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Electronic band structure of Cu3Au An angle-resolved photoemission study along the [111]-direction.

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Ann. Physik 2 (1993) 450-464
Annalen
der Physik
@ Johann Ambrosius Barth 1993
Electronic band structure of CusAu: An angle-resolved
photoemission study along the [llll-direction
’,
Markus Lau Stefan Liibus’, Ralf Courths’, Samed Halilov2, Herbert Gollisch2,
and Roland Feder2
* Laboratorium fur Festktirperphysik
2Theoretische Festkerperphysik, Fachbereich Physik der Universittit D-47048 Duisburg, Germany
Received 17 March 1993, accepted 16 April 1993
Abstract. High-resolution normal photoemission (ARPE) spectra have been recorded for
Cu3Au(l1 I) with the use of polarized synchrotron and rare-gas resonance radiation in the photon
energy range from 9 to 27 eV. It is for the first time that dispersions of the gold-like bands have been
found experimentally. Using a fully relativistic layer-KKR photoemission formalism, occupied and
unoccupied bands as well as one-step-model photoemission spectra have been calculated. The comparison of calculated spectra with experimental ones and the observation of direct-transition resonances
upon photon energy near the Brillouin zone-center reveal a shift of the unoccupied ground-state bands
by about +2.5 eV (self-energy shift). The direct-transition structures in the experimental spectra have
been exploited to determine the dispersions of the occupied bands along the [ 11 I] direction (A line
in k space). In order to determine the wave vector of the experimental direct transitions we used as
final state that calculated unoccupied band along [ 1 1 I], which also exists in pure copper and gold up
to about 20 eV above the Fermi energy (“unfolded” band structure), shifted by + 2.5 eV. The experimental occupied bands with Cu character are in very good agreement with theory after shifting the latter
by about 0.3 eV to lower energy, whereas somewhat bigger discrepancies exist for the gold-like bands.
Keywords: Photoemission; Electronic band structure; Calculation (of photoemission spectra).
1 Introduction
The electronic structure of the noble metal alloy Cu3Au is of great interest in order to
study alloying effects and to understand the classical order-disorder phase transition
found at 663 K. Several bulk band-structure calculations [l - 111 and experimental investigations probing the electronic structure such as photoemission (PE) [3, 7, 8,
12 - 201, X-ray absorption (XANES) [21], Fermi-surface (de Haas-van Alphen effect)
[22] and Mossbauer [23] studies have been performed. However, from the experimental
point of view, the electronic structure of Cu3Au is still a matter of controversy.
Band structure calculations show that in ordered Cu3Au, due to the hybridization of
states of mainly next nearest neighbours, none of the band states is of pure Cu or Au
atomic origin. The large spin-orbit coupling of Au also enhances the mixing of states.
It has been found that the Au 5 d states narrow and shift away from the Fermi level down
by about 1.5 eV as compared to pure Au, whereas the energies of the Cu 3d states are
much weaker influenced. The shift of the Au states, which experimentally becomes ap-
M. Lau et al., Electronic band structure of Cu,Au
45 1
parent in a higher binding energy of core electrons as compared to pure Au [15, 161,
is due to a loss of d charge on the Au atoms, which has been demonstrated by XANES
measurements [21]. Cu and Au atoms share a common s-band and common d-bands,
but because of the large potential shift at the Au atom it is nevertheless meaningful to
distinguish between Au-like bands between 7 and 4eV energy below EF and Cu-like
bands between 4 and 2 eV, respectively, although one should not ignore that the atomic
character is not pure (about 70%). The band structure of the Cu-like bands is rather
complex because of back-folding effects due to the reduction of the fcc Brillouin zone
(BZ) of the pure metal to the smaller simple cubic BZ of Cu3Au.
