Electronic structure of CeSe probed by resonant photoemission spectroscopy: A test case for the single-impurity Anderson Hamiltonian

Article abstract of DOI:10.1103/PhysRevB.57.12030

One of the most interesting problems, in the study of the electronic structure of Ce compounds, is the evaluation of the intrinsic linewidth of the atomiclike Ce 4f states in low Kondo temperature compositions. In this context, the case of CeSe is of particular interest, because of the energy location of the Ce 4f⁰ peak in a pseudogap formed mainly between the Se 4p and the Ce 5d density of states (DOS). This fact results experimentally in the most narrow Ce 4f⁰ final state so far reported (～280 meV), and represents at the same time an experimental upper limit for the lifetime broadening of this state in low Kondo temperature compounds, and extra information useful in the refinement of theoretical fitting of the data. We present single impurity Anderson Hamiltonian calculations which take advantage of the Ce 5d calculated local density approximation DOS to simulate the delocalized valence band continuum that mixes with the 4f impurity state. These calculations fit the experimental data and reproduce a certain degree of mixing between the Ce 4f and Se 4p states reasonably well.

Full text of DOI:10.1103/PhysRevB.57.12030

PHYSICAL REVIEW B
VOLUME 57, NUMBER 19
15 MAY 1998-I
Electronic structure of CeSe probed by resonant photoemission spectroscopy:
A test case for the single-impurity Anderson Hamiltonian
G. Chiaia and L. Duo`
INFM - Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo Da Vinci 32, I-20133, Milano, Italy
O. Tjernberg,* M. G o¨ thelid, and M. Bj o¨ rkqvist
Material Physics, Department of Physics, Royal Institute of Technology, S-10044, Stockholm, Sweden
†
H. Kumigashira, S.-H. Yang, T. Takahashi, and T. Suzuki
Department of Physics, Tohoku University, Sendai 980-77, Japan
I. Lindau
Department of Synchrotron Radiation Research, Lund University, S o¨ lvegatan 14, S-22362, Lund, Sweden
͑
Received 25 November 1997; revised manuscript received 21 January 1998͒
One of the most interesting problems, in the study of the electronic structure of Ce compounds, is the
evaluation of the intrinsic linewidth of the atomiclike Ce 4f states in low Kondo temperature compositions. In
0
this context, the case of CeSe is of particular interest, because of the energy location of the Ce 4f peak in a
pseudogap formed mainly between the Se 4p and the Ce 5d density of states ͑DOS͒. This fact results
0
experimentally in the most narrow Ce 4f final state so far reported ͑ϳ280 meV͒, and represents at the same
time an experimental upper limit for the lifetime broadening of this state in low Kondo temperature com-
pounds, and extra information useful in the refinement of theoretical fitting of the data. We present single
impurity Anderson Hamiltonian calculations which take advantage of the Ce 5d calculated local density
approximation DOS to simulate the delocalized valence band continuum that mixes with the 4f impurity state.
These calculations fit the experimental data and reproduce a certain degree of mixing between the Ce 4f and
Se 4p states reasonably well. ͓S0163-1829͑98͒07819-9͔
I. INTRODUCTION
experimental point of view, different aspects of a specific Ce
composition can concur to hinder the model interpretation of
the Ce 4f electronic structure in VB photoemission measure-
ments. First it is not always easy to disentangle the 4f spec-
tral weight from the remaining part of the VB, either because
of cross section considerations or unfavorable stoichiometry.
