic scattering through
greater overlap with final state wave functions.
Full text:[
arxiv]
Phys. Rev. Lett. 95 029701 (2005).
Phase coherence length and quantum interference patterns at step edges
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
J. Kröger, H. Jensen, and R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
Abstract
A comment on the work of Wahl et al.,
Phys. Rev. Lett. 91, 106802 (2003)
Full text:[
arxiv]
Phys. Rev. B 71 155417 (2005).
Electron dynamics in vacancy islands: scanning tunnelling spectroscopy on
Ag(111)
H. Jensen, J. Kröger, and R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
The dynamics of Ag(111) surface state electrons confined to nanoscale
hexagonal and triangular vacancy islands have been
investigated using scanning tunneling spectroscopy. We find that the
lifetimes of quantised states with significant amplitude near the centers of
the vacancies are only weakly affected by the geometry of the confining
cavity. A theoretical model is used to describe the dependence of the
lifetime on electron energy, vacancy size, step reflectivity and the
phase coherence length due to inelastic electron-electron and
electron-phonon scattering. Lossy scattering is found to be the dominant
lifetime-limiting process for Ag(111) surface vacancy islands with
areas in the range 40-220 nm2.
Phys. Rev. B 71 155120 (2005).
An embedding potential definition of channel functions
J. E. Inglesfield
School of Physics and Astronomy,Cardiff University,
Cardiff, CF24 3YB, United Kingdom
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
H. Ishida
College of Humanities and Sciences, Nihon University,
Sakura-josui, Tokyo 156-8550, Japan
Abstract
We show that the imaginary part of the embedding potential, a generalised
logarithmic derivative, defined over the
interface between an electrical lead and some conductor,
has orthogonal eigenfunctions which define scattering channels into and out of
the lead.
In the case of an infinitely extended interface we establish the relationship
between these eigenfunctions and the Bloch
states evaluated over the interface. Using the new channel functions,
a well-known result for the total transmission through the conductor
system is simply derived.
Full text:[
arxiv]
J. Phys: Condens. Matter 16 8875-8889 (2004).
An embedding scheme for the Dirac Equation
S Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
An embedding scheme is developed for the Dirac Hamiltonian H.
Dividing space into
regions I and II separated by surface S,
an expression is derived for the
expectation value of H which makes explicit reference to a
trial function defined in I alone, with all details of region II replaced by
an effective potential acting on S and which is related to the Green
function of region II. Stationary solutions provide approximations to
the eigenstates of H within I. The Green function for the
embedded Hamiltonian is equal to the Green function for the entire system
in region I.
Application of the method is illustrated for the problem of a hydrogen atom
in a spherical cavity and an Au(001)/Ag/Au(001) sandwich structure
using basis sets that satisfy kinetic balance.
Full text:[
arxiv|
JPCM]
J. Phys: Condens. Matter 16 6841-6849 (2004).
Spin-orbit splitting of image states
J R McLaughlan, E M Llewellyn-Samuel and
S Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
We quantify the effect of the spin-orbit interaction on the Rydberg-like
series of image state electrons at the (111) and (001) surface of Ir, Pt
and Au. Using relativistic multiple-scattering methods we find Rashba-like
dispersions with ΔESO(K)=γK
with values of γ for
n=1 states in the range 38-88 meV Å. Extending
the
phase-accumulation model to include spin-orbit scattering we find that the
splittings vary like 1/(n+a)3 where a is the
quantum defect and that
they are related to the probability of spin-flip scattering at the
surface. The splittings should be observable experimentally being larger
in magnitude than some exchange-splittings that have been resolved by
inverse photoemission, and are comparable to linewidths from inelastic
lifetimes.
Full text:[
arxiv|
JPCM]
Phil. Trans. R. Soc. Lond. A 362 1149-1161 (2004).
Electron states in quantum corrals
S Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
Quantum corrals are nanoscale structures formed by positioning
individual atoms using the scanning tunneling microscope into geometrical
arrangements that form closed structures. They can be used to
control the spatial and spectral distribution of surface electrons.
The theoretical modelling of these systems is described and illustrated,
and the application of the corrals as quantum laboratories for
controling the interactions of surface state electrons is described.
A new three-dimensional scattering model is introduced that extends the
description of the electron states within quantum corrals and which
can form the basis of many-body calculations of the
lifetimes of confined electrons.
Phys. Rev. B 68 195422 (2003).
Hole dynamics in a quantum-well state at Na/Cu(111)
E. V. Chulkov
Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal, 4,
20018 San Sebastián/Donostia, Basque Country, Spain
and
Departamento de Física de Materiales and Centro Mixto CSIC-UPV/EHU,
Facultad de Ciencias Químicas, UPV/EHU, Apartado Postal 1072, 20080
San Sebastián/Donostia, Basque Country, Spain
J. Kliewer and R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
V. M. Silkin
Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal, 4,
20018 San Sebastián/Donostia, Basque Country, Spain
B. Hellsing
Experimental Physics, Chalmers University of Technology and Göteborg
University, S-412 96 Göteborg, Sweden
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
P.M. Echenique
Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal, 4,
20018 San Sebastián/Donostia, Basque Country, Spain
and
Departamento de Física de Materiales and Centro Mixto CSIC-UPV/EHU,
Facultad de Ciencias Químicas, UPV/EHU, Apartado Postal 1072, 20080
San Sebastián/Donostia, Basque Country, Spain
Abstract
Theoretical calculations and scanning-tunneling spectroscopy measurements of
the hole lifetime broadening, τ-1,
in a quantum-well state for 0.95 and 1.0 monolayers of Na on
Cu(111) are reported. A model potential is proposed for calculating
quantum-well states in a
monolayer on metal surfaces. The inelastic electron-electron contribution,
(τe-e)-1, is evaluated
within the GW approximation by using eigenfunctions and eigenenergies obtained with this
model potential. The electron-phonon contribution,
(τe-ph)-1 is computed by employing Debye
and Einstein models as well as a first-principle ultrasoft pseudopotential
method. The obtained theoretical results are in excellent agreement with
experimental data, both showing a surprisingly large difference in the
lifetime broadening for 0.95 and 1.0 monolayers which is
attributed mostly to changes in the electronic structure.
Comp. Phys. Comm. 151 251-264 (2003).
