Robust Spin Polarization and Spin Textures on Stepped Au(111) Surfaces
Jorge Lobo-Checa,1,2,3Fabian Meier,2,3Jan Hugo Dil,2,3Taichi Okuda,2,4Martina Corso,2Vladimir N. Petrov,5
Matthias Hengsberger,2Luc Patthey,3and Ju ¨rg Osterwalder2
1Centre d’Investigacio ` en Nanocie `ncia i Nanotecnologia, CIN2 (CSIC-ICN), Esfera UAB, Campus de Bellaterra,
2Physik-Institut, Universita ¨t Zurich-Irchel, Winterthurerstrasse 190, CH-8057 Zu ¨rich, Switzerland
3Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland
4The Institute for Solid State Physics, The University of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan
5St. Petersburg Technical University, 29 Polytechnicheskaya Street, St. Petersburg 195251, Russia
(Received 3 December 2009; published 7 May 2010)
The influence of structural defects, in the form of step lattices, on the spin polarization of the spin-orbit
split Shockley surface state of Au(111) has been investigated. Spin- and angle-resolved photoemission
data from three vicinal surfaces with different step densities are presented. The spin splitting is preserved
in all three cases, and there is no reduction of the spin polarization of individual subbands, including the
umklapp bands induced by the step lattice. On the sample with the highest step density studied, where the
wave functions are delocalized over several terraces, the spin splitting is enhanced substantially, likely as
an effect of the effective surface corrugation as on related surface alloys. The spin texture shows in all
cases spin polarization vectors tangential to the Fermi circles, with the same helicities as on Au(111).
DOI: 10.1103/PhysRevLett.104.187602PACS numbers: 79.60.Bm, 72.25.?b, 73.20.At
The Rashba effect is one of the cornerstones of spin-
tronics . It applies to an electron gas confined to two
dimensions (2D) by an asymmetric potential and leads to a
momentum-dependent spin splitting of the electronic
states, induced by the spin-orbit interaction . The split-
ting can be controlled by applying an electric field along
the confinement direction, thus providing effective control
of injected spin currents. Such systems have been realized
in semiconductor heterostructures , but they exist also
naturally on noble metal surfaces , as has been shown
directly by spin- and angle-resolved photoemission spec-
troscopy (SARPES) . While these latter systems are
obviously less suitable for device applications, they offer
a convenient platform for fundamental studies of these
In this Letter we address the influence of lateral con-
finement and presence of structural defects on the spin
polarization and on the spin splitting. Vicinal Au(111)
surfaces are used as model systems, because the
Shockley surface state on Au(111) shows the largest
spin-orbit splitting of the noble metal surfaces, with
100% spin polarized subbands. Such vicinals exhibit regu-
lar lattices of monoatomic steps, and flat terraces in be-
tween . Linear steps represent one kind of structural
defects; they act as repulsive potential barriers for surface
state electrons that can lead to partial or even complete
lateral confinement of the surface state wave function,
depending on the terrace width . According to
Bihlmayer et al., a large contribution to the spin splitting
on Au(111) originates from the topmost atomic layer ,
and it should thus be susceptible to the presence of steps.
On the flat Au(111) surface, the parabolic subbands are
shifted in momentum by 0:026?A?1with respect to each
the Fermi level thus consists of two concentric rings, with
spin polarizationvectors lying mainly in-plane and tangen-
tial to the circular shape [4,5]. Interestingly, the 2D Fourier
analysis of surface state standing wave patterns, originat-
ing from defect scattering and imaged by scanning tunnel-
ing microscopy (STM), produces only a single circle at the
Fermi energy . This apparent inconsistency was ex-
plained by introducing an additional spin selection rule,
allowing for interference effects only between bands with
parallel spin polarization [11,12]. While this represented a
nice confirmation of the spin texture of these states in
momentum space, a direct investigation of the interaction
of these states and their spin polarization with surface
defects can only be achieved by SARPES. Indeed, a
(spin-integrated) angle-resolved photoemission (ARPES)
investigation of some vicinal Au(111) surfaces has shown
that the spin splitting persists for surfaces with large ter-
The effects of a regular array of steps on the Au(111)
Shockley state are fourfold: First, the energy of the band
bottom shifts towards the Fermi energy because of the
repulsive scattering potential [14,15]. Second, a momen-
tum shift of the band bottom occurs in the direction per-
pendicular to the steps. Its magnitude is related to both the
complex potential landscape created by the steps and the
existence of a projected gap at the
Qualitatively, this effect is explained as a change in the
reference of the electron wave function: For large separa-
tion between steps the electrons are confined within each
(111) terrace [Fig. 1(a)] and openings of small energy gaps
have been observed [13–15]. For small step separation the
electrons interact with several steps. Their wave functions
?? point .