Second, also when the 4f contribution is more or less iso-
lated from the rest, the results from polycrystalline composi-
tions often present superimposed Ce 4f structures from non-
equivalent Ce sites with the consequence of smearing out the
features. Third, the differences in the Ce 4f electronic struc-
ture between surface and bulk layers due to the different
coordination of the Ce ion often end up in an extra compo-
The investigation of the electronic structure of Ce and its
compounds has involved the interplay of both experimental
and theoretical developments in the field of strongly corre-
lated electron systems: on the experimental side, the avail-
ability of highly energy resolved intense beamlines at differ-
ent synchrotrons that cover a wide photon energy range
containing the most intense core level thresholds of the Ce
atom ͑Ce 3d-4f at ϳ880 eV and Ce 4d-4f at ϳ120 eV͒; on
the theoretical side the proposition of different models for
the calculation of the electronic structure that could properly
account for both the delocalized valence band ͑VB͒ states
involved in the bonding and the more localized nature of the
Ce 4f shell. The experimental and theoretical achievements
in the field have been well summarized and discussed in a
0
9–11
nent for the Ce 4f final state in photoemission spectra.
Finally, the surface contamination which reduces the lifetime
of freshly produced surfaces, even when operating in ultra-
high vacuum conditions ͑UHV͒, has a limiting influence on
the reproducibility of the results. For this set of reasons, par-
ticularly when the aim of the investigation is the comparison
of different model calculations, a proper choice of the Ce
compound is of main importance.
This work presents photoemission results on a single crys-
tal CeSe. This compound is a low Kondo temperature (TK)
composition, with NaCl crystal structure, and it is easily
cleavable along the ͑100͒ surfaces. The temperature depen-
dence of the electrical resistivity shows Kondo behavior with
TK in the range of 10–20 K.12 Measurements of the reduced
sublattice magnetization give a N e´ el temperature of 5.12 K,13
1
review article by Allen et al. While all experimentalists in-
volved in this agree in the quest for higher energy resolution
and better sample quality, a fierce controversy has been
raised among both theorists and experimentalists on the most
relevant models that account for the strong correlation prop-
erties of these compounds.2 In particular, the limits and
–6
7
prediction capabilities of local density approximation
LDA͒ or single impurity Anderson Hamiltonian ͑SIAH͒
8
͑
calculations are the center of the attention, being critically
confronted and discussed.
Most often in this discussion, results are presented for one
particular Ce compound that either satisfies or contradicts the
predictions of one or the other model. Particularly in the
while the optical and magneto-optical properties show a cer-
0
163-1829/98/57͑19͒/12030͑6͒/$15.00
57
12 030
© 1998 The American Physical Society

57
ELECTRONIC STRUCTURE OF CeSe PROBED BY . . .
12 031
local density of states ͑DOS͔͒, different images were taken
with both negative and positive values of the tip voltage, thus
involving both the empty and the filled states. The purpose
was to detect preferentially the Ce sites, because of the high
0
Ce 4f density of states either below ͑Ce 4f ) or above ͑Ce
1
4
f ) the Fermi level. However, no changes were seen in the
recorded images, probably because the dominant tunneling is
due to the delocalized VB states, with a negligible, if any,
contribution from the Ce 4f orbitals.
III. LDA CALCULATIONS
Density functional LDA calculations for CeSe were per-
FIG. 1. STM picture of the ͑100͒ cleaved surface of CeSe.
1
6
formed by the Max-Planck Institute in Dresden. These cal-
culations were carried out using the standard Hedin-
Lundqvist exchange-correlation potential,17 and employing
the optimized linear combination of atomic orbitals ͑LCAO͒
tain degree of Se 4p–Ce 4f and Ce 5d–Ce 4f mixing.14
Our interest in the CeSe compound is focused on the energy
position of the Ce 4f level which is expected to be within the
pseudogap formed between the Ce 5d conduction band and
the Se 4p VB, thus allowing a more straightforward com-
parison with model calculations.