Complex frequency technique for linear and second harmonic optical
properties of metallic surfaces
L. Calmels
CEMES-CNRS, 29 rue Jeanne Marvig,BP 4347, 31055 Toulouse Cedex 4, F
rance,
and
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
J. E. Inglesfield
Department of Physics and Astronomy, University of Wales,
PO Box 913, Cardiff, CF24 3YB, United Kingdom
S Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
E. Arola
Department of Physics, School of Chemistry and Physics,
Keele University, Keele, Staffordshire, ST5 5BG, United Kingdom
Th. Rasing
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1,
6525 ED Nijmegen, The Netherlands
Abstract
We describe a complex frequency technique for evaluating the linear
and quadratic dielectric responses of metal surfaces, illustrated
by application to the surface of jellium. The electric
susceptibilities are shorter-range functions of the spatial
coordinates at complex frequency, whereas their general behaviour
is complicated, long-range and highly oscillatory at real frequency.
As a result the linear and the second harmonic electric charges induced by an
optical perturbation are then numerically easier to calculate at complex
frequency. As the functions which characterise the optical behaviour
of the metal surface are analytic in the upper complex frequency
half-plane, the dielectric response at real frequency can be deduced
by analytic continuation from the results at complex frequency.
We illustrate and discuss this approach,
which should be useful for studying more realistic models of a
surface in which the crystal potential is included, and where
a direct calculation of the dielectric response is difficult to obtain
at real frequency.
Comp. Phys. Commun. 146 274-275 (2002).
Reply to Comment on "Ewald summation technique for one-dimensional charge
distributions"
D.J. Langridge, J.F. Hart, and S. Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
We explain why the methods in Langridge, Hart and Crampin
[Comput. Phys. Commun. 134 (2001) 78] suffice for the evaluation
of the lattice sums entering the Madelung matrix describing multipole
interactions in systems with one-dimensional translational periodicity.
New Journal of Physics 3 (2001) 22.1-22.11
Scanning tunnelling spectroscopy of electron resonators
J. Kliewer and R. Berndt
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel,
D-24098 Kiel,
Germany
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
The electronic structure of artificial Mn atom arrays on Ag(111) is
characterized in detail with scanning tunnelling spectroscopy
and spectroscopic imaging at low temperature. We demonstrate the degree to
which variations in geometry may be used to control spatial
and spectral distributions of surface state electrons confined within
the arrays, how these are influenced by atoms placed within the
structure and how the ability to induce spectral features at specific
energies may be exploited through lineshape analyses to deduce
quasiparticle lifetimes near the Fermi level. Through extensive comparison
of dI/dV maps and spectra we demonstrate the utility of a model
based upon two-dimensional s-wave scatterers for describing and predicting
the characteristics of specific resonators.
[
Full-text]
Phys. Rev. B 64 (2001) pp. 125416.1-125416.8
Local-field effects on the near-surface and near-interface screened electric field in noble metals
L. Calmels
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1,
6525 ED Nijmegen, The Netherlands
and
Department of Physics and Astronomy,
University of Wales Cardiff,
P.O. Box 913, Cardiff, CF2 3YB, United Kingdom
J.E. Inglesfield
Department of Physics and Astronomy,
University of Wales Cardiff,
P.O. Box 913, Cardiff, CF2 3YB, United Kingdom
E. Arola and S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Th. Rasing
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1,
6525 ED Nijmegen, The Netherlands
Abstract
The screening of an optical electric field at a noble metal surface is
evaluated within a semiclassical model where the non-locality of the
d-electron response is taken into account via a set of interacting atomic
dipoles. The dipole moments in the first few atomic layers differ from
the expected bulk value due to the symmetry breakdown at the surface.
These effects give rise to surface-induced electric charges and currents
and to a surface-induced electric field which vanishes in the bulk but
can be important in the top atomic layers. This field takes into account
local-field effects, is frequency-dependent and is strongly enhanced in a
frequency range characteristic of the metal surface. Results are first given
for an electric field perpendicular to the metal surface, and the enhancement
of the surface response is mainly due to interband electronic transitions
for the Cu and Au surfaces, while it originates from a coupling with the
bulk plasmon excitations for a Ag surface. The anisotropy in the surface
response is studied for an electric field parallel to the anisotropic
Ag(110) surface. Finally, the calculation is generalised to describe
screening effects at an interface between two different noble metals.
The simple surface model used in this paper shows that the surface-induced
electric field should be taken into account in the simulations of surface
spectroscopy, where the calculated signal directly depends on the linearly
screened field at the surface.
Surf. Sci. 482-485 (2001) pp. 1050-1055
Surface states and second harmonic generation at the (110) nickel surface
from a first principles calculation
L. Calmels
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1,
6525 ED Nijmegen, The Netherlands
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
J.E. Inglesfield
Department of Physics and Astronomy,
University of Wales Cardiff,
P.O. Box 913, Cardiff, CF2 3YB, United Kingdom
Th. Rasing
Research Institute for Materials, University of Nijmegen,
Toernooiveld 1,
6525 ED Nijmegen, The Netherlands
Abstract
The electronic and magnetic structure of the ferromagnetic (110) nickel
surface is calculated within the first-principles Layer Korringa
Kohn Rostocker (LKKR) method. Spin-dependent results are given for the
local density of states which show the existence of several
empty surface states at the high symmetry directions of the surface Brillouin
zone. Unoccupied surface states with their dispersion are
described in detail and compared with inverse photoemission measurements.
Second harmonic generation can be calculated in magnetic systems within
the framework of the LKKR method. We present preliminary results which
show that surface states are responsible for an enhancement of the second
harmonic electric current in the vicinity of the (110) nickel surface.
Such a surface state contribution to the second harmonic signal has
recently been observed in Ni(110).
J. Phys. Condens. Matter 13 (2001) pp. L607-L612
Reflection anisotropy spectroscopy of W(110): an optical probe of surface
electronic structure
D. S. Martin, O. Zeybek, B. Sheridan, S.D. Barrett and P. Weightman
Surface Science Research Centre,
The University of Liverpool,
PO Box 147, Liverpool, L69 3BX, UK
J.E. Inglesfield
Department of Physics and Astronomy,
University of Wales Cardiff,
P.O. Box 913, Cardiff, CF2 3YB, United Kingdom
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
The reflection anisotropy (RA) spectrum of W(110) has been
measured, showing a large resonance feature which is due to
transitions from occupied surface states. To understand the
origin of the spectral profile a layer-KKR calculation of the
surface electronic structure has been performed and from the
joint density of states the important transitions have been
identified. These are due to transitions from surface states with
a large p-component to unoccupied d-states, the anisotropy
arising from the relative weight of px and py. These
surface states have been previously measured in angle-resolved
photoemission. The adsorption of oxygen on the W(110) surface has
been studied, showing a decrease in anisotropy with increasing O
coverage and confirming the surface sensitivity. For the first
time the consideration of the density of states upon the initial
and final electronic states participating in RA transitions is
made.
