Progress of Theoretical Physics Supplement No.
271
101, 1990
Electron-Electron Correlation, Resonant Photoemission
and X-Ray Emission Spectra
Jean-Claude PARLEBAS, Akio KOTANI*·t> and Satoshi TANAKA*
Institut de Physique et Chimie des Materiaux ( UM 46 CNRS)
ULP 4 rue Blaise Pascal, 67070 Strasbourg Cedex, France
*Department of Physics, Tohoku University, Sendai 980
(Received July
24, 1990)
In this short review paper we essentially focus on the high energy spectroscopies which
involve second order quantum processes, i.e., resonance photoemission, Auger and X-ray
emission spectroscopies, denoted respectively by RXPS, AES and XES. First, we summarize
the main 3P-RXPS and AES results obtained in Cu and Ni metals; especially we recall that
the satellite near the 3P-threshold in the spectra, which arises from a d-hole pair bound state,
needs a careful treatment of the electron-electron correlation. Then we analyze the RXPS
spectra in a few Ce compounds (Ce02, Ce20a and CeFa) involving 3d or 4d core levels and we
interpret the spectra consistently with the other spectroscopies, such as core XPS and XAS
which are first order quantum processes. Finally within the same one-impurity model and
basically with the same sets of parameters, we review a theory for the Ce 5p-+ 3d XES, as well
as for the corresponding RXES, where (1) the incident X-ray is tuned to resonate with the 3d
-+4! transition and (2) the X-ray emission due to the 5p-+3d transition is actually observed.
The paper ends with a general discussion.
§ 1.
Introduction
In the study of the electronic properties of transition metals or rare earth based
materials, important information has been provided by the various modern high
energy spectroscopies/> i.e., valence photoemission spectroscopy (v-XPS), its resonance process (RXPS), its inverse process called bremsstrahlung isochromat spectroscopy (BIS), core level-X-ray photoemission spectroscopy (XPS), X-ray absorption
spectroscopy (XAS), X-ray emission spectroscopy (XES) and Auger electron spectroscopy (AES). With these spectroscopies the electronic degrees of freedom in the solid
can be tested as well as the correlated nature of the d or f electrons. Moreover the
high energy spectroscopies are an ideal testing ground for theories dealing with many
electrons wave functions and necessarily used in 3d, 4/ or 5/ electron systems. Also,
because in each of these spectroscopic experiments a different response of the valence
(conduction) electron is probed, highly differing line shapes are obtained; the challenge is then to reproduce all these responses with a single model theory. In this
short review paper, after recalling some RXPS and AES results for Ni and Cu metals
we focus on RXPS and XES spectra of light rare earth systems, especially of Ce
n Present address: Institute for Solid State Physics, University of Tokyo,
Tokyo 106.
7-22·1,
Roppongi, Minato-ku,
272
J. C. Parlebas, A. Kotani and S. Tanaka
compounds. We interpret the spectra, consistently with core XPS and XAS spectra,
and using the same one-impurity many-electron model theory.
In RXPS, AES and XES processes, which we discuss in this paper, a core electron
is first excited by an incident photon (or sometimes by an incident electron in the case
of AES and XES), and then an Auger transition (for RXPS and AES), or a radiative
transition (for XES) occurs to fill the core level. Therefore, these processes are
essentially second order quantum processes, whereas the other spectroscopies such as
XPS, XAS and BIS are first order quantum processes. In RXPS, the kinetic energy
of the emitted electron, E, depends on the incident photon energy w, while E is
independent of w in AES. RXPS occurs near the threshold of the core-electron
excitation, while AES occurs above the threshold. XES is usually observed well
above the threshold, but when XES occurs near the threshold, we denote it by the
resonance XES (RXES). It is to be noted that RXPS and RXES (AES and XES) are
two different decay channels of the same intermediate states, and thus they can be
described within the same theoretical framework.
The first observation of RXPS has been performed in Ni metal by Guillot et al. 2>
In the observed spectra, the intensity of the so-called 6 eV satellite was strongly
enhanced at the 3p excitation threshold and it has then been interpreted through the
strong electron correlations in the 3d states. After the RXPS spectra had been
observed for Ni metal, there were several experimental and theoretical studies of
RXPS in other transition metals, 3 > including Cu, as well as in the corresponding 3d
compounds, including high Tc superconductors (see Ref. 4) and references therein).