18
19
method in its scalar relativistic version. In this scheme,
the Bloch wave function is approximated by a linear combi-
nation of compressed atomic states forming a sufficiently
complete basis in the energy region up to some 5 eV above
the Fermi level. The basis includes Se 4s and 4p states, and
Ce 4f, 6s, 6p, and 5d states. The k sums were done using the
linear tetrahedron method at a mesh containing about 500 k
points in the irreducible part of the Brillouin zone. Since it is
commonly assumed that LDA calculations work well in de-
termining the spectral weight of delocalized states in the VB,
but they cannot take into proper account correlation effects,
the aim of these calculations was to determine the non-f part
of the CeSe electronic structure. The outcome is therefore
useful in two ways. On one side it helps the spectral assign-
ment, allowing us to distinguish between the different com-
ponents that build up the VB: Ce 5d, Se 4p, Se 4s, Ce 6p,
Ce 6s, and, by exclusion, Ce 4f. On the other side LDA
calculations provide a nonheuristic way to evaluate a total
II. EXPERIMENT
CeSe single crystals were grown by the Bridgman method
with a sealed tungsten crucible and a high frequency induc-
tion furnace. High purity Ce and Se metals with the respec-
tive composition ratio were used as starting materials. The
samples obtained were characterized by the Debye-Scherrer
method.
All photoemission experiments presented in this work
were performed using the synchrotron light from beamline
15
2
2 of the Max Laboratory in Lund, Sweden. This beamline
is equipped with a plane grating monochromator SX-700,
and a 200 mm hemispherical electron energy analyzer with
multichannel detection, by means of a charge-coupled device
density of states at the Fermi level (E ) that can be further
͑
CCD͒ camera. The resonant photoemission data with pho-
ton energies tuned to the Ce 4d-4f absorption threshold
ϳ120 eV͒ were recorded with an energy resolution of ap-
proximately 70 meV. The CeSe single crystal was kept in
F
used as an input in SIAH calculations to account for the
hybridization strength with the f states, as will be further
illustrated in Sec. V.
The results of the LDA calculations are presented in Fig.
, for all the VB contributions except for Ce 4f and Se 4s,
since the Se 4s DOS gives a contribution only at about 15 eV
of binding energy ͑BE͒ and the LDA calculated Ce 4f DOS
is unreliable since it does not include the f-f correlation. In
fact, calculations that include the Ce 4f state in the basis set,
without explicitly taking into account the f-f Coulomb re-
pulsion, end up in an f narrow band crossing the Fermi level.
On the contrary, all photoemission measurements on Ce
compounds identify some Ce 4f spectral weight at about 2–3
͑
Ϫ11
UHV conditions at a base pressure of about 7ϫ10
mbar
2
and continuously cooled to liquid nitrogen temperature all
through the experiment, to prevent possible segregations of
impurities from the bulk. No traces of C 1s or O 1s peaks
were ever detected, confirming the quality of the surfaces.
Fresh CeSe ͑100͒ surfaces were obtained by cleavage in
UHV. This was achieved by gluing a post on top of the
sample in air, and inducing cleavage in UHV by pushing the
post with a wobble stick. Sharp 1ϫ1 low energy electron
diffraction ͑LEED͒ patterns were seen to confirm the order
and quality of the fresh surfaces.
eV below E and interpret this energy separation from E as
F
F
Scanning tunneling microscopy ͑STM͒ images were also
recorded at the Royal Institute of Technology in Stockholm
by using a commercial Omicron system, in UHV conditions
and at room temperature. An image of the sample ͑100͒ sur-
face is shown in Fig. 1. This figure evidences a clear array of
atoms, separated by approximately 3 Å with each row corre-
sponding to a Ce-Se-Ce-Se . . . series. The surface remained
stable for several hours at room temperature and atomic reso-
lution was still achievable one day after the cleavage. With
the aim of discriminating the Se from the Ce atoms ͓i.e., the
the energy required to localize an f hole on a Ce 4f orbital.