Appl. Phys. A 72 (2001) pp. S147-S148
Electronic structure of an adsorbate in a resonator
J. Kliewer and R. Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
and
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel,
D-24098 Kiel,
Germany
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
We report the controlled modification of the electronic
structure on a single Mn adsorbate. This modification was achieved by
placing the Mn atom within geometrical arrays of adatoms on Ag(111), and
observed with local tunnelling spectroscopy. The changes result from the
coupling between the Mn $s$ level and surface electronic states of the
substrate, which are strongly influenced by the size and geometry of the
nanocavity. The dimension and geometry of the adatom array thus provide a
degree of control over the induced changes.
Comp. Phys. Commun 134 78-85 (2001).
Ewald summation technique for one-dimensional charge distributions
D.J. Langridge, J.F. Hart, and S. Crampin
Department of Physics,
University of Bath,
Bath BA2 7AY,
United Kingdom
Abstract
We address the numerical evaluation of problematic
lattice sums that occur when dealing with long-range electrostatic
interactions in systems with one-dimensional periodicity. An Ewald-type
solution is developed yielding rapidly convergent sums. Explicit
expressions are given for the Madelung matrices that enter the potential
and total energy in self-consistent electronic structure calculations
for systems such as atomic wires and steps.
Phys. Rev. Lett. 85 (2000) pp. 4936-4939
Controlled modification of individual adsorbate electronic structure
J. Kliewer and R. Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
and
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel,
D-24098 Kiel,
Germany
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
Modification of the electronic structure of a single Mn adsorbate placed
within a geometrical array of adatoms on Ag(111) is observed using local
spectroscopy with the scanning tunneling microscope. The changes
result from coupling between the adsorbate level and surface electronic
states of the substrate. These surface states are scattered coherently
within the adatom array, mediating the presence and shape of the array to
the adsorbate within. The dimension and geometry of the adatom array thus
provide a degree of control over the induced changes.
J. Elec. Spec. and Relat. Phenom. 109 (2000) pp. 51-61
Scanning tunneling spectroscopy of surfaces where surface states dominate
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
The spectroscopic study with the scanning tunneling microscope (STM) of systems
where surface states are prominent is discussed. The observation of surface
states in the STM and the success of perturbative calculations of the
tunneling current in such cases is attributed to a common cause, namely
the finite intrinsic lifetime of electrons in the surface state.
A computational framework is described for modeling scanning tunneling
microscopy and spectroscopy of Shockley surface states on close-packed
faces of the noble metals, including their interactions with
surface structures. This is used to model experiments on both clean surfaces
and within atomic corrals, highlighting the role of the STM in investigating
both elastic and inelastic scattering mechanisms at surfaces.
J. Elec. Spec. and Relat. Phenom. 109 (2000) pp. 71-84
STM and STS of bulk electron scattering by subsurface objects
M. Schmid
Institut für Allgemeine Physik,
Technische Universität Wien,
A-1040 Wien, Austria
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
P. Varga
Institut für Allgemeine Physik,
Technische Universität Wien,
A-1040 Wien, Austria
Abstract
Results obtained on aluminum and copper surfaces are used to
demonstrate the ability of scanning tunneling microscopy (STM) and
spectroscopy (STS) to detect subsurface structures through their
influence on the electronic structure.
Subsurface Ar bubbles in Al lead
to a quantum well bounded by the outer surface and the top of the
bubbles.
Using z(V) spectroscopy, where the STM feedback loop keeps the
current constant while ramping the voltage, it is possible to
detect the energy steps between the quantum well states;
combined with a one-dimensional model
employing a realistic potential for the electrons, this allows an
estimate of the thickness of the quantum well, i.e., the depth of the
bubbles. Simulated STM images calculated with a three-dimensional scattering
theory reproduce many details of the interference pattern, and confirm
the size and shape of the bubbles.
Interference patterns attributed to subsurface scatterers have also been
detected on Cu(111) and Cu(100). We propose that the patterns observed
on Cu(111) are due to focusing of electron waves in certain
crystallographic directions, whereas those on Cu(100) are unexplained up
to now.
J. Phys.: Condens. Matt. 12 (2000) pp. L489-L496
Nature of Friedel Oscillations around Si dopants in the
GaAs(110) accumulation layer
J.E. Inglesfield
Department of Physics and Astronomy,
University of Wales Cardiff,
P.O. Box 913, Cardiff, CF2 3YB, United Kingdom
M.H. Boon
Institute for Theoretical Physics,
University of Nijmegen,
P.O. Box 9010, NL-6500 GL Nijmegen, Netherlands
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
The screening of sub-surface Si impurities in an accumulation layer at
the GaAs(110) surface is calculated. Such an accumulation layer can be
induced by a scanning tunneling microscope tip, and surface Friedel
oscillations have been imaged around the Si dopants. This study uses
the effective mass approximation to describe the electrons in the GaAs
conduction band, and a fitted model potential for the impurity.
Two-dimensional effects dominate, with a doubly occupied bound state
pulled off the lowest sub-band by the impurity, and a depletion of one
electron in the conduction states. The bound state gives a large central
peak in the surface induced charge, with the Friedel oscillations
coming from the change in the conduction states. To explain
the amplitude of the observed oscillations, it is necessary
to reduce the tunneling contribution from the bound state.
Phys. Rev. B 61 (2000) pp. 15596-15599
Envelope functions for conduction electron states at GaAs(110)
J.E. Inglesfield
Department of Physics and Astronomy,
University of Wales Cardiff,
P.O. Box 913, Cardiff, CF2 3YB, United Kingdom
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
Low-lying conduction band wave-functions are calculated for
semi-infinite GaAs(110), using the layer-KKR method. It is found
that the envelope functions for the orbitals with even
mirror symmetry are in quadrature with the envelopes for the
odd orbitals. The even orbitals dominate, and a single envelope
function with a node close to the surface works well. The tunneling
into the surface barrier is rather constant for the states considered,
within 0.28 eV of the bottom of the conduction band. Thus recent STM
experiments on sub-surface impurity screening in accumulation layers
with this amount of band-bending probe the surface charge density.