Whereas RXPS in transition metals (solid and films) was observed a bit prior to the
observations both in atoms (vapours) and compounds and then compared to them, the
corresponding theory for transition metals is actually quite different from atomic
physics and is somewhat similar to the theory for the compounds. A major aspect of
the theory for the metallic state is the concept of a pair of (quasi) localized d holes
that arises in XPS from the valence bands, as well as in RXPS and in AES spectra.
Situations involving more than one hole in the d shell are no longer described by
one-electron band theory, but need configuration interaction models (cluster model,
impurity model) and point out the importance of correlation effects. However as
indicated by band structure calculations and confirmed by experiments, there are also
itinerant valence and conduction bands present at relatively low energies in the
3d-compounds which arise from the ligand p and transition metal4s states. We have
therefore to deal simultaneously with the strongly correlated 3d-electrons and other
states which are essentially itinerant. For example the formation of a bound state of
two d holes and one conduction electron (sometimes called trion) has been recently
studied within the RXPS spectra by solving a three-body problem in a two band
Hubbard model. 5 > In the present paper a somewhat similar band model has been used
for the calculation of RXPS and AES spectra of Ni and Cu metals.
Another field of interest called much attention since several years; it is the strange
behaviour of the 4/ (5/) electrons in rare earth (actinide) systems, especially in the
mixed valence and heavy fermion systems (e.g., see Ref. 6) and references therein).
XPS and XAS techniques, especially those involving core levels7> are also very
powerful means to investigate the 4/ (5/) electron states. Moreover RXPS is of
Electron-Electron Correlation, Resonant Photoemission
273
great practical importance for the study of Ce compounds, as a technique to separate
out the /-symmetric states from other states in v-XPS. On the other hand, there has
been only a few XES measurements compared with RXPS, XPS and XAS. For
example there have been a certain number of XES experimental investigations for
rare earth systems so far carried out. 8l-HJ However most of them were performed by
using the technique of electron bombardment to excite Gore electrons. By the electron stimulation the injected electrons induce various complicated processes, which
make the interpretation of the observed XES spectra very difficult. Therefore the
selective excitation by using the X-ray stimulation is highly recommended for XES,
but only a very few works have been performed in such a way. 12 J Furthermore RXES
is an interesting new subject to be studied in future by using synchrotron radiation
sources.
In the case of light rare earth systems for which the I band energy dispersion is
quite small, the impurity Anderson modeP 3l' 14 J has been widely applied for the calculation of various core XPS and XAS spectra (Ref. 7) and references therein).
Gunnarsson and Li 15 J developed a theory for RXPS in metallic /-electron materials
and used it in the cases of Ce compounds; their model is based on a 1/Nf expansion
where Nf is the orbital and spin degeneracy of the I level. For RXPS in insulating
/-electron systems, Nakano et al_l 6 l developed a formulation and applied it to the
analysis of Ce203. For XES and RXES little theoretical investigations have been
performed; recently Kayanuma and Kotani,l7l and Tanaka et aV 8 l proposed a theory
for insulating La and Ce compounds and they took into account the electron correlation effects within the above mentioned impurity Anderson model (with a filled
valence band).
The present review is organized as follows: In § 2 we summarize the main
3p-RXPS and AES results obtained in copper metals, para and ferromagnetic nickel
for which a strong spin polarization is shown for the 6 eV satellite. Section 3 is
devoted to an analysis of 3d or 4d-RXPS spectra in some Ce compounds (Ce02, Ce203
and CeFg), recalling the link with the other spectroscopies (v-XPS, BIS, core XPS and
XAS). Finally in§ 4, the previously considered theory in§ 3 is extended to the study
of Ce 5P--+3d XES and RXES; in the latter case the incident X-ray is tuned to resonate
with the 3d --+4/ transition, then an X-ray is emitted due to the 5p--+ 3d transition. In
§ 5 we present a general discussion on the present review.