By looking at Fig. 2 it is then clear that some mixing
occurs between the Ce 5d and the Se 4p states in the binding
energy region of 4–6 eV, and that most of the non-f spectral
weight at the Fermi level comes from the Ce 5d states, which
are therefore responsible for the metallic behavior of this
compound. The gray area in the figure corresponds to the
expected ionization energy range ͑2–3 eV͒ for an atomiclike
Ce 4f impurity immersed into a continuum of VB states. The
LDA calculations therefore show that the Ce 4f photoemis-

1
2 032
G. CHIAIA et al.
57
channels are enhanced, as indicated in the figure by A, B,
and C. Since the resonance involves the Ce site, all three
channels should contain either Ce 4f or Ce 5d ͑or both͒
spectral weights. Feature B is easily assigned to the Ce 4f0
final state: first because it does not find any counterpart in the
LDA calculation; second for its almost atomiclike line shape;
third for the intensity of its enhancement across the Ce 4d-4f
threshold, typical of Ce 4f final states; fourth in comparison
with all the other low TK Ce compounds which present a
similarly resonating peak in this BE range, where the energy
separation from E corresponds to the energy needed to put
F
a hole on a localized 4f orbital. It is worthwhile to mention
the particularly narrow full width at half maximum ͑FWHM͒
of this peak, about 280 meV, which is fitted by a 200 meV
FWHM Lorentzian curve, convoluted with a 200 meV
FWHM Gaussian curve, as shown by the solid line curve in
the figure. To the authors’ knowledge, this FWHM value of
FIG. 2. LDA partial DOS for CeSe. The gray area ͑between
Ϫ3 and Ϫ2 eV͒ corresponds to the expected ionization energy
range for a Ce 4f impurity.
2
80 meV is by far the smallest ever reported on low TK Ce
compounds and should be considered as an experimental up-
per limit, to be used for comparison with model calculations
FWHM. Feature C carries all the fingerprints of the Ce 4f1
final state, with the f7/2-f5/2 spin orbit doublet separated by
sion final state should lie in an energy region of low total
density of states.
2
80 meV ͑with f7/2 at higher BE and f5/2 at the Fermi level͒.
1
This final state originates from the overlap of the 4f ground
IV. VB SPECTRAL ASSIGNMENT
state with the delocalized VB states at the Fermi level, and
0
its presence and intensity, as compared to the 4f peak, is an
The LDA calculations, together with the experimental
resonance enhancement of the Ce derived states at the Ce
d-4f absorption threshold, are very usefully combined in
this section to achieve a spectral assignment of the VB states.
Figure 3 collects the resonantly enhanced VB spectra ob-
tained by tuning the photon energy across the Ce 4d-4f
threshold: the photon energy corresponding to each spectrum
is given on the right side of each curve. In the photon energy
range spanned by the resonance ͑114 eV for the antireso-
nance, 122 eV for the resonance maximum͒ three energy
indication of the hybridization strength between f and non-f
states in the VB. It should be further mentioned, as it will be
analyzed more thoroughly later, that a non-negligible contri-
bution to the overall resonance of the C channel comes from
Ce 5d states which cross the Fermi level as predicted by
LDA calculations. The resonant enhancement of channel A
should also be ascribed to the presence of Ce 5d states, as
can be seen from the calculated partial DOS of Fig. 2. How-
ever, these states, as previously mentioned, strongly mix
with the Se 4p VB states with which they overlap in this BE
region.
4
This explains the strong line-shape variation of region A
at different photon energies, due to the different photoioniza-
tion cross sections of Se 4p and Ce 5d states, as illustrated in
Fig. 4. In the uppermost spectrum of this figure, recorded
with a photon energy of 40 eV, the BE region between 6 and
4
eV is dominated by three features (a, b, and c), corre-
sponding to the features indicated in the Se 4p partial DOS
of Fig. 2. Once the photon energy is increased to 80 eV, the
line shape of this BE region changes, and a broader feature
bЈ appears with its maximum at the same energy of feature
b. This shape change corresponds to the increase of the
(
Ce 5d)/(Se 4p) photoionization cross section ratio, as
20
predicted by atomic calculations. Therefore the spectrum at
0 eV is the most sensitive to the Ce 5d. By increasing the
8
photon energy even further, the (Ce 5d)/(Se 4p) intensity
ratio decreases again and for the photon energy correspond-
ing to the Ce 4d-4f antiresonance ͑114 eV͒ the BE range
between 6 and 4 eV is again dominated by the Se 4p spectral
weight. Besides, at this photon energy, almost all the Ce 4f
spectral weight is suppressed.