Science 288 (2000) pp. 1399-1402
Dimensionality effects in the lifetime of surface states
J. Kliewer
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
R. Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
and
Institut für Experimentelle und Angewandte Physik,
Christian-Albrechts-Universität zu Kiel,
D-24098 Kiel,
Germany
E.V. Chulkov, V.M. Silkin and P.M. Echenique
Departamento de Física de Materiales, Facultad de Química,
Universidad del Pais Vasco
and
Centro Mixto UPV-CSIC and Donostia International Physics Center,
Apdo. 1072,
20080 San Sebastian/Donostia,
Spain
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
A long standing discrepancy between measured and calculated values
for the lifetimes of holes in the surface state electron bands on
noble metal surfaces is resolved, with both found to have been in error.
The ability of the
scanning tunneling microscope to verify surface quality before
taking spectroscopic measurements is exploited to remove the effects of defect
scattering on experimental lifetimes, found to have been a significant
contribution to prior determinations.
A new theoretical treatment of inelastic electron-electron scattering
is developed which explicitly includes hitherto ignored
intra-band transitions within the surface state band.
The new physical picture to emerge has two-dimensional decay channels
dominating the electron-electron interactions that contribute to the
hole decay, screened by both s-p and d electron states of the
underlying three-dimensional electron system.
Appl. Phys. A 69 (1999) pp. 503-506
Surface-state linewidth from scanning tunnelling spectroscopy
Richard Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
Jiutao Li and Wolf-Dieter Schneider
Institut de Physique Experimentale,
Universite de Lausanne,
CH-1015 Lausanne,
Switzerland
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
The STM can be used to investigate lifetimes of hot holes in a surface state
at low temperatures. We analysed dI/dV data from a Ag(111) using detailed tunnelling
calculations and a simple model and found an electron self-energy of Sigma=4.9 +/- 0.6 meV.
The corresponding lifetime tau = 67 +/- 8 fs is considerably higher than those determined
by angle-resolved photoemission, although it remains below theoretical predictions.
Spatially resolved dI/dV spectra reveal that the lifetime decreases drastically
in proximity to defects such as surface steps.
Surf. Sci. 422 (1999) pp. 95-106
Tunnelling spectroscopy of surface state scattering and confinement
Jiutao Li and Wolf-Dieter Schneider
Institut de Physique Experimentale,
Universite de Lausanne,
CH-1015 Lausanne,
Switzerland
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Richard Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
Abstract
Using low-temperature scanning tunnelling microscopy we have
investigated confinement of electronic surface states to hexagonal
islands and other nanoscale structures on Ag(111). Local
spectroscopy and spatial maps of the differential conductance are
analysed using simple models of the electronic structure. We find
that the concept of confinement of a two-dimensional surface state
applies down to very small structures, and observe in real space how
proximity to defects affects surface state lifetimes.
Phys. Rev. Lett. 81 (1998) pp. 4464-4467
Surface state lifetime measured by scanning tunneling spectroscopy
Jiutao Li and Wolf-Dieter Schneider
Institut de Physique Experimentale,
Universite de Lausanne,
CH-1015 Lausanne,
Switzerland
Richard Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
O.R. Bryant and S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
Quasiparticle interactions broaden spectral features at surfaces,
which can be measured using the scanning tunneling microscope (STM).
We report the first study of lifetimes effects on Shockley surface state electrons
using low-temperature STM spectroscopy. Data taken from Ag(111) are analysed and
understood using detailed tunneling calculations and a simple model, and found to
correspond to a self-energy of Sigma=4.9 +/- 0.6 meV. This is considerably below values
determined by angle-resolved photoemission, but remains higher than theoretical
predictions.
Phys. Rev. Lett. 80 (1998) pp. 3332-3335
Electron confinement to nanoscale Ag islands on Ag(111): a quantitative study
Jiutao Li and Wolf-Dieter Schneider
Institut de Physique Experimentale,
Universite de Lausanne,
CH-1015 Lausanne,
Switzerland
Richard Berndt
2. Physikalisches Institut,
RWTH Aachen,
D-52056 Aachen,
Germany
S. Crampin
Department of Physics,
University of Bath,
BA2 7AY,
United Kingdom
Abstract
Lateral confinement has been suggested as a possible mechanism for depopulation of surface
state levels and concomitant modification of metal surface related properties. Studies to
date give conflicting accounts of the effectiveness of confinement due to scattering at
step edges. We present a quantitative study of surface states on nanoscale Ag islands
on Ag(111), using low-temperature scanning tunneling microscopy and electronic structure
calculations. These results confirm the validity of the confinement picture down to the
smallest of island sizes.
Journal of Chemical Physics 107 (1997) pp.8103-8109
Ab-initio diffusional potential energy surface for
CO chemisorption on
Pd{100} at high coverage: Coupled translation and rotation
P. Hu
University of Cambridge, Department of Chemistry, Cambridge CB2 1EW, UK
and
School of Chemistry, The Queen's University of Belfast, Belfast BT9 5AG, UK
D. A. King
University of Cambridge, Department of Chemistry, Cambridge CB2 1EW, UK
S. Crampin, M. H. Lee, M. C. Payne
University of Cambridge, Cavendish Laboratory, Cambridge CB3 0HE, UK
Abstract
The ground state potential energy surface for CO chemisorption across Pd{110}
has been calculated using density functional theory with gradient corrections
at monolayer coverage. The most stable site corresponds well with the
experimental adsorption heat, and it is found that the strength of binding
to sites is in the following order: pseudo-short-bridge > atop > long-bridge >
hollow. Pathways and transition states for CO surface diffusion, involving a
correlation between translation and orientation, are proposed and discussed.
Phys. Rev. B 54 (1996) pp. 17367-17370
Fully three-dimensional scattering calculations of standing electron waves in
quantum nanostructures: the importance of quasiparticle interactions.
S. Crampin and O.R. Bryant
School of Physics, University of Bath, BA2 7AY, United Kingdom
Abstract
We describe full multiple scattering calculations of surface state
electrons in quantum nanostructures built from of a small number of adatoms.