We summarize in short some of the most important results of published PE investigations concerning bulk bands in Cu3Au in order to demonstrate the need for additional
PE studies. Schneider et al. [20] have applied the technique of spin- and angle-resolved
photoemission to Cu3Au(OOl) to study the spin-orbit splitting of electronic bands.
Near the X point, they found a splitting of 0.8 eV of the Au-like bands, which is in
agreement with the calculation of Davenport et al. [5, 181 (0.85 eV). However, because
the (001) surface is rich of surfaces states [16, 241, it has to be checked whether all of
the observed spectral features in Ref. 20 are of bulk origin. Schneider et al. [20] also
found a spin-orbit splitting of about 0.2 eV in the Cu-like bands (if the origin of the
spectral features is correctly interpreted), which is more than in pure Cu and
demonstrates the hybridization with the Au-like states. The authors [20] note that the
experimental features agree better with Davenport’s calculation [5, 171 after shifting the
theoretical bands by 0.4 eV to lower energy. Wang et al. [17] have tried to perform a
band-mapping along the [OOl] direction with the use of angle resolved photoemission
(ARPE) from Cu3Au(O01). In that study, the valence band positions in bulk k space
have been obtained by assuming a free-electron-like final state. However, it was not
possible to make a detailed comparison between the calculated bands [5] and the structures in the experimental spectra because of a lack experimental resolution. At the r
point the experimental energies seem to be in good agreement with the fully relativistic
calculation of Davenport et al. [5] (Fig. 2 of Ref. 17). However, this result is accidental
as will be demonstrated by our investigation. Three Au-like bands have been detected
[17], which show very small or even no dispersions and differ by some tenth eV from
theory. In another band-mapping PE study of Cu3Au(O01), Sohal et al. [S] found three
Cu-like bands showing dispersions like folded d-bands of pure Cu and three Au-like
structures. Comparison of the experimental bands with those of a fully relativistic
LMTO calculation led the authors to the conclusion of a fair agreement (within 0.5 eV,
as is evident from Fig. 2 of Ref. 8). Krummacher et al. [18]concluded from their angleintegrated PE study on Cu3Au(O01)and (1 10) that good agreement with Davenport’s
calculation is obtained if a 0.6eV correction of the theoretical Fermi level to higher
energy is included. Stuck et al. [19] have determined the partial densities-of-states of
the constituents applying the technique of X-ray-photoelectron diffraction (XPED) to
Cu3Au(O01). The hybridizations of Cu and Au states are nicely seen with this method
and the derived partial densities show good agreement with calculated ones [6, 81 within
the limited energy resolution of XPED. However, a shift of about 0.5 eV between experiment (lower energies) and theory is seen (compare Fig. 3 of Ref. 19 with Fig. 3 of Ref. 8).
This energy shift between theory and experiment has also been found by Weinberger
et al. [6] in a theoretical analysis of experimental [I61 XPE spectra.
Summarizing the published PE investigations of bulk bands in Cu3Au, we find the
situation unsatisfying. Energy shifts between calculations and experiments (about
0.5 eV lower experimental energies for the Cu-like bands and some tenth eV higher ex-
452
Ann. Physik 2 (1993)
penmental energies for the Au-like bands) have been found in most investigations, however, no detailed comparison with calculated bands was possible. This has motivated us
to perform a thorough investigation of the band structure with the use of ARPE with
high energy and angle resolution. In this study we report ARPE measurements along
the surface normal of a Cu3Au(l11) single crystal in the ordered phase and results for
the band structure along the [I 1 I] direction. We confirm that published band structures
[3, 5, 6, 8, 9, 111 have to be shifted down in energy by about 0.5 eV as compared with
experiment. We also give energies of several Cu-like and Au-like bands at the f point
and dispersions of some Cu- and Au-like bands along [Ill], which can be identified
unambiguously in the theoretical band structure. This has been achieved by comparing
our experimental band dispersions with a bulk band-structure calculation and one-stepmodel PE spectra obtained by a fully relativistic layer-KKR method.