PRL 104, 187602 (2010)
7 MAY 2010
? 2010 The American Physical Society
are therefore delocalized and sensitive to the step lattice
the surface-projected bulk energy gap at the?? point, trans-
forming the Shockley surface state intoa surface resonance
[16,17].Third,the step superlatticealso generates umklapp
states, i.e., replica bands shifted in momentum in the
direction perpendicular to the steps by 2?=d [Fig. 1(c)]
[13–15]. Finally, the spin-orbit induced splitting of the sub-
bands is progressively lost in the ARPES spectra due to the
peak broadening resulting from the large terrace width
distributions (TWD). This splitting can only be observed
with optimally prepared surfaces, at low temperatures, and
only for the largest terrace widths of the order of ?50?A
Au(11 12 12), Au(7 8 8) and Au(2 2 3). The relevant
structural parameters are introduced in Fig. 1(d) and sum-
marized in Fig. 2. Au(11 12 12) and Au(7 8 8) have large
terraces and show surface reconstructions similar to
Au(111), whereas Au(2 2 3) exhibits small terraces, so
that the aforementioned localization transition occurs in
this set. All surfaces were prepared in situ in ultrahigh
vacuum (UHV) by repeated cycles of Arþsputtering at
0.75 kVand annealing to 700 K. The quality of the surfaces
was checked from the spot splitting in low-energy electron
diffraction (LEED)patternsand theline shapeandwidth of
the surface state in spin-integrated ARPES. No minigaps
were observed in the surface state dispersion due to a
combination of TWD, acquisition temperature and insuffi-
cient instrumental resolution . Spin-integrated and spin-
resolved ARPES data were taken at the COPHEE end
station  located at the Surface and Interface
Spectroscopy (SIS) beam line at the Swiss Light Source.
All measurements were performed at room temperature
(RT) in a UHV chamber with 1 ? 10?10mbar base pres-
sure using linear horizontal polarized light. The energy and
angular resolution of our SARPES measurements were
70 meVand ?0:5?at 21 eV photon energy. Spin-resolved
momentum distribution curves (MDCs) were obtained by
recording intensities and scattering asymmetries in two
orthogonal Mott detectors  for different emission
Figure 2 summarizes the spin-integrated Fermi surface
maps and band dispersion measurements perpendicular to
the steps for the three vicinal surfaces, showing the para-
bolic dispersion of the Shockley surface state. Although
similar data were already reported in literature [6,13,14],
they are included here to serve as a guideline for the
discussion of the spin-resolved data. No spin splitting can
be resolved in these data because the bandsare intrinsically
broad. This is a consequence of the large TWD in these
samples, and of the measurement temperature (RT). Weak
replica bands, shifted to larger kxvalues, are observed for
Au(11 12 12) and Au(7 8 8), both in the energy distribution
curves (EDCs) and Fermi surface maps (FSMs). They are
due to umklapp scattering within the step lattice. It is not
observed for Au(2 2 3), because the displayed momentum
range is too small (the center of the replica is found at kx¼
The evolution of the spin polarization and spin texture of
thesurface statewith increasingstep density is investigated
through spin-resolved MDCs measured along kx, i.e., the
direction perpendicular to the steps (Fig. 3). Two orthogo-
nal Mott polarimeters yield simultaneously the spin-
FIG. 1 (color online).
extreme cases of step densities on vicinal Au(111): (a) the
electrons are confined within each terrace and (b) they are
delocalized on the average surface. (c) Graphical representation,
for case (a), of the main Fermi surfaces (solid circles) and the
umklapp states (dotted circles) induced by the step superlattice.
Directions of the tangential in-plane spin polarization vectors are
included. The sample coordinate system and the experimental
setup are schematically represented in (d) and (e), respectively. ?
is the miscut angle and d is the distance between steps. A slight
sample tilt around the x-axis could not be corrected, therefore
momentum scans along kx follow the green dashed line in
(c) rather than the high symmetry gray line.
Surface state wave functions for two
Au(7 8 8) and Au(2 2 3), representing Fermi surface maps
(a)–(c) and band dispersions perpendicular to the steps (d)–(f),
taken with 21 eV photon energy. The surface state bands are
broadened due to the terrace width distribution, completely
masking the spin splitting. For Au(11 12 12) and Au(7 8 8)
weak replica due to umklapp scattering are observed.