These are structures which have been assembled and studied in recent
cryogenic STM experiments. Our calculations confirm the nature of electron
confinement deduced from a previous continuum model. We highlight the
role of the intrinsic electron lifetime in determining spectral
features, arguing that atomic corrals could serve as useful ``nanoscale
quantum laboratories'' of many-body processes at surfaces. Results for
structures assembled from several different atomic species show
remarkable similarities, a specific prediction of our theory.
Surf. Sci. Lett. 364 (1996) pp. L595-L599
Ab-initio results for the adiabatic atom-surface
interaction for helium and neon on a simple metal
F. Montalenti, M.I. Trioni and G.P. Brivio
Istituto Nazionale di Fisica della materia-Dipartimento di Fisica, Universita
di Milano,
Via Celoria 16, 20133 Milano, Italy
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
Abstract
We report an ab-initio calculation of the adiabatic electronic
properties of He and Ne atoms interacting with a jellium
(Al-like)
surface, in the framework of the embedding method and using density
functional theory in the local density approximation.
In particular, attention is focused on the repulsive
atom--surface potential.
For incident atoms with initial kinetic energies in the typical
experimental range (up to about 200 meV), it is shown that Ne gets
closer to the metal than He.
This is in agreement with the experimental observation of a greater
sensitivity to the surface electronic structure of Ne than of He,
but in contrast with results obtained by simply applying the
effective medium theory to the Ne/metal system.
J. Magn. Magn. Mater. 156 (1996) pp. 107-108
Empty electron states in ultrathin Fe/Au(100) films
S. De Rossi
Istituto Nazionale di Fisica della Materia-Dipartimento di
Fisica, Politecnico di Milano,
piazza Leonardo da Vinci 32, I-20133 Milano, Italy
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
F. Ciccacci
Istituto Nazionale di Fisica della Materia-Dipartimento di
Fisica, Politecnico di Milano,
piazza Leonardo da Vinci 32, I-20133 Milano, Italy
Abstract
We report a spin-resolved inverse photoemission study of the Fe films grown
on Au(100), in which we have identified empty states with majority and
minority spin character. We have also identified a spin-polarised interface
states present in ultrathin films.
Phys. Rev. Lett. 77 (1996) pp. 908-911
Unexpected Negative Exchange Splitting of the Fe(001) Image State
S. De Rossi and F. Ciccacci
Istituto Nazionale di Fisica della Materia-Dipartimento di
Fisica, Politecnico di Milano,
piazza Leonardo da Vinci 32, I-20133 Milano, Italy
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
Abstract
We have observed a surprising negative exchange splitting of the n = 1
image-potential surface state at Fe(001) using spin resolved inverse
photoemission, indicating that the minority-spin level has a lower energy than
the majority-spin level. Calculations show the negative sign results
from two superimposing effects. A true reverse polarization of the image
state, which hybridizes with bulk bands, which is then enhanced by
matrix element effects in inverse photoemission.
Phys. Rev. B 54 (1996) pp. R2343-R2346
Effects of interface magnetic moments and quantum-well states on
magnetisation-induced second harmonic generation
P. van Gelderen
Research Institute for Materials, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
Th. Rasing and J.E. Inglesfield
Research Institute for Materials, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We develop a model for magnetisation-induced second-harmonic-generation (MSHG)
experiments on Co/Cu(001) and Cu/Co(001) overlayers by expanding the nonlinear
optical susceptibility to lowest order in the magnetisation, and taking the
latter to be given by the interface moments from ab-initio
electronic-structure calculations. The model accounts well for the relative
MSHG signal from Co/Cu(001), but contrary to experiment predicts a nearly
constant signal for Cu/Co(001). We discuss the possibility of quantum-well
states accounting for the failure in the latter case.
Phys. Rev. B 53 (1996) pp. 13817-13823
Integrity of quantum-well resonances in metallic overlayers
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
S. De Rossi and F. Ciccacci
Istituto Nazionale di Fisica della Materia-Dipartimento di
Fisica, Politecnico di Milano,
piazza Leonardo da Vinci 32, I-20133 Milano, Italy
Abstract
Spin-polarized quantum well states in Ag/Fe(001) have been studied by
spin-resolved inverse photoemission and ab-initio electronic structure
calculations. We find excellent agreement between predicted and measured
sp-quantum well states, including majority-spin resonances previously
unobserved in this system.
These exhibit unusual behaviour, narrowing as they move
further into the continuum energy range. With increasing Ag coverage the
resonance widths are shown to reduce in line with level spacings,
indicating the quantum well levels retain their integrity in thick films.
Phys. Rev. B 53 (1996) pp. 9115-9122
Quantum well states in Cu/Co overlayers and sandwiches
P. van Gelderen
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
J.E. Inglesfield
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We report ab initio calculations of quantum well states in
Cu/Co(001) and Co/Cu(001) overlayers and in Co/Cu/Co(001) sandwiches.
Overlayer states are found which coincide well with those previously
identified in photoemission and inverse photoemission experiments.
In Cu/Co and at energies overlapping with the substrate continuum,
minority spin resonances are clearly identifiable. However in the
majority spin channel coupling to the substrate is strong enough to
effectively destroy quantum well features. In Co/Cu/Co(001)
sandwiches discrete states are found at similar energies to those
in overlayers of corresponding Cu thicknesses, but well defined
resonance states
are absent in both spin channels. There is no longer a
strongly size-dependent electronic structure at the Fermi energy.
We conclude care must be taken in extrapolating from the electronic
structure of overlayer systems to that of other modulated structures.
Phys. Rev. B 53 (1996) pp. 8052-8064
Embedding approach to the isolated adsorbate
M.I. Trioni and G.P. Brivio
Istituto Nazionale di Fisica della materia-Dipartimento di Fisica, Universita
di Milano,
Via Celoria 16, 20133 Milano, Italy
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
J.E. Inglesfield
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
An embedding method is proposed, based upon Green function matching,
for calculating the electronic properties of an isolated adsorbate.
The self-consistent single-particle Schrodinger equation is solved
in a localized region containing the adsorbate and that part of the
substrate mainly perturbed by it.
The extended substrate is taken into account exactly
by an effective embedding potential.
The advantages of the method for the adsorption problem are discussed
and tested by a calculation of the electronic properties of isolated
Si and N adatoms on Al, modelled as jellium.