Angle-resolved photoemission (ARPE) is a powerful tool for the determination of the
dispersion of bulk and surface electronic bands in crystals, and various aspects of this
method and results have been described in review articles [25 -271. The normal emission
variant of ARPE has been applied with success to the noble metals copper [28, 291,
silver [30] and gold [31]. For these metals a considerable amount of details of the
valence and conduction band states has been gathered. The state dispersions have been
determined by the observation of direct interband transitions, which can be swept over
the Brillouin zone (BZ) by using tunable synchrotron radiation. The location of the
direct transitions in k-space is one of the major problems in determining the bulk band
structure from experiment. This is due to the fact, that the component of the full
wavevector R = l+ G of the photoelectron (& is the reduced wavevector and is a
reciprocal lattice vector) perpendicular to the surface (EL)
is not conserved in the
photoemission process, whereas the parallel component (XI,
) is conserved. The
strength of the observed direct transitions vanes considerably with photon energy [32]
and emission angle, which often complicates the procedure on the one hand but also
offers the possibility of adjusting the final-state band energy [30, 311. As final state
often free-electron (FE) like bands are used [17, 28, 291, but the FE approximation
(FEA) neglects band gaps and yields distorted dispersions due to the bad approximation
to the dispersion of the “true” final state. The use of calculated unoccupied bands of
the real band structure (with the use of a real potential) as final states, which have to
be adjusted in energy properly, have yielded much better results [30, 311. In principle,
however, one-step PE calculations, which include excitation effects and influences of the
surface, provide the most appropriate comparison between theory and experiment.
e
2 Theoretical
The relativistic bulk band structure - for occupied and unoccupied states - and onestep-model photoemission spectra were calculated using a fully relativistic layer-KKR
formalism ([33] and references therein), which was recently generalized to handle several
atoms per unit cell [34]. The real potential input (within the muffin tin approximation)
was obtained by means of a relativistic self-consistent LMTO calculation using the von
Barth-Hedin [41] exchange-correlationapproximation. The real part of the uniform inner potential and the work function were taken as 14.54 eV and 5.0 eV, respectively. The
bulk band structure was calculated for this real potential. We note that the occupied
bands obtained by our layer-KKR method are practically the same as those from the
original LMTO calculation. We neglect the real self-energy correction - to be deter-
M. Lau et al., Electronic band structure of Cu,Au
453
mined ex post as an energy shift of the upper bands by comparison with experiment
- and its imaginary part, which should strictly speaking be taken into account to obtain the experimentally relevant quasi-particle bands for the final (unoccupied) states.
In the photoemission calculations, however, we considered a real self-energy correction
for the upper states (up to 2.5 eV). The imaginary part was taken spatially uniform and
energy dependent as 5 , = ( B - E ~ ) - 0 . 2eV
5 for occupied states of energy E and for the
unoccupied states as Vi2= -0.5 eV (- 1.0 eV) for photon energies 9 and 12 eV
(21.2 ev).
The thus obtained occupied and unoccupied bulk bands along the [I 111 direction are
presented in Fig. 1. There are many more bands in theory than can be resolved experimentally (see below). The explanation lies in the effect of the band folding [17]. The
Cu-like bands above -4 eV resemble those of fcc copper folded back from the fcc BZ
with diameter 2(2n/ao) (along the cubic axis) into the smaller simple-cubic BZ with
diameter 2(n/ao). Due to the relativistic selection rules [32, 351 only final (unoccupied) states with A6 symmetry can emit along the A surface normal of an (1 1 I) terminated crystal. The A6 band labeled f i n Fig. I correspond to the free-electron like A l
band in pure Cu, which is exclusively present in that metal in the energy region between
.......