§ 2.
Resonant photoemission in copper and nickel metals
In this section, we review a theory for the resonant photoemission in Cu and Ni
metals, using a simplified s- and d- hybridized band model. First of all (§ 2.1) we
recall some experimental data on the resonance and Auger spectra near the 3p
threshold, i.e., 3P-RXPS, and AES in Ni and Cu metals which motivated the following
theory and calculations. Next (§ 2.2) the Hamiltonian of the problem as well as a
general expression for the RXPS spectra are written down, including the interference
effect with the direct photoemission process. Afterwards, on the basis of a onedimensional energy band model for a finite system, the satellite and Auger spectra are
calculated in copper metal as well as paramagnetic nickel (§ 2.3) and their spin
274
]. C. Parlebas, A. Kotani and S. Tanaka
polarization are obtained in the case of ferromagnetic nickel (§ 2.4). Section 2.5 is
devoted to a few concluding remarks.
2.1.
Summary of a few experimental data and general remarks
Many years ago an original picture of electron correlation effects on the 3d
photoemission spectra (3d-XPS) of Ni metal was proposed by Htifner and Wertheim19 >
as well as, Kemeney and Schevchik 20 > in order to explain the occurrence of the
so-called 6 eV satellite: They observed both the 3d-XPS spectra (direct photoemission) and the 2P-XPS spectra (core photoemission) and found that both kinds of
spectra exhibited a very similar satellite structure, so that the mechanism of the
satellite ought to be similar too in both cases. It has then been recognized that the
satellite reflected directly the correlation effect of a pair of 3d -holes, and from this
viewpoint, much attention has been paid to this phenomenon.
In the direct photoemission process of Ni metal, a photoproduced 3d -hole is
subjected to multiple scattering21 >with other 3d -holes through the intraatomic Coulomb interaction Udd· Therefore, the satellite arises in the 3d-XPS spectrum from
the final state where a two d -hole bound state is formed by the multiple scatterings,
while the main 3d-XPS peak corresponds to the system state where d-holes are
moving well apart from each other. 22 >' 23 > Actually there has been a remarkable
progress in this field, and additional experimental facts have then been obtained both
on the main line and on the satellite. On the main line, the angle resolved XPS
experiment has been performed in Ni and thereby the 3d -band width and the
exchange splitting could be estimated experimentally. 24 > On the satellite, it has been
discovered that its intensity is resonantly enhanced when the incident photon energy
w approaches the threshold Wo of the 3P-core electron excitation. This phenomenon2>'25> is called resonant photoemission
(3P-RXPS) and has been first observed in
Ni
Ni metal and then in Cu metal. 26 >
Whereas the binding energy of the satel83
lite in Ni is about 6 eV (and wo~67 eV),
the satellite of Cu lies at about 15 eV
79
Auger
Cu
(and Wo ~ 75 e V). Moreover it is seen
XJ I I
satellite
75
(Fig. 1) that not only the satellite inten?:
' ' ' ()
"iii
c:
sity increases when the incident photon
~
a.
-~
c 71
energy w is close to Wo, but when w
.!
c:
c:
becomes
larger than Wo, then the so0
67
c:
"iii
called Auger peak appears whereas the
0
.E
"iii
satellite
does persist. These features
8
.E
0
have
been
observed both in Ni and Cu
.s::.
8
a.
metals, so that the fundamental mecha.a.
2
nism of the 3p-RXPS is expected to be
the same for both types of metallic
(eV)
-20
0 =~ (eV) -20
-10
0=£F (3d 4s) systems.
Binding energy
Binding energy
In the next subsection the resonant
Fig. 1. Experimental 3p-RXPS spectra in Ni and
enhancement
of the satellite intensity
Cu metals (after Refs. 2) and 27) respectively).
-
Electron-Electron Correlation, Resonant Photoemission
275
will be interpreted as the coherent second order process consisting of (i) the optical
excitation of a 3p-core electron to the 3d and (or) 4s bands and (ii) the creation of a
two-d-hole bound state and a photoelectron by the super Coster-Kronig transition.
When the processes (i) and (ii) occur independently, we obtain the Auger spectrum.