In the former case excellent agreement is found with the results
previously computed by other methods, in the latter, not previously
investigated by a first principles approach, the ionic-like character
of the bond is seen in the calculated charge densities and densities
of states.
Finally the problem of the lack of screening due to the presence of an
adatom on a simple metal surface is estimated by the generalized
phase shift theory.
This effect turns out to be an important contribution to the atom-surface
interaction energies, and it is corrected to first order by the use of
the grand-canonical energy functional.
Phys. Rev. Lett. 76 (1996) pp. 2298-2301
Quantum wells and electron interference phenomena in Al due to subsurface noble gas bubbles
M. Schmid, W. Hebenstreit, and P. Varga
Institut für Allgemeine Physik, Technische Universität Wien,
A-1040 Wien, Austria
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
Abstract
Scanning tunneling miscroscopy on Ar ion bombarded and annealed aluminum
surfaces shows electron interference between the surface and subsurface
bubbles of implanted gas. The depth of the bubbles as determined from the
energy dependence of the standing waves indicates a minimum around 6-7
layers on Al(111). The appearance and energy dependence of the interference
pattern is in good agreement with scattering theory based on free electrons,
and indicates the bubbles have a shape given by the Wulff construction.
Phys. Rev. B 52 (1995) pp. 3063-3066
Magnetism of Fe on Au(100) in the monolayer limit
S. De Rossi and F. Ciccacci
Istituto Nazionale di Fisica della Materia-Dipartimento di
Fisica, Politecnico di Milano,
piazza Leonardo da Vinci 32, I-20133 Milano, Italy
S. Crampin
School of Physics, University of Bath, BA2 7AY, United Kingdom
Abstract
We report a spin-resolved inverse photoemission study of the electronic
structure of Fe/Au(100) thin films, concentrating on states at the center
of the surface Brillouin zone and film thicknesses in the monolayer regime.
We identify states with minority-spin character 0.7 eV above the Fermi level,
confirming previous tentative assignments based upon spin-integrated studies.
However, a feature previously assigned to a quantum-well state is found to be
exchange split by only 200 meV, too small to originate from Fe-derived states,
but in line with self-consistent band-structure calculations that predict an
Au-derived interface state.
Phys. Rev. B 51 (1995) pp. 7318-7321
The embedding method for confined quantum systems
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, United Kingdom
M. Nekovee and J.E. Inglesfield
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We discuss the application of the embedding method to the
problem of finding the eigenstates of confined quantum
systems. Embedding is a general way of tackling boundary condition
problems, giving a true variational principle, and we apply it to
the confinement problem by embedding within an isotropic medium with
a very large potential.
Corrections for incomplete confinement are described.
The method is tested on examples recently studied by
Brownstein [Phys. Rev. Lett. 71, 1427 (1993)], namely an
electron in two dimensions confined within the quadrant of a
circle, and a H atom off centre in a spherical cavity.
[
Full text (pdf)] (93Kb)
Electronic Surface and Interface States on Metallic Systems,
E. Bertel and M. Donath, eds., (World Scientific, 1995), pp. 187-201.
Two- and three-dimensional aspects of surface state confinement
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, United Kingdom
M.H. Boon and J.E. Inglesfield
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
The confinement of surface state electrons on Cu(111) by nanoscale structures
is modelled in this paper by a cylindrical sheath potential on the surface.
The confined states can leak through the potential barrier and are also
scattered into bulk states, and the contributions of these processes to the
lifetime are discussed. Scattering into bulk states provides the most
important energy broadening mechanism in this calculation, but contrary to
experiment the broadening vanishes as the energy approaches the bottom of the
surface state band. The limitations of a two-dimensional treatment of the
scattering of surface states by surface potentials are discussed.
In a two-dimensional approximation, the sheath model potential can reproduce
very well the local density of states at the centre of a ring of discrete
s-wave scatterers.
Phys. Rev. B 50 (1994) pp. 18564-18571
Effective cluster interactions at alloy surfaces and charge
self-consistency: Surface segregation in Ni-10 at.% Al and Cu-Ni
T.Schulthess and R. Monnier
Laboratorium für Festkörperphysik, ETH-Hönggerberg,
CH-8093 Zürich, Switzerland
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
Abstract
First principles results are presented for the effective cluster
interactions at the surface of a random Ni-10 at.% Al alloy. The
derivation is based on an extension of the generalized perturbation
method to semi-infinite inhomogeneous binary alloys, using a layer
version of the Korringa Kohn Rostocker multiple scattering approach in
conjunction with the single site coherent potential approximation to
compute the self-consistent electronic structure of the system. When
applied to the bulk, the method yields effective pair interactions
which have the full point group symmetry of the lattice to a very high
level of numerical accuracy, despite of the fact that intra- and
interlayer couplings (scattering path operators) are treated
differently, and which are in perfect agreement with those of a recent
3-dimensional treatment. Besides the pair terms, a selected class of
triplet and quadruplet interactions are calculated, as well as the
point interactions induced by the presence of the surface. The value
of the latter in the first lattice plane is strongly exaggerated in
our approach, leading to a complete segregation of the minority
species to the surface. Using a value corresponding to the difference
in the surface energies of the pure components for this term leads to
the observed Al concentration of approximately 25% at the surface.
Possible reasons for the shortcoming of the theory are analyzed, and
test calculations for the well studied Cu-Ni system show that the free
energy of the seminfinite alloy cannot be approximated by the sum over
the single particle band energies, once charge selfconsistency is
enforced at the surface.
Chemical Physics Letters 230 (1994) pp.501-506
Gradient Corrections in Density Functional Theory Calculations for
Surfaces: CO on Pd(110)
P. Hu, D. A. King
University of Cambridge, Department of Chemistry, Cambridge CB2 1EW, England
S. Crampin, M. H. Lee, M. C. Payne
University of Cambridge, Cavendish Laboratory, Cambridge CB3 0HE, England
Abstract
Ab initio total energy calculations have been performed for CO
chemisorption on Pd(110). Local density approximation (LDA)
calculations yield chemisorption energies which are
significantly higher than experimental values but inclusion of
the generalised gradient approximation (GGA) gives better
agreement. In general, sites with higher coordination of the
adsorbate to surface atoms lead to a larger degree of
overbinding with LDA, and give larger corrections with GGA. The
reason is discussed using a first-order perturbation
approximation. It is concluded that this may be a general
failure of LDA for chemisorption energy calculations. This
conclusion may be extended to many surface calculations, such
as potential energy surfaces for diffusion.