-9
.--.__
..-_
Fig. 1 Theoretical ground-state band-structure for Cu,Au along the A line ([ 1111 direction) with A ,
and A4+5symmetry. Left panels: occupied states below the Fermi energy EF. Right panels: Unoccupied states above Ef-The dots represent the calculated E ( k ) values, whereas the connecting dashes
only serve as guides for the eyes. The unoccupied A, band f drawn with bold Line carries most of the
electron flux along the [ 1111 surface normal. The dashed-dotted curve f * is the "experimental" final
state used in this work for the evaluation of the experimental data and is the calculated band f shifted
upwards by 2.5 eV.
454
Ann. Physik 2 (1993)
ARPE
normal emissiol
hv -21.2 eV
c u (111)
-
L
I
Copper
-
I
1
Fig.2 Above: Comparison of normal
photoemission spectra of Cu,Au(lll)
(data points) and Cu(ll1) (solid line)
taken with unpolarized He1 radiation
(hv = 21.22 eV). For Cu, the structures
A-D represent direct transitions from
the d-bands, and S1 and S 2 are surface
emissions. Below: Occupied ground-state
band-structure of Cu along [ l l l ] and
location of direct transitions given by
the intersections with the unoccupied
band 7 (corresponding to band f in
Fig. 1) lowered by the photon energy.
The theoretical band structure of Ref. 39
has been used.
[-ffrrl
17! \ 7
'
band 7-hv
-L
-3
-2
-1
0
the Fermi energy and about 23 eV above EF (see also Fig. 2). The other A6 bands in
Cu3Au result from the back-folding effect and certainly emit electrons with much less
probability along the [I 1 I] direction. It is therefore not astonishing that the photoemission spectrum from Cu3Au(l11) taken along the surface normal resembles very much
the corresponding Cu(l11) spectrum (Fig. 2), because the normal photoemission current due to the excitation out of occupied back-folded bands and due to excitation into
unoccupied back-folded bands is low. The band labeled f* in Fig. 1 represents the
dominating final band f shifted by 2.5 eV to higher energy. It will be shown that the use
of this shifted final state f* explains our experimental spectra very well.
3 Experimental
The experiments were performed at the synchrotron light source BESSY at Berlin on
beamline TGM2 and in the home laboratory with rare gas resonance radiation, respectively. Photons with energies between 9 and 27 eV were used. As photoelectron spectrometers an ADES 300 (BESSY) and an ESCALAB system from Vacuum Generators
were used. For the synchrotron radiation experiments the total energy resolution
(photons plus electrons, full width) was about 100 meV for h v I24 eV and increased to
about 150 meV at h v = 27 eV, whereas for the laboratory experiments the resolution was
about 60 meV. The electron angular resolution was about 3 (full angle of acceptance).
The light was incident in the (1lo)-- mirror plane with an angle Op Y'th respect to the
surface normal Z (x,jj and Z are the surface adapted coordinates, p = [112]). The linearly
polarized synchrotron light (- 90% degree of polarization) was oriented in the plane of
incidence (p or polarization) and photoemission spectra were taken with 0, = 62.5
( Z @ ) light) and 0,= 22.5" Q ( 2 ) light), respectively, in order to vary the light components perpendicular (2) and parallel (jj) to the surface. The light from the resonance
lamp was incident at 0, = 40 O and was either unpolarized or (p) or X(s)polarized
(with the use of a triple reflection polarizer with -90% degree of polarization).
O
45 5
M. Lau et al., Electronic band structure of Cu,Au
~~~~
The single crystal of ordered Cu3Au(lll) was cleaned in situ by repeated cycles of
(- 500 eV beam energy) and subsequent annealing up to 640 K
(below the phase transition temperature of 663 K) for several hours. This procedure was
done until sharp superstructure LEED spots (a 2 x 2 structure as compared with the
Cu(l11) LEED pattern) indicated a well ordered surface at room temperature. The intensity and the energetic position of the emission from a surface state at 0.4 eV energy
below the Fermi energy [361 (see structure S1 in Fig.2) was also used to check the
quality and the orientation of the (1 1I) surface with respect to the analyzer. This emission corresponds to the well known Shockley-type surface state on the noble metal (1 1 1)
surfaces [27, 37, 381. To our knowledge the ( i l l ) surface of Cu3Au has not been
studied by means of surface structural methods until yet. The chemical cleanliness of
the surface was checked by means of X-ray excited core-level emission (XPS). In addition, ARPE spectra from a Cu( 1 I 1) sample were measured for comparison (see Fig. 2).