Spin-integrated ARPES data from Au(11 12 12),
PRL 104, 187602 (2010)
7 MAY 2010
integrated intensities and the three spin polarization com-
ponents Px, Pyand Pz. In order to quantify the relative
contributions of all the sub-bands the analysis of these data
was based on a two-step fitting procedure described in
detail elsewhere [20,21]. For these fits four pairs of Voigt
peaks were used for Au(11 12 12) and Au(7 8 8) (the
umklapp peaks are interweaved with the main peaks) and
only two pairs for Au(2 2 3) on a linear background (see
Ref.  for details). The use of pairs of peaks is required
due to the strong modulation observed in the spin polar-
ization data. In order to comply with the Rashba model ,
the spinsplittingswere forcedtobeequalforallpeakpairs.
This analysis yields the value of the splitting, the degree of
spin polarization of each peak, and the orientations of the
polarization vectors, which are summarized for each sur-
face in Figs. 3(g) to 3(i). The splittings ?k and the peak
widths are listed in Table I. The widths of all main peaks
are quite similar for a particular surface, and average val-
ues are thereforegiven. The same holds forumklapp peaks.
Several conclusions can be drawn from these data and
their fits. (i) The surface states show clear spin polarization
signals for all three surfaces. (ii) Excellent fits could be
obtained when setting all values ci¼ 1:0; i.e., all peaks
appear tobe 100%spinpolarized.(iii)Allspinpolarization
vectors lie mainly in-plane as in the case of the flat (111)
surface. All paired peaks have opposite polarization vec-
tors. (iv) The spin polarization vectors of the umklapp
states follow closely, in direction and magnitude, those of
the main states. (v) The widths of the components increase
with decreasing terrace size, as previously observed and
related to an increase of the TWD [14,15]. The umklapp
peaks are broader than the main peaks but follow the same
tendency. (vi) Au(11 12 12) and Au(7 8 8) show the same
spin splitting ?k as Au(111) (0:026?A?1). On the other
hand, Au(2 2 3) shows a substantially larger splitting of
?A?1), and average peak widths (in?A?1) obtained from the fits to
the data of Fig. 3 [binding energies: 0.10 eV for Au(11 12 12)
and Au(7 8 8), 0.05 eV for Au(2 2 3)]. Au(111) is added for
Spin splittings, expressed as momentum shift ?k (in
Au(1 1 1)
Au(11 12 12)
Au(7 8 8)
Au(2 2 3)
FIG. 3 (color).
0.10 eV for Au(11 12 12) and Au(7 8 8), 0.05 eV for Au(2 2 3)] obtained by rotation of ?sin Fig. 1(e). The top graphs (a)–(c) give the
spin-integrated intensities, showing also the fitted peak profiles used for the two-step fitting routine described in the text. In the graphs
(d)–(f), the corresponding spin polarization curves and errors for the x (green open circles), y (magenta open squares), and z (black
triangles) components are represented. The polarization fits (see text) are shown as continuous lines in the corresponding color. The
discontinuous line in (f) corresponds to the y polarization fit when fixing the splitting to the flat Au(111) value. The bottom panels (g)–
(i) show the resulting polarization vectors for the individual peaks. In the top and bottom graphs the components from the main
(umklapp) states are indicated as continuous (discontinuous) lines using the same color codes. Each of the bottom panels gives the in-
plane (left) and the out-of-plane (right) orientation of the spin polarization vectors.
Spin-resolved MDCs from the three investigated vicinal surfaces taken with 23 eV photon energy [binding energies:
PRL 104, 187602 (2010)
7 MAY 2010
The fact that the surface state electrons remain fully spin
polarized on these three stepped surfaces merits further
discussion. It indicates a high robustness of spin currents in
the presence of such structural defects. Spin polarization is
neither lost by scattering within the ordered step lattice nor
by the high degree of disorder that is obvious by the large
TWDs. Even umklapp bands preserve the full spin polar-
ization. The close resemblance of all measured surfaces to
the Au(111) case strongly suggests that the observed spin
polarization vectors essentially reflect the initial state spin
With regard to the spin texture, all vicinal surfaces show
directions of spin polarization vectors similar to those on
the flat Au(111) surface along the direction perpendicular
to the steps (kx), i.e., the spin vectors point mainly along
the tangential ?y axis , with the same helicities for the
corresponding subbands. Umklapp bands closely follow
their corresponding main bands. Deviations from a purely
tangential in-plane spin texture appear as modulations in
the measured Pxcurves. They are assigned to a small
sample tilt of the order of 1?that cannot be corrected in
our experimental setup. Because of the small Fermi surface
radii, it translates into a much larger rotation of the spin
polarization vectors [Fig. 1(c)].
Finally, we discuss the strong enhancement of the spin
splitting ?k by ?60% in the case of Au(2 2 3) with respect
to the flat Au(111) and the other two investigated surfaces.