J. Phys.: Condens. Matter 6 (1994) pp. L613-L618
Surface states as probes of buried impurities
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
Abstract
Shockley surface states at metal surfaces decay exponentially into
the crystal, typically penetrating several interplanar spacings.
Within this distance defects such as impurity atoms will scatter
the surface state electrons and give rise to characteristic standing
wave patterns in the local density of states outside the surface,
similar to those recently detected with the STM due to scattering
by adatoms. A multiple scattering theory is developed to model
this situation and applied to impurities near the Cu(111) surface.
The results are discussed within a two-dimensional scattering model
and the prospects for observation with the STM considered.
Phys. Rev. Lett. 73 (1994) pp. 1015-1018
Influence of bulk states on laterally confined surface state
electrons
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, United Kingdom
M.H. Boon and J.E. Inglesfield
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
Strong scattering by adatoms positioned with the tip of an STM has
recently
been used to confine surface state electrons to nanoscale structures.
We develop a model for confinement by a circular potential on a metal
surface, including substrate band structure effects. Scattering into
bulk states provides an important broadening mechanism for partially
confined states. Contrary to experiment the level width vanishes
as the energy approaches the surface state band edge, indicating an
additional dominant broadening mechanism for laterally confined
surface state levels seen in the STM.
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J. Phys.: Condens. Matter 6 (1994) pp. 7227-7237
Unoccupied electronic states in Au(100) surfaces
F. Ciccacci, S. De Rossi, and A. Taglia
Dipartimento di Fisica, Politecnico di Milano,
piazza Leonardo da Vinci 32, I-20133 Milano, Italy
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
Abstract
We present a joint experimental and theoretical work on the emply electronic
states of Au(100) surfaces. Bothe the stable 5 x 10 reconstructued and the
metastable defect-stabilised 1 x 1 surfaces have been investigated by means
of angle-resolved inverse photoemission, and the electronic structure has
been determined theoretically for the 1 x 1 surface within the local density
approximation. The experimental spectra for the two surfaces are very similar,
showing in both cases bulk derived transitions and a surface feature
corresponding to the n=1 image potential state. In the spectra from
the metastable surface, a strong n=0 surface resonance is also observed.
Comparison with theoretical calculations for the 1 x 1 surface gives generally
good agreement for the bulk transitions, but suggests that surface defects
strongly influence surface states localised near the surface layer.
Phys. Rev. B 49 (1994) pp. 14035-14038
Partial wave summations in atomic-sphere surface calculations
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
Abstract
Using a simple model it is demonstrated that l=3 partial
waves contribute significantly to the description of the
exponentially
decaying charge distribution at metal surfaces calculated within the
atomic-sphere approximation.
Despite a partially compensating error in the calculated Fermi level,
truncating at l=2 overestimates calculated work functions
by up to 0.7eV or 15%, whilst trends are well established.
The better converged results improve agreement with experiment for
the late-row metals, but generally result in poorer agreement for the
BCC transition metals.
Surf. Sci. 307/309 (1994) pp. 41-45
The embedding method for surface adsorption
M.I. Trioni
Istituto Nazionale di Fisica della materia-Dipartimento di Fisica, Universita
di Milano,
Via Celoria 16, 20133 Milano, Italy
J.B.A.N. van Hoof
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
S. Crampin
Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
G.P. Brivio
Istituto Nazionale di Fisica della materia-Dipartimento di Fisica, Universita
di Milano,
Via Celoria 16, 20133 Milano, Italy
J.E. Inglesfield
Institute for Theoretical Physics, University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We report preliminary results for the electronic properties of an
adsorbate on jellium obtained by solving self-consistently the
one-electron
Schrodinger equation within a localized spherical (embedding)
region containing the adatom. The extended substrate is taken into
account by an effective potential defined on the surface
of the sphere. The charge density of the clean
surface and of Si on jellium are in excellent agreement
with those previously computed by other methods, and
we highlight the advantages of our new approach to the
adsorption problem.
J. Phys.: Condens. Matter 5 (1993) pp. L443-L448
Segregation and the work function of a random alloy: PdAg(111)
S. Crampin
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
Self-consistent parameter-free calculations of the surface electronic structure of a
random alloy are used to discuss the composition dependance of the work function (phi)
of the PdAg(111) random alloy surface. For crystals with uniform composition profile phi
varies almost linearly between the pure metal limits, and in the presence of segregation is
found to be a measure of the surface layer composition. Good agreement with measured
polycrystalline work functions is found using experimentally determined segregation
data. The results are used to understand screening within PdAg alloys and point to possible
surface-alloy formation during the growth of Pd on Ag.
Solid State Commun. 87 (1993) pp. 317-320
Influence of interdiffusion on the interfacial magnetism in Fe/Ru superlattices
T. Schulthess
Institut für Angewandte Physik, ETH-Hönggerberg, CH-8093 Zürich,
Switzerland
S. Crampin
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
R. Monnier
Laboratorium für Festkörperphysik, ETH-Hönggerberg, CH-8093 Zürich,
Switzerland
Abstract
We study the effect of interdiffusion on the magnetism of two Fe/Ru superlattices
representative of the two structures proposed in the literature. Our approach is
a combination of the layer Korringa-Kohn-Rostoker method with the multiple-scattering
spin-polarised version of the coherent-potential approximation. We find that even a 20%
alloying in the boundary planes produces only an insignificant reduction of the Fe
moments at the interface, so that interdiffusion cannot be at the origin of the
magnetically dead layers observed in these systems. From an analysis of results
for bulk alloys we deduce that local geometrical relaxation and possibly on-site Coulomb
interactions of the Fe 3d electrons are responsible for the moment suppression.
J. Phys.: Condens. Matter 5 (1993) pp. 4647-4664
Fe on Au(001): magnetism and band formation
S. Crampin
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
The development of thin-film electronic and magnetic properties with film size are
addressed in a study of Fe on Au(001), up to 10 Fe layers thick and including the
Au overlayer formed during normal growth conditions. Enhanced moments at the
Fe/Au interface are observed, decaying to bulk over 3 Fe layers, and the weak
Fe-Au interaction is reflected in moments similar to those of the Fe(001)
surface and in a very small asymmetry in the magnetic properties of the Fe film.