Ar' ion bombardment
4 Results and discussion
Normal-emission energy-distribution-curves(EDC's) taken in the photon energy range
9 eV 5 h v I27 eV and representing the strong intensity emissions from the copper-like
states between 2 and 4 eV binding energy EB (EB= -(I?-&))
are shown in Fig. 3. The
I
I
I
I
I
I
I
1
I
I
-4
-3
-2
Energy Below EF (eV)
-6
-3
-2
Energy Below EF (eV)
Fig. 3 Series of normal-emission electron-energy-distribution-curvesfrom Cu3Au(l11) with photon
energies between 9 and 27eV. The spectra represent the emissions from the Cu-like states. Left:
9 eV 5 h v 5 18 eV and Z ( j j ) light. Right: 19 eV c h v s 27 eV and y (z)light. The curves have been normalized to the same background intensity at 4.5 eV binding energy. For the light polarizations see main text.
45 6
Ann. Physik 2 (1993)
emissions from the gold-like bands between 5 and 7 eV (see Fig. 2), which exhibit much
lower intensities, will be presented below. The spectral features 5 -7 in the EDC’s are
immediately identified as bulk direct-transition structures by their dispersion with
photon energy. One also recognizes strong intensity variations of these structures with
photon energy around h v = 23 eV (indicated by arrows in Fig. 3). Here, structure 5
reaches a minimum of intensity and structures 6 and 7 reach a maximum, respectively.
These intensity “resonances” will serve below for the energy calibration of the final
state of the direct transitions [30, 3 11. From data like those shown in Fig. 3 we determined the initial state energies of the direct transitions and their dependence on hv. The
corresponding results are summarized in the left panel of Fig. 4. The additional structures 1-4 given in that figure are visible as shoulders to the dominating peaks and are
discussed below.
In order to better understand the following discussion and the data evaluation performed, we first remember the interpretation of the experimental Cu(i11) 21.2 eV spectrum of Fig. 2. This well-known EDC has been analyzed in terms of direct transitions
(features A - D ) and surface emissions (features Sland Sa [27, and references therein].
For a comparison with theory we have chosen the band structure calculated by
Eckhardt, Noffke and Fritsche [39], which is known to fit the experimental ARPE data
from Cu very well [27]. The location of the direct transitionsA - D in the band structure
along the [11 11 direction ( A line in k space) is indicated in this figure by the intersection
of the Cu d-bands (bands 2- 5) with the unoccupied final-state band 7, which is lowered
1 p ‘y
,
4’
,
h
:i;,;
,, ,,,
Iy(z1light
l0
,,,, ,
15
20
25
Photon Energy hv (eV)
1
30
Fig. 4 Left: Energy dispersions with photon energy of the Cu-like structures in the normal emission
spectra shown in Fig. 3. The lines through the data points are guides for the eye The dashed-dotted
line represents a constant final-state energy of 19.7 eV lowered by the photon energy and is discussed
in the main text. Right: Comparison between experimental and calculated Cu-like occupied band structure of Cu,Au along [Ill]. The theoretical bands are shifted to lower energy by 0.31 eV.
457
M. Lau et al.. Electronic band structure of Cu,Au
by the photon energy for this purpose. The direct transition from the s-band (band 1)
is not visible due to a very low transition strength. Feature Slis the emission from the
Shockley-type surface band in the gap around the Fermi energy, and the shoulder-like
structure S, may be due to another surface state [40] or to a density-of-states effect
~71.