The contribution of Ce 5d in channel C of Fig. 3 is fur-
ther confirmed by the dynamic evolution of channels A, B,
and C across the Ce 4d-4f edge, as shown in Fig. 5. Each
FIG. 3. Resonant photoemission spectra of CeSe with the pho-
ton energy ranging across the Ce 4d-4f absorption threshold ͑114–
0
1
22 eV͒. Peak B, assigned to the Ce 4f final state, has a FWHM of
about 280 meV. It is fitted with a Lorentzian curve with 200 meV of
FWHM, which was convoluted with a Gaussian curve with 200
meV of FWHM. The solid curve represents the Lorentzian-
Gaussian fitting curve, summed to the integral background ͑solid
line͒ of peak B.

57
ELECTRONIC STRUCTURE OF CeSe PROBED BY . . .
12 033
FIG. 6. Curve fitting of the Se 3d core level at photon energy of
50 eV.
1
FIG. 4. Photoemission spectra of CeSe at five different photon
energies.
spectrum is shown as a dotted curve, recorded with a photon
energy of 150 eV, and after an integral background subtrac-
tion. Four peaks, indicated by 1, 2, 3, and 4, are clearly
resolved, which correspond to the Se 3d3/2 bulk component,
the Se 3d3/2 surface component, the Se 3d5/2 bulk compo-
nent, and the Se 3d5/2 surface component, respectively, with
a surface core level shift of about 400 meV. The assignment
of the bulk and surface components to each spin-orbit com-
ponent has been verified by performing photoemission mea-
surements of the same core level at different photon energies
and by checking the changes in the intensity ratio of peak 2
over 1 (4 over 3) as a function of the different surface
sensitivities. The solid line represents the fitting of the ex-
perimental curve by four Lorentzian curves, all with a
FWHM of 230 meV and BE of 55.86, 55.47, 55.01, and
curve is obtained by subtracting two photoemission spectra
separated by 2 eV of increasing photon energy, as indicated
on the labels in the figure; therefore each curve represents the
enhancement of the spectral weight after a 2 eV increase of
the photon energy. Each difference curve is then normalized
to an equal height of channel B. It is first clear that channels
A and C resonate before B: in fact at the beginning of the
series ͑116–114͒ A, B, and C are almost equally enhanced,
but when h␯ increases, the enhancements of A and C almost
saturate, while channel B continues to increase in intensity.
Furthermore, the similarity in the behavior of channels A and
C supports our conclusion that the resonance behavior in
both of these channels is mainly due to the presence of Ce
5d spectral weight.
5
4.62 eV, respectively. The best fit is obtained when all four
Another interesting feature of this compound is the almost
Lorentzian curves have the same FWHM, which is quite in-
teresting. On one hand, the equal width of the bulk and sur-
face components 1 and 2 (3 and 4) originates from the high
degree of order at the surface as seen in the STM image in
Fig. 1, since the presence of inequivalent sites would result
in a broadening of the surface component. On the other hand,
the equal width of peaks 1 and 3 ͑2 and 4͒ implies that the
M M N Coster-Kronig transition that should broaden the
complete lack of Se derived DOS at the Fermi level, as wit-
nessed both by LDA calculations and by the experimental
evidence presented in Fig. 6. There, the Se 3d photoemission
4
5
45
3
d3/2 peaks ͑1 and 2͒ is energetically forbidden. This means
that the energy released by this transition, i.e., the BE differ-
ence between the M and the M Se holes ͑ϳ1 eV͒, is not
4
5
big enough to excite a filled Se VB state above the Fermi
level. Therefore the Se partial DOS within 1 eV below E is
F
practically negligible.