In addition to this second order process, as already mentioned, there exists the direct
3d-XPS which can provide the same final state with a pair of d-holes as that of the
previously considered second order process, especially within the partially unoccupied
3d-band of Ni. Thus the second order process can interfere27 > with the direct one
(§ 2.2). Moreover a strong spin polarization has been observed for the satellite peak
in ferromagnetic Ni 28 > as predicted within an atomic model by Feldkamp and Davis. 29 >
It is also another purpose of this section (§ 2.4) to discuss the spin polarization of
the RXPS spectra in Ni. But let us first present quite a general formulation for RXPS
in Ni and Cu.
2.2.
General formulation of RXPS spectra in noble or transition metals
We consider a system30 H
4> consisting
of a broad 4s band
{€sk},
narrow 3d bands
{€dk0"} and 3p core levels €c, as shown schematically for Cu metal and ferromagnetic
Ni in Fig. 2. The orbital degeneracies of the 3d and 3p states are disregarded, for
simplicity. In the initial state of the RXPS process, the Hamiltonian Hg is written as
a periodic Anderson Hamiltonian, apart from the Coulomb interaction Udd which we
will take explicitly into account only in the final state of the RXPS:
(2 ·1)
where aJkO" (a~kcr) denotes the creation operator of the 4s (3d) electron with wave
vector k and spin a, and vksd represents the sd hybridization. In the intermediate
state of the 3P-RXPS, a 3P-core electron is excited to the 3d- or 4s- band, so that Hg
is replaced by the intermediate Hamiltonian Hm:
(2·2)
Ni
t spin
~spin
Cu
( m1nority)
5-state super C-K
transition
Fig. 2. Schematic 3P core level and 3d 4s band structure of Ni and Cu metals showing the formation
of a two d-hole bound state in a 3p-RXPS process.
J. C. Parlebas, A. Kotani and S. Tanaka
276
where Ups( Upd) describes the attractive (negative) potential of the 3P-core hole acting
on 4s (3d) states. 30 >
The intermediate state decays then by super Coster-Kronig transitions into the
final state of the 3p-RXPS with i) the core level filled, ii) the emission of a
photoelectron of energy € and iii) the creation of a pair of 3d -holes which is assumed
to be bound at the irradiated atom due to the intraatomic Coulomb interaction Udd.
By the presence of a 3d-hole pair, the d and s electrons are subject to the attractive
(electron-hole) potentials - UdiUdd>O) and Uds (Uds<O), respectively. Thus the
Hamiltonian in the final state is given by 32 >·33 >
(2·3)
where the second term of the right-hand side represents the additional Coulomb
energy between the bound d-holes when they are built up. With the third term, the
formation of the 3d-hole pair is treated self-consistently since a bound state is
produced below the bottom of the dO"-bands by the attractive Coulomb potential
-udd.
The total photoemission spectrum for the electron emitted with spin O" is expressed by taking into account the interference between the second order process of the
3d-RXPS and the direct 3d-XPS, including virtual transitions from the initial to the
final state accompanied by the process going into and returning from various intermediate states: 33 >
+ L:
(d
mf'P EP
X
( )
€
<JIHslm><mlHsl!'><J'IHvcrlg>
(m+Ec+Eu-Em+iT)(m+Eu-Ef'-€)
o(EB+ Ef+ Eu- €F)'
2
1
(2·4)
where EB is the binding energy (EB=m-E), w the incident photon energy, EF the Fermi
energy, Jg> the ground state of Hu with energy Eu, lm> and If> the eigenstates of Hm
and Hf with energies Em and Ef; r represents the life time effect of the 3p-core hole.
The interactions Hvcr, HRcr and Hs describe the direct photoexcitation of a d-electron,
the radiative photoexcitation of a core electron to the sd bands, and the super
Coster-Kronig transition, respectively: After eliminating the core electron and
photoelectron operators, they are written as:
(2·5)
(2·6)
(2·7)
For more explicit details we defer to Parlebas et al. 31 > and Jo et al. 33 > Next we
give some numerical results of 3P-RXPS for Cu and paramagnetic Ni metals.
Electron-Electron Correlation, Resonant Photoemission
2.3.
277
Culculated 3P-RXPS spectra in copper metal and paramagnetic nickel
Within the previously considered theory, numerical calculations of 3P-RXPS
spectra were first performed for Cu metal 31 > and paramagnetic Ni metal 32 > by neglecting the direct 3d-XPS term and thus any interference with that direct process, i.e., by
neglecting the second and third contributions in Eq. (2·4). For ksk} and {edk}, one
dimensional energy bands with linear dispersions were assumed as well as a finite
number of atoms (N =40), sufficiently large to provide numerical convergence. Also
a sinusoidal hybridization was introduced.
The calculated spin integrated RXPS spectra for Cu metal:
(2·8)
is shown (Fig. 3) as a function of the binding energy EB counted from the center of the
satellite EB 0 with the incident photon energy w as a parameter; an occupied s-band
width of about 9 e V is taken as the energy unit. In agreement with experiment (see
Fig. 1), the amplitude of the satellite increases as w approaches the core-level threshold energy Wo, and for w>wo, the Auger peak appears at EB-EB 0 =w-wo, but the
satellite does persist. The persistence of the satellite could only be explained by
considering the s-screening effect around the two d-hole bound state: Without the
s-screening effect, the super Coster-Kronig transition becomes independent from the
3P-electron excitation, so that only the Auger peak appears. As shown in the inset of
Fig. 3, the integrated intensity of the satellite is enhanced rather symmetrically
around Wo, whereas the Auger intensity grows rapidly starting from Wo and then
saturates for larger w, in accord with experiment. 26 > Also it is to be emphasized that
. . . . - - - - - - - - - - . r.w-"hwo=
0.0
Ni
Ea-eg
Fig. 3. RXPS spectra F(EB, w) in Cu calculated as
a function of the binding energy, EB- EB", EB"
being the center of the satellite, for various
incident photon energies, w- Wo, Wo being the
3P-threshold energy and Uds= -1; Ups= UPd
=0. The inset shows the w-dependence of
satellite, Auger and total (binding energy)
integrated intensities. The energy unit is 9 eV.
0.0
Fig. 4. RXPS spectra F(EB, w) in paramagnetic
Ni with Udd=2; Uds= -1 and Ups= Upd=D.
The inset shows the w-dependence of satellite,
Auger and total integrated intensities. The
energy unit is 10 eV.
278
]. C. Parlebas, A. Kotani and S. Tanaka
the s-screening effect is important in reducing the interaction udd between d -holes:
Especially it has been shown that the bare Coulomb interaction Udd(Cu)~27 eV is
reduced to the effective interaction Ud'Jf(Cu)~s eV by the s-screening effect.3ll The
value of Udd(Cu) has been estimated from the experimental spectra in accord with an
atomic Coulomb energy reported by Antonides et al. 35 J
In the case of paramagnetic Ni metal, 32 J the 3d-density of states (DOS) is very
high at EF and decreases rapidly with increasing energy. Therefore the 3P-electron
can be strongly excited to the 3d-band in the vicinity of the resonance w=wa, which
makes the resonance effect in Ni much sharper than in Cu metal, as seen from Fig. 4.
The persistence of the satellite for w > Wo in Ni originates from the sharp peak of the
empty 3d-DOS, in addition to the 4s-screening effect mentioned before. As shown in
the inset of Fig. 4, the integrated intensity of the Auger peak decreases for large win
contrast with that in Cu. This trend, which is in agreement with experimene6 J is only
explainable by taking into account both the s-and d- bands coupled through hybridization. In paramagnetic Ni, the s-screening effect reduces the bare Coulomb interaction UdiNi)~20 eV to the effective value Ud'Jf(Ni)~4 eV. 32J In ferromagnetic Ni
similar results have been found. 33 J In the following section we report on the spin
polarization of the 3p-RXPS in ferromagnetic nickel, 33 J including the interference
effect which has been numerically disregarded in the present section.
2.4.
Calculated spin polarization of the 3P-RXPS in ferromagnetic Ni
Again we assume one dimensional energy bands with a sinusoidal hybridization
so that intraatomic mixing between s- and d-states is avoided. The value of Md/Ms
is taken as unity and a=Mn/Md is varied as a parameter in order to st_udy the
interference effect. Numerical calculations were performed with the following potential values: Udd=20 eV; Uds= -10 eV; Upd= -10 eV and Ups=O.
It is to be noted that there exist four independent processes "in the resonant second
order process (Fig. 5), i.e., 3P6-->3d6 and 3P6-->4s6 photoexcitations for the 3p core
level followed by the emission of a- 6 spin photoelectron ( 6= i , -l- ), where the d hole
pair has been assumed to be a spin singlet. In the case when the direct 3d-XPS is
absent, i.e., Mn=O, Fig. 5 shows the binding energy dependence of the 3P6-RXPS
spectral amplitude F(EB, w, 6), coming from the four processes, separately. The
persistence of the sa~ellite beyond the resonance threshold wa originates from two
different effects depending which process is considered: i) for 3Pi -->4si and 3p! -->4s!
processes, the persistence of the satellite comes from the s-screening effect similarly
as in Cu metal ii) for 3p! ...... 3d! process, it is mainly due the (unfilled) high 3d! DOS.
The (binding energy) integrated intensities of the satellite and Auger peaks are
exhibited in Fig. 6. First, in the case Mn=O (a=O), the satellite intensity is enhanced
symmetrically around w= Wa and the Auger intensity starts growing at w?:. Wa.
Then, when a is finite, the satellite intensity becomes asymmetric around w=wa
(decreased for w < Wa and increased for w > wa) due to the interference effect between
the direct and second order processes. According to the experiments by Guillot
et al. 2 J and Barth et al., 25 J the satellite intensity is actually found asymmetric which
points out the importance of the interference effect. However, according to Fig. 6,
the Auger intensity is not so much influenced by the interference.
Electron-Electron Correlation, Resonant Photoemission
279
6(hw)= 0.0
(3p,t)-+(s,t)
Ul
·c:
::I
...0
..0
>
I-
6(hw)= 0.0
V)
z
UJ
(3p,1')-+(d,t)
1-
z
.2
5
.0
Fig. 5. The four independent processes contributing to the 3p-RXPS spectra of ferromagnetic
Ni when the direct 3d-XPS is absent (MD=O).
The values of the various parameters are given
in the text.
'hw-'hwo(eV)
Fig. 6. Integrated intensities of the satellite and
Auger peaks in ferromagnetic Ni.
Finally we summarize the main results obtained for the spin polarization P of the
satellite and Auger peaks:
P=(Q-1)/(Q+ 1),
f
Q= F(EB,
(J),
'i )dEB
(2·9)
IfF(EB,
(J),
.1-
)dEB'
(2·10)
where Q denotes the majority to minority spin intensity ratio. As already seen, the
process 3p.l- --+3d .1- is dominant for the
satellite when w ~ Wo (Fig. 5). This is
100 p ("/o)
then the reason of the large spin polariSatellite
zation of the satellite near the resonance
80
a= 0.3
threshold (w~ wa) as can be seen.in Fig.
7 for a=O. When w is smaller or larger
than Wo, the intensity of the 3p.l- --+3d.!process decreases and becomes compa- .
rable to 3p0"--+4sO' processes, so that the
spin polarization of the satellite
decreases. Moreover, as long as a=O,
the decrease of P for w > Wo is more
l'lw-?lluo (eV)
rapid than that for w < Wo, whereas P
Fig. 7. Spin polarization P of the satellite and
Auger peaks in ferromagnetic Ni.
decreases more rapidly for w < Wo than
280
]. C. Parlebas, A. Kotani and S. Tanaka
for (1) > (J)o as soon as a is finite (Fig. 7). This can be explained because the intensity
of the 3pt --+3d J, process, which gives a large contribution to the spin polarization,
decreases for (1) < (J)o and increases for (1) > (J)o by the interference effect (Fig. 6).
According to Clauberg et al.,Z8 > the polarization of the satellite actually decreases
more rapidly for (1) < (J)o than for (1) > (J)o in agreement with the present theory. Also
the observed polarization of the Auger peak is much smaller than that of the satellite
in agreement with the results of Fig. 7.
2.5.
Brief outlook
Up to now we only considered the cases of Ni and Cu metals. More generally as
far as transition metal compounds are concerned, including the new series of high Tc
Cu based compounds (see Ref. 4) and references therein), the two d holes which have
been considered in the present section are sometimes so strongly bound that they are
(almost) localized at the same (irradiated) site. In that case it is no longer necessary
to solve a periodic Anderson type model, as it is the case for the final state of RXPS
in Eq. (2·3); it should be sufficient to perform a single impurity (or single cluster)
Anderson calculation. This remark is even more valid for rare earth compounds
because the rare-earth ions can be viewed as isolated entities to a good approximation
(especially, if we except the cases of heavy fermion compounds (see Ref. 6) and
references therein)). The remaining part of the present review is devoted to such
light rare-earth (Ce) compounds.
§ 3.
Resonant photoemission in rare-earth compounds
In this section, RXPS spectra in Ce based compounds with strong //(Ce) correlations are studied by using an adapted version of the Single Impurity Anderson Model
(SIAM). 14 >' 15 > For instance, in Ce insulating oxides like CeOz and Cez03, the hybridization between a Ce 4/ state and an 0 2p state as well as the Coulomb repulsion Uff
between Ce 4/ electrons are taken into account (§ 3.1). Next, the valence photoemission spectra (v-XPS), the bremsstrahlung isochromat spectra (BIS), the 3d core
absorption spectra (3d-XAS) and the 3d core photoemission spectra (3d-XPS) are
theoretically reviewed for Ce oxides by using the filled band version of the SIAM: It
is found out that Cez03 is in an almost trivalent state whereas CeOz is in a mixed
valence state(§ 3.2). Then RXPS spectra are calculated forCe compounds and it is
shown that the resulting spectra can be analyzed consistently with the various
previously considered spectra and can be compared satisfactorily with experiments,
especially for Cez03 and CeF3 (§ 3.3).
3.1.
Genaral remarks on Ce compounds
By the analysis of core level XPS (and XAS) data, the 4/ state of intermetallic
compounds like CeRh3, CeRuz, CeCoz (for a review see Allen et al. 36 >) as well as
insulating compounds like CeOz (for a review see Kotani et ai.7l) were found to be in
a mixed valence state whereas, traditionally, they have been considered to be in a
tetravalent (Ce4+) state. Moreover in rare-earth based systems, the v-XPS spectra
analysis, where the 4/ and other valence (conduction) electrons are photoemitted, is
Electron-Electron Correlation, Resonant Photoemission
281
an additional useful tool to study the 4/
state and its hybridization with the other
!-level ~;t;;;:h:l£.
valence (conduction) states. Also, the
· r.'NJI'>'fl7'k'
banc;l
bremsstrahlung isochromat spectroI
3d-xPS scopy (BIS), in which incident electrons
are absorbed and photons are emitted, is
able to provide information on the
strong
correlations between 4/ eleccore
level
--<itrons.
Furthermore
the RXPS has also
Ce02
parameters
(V•O)
been observed at the 4d threshold of
Fig. 8. Schematic core level and 2p 4/ band strucvarious rare-earth systems (see for
ture of Ce02 and Ce20a showing the mechanism
example Peterman et al. 37 >). Similarly
of core-XAS and XPS as well as v-XPS and
to the 3P-RXPS in Ni metal, presented in
BIS.
the previous section 2, the mechanism of
the 4d-RXPS in rare earth based systems is described as follows: A 4d core electron
is first excited to the 4/ state by absorbing an incident photon of energy w (leading to
the 4d-XAS phenomenon) and then the super Coster-Kronig transition occurs, i.e., a
4/ electron makes a transition back to the 4d level and another 4/ electron is emitted.
Therefore only the 4/ derived XPS of the v-XPS spectrum is enhanced at the 4d
threshold and this phenomenon is used as a possible technique to separate out the
/-symmetric states from other states.37l The v-XPS, BIS and RXPS have been
observed in CeOz and Cez03 by Allen. 38 >
One of the purposes of the present section is to review the RXPS spectra in a few
typical rare earth systems with strong I electron correlation: In fact we shall
essentially focus on Ce oxides. First of all, in next subsection 3.2, various spectra
-3d-XPS, 3d-XAS, v-XPS and BIS- of Ce oxides are reviewed as interesting
preliminary steps towards RXPS. Basically, in the limit of vanishing hybridization,
the ground state of CeOz consists of the filled 0 2P valence band (VB) with no 4/
electron occupation, whereas that of Cez03 consists of the filled VB with one extra 4/
electron (Fig. 8). Let us just recall here that if the binding energy Es (see Eq. (2·4)
for example) is kept constant while the incident photon energy w is varied, then it is
possible to obtain the constant initial state spectrum (CIS); from the point of view of
the one electron picture, the CIS spectrum provides information on the final state of
the photoexcitation. In§ 3.3 the RXPS of Ce oxides is calculated and the CIS spectra
of CeOz and Cez03 compounds are analyzed by using the same parameter values as
determined in § 3.2; a comparison is made between Cez03 and CeF3\
\
\
\
3.2.
v-XPS, BIS, 3d-XPS and 3d-XAS in Ce oxides
The first analysis of 3d -XPS spectra in Ce oxides, especially in CeO z
compounds39 H 1> was performed by Fujimori 42 > by using a CeOs cluster model. Then
more detailed analysis were carried out by Wuilloud et al. 43 > Kotani and Parlebas, 44 >
Parlebas and Kotani, 45 > Kotani et al. 46 > by using the SIAM with a filled oxygen 2P
valence band (VB). In this model, as shown in Fig. 8, we consider a finite system
consisting of a simplified VB and a 4/ level Ef on a single Ce site. Moreover, for CeOz
compounds, extensive studies of the 4/ states have also been worked out by measure-
282
]. C. Parlebas, A. Kotani and S. Tanaka
ments of 2P-XAS, 41 > 3d-XAS,47) vXPS,43)'38>'48> BIS, 43 >' 38 >' 48 > and their theoCal
.·
,-.;:..
retical interpretations. 43 >' 48 >-s 2> In § 3.2.1
! :.
j
.
\ _...,,..._,..:
l·
we recall the formulation of the 3d-XPS,
·'
3d-XAS, v-XPS and BIS spectra within
the filled band SIAM. Then in § 3.2.2
we present a brief review of the corresponding calculated spectra in the case
900
875
925
of Ce02 and in comparison with the
BINDING ENERGY (eV)
available experimental data. For the
other insulating Ce203 oxide, much less
study has been performed. Fuggle et al. 40 >
3d-XPS
(b)
observed the 3d-XPS spectra and
Allen, 38 >and Le Normand et al. 53 >measv
ured the v-XPS and 3d-XPS for a Ce02
>
sample converted progressively to Ce203.
1ii'i
According to these data, the 3d-XPS
z
LIJ
1spectrum
of Ce203 only exhibits two
z
peaks (apart from the spin orbit splitting
of the 3d level) whereas for Ce02 the
3d-XPS
spectrum shows a well known
BINDING ENERGV(eV)
three-peaks
structure (Fig. 9(a)). MoreFig. 9. Experimental (a) and calculated (b)
3d-XPS spectra for CeO. and Ce.Os. (Experiover the v- XPS spectrum has two peaks
mental data are taken from Ref. 38).)
in Ce203 while only one structure in Ce02
(Fig. lO(a)). In § 3.2.3 we briefly present the method of calculation of the various spectra for Ce203 still within the filled
band SIAM; comparison is made with the experimental spectra. Finally let us
remark that we use either a spin singlet ground state (case of Ce02 in §3.2.2) or a spin
doublet ground state (case of Ce203 in §3.2.3) and the differences in the various spectra
between Ce203 and Ce02 are also discussed.
3d-XPS
~·
3.2.1. Formulation
The Hamiltonian H of the considered finite system is written as:
H=~Ekalvakv+E/~a}vafv+
uff ~ a}vafva}v'afv'+ ~~(alvafv+h.c.).
ku
v>v'
y N kJJ
JJ
(