As has already been discussed above, the striking similarity of the 21.2 eV spectra
from Cu,Au(Ili) and Cu(l11) in the region of the Cu-like bands (Fig. 2) is due to the
low emission strength of the “back-folded” bands in CqAu. However, some additional
low-intensity features due to excitations from these “back-folded”bands are observable
especially in the lower energy region. This “fine structure“ in the 21.2 eV spectrum is
presented in an enlarged scale in Fig. 5, where the corresponding spectra taken with
Fig.5 Upper two panels: Nor-
mal photoemission spectra from
Cu,Au(llI) taken with unpolarized He1 (hY = 21.22 ev) radiation
(above) and with %,p(Z)- and
i(y)-light (center). The spectra
give only the emissions from the
Cu-like states. The second
derivative of the “unpolarized”
spectrum is also given (above).
The vertical dashes give the
energetic positions of the identified structures. Lower panel:
Comparison with the ground-state
band-structure given in Fig. 1.
The dashed dotted line is the experimental final state band f*
(see Fig. 1) lowered by the photon
energy, in order to localize the
possible direct transitions into
this band (filled dots). The
calculated occupied bands have
been shifted by 0.31 eV to lower
energy.
,
>
.
458
Ann. Physik 2 (1993)
polarized light are also given. Besides the dominant features 5, 6 and 7, the five additional shoulder-like structures 1-4 (at about 2eV binding energy) and 8 (at 4eV) are
unambiguously detected as peaks in the second derivative of the “unpolarized” EDC
(upper panel of Fig. 5).
It was not possible to take all the spectra shown in Fig. 3 with such good statistics
as has been done for the 21.2 eV spectrum of Fig. 5, and therefore the energies of all
these “extra” structures given in Fig. 4 could not be determined very accurately as function of photon energy. It is also possible that each of the structures 2-4 may represent
an average over more than one spectral feature. Further, the very weak structure 1 could
only be detected unambiguously in the 21.2 eV EDC. However, the dispersion of the
dominant emissions 5 - 8 from the “unfolded” bands with photon energy could be
determined with rather high accuracy.
It will be shown now that most of the observed spectral structures can be explained
by direct transitions from the calculated bands to the final state band f* shifted by
+2.5 eV as compared to the ground-state calculation (Fig. 1). First, we consider the intensity “resonances” occurring around h v = 23 eV (Fig. 3, right panel). These
“resonances” have also been found in the corresponding ARPE spectra of the noble
metals [30, 311 and result from a combined effect of the matrix-elements for excitation
of direct-transitions [32] and the probability for transmission of excited electrons
through the surface [30, 311. The direct transitions from the d bands along [I 1 I] show
a maximum or a minimum of intensity if they approach the r point, where the transitions end into the flat-band part of band f *. More precisely, the strength of excitation
into this band is minimal for the 3deg states (bands 5 and 6 in Fig. 2 near the r point)
and is maximum for the 3dt2, states (bands 2-4 in Fig. 2), when sweeping the direct
transitions through the center of the bulk BZ. ,Second, the energy dispersions of the
structures 5 - 7 vanishes around h v = 23 eV (left panel of Fig. 4). Combining these two
observations and by analogy with the noble metal results, we conclude that one samples
the region around the r point at h Y = 23 eV. For these photon energies structure 5 has
eg character and structures 6 and 7 have t2gcharacter. The splitting of the latter reflects
the spin-orbit interaction. From the experimental binding energies in this flat-band
region around the r point (5 (eg): -2.9 eV, 6(tZg): -3.6 eV, 7 (tZg):- 3.82 eV) and the
resonance energy h v = 23 eV, the flat band part of the “experimental” final band f * is
deduced to be at 19.7 (k0.4) eV above EF, and is thus about 2.5 eV higher than band
f of the ground-state calculation (Fig. 1).