V. SIAH MODEL CALCULATIONS
All the SIAH calculations presented here have been per-
formed by using a Gunnarsson-Sch o¨ nhammer model in the
8
limit of an infinite f-f interaction energy (U→ϱ), which
was implemented in a software code that calculates the Ce
4
f spectral weight as a function of an input parameters’ set.
FIG. 5. Dynamic behavior of the CeSe resonant spectra across
the Ce 4d-4f threshold. Each curve is the difference between two
spectra taken with 2 eV of difference in the photon energy.
The code allows the choice of the model DOS to be used for
simulating the hybridization with the Ce 4f orbitals: in this

12 034
G. CHIAIA et al.
57
hybridization strength and vice versa. In this way, after the
Ce 5d correction, the value obtained for the Kondo energy
(
kT ) for the best fit of Fig. 7 is 1.8 meV, which corre-
K
sponds to a Kondo temperature of about 20 K, similar to the
experimental value estimated by electrical resistivity mea-
surements ͑10–20 K͒.
Particularly interesting is the comparison between the cal-
culations that correspond to different choices of the input
model DOS ͑1 and 2͒. In Fig. 7, curve 5 reproduces the
positions and shapes of peaks a and b well: however, if a
proper choice of ⑀ and ⌬ always ends up in curves with the
f
right BE of a and the right b /b intensity ratio, the shape of
2
1
a ͑FWHM of about 280 meV͒ and the a/b intensity ratio can
only be fitted with a proper choice of the FWHM of the
Lorentzian DOS (W). In this case a choice of 1.4 eV for W
results in a very good fit of the experimental data, which can
be attributed to the fact that for this value of W the Lorent-
zian DOS approximates the LDA calculated Ce 5d DOS very
well, as seen in the figure inset. Moreover the curves 1 and 2
have the same intensity at a BE of 2.25 eV ͑vertical line in
FIG. 7. SIAH fitting of the Ce 4f spectral weight: curve 4 is the
experimental spectrum, curve 3 is the SIAH calculated curve using
the Ce 5d LDA DOS ͑curve 1 in the inset͒ to simulate the VB band,
curve 5 is the SIAH calculated curve using the Lorentzian model
DOS ͑curve 2 in the inset͒ with W of 1.4 eV.
the figure͒, which is the value of the ⑀ used in the fitting,
f
therefore suggesting the importance, in the SIAH model cal-
culations, of reproducing the intensity of the delocalized
states at about the ionization energy of the 4f impurity well.
If, on the other hand, the LDA calculated Ce 5d DOS ͑1͒ is
used, a reasonable fit of a and b is achieved ͑curve 3͒, this
work we compare the results obtained either by adopting a
Lorentzian DOS centered at the Fermi level or a LDA cal-
culated DOS. The input parameters’ set includes, among oth-
ers, the unhybridized BE of the Ce 4f impurity (⑀ ), the
spin-orbit splitting ͑SOS͒ for the Ce 4f state, and the aver-
time simply by finding the right values of ⑀ and ⌬, which
are the line shape of the model DOS now fixed.
f
f
1
age 4f hybridization strength energy (⌬).