Calculated hyperfine fields are found to exhibit a strong dependence upon
film thickness and no simple relationship with the local spin moments.
Densities of states and core-level shifts reflect changes in nearest-neighbour
species and give a consistent picture of the interface bonding. The development
of zone-centre states with film thickness is followed, and bulk-band overlap
and interfacial bonding are found to influence the distribution of quantum well
states strongly.
Phys. Rev. Lett. 70 (1993) pp. 3099-3102
Magnetic splitting of image states at Fe(011)
M. Nekovee, S. Crampin and J.E. Inglesfield
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
The exchange splitting of image-induced surface states on Fe(110)is calculated
by spin-polarised near-surface embedding. The splitting is 55 meV for the n=1
state and is primarily a result of coupling to the spin-polarised substrate
potential. The effect of the spin-polarised surface barrier is relatively small and
of opposite sign to the substrate contribution. This surprising result is a direct
consequence of the negative spin density fof surface electrons at the Fermi energy,
illustrating the sensitivity of spin-split image states to surface magnetic properties.
Phys. Rev. B 47 (1993) pp. 4810-4813
Magnetic structure near (310) tilt boundaries in iron
K. Hampel and D.D. Vvedensky
The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
S. Crampin
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
The layer Korringa-Kohn-Rostoker method has been used to investigate the electronic
and magnetic structure of an isolated Sigma-5 Fe (310) tilt boundary. The calculation
shows an enhancement of the local magnetic moment at the grain boundary, which decays
away rapidly from the region of the interface. The magnitude and form of the enhancement
is similar to that found near iron surfaces from recent tight-binding calculations.
Phil. Mag. A 67 (1993) pp. 1447-1457
Stacking fault energies of random metallic alloys
S. Crampin
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
D.D. Vvedensky
The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
R. Monnier
Laboratorium für Festkörperphysik, ETH-Hönggerberg, CH-8093 Zürich,
Switzerland
Abstract
Stacking fault energies in dilute Cu(Al) alloys and across the composition range of
PdAg alloys are calculated from first-principles using the layer
Korringa-Kohn-Rostoker method and treating the compositional disorder within the
coherent potential approximation. In Cu(Al), rigid band behaviour results in a sharp
reduction in the fault energy with Al concentration. The non-uniform variation
of the fault energy in PdAg is understood in terms of the relative band-widths
and d-resonance energies of Pd and Ag.
Surf. Sci. 287/288 (1993) pp. 732-735
Subvolume embedding for interfacial electronic structure
S. Crampin, M. Nekovee, J.B.A.N. van Hoof and J.E. Inglesfield
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We discuss aspects of a new method for interfacial electronic structure calculations
which combines full potential accuracy and linear scaling of cpu/memory requirements
with the number of atomic planes. The basic method is to partition space into
subvolumes, with a separate expansion of the one-electron Green function made
within each subvolume. Adjacent subvolumes are coupled via embedding potentials.
We comment upon the advantages of the method, and illustrate with some applications
to the stepped jellium surface.
J. Phys.: Condens. Matter 4 (1992) pp. 8477-8488
The surface state-surface resonance transition on Ta(011)
J.B.A.N. van Hoof, S. Crampin and J.E. Inglesfield
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We study an unusual surface state-surface resonance transition recently identified
in photoemission on Ta(011) using surface electronic structure calculations performed
with the surface embedded Green function method. The transition is understood in terms
of the relative movement of the bulk bands and surface potential with increasing parallel
momentum, which switches the condition for a surface state below the band at the zone
centre to a resonance within the band beyond 0.11 inverse Angstrom along Gamma-bar.
A simple two-band model is constructed to illustrate the effect. Comparison of the
calculated and experimental surface bands away from the zone centre shows sizeable
differences, and we predict the existence of several unnocupied surface states which
should be visible to inverse photoemission.
J. Phys.: Condens. Matter 4 (1992) pp. 1475-1488
Full-potential embedding for surfaces and interfaces
S. Crampin, J.B.A.N. van Hoof, M. Nekovee and J.E. Inglesfield
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
Abstract
We extend the surface-embedded Green function technique for calculating the electronic
structure of surfaces and interfaces by presenting a method for determining substrate
embedding potentials which makes no approximations to the substrate potential. We first
present an alternative derivation of the surface embedded Green function method, to
clarify the use of a planar surface in simulating embeddeing on a more complicated surface,
and illustrate this with rigorous tests. Considering the case of a region embedded on two
surfaces, we determine the conditions under which the resulting Green function may
itself be used as a substrate embedding potential, and thereby derive a precedure
for obtaining anembedding potential which makes no approximation to the substrate
potential. In the case of a substrate with semi-infinite preiodicity this reduces
to a self-consistency relation, for which we describe a first-order iterative solution.
Finally, a particularly efficient scheme for obtaining local properties within a surface
or interface region is outlined. This constitutes a full-potential solution to the
one-electron Schrödinger equation for systems of two-dimensional periodicity,
whose calculation time scales linearly with the number of atomic planes.
Phys. Rev. B 45 (1992) pp. 464-467
Interdiffusion and magnetism in Cu/Ni/Cu sandwiches
S. Crampin
Institute for Theoretical Physics, Catholic University of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, The Netherlands
R. Monnier
Laboratorium für Festkörperphysik, ETH-Hönggerberg, CH-8093 Zürich,
Switzerland
T. Schulthess
Institut für Angewandte Physik, ETH-Hönggerberg, CH-8093 Zürich,
Switzerland
G.H. Schadler
Laboratorium für Festkörperphysik, ETH-Hönggerberg, CH-8093 Zürich,
Switzerland
D.D. Vvedensky
The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
Abstract
Results are presented for the magnetic-moment distribution in a (111) sandwich consisting
originally of three perfect layers of nickel bounded on each side by a semi-infinite
copper crystal, for different degrees of interdiffusion. The approach used is a
combination of the recently developed layer Korringa-Kohn-Rostoker method, with the
multiple-scattering spin-polarised version of the coherent-potential-approximation.
When applied to bulk homogeneous CuxNi1-x, it yields average
and Ni moments in excellent agreement with experiment. The sandwich geometry is found to
favor magnetism at Ni concentrations far below the bulk critical value.