The “quality” of this choice of a shifted ground-state band f as final state along [I 111
will be checked now by comparing three selected experimental spectra of Fig. 3 both
with the theoretical predictions for direct transitions from the occupied bands of Fig. 1
into f * and with theoretical spectra calculated within the one-step-photoemission formalism. Figures 5 and 6 show this detailed comparison for the 21.2 eV spectra. It is seen
from Fig. 5 that, concerning the energy location of direct transitions from the Cu-like
bands into f*, nearly perfect agreement between theory and experiment can be achieved
by shifting the calculated occupied bands to lower energy by 0.31 eV. The comparison
of the experimental and theoretical spectra (Fig. 6 ) confirm the energy shifts in the final
and initial states for the copper-like region, because energies and intensities of most of
the calculated structures show better agreement with experiment if the shifts are taken
into account (solid lines). However, the conclusions drawn from the gold-like region are
ambiguous, and this will be discussed below. Figures 7 and 8 show the corresponding
comparisons for h v = 12 eV and 9 eV, respectively, where only Cu-like bands are excited.
Here, the necessity of an inclusion of the shifts in the final and initial bands of the
459
M. Lau et al.. Electronic band structure of Cu,Au
I
I
I
I
I
C UAU(ll1)
~
-
ARPE hv=21.2eV
normal emission
.
.... experiment
=
h
2
Fig. 6 Comparison of the experimental spectra
from Cu,Au(lIl) taken with polarized 21.2eV
radiation (data points and see Fig. 5 ) with the
corresponding theoretical spectra calculated on
the basis of the one-step layer-KKR photoemission method both with real self-energy correction of 2.5 eV for the upper states (solid curves)
and without this correction (dashed curves).
The theoretical curves have been shifted by
0.31 eV to lower energy.
3
I
-7
-6
-5
-L
-3
Energy below EFleV)
-2
r
I
F
normal emission
I
Fig. 7 Same as in Figs. 5 and 6
for h v = 12 eV.
-4
I
I
-3
I
Energy below EF [eV)
I
-2
460
Ann. Physik 2 (1993)
-L
-3
-2
Energy below EF 1eV)
Fig. 8 Same as in Figs. 5 for
hv=9eV.
theory is evident. Discrepancies between theory and experiment are visible in the relative
intensities in the spectra excited with 2 0 ) and J ( 2 )polarized light, which cannot be explained by us until yet. It follows at least for the Cu-like valence states that all dominant
and most of the weak spectral features are due to direct transitions into band f * along
[I 111. The only exceptions are the weak structures 1 and 2, which have no counterpart
in theory.
The experimental occupied band structure along [I 1 I] can then be derived using the
“experimental” empty band f * and the equation for direct transitions:
Ei(k)= E f * ( k ) - h v and Ei= -EB
(1)
which neglects any excitation correction. The result is shown in the right panel of Fig. 4.
Filled symbols represent those spectral features which can be interpreted as direct transitions. In this figure, the calculated occupied bands are shifted down in energy by 0.3 1 eV,
in agreement with the discussion above. Good overall agreement between experiment
and theory is achieved. Especially the dispersion of the two spin-orbit split bands 5,
originating from the 3deg state at r, are reproduced by experiment almost completely.
The dispersions of the structures 6 and 7, which give to the spin-orbit splitting of the
t,, state at r, also fit very well with to the calculation, but midway between r and R
they probably represent averages over several interfering bands. The experimental spin-
46 1
M. Lau et al., Electronic band structure of Cu,Au
orbit splitting of 0.22 eV is a bit smaller than the calculated one (0.28 eV). Structures
2, 4 and 8 (and the structure seen at - 3.2 eV around h v = 1 4 eV) cannot be interpreted
as direct transitions to band f* (as one might suggest from Figs. 5 and 6).