The results, presented in Fig. 7, are obtained by choosing
a value for the SOS of 280 meV, and by changing the values
In this regard it is particularly interesting that when using
curve 1 as the model DOS, the output of the calculation code
shows some spectral intensity in the BE region between 4
and 6 eV, in correspondence with the resonating channel A
of Figs. 3 and 5, while this does not happen for a model DOS
like 2. Since the Gunnarsson-Sch o¨ nhammer model imple-
0
of ⑀ and ⌬ in order to best fit the BE of the Ce 4f experi-
f
1
mental final state (a) and the 4f final state line shape (b),
particularly with regard to the f5/2 /f7/2 intensity ratio
(
b /b ). The experimental curve ͑4͒ is here compared with
mented in the code calculates only the 4f spectra weight, this
fact implies the presence of some f weight in this BE area,
therefore suggesting a certain degree of p-f mixing. This
result is experimentally supported by looking at the
magneto-optical polar Kerr rotation for the monochalco-
genide CeS, CeTe, and CeSe.14
2
1
two calculated curves ͑3 and 5͒: curve 3 is the result from
calculations that use the LDA Ce 5d DOS ͑curve 1 in the
figure inset͒ as the model DOS for the delocalized states, and
curve 5 corresponds instead to the use of a Lorentzian model
DOS with a FWHM of 1.4 eV ͑curve 2 in the figure inset͒.
The experimental curve 4 was first obtained by subtracting
from the on-resonance VB spectrum (h␯ϭ122 eV͒ the off-
resonance one (h␯ϭ114 eV͒, thus eliminating most of the
non-f spectral weight. However, the presence of a Ce 5d
VI. CONCLUSIONS
We have investigated the electronic structure of CeSe
which represents an interesting benchmark for the SIAH
resonance close to E , as shown previously, is not com-
F
0
pletely eliminated by this operation. Therefore a further sub-
traction of the LDA calculated Ce 5d partial DOS, multiplied
by a Fermi step function and convoluted with a 100 meV
FWHM Gaussian function, was performed. The Ce 5d spec-
tral weight, before being subtracted, was normalized in such
a way as to constitute about 30% of the total intensity in the
region close to the Fermi level. The choice of this relative
weight was done in consideration of what has been observed
experimentally for other Ce compounds at the Ce 4d-4f
resonance maximum.21 Besides, since the Ce 5d partial DOS
model, due to the experimentally narrow Ce 4f final state.
Different model DOS’s were compared in the calculations,
and the choice of the LDA calculated Ce 5d DOS results in
a good fit and suggests a certain degree of p-f mixing.
ACKNOWLEDGMENTS
This work was supported by the Swedish Natural Science
Research Council, by the Human Capital and Mobility Pro-
gramme of the European Community, and by grants from the
Japanese Atomic Energy Research Institute ͑REIMEI͒ and
the Ministry of Education, Science and Culture of Japan. We
would particularly like to acknowledge the contributions of
Dr. Victor Antonov and Dr. Manuel Richter from the Max-
Planck Institute in Dresden for performing the LDA calcula-
tions.
͑
Fig. 2͒ is mostly a linearly increasing function across the
Fermi level, its subtraction from the resonance spectrum de-
creases the f5/2 /f7/2 (b /b ) intensity ratio, therefore lower-
ing the ⌬ value ͑and consequently the estimated Kondo tem-
perature͒ needed to fit the experimental data. As a matter of
fact a high b /b intensity ratio points to a high value of the
2
1
2
1

57
ELECTRONIC STRUCTURE OF CeSe PROBED BY . . .
12 035
*
Present address: ESRF, Experiments Division, ESRF-BP220, F-
8043 Grenoble Cedex, France.
Kohn and L. J. Sham, ibid. 140, A1133 ͑1965͒.
O. Gunnarsson and K. Sch o¨ nhammer, Phys. Rev. Lett. 50, 604
͑1983͒; Phys. Rev. B 28, 4315 ͑1983͒.
C. Laubschat, E. Weschke, C. Holtz, M. Domke, O. Strebel, and
G. Kaindl, Phys. Rev. Lett. 65, 1639 ͑1990͒.
E. Weschke, C. Laubschat, T. Simmons, M. Domke, O. Strebel,
and G. Kaindl, Phys. Rev. B 44, 8304 ͑1991͒; C. Laubschat, E.
Weschke, M. Domke, C. T. Simmons, and G. Kaindl, Surf. Sci.
269/270, 605 ͑1992͒.