This finding is completely hidden in the broad peak widths
found on this surface and can only be revealed by a careful
spin analysis. We have verified the validity of this result by
imposing a splitting of 0:026?A?1, which is the splitting on
Au(111), in a constrained fit. While the intensity fit is still
excellent, the Pyfit [shown as a dashed line in Fig. 3(f)] is
much worse than the fit yielding 0:042?A?1(continuous
blue line). We propose that the enhanced spin splitting is
related to the short terrace width and the concomitant
change in reference frame for the electron wave function
[see Fig. 1(b)]. In the case of Au(11 12 12) and Au(7 8 8)
the electrons are confined and referred to single (111)
terraces, whereas for Au(2 2 3) the electrons propagate
with respectto the average
Accordingly, the electrons interact with several steps, and
their wave functions ‘‘feel’’ a strong increase of the effec-
tive surface corrugation on the densely stepped Au(2 2 3)
surface. In the case of surface alloys, it has been demon-
strated that the enhanced potential gradient at the surface
induced by the surface corrugation is responsible for the
unexpected increase in the magnitude of the Rashba split-
ting[23–26].Therefore,we speculatethat thesame mecha-
nism applies for the vicinal Au(111) surfaces, but only
above a critical step density leading to propagating wave
functions. According to the literature, the transition occurs
at terrace widths of ?20?A.
In summary, we have studied the interaction of spin
polarized surface state electrons with a periodic distribu-
tion of steps by means of spin-resolved ARPES. We ob-
serve the existence of spin splittings even when spin-
integrated ARPES cannot resolve them. Moreover, our
analysis shows that the spin polarization and the spin
textures on vicinal surfaces are closely related to those
on the flat Au(111) surface. All subbands, including um-
klapp bands due to the step lattice, are 100% polarized and
show essentially tangential spins and the original spin
helicity of Au(111), in spite of a relatively high degree of
disorder as reflected in the broad photoemission peaks. For
the highest step density, we observe that the spin splitting
increases substantially as the electron wave functions ef-
fectively probe an increased surface corrugation.
We wish to express our gratitude to J.E. Ortega and
R. Fasel for lending us the crystals studied in this work, to
T. Greber for cunning and stimulating discussions, to M.
Klo ¨ckner for technical assistance, and to the staff of the
Surface and Interface Spectroscopy (SIS) beam line of the
Swiss Light Source (Paul Scherrer Institut, Switzerland),
where these experiments were performed. This work has
been supported by the Swiss National Science Foundation
and by the Spanish Ramo ´n y Cajal Program.
 S.A. Wolf et al., Science 294, 1488 (2001).
 Y.A. Bychkov and E.I. Rashba, JETP Lett. 39, 78 (1984).
 J. Nitta et al., Phys. Rev. Lett. 78, 1335 (1997).
 S. LaShell, B.A. McDougall, and E. Jensen, Phys. Rev.
Lett. 77, 3419 (1996).
 M. Hoesch et al., Phys. Rev. B 69, 241401(R) (2004).
 M. Corso et al., J. Phys. Condens. Matter 21, 353001
 J.E. Ortega et al., Phys. Rev. B 65, 165413 (2002).
 G. Bihlmayer et al., Surf. Sci. 600, 3888 (2006).
 F. Reinert et al., Phys. Rev. B 63, 115415 (2001).
 L. Petersen et al., Surf. Sci. 443, 154 (1999).
 L. Petersen et al., Surf. Sci. 459, 49 (2000).
 J.I. Pascual et al., Phys. Rev. Lett. 93, 196802 (2004).
 A. Mugarza et al., Phys. Rev. B 66, 245419 (2002).
 A. Mugarza and J.E. Ortega, J. Phys. Condens. Matter 15,
 F. Baumberger et al., Phys. Rev. Lett. 92, 196805 (2004).
 J.E. Ortega et al., Phys. Rev. Lett. 84, 6110 (2000).
 J.E. Ortega et al., Surf. Sci. 482–485, 764 (2001).
 M. Hoesch et al., J. Electron Spectrosc. Relat. Phenom.
124, 263 (2002).
supplemental/10.1103/PhysRevLett.104.187602 for more
information on ARPES data, the SARPES fit procedure,
and error analysis.
 F. Meier et al., Phys. Rev. B 77, 165431 (2008).
 F. Meier, J.H. Dil, and J. Osterwalder, New J. Phys. 11,
 J. Henk et al., J. Phys. Condens. Matter 16, 7581 (2004).
 K. Sugawara et al., Phys. Rev. Lett. 96, 046411 (2006).
 C.R. Ast et al., Phys. Rev. Lett. 98, 186807 (2007).
 G. Bihlmayer S. Blugel, and E.V. Chulkov, Phys. Rev. B
75, 195414 (2007).
 J.H. Dil, J. Phys. Condens. Matter 21, 403001 (2009).
PRL 104, 187602 (2010)
7 MAY 2010