The emissions from the gold-like bands, their dispersions with photon energy and
their interpretation as direct transitions within the band structure of Fig. 1 (using the
experimental final state f*)are given in Figs. 9- 11, respectively. We emphasize that
dispersion of gold-like bands have been detected experimentally for the first time.
Therefore, there is no doubt of a band-like behaviour of all valence states in this alloy.
In agreement with the higher binding energies of the gold like states of about 6 eV (average), the region around the r point is reached at about h v = 25 -26 eV, and this again
justifies the use of the shifted final statef? Generally, the agreement with the calculated
valence bands is mixed. The dominant structures b and e show a clear dispersion similar
to the corresponding calculated bands, however, the dispersion amplitudes seem to be
smaller than in theory. The theoretical spin-orbit splitting of the “t2gyy states of 0.35 eV
at r (structures d and e ) is reproduced by the experiment. However, the experimental
energies at this symmetry point are higher than in theory, by about 0.1 eV for the upper
states and by 0.4 eV for the lower states (after shifting the theory downwards by 0.31 ev).
Near r the experimental dispersions are weaker then predicted by theory. Until now we
have no explanation for the partial disagreement between experiment and theory in the
region of the gold-like bands.
5 Summary
We have presented angle-resolved photoemission experiments on Cu3Au(1 I I) ordered
single-crystal and a first-principle band-structure calculation along [I 1 11 as well as
-
I
C
1
s
--
I
r
c
u)
0
C
-8
-7
-6
-5
-7
-L -8
Energy below EF lev)
-6
-5
-L
Energy below EFleV)
Fig. 9 Normal emission EDC’s from Cu,Au(lll) in the photon energy region 9 eV S h v I19 eV. The
light. Right: p(Z) light.
spectra represent the emission from the Au-like bands. Left:
Zu)
462
Ann. Physik 2 (1993)
I
-8
-7
I
I
I
-6
-5
-2
Energy below EF lev1
Fig. 10 Normal emission EDC's from Cu,Au(l 1 1)
in the photon energy region 20 eV Ih v I 27 eV
taken with Zv) light (open dots) and y(Z) light
(filled dots), respectively. The spectra represent the
emission from the Au-like bands.
4.5
ARPES
-5
L
-5 5
-7t
-7.5
10
i
U
15
20
25
Photon Energy hv lev)
I
30
Wave vector along 11111
Fig. 11 Left: Energy dispersions with photon energy of the Au-like structures in the normal emission
spectra shown in Figs. 9 and 10. The lines through the data points are guides for the eye. The dasheddotted line represents a constant final-state energy of 19.7 eV lowered by the photon energy and is
discussed in the main text. Right: Comparison between experimental and calculated occupied Au-like
band structure of Cu,Au along [ l l l ] . The theoretical bands are shifted to lower energy by 0.31 eV.
M. Lau et al., Electronic band structure of Cu,Au
463
calculated one-step-model spectra using a fully relativistic layer-KKR photoemission
formalism. The experimental data have been analyzed in terms of direct transitions
along [l 1I].
It is found that the experimental energies of the occupied copper-like states
are about 0.3 eV lower than in the calculation. This rigid shift cannot be explained with
relaxation effects due to the excitation of photoelectrons. In the region of the Cu-like
bands above 4 eV binding energy the experimental dispersions of the experimental spectral structures agree with those of the “unfolded” bands in theory. Experimental disper-.
sions of some of the Au-like bands below 4.5 eV binding energy have been found for
the first time, thus providing the band-like character of these states. However, there is
minor agreement between theoretical and experimental band dispersions in this energy
region.
This work was supported by the “Deutsche Forschungsgemeinschaft” (SFB 166) and by the
“Bundesminister fur Forschung und Technology” (BMFT Grant no 055PGAAB6). We thankfully
acknowledge the skillful help of S. Witzel and W. Braun during the measurements at BESSY. We also
wish to thank F. Miiller and R. Heise for their technical assistance.
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