L. Z. Liu, J. W. Allen, O. Gunnarsson, N. E. Christensen, and O.
K. Andersen, Phys. Rev. B 45, 8934 ͑1992͒.
8
9
0
3
†
Present address: Department of Physics, Seoul National Univer-
sity, Seoul 151-742, Korea.
J. W. Allen, S. J. Oh, O. Gunnarsson, L. Sch o¨ nhammer, M. B.
Maple, M. S. Torikachvili, and I. Lindau, Adv. Phys. 35, 275
1
1
͑
1986͒.
2
F. Patthey, B. Delley, W. D. Schneider, and Y. Baer, Phys. Rev.
Lett. 55, 1518 ͑1985͒.
E. Weschke, C. Laubschat, R. Ecker, A. H o¨ hr, M. Domke, G.
Kaindl, L. Severin, and B. Johansson, Phys. Rev. Lett. 69, 1792
3
11
1
1
2
3
͑
1992͒; D. Malterre, M. Grioni, Y. Baer, L. Braicovich, L. Du o` ,
J. Schoenes and F. Hulliger, J. Magn. Magn. Mater. 63&64, 43
͑1987͒.
A. D o¨ nni, A. Furrer, P. Fischer, and F. Hulliger, Physica B 186-
P. Vavassori, and G. L. Olcese, ibid. 73, 2005 ͑1994͒; E. We-
schke, C. Laubschat, A. H o¨ hr, M. Domke, G. Kaindl, L. Sev-
erin, and B. Johansson, ibid. 73, 2006 ͑1994͒.
188, 541 ͑1993͒.
R. Pittini, J. Schoenes, and P. Watcher, Physica B 206&207, 92
͑1995͒.
J. N. Andersen, O. Bj o¨ rneholm, A. Sandell, R. Nyholm, J.
Forsell, L. Th a˚ nell, A. Nilsson, and N. M a˚ rtensson, Synchrotron
Radiation News 4, 15 ͑1991͒.
4
5
14
D. Malterre, M. Grioni, P. Weibel, B. Dardel, and Y. Baer, Phys.
Rev. Lett. 68, 2656 ͑1992͒; R. I. R. Blyth, J. J. Joyce, and A. J.
Arko, ibid. 69, 3418 ͑1992͒; D. Malterre, M. Grioni, P. Weibel,
B. Dardel, and Y. Baer, ibid. 69, 3419 ͑1992͒.
J. J. Joyce, A. J. Arko, J. Lawrence, P. C. Canfield, Z. Fisk, R. J.
Bartlett, and J. D. Thompson, Phys. Rev. Lett. 68, 236 ͑1992͒; F.
Patthey, W. D. Schneider, M. Grioni, D. Malterre, Y. Baer, and
B. Delley, ibid. 70, 1179 ͑1993͒; J. W. Allen and O. Gunnars-
son, ibid. 70, 1180 ͑1993͒; J. J. Joyce and A. J. Arko, ibid. 70,
1
5
1
1
1
6
7
8
M. Richter ͑private communication͒.
L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 ͑1971͒.
H. Eschrig, Optimized LCAO Method and the Electronic Struc-
ture of Extended Systems ͑Springer, Berlin, 1989͒.
M. Richter and H. Eschrig, Solid State Commun. 72, 263 ͑1989͒.
J. J. Yeh and I. Lindau, At. Data Nucl. Data Tables 32, 1 ͑1985͒.
J. M. Lawrence, A. J. Arko, J. J. Joyce, R. I. R. Blyth, R. J.
Bartlett, P. C. Canfield, Z. Fisk, and P. S. Riseborough, Phys.
Rev. B 47, 15 460 ͑1993͒.
1
9
1181 ͑1993͒.
6
7
20
A. B. Andrews, J. J. Joyce, A. J. Arko, J. D. Thompson, J. Tang,
J. M. Lawrence, and J. C. Hemminger, Phys. Rev. B 51, 3277
2
1
͑
1995͒.
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 ͑1964͒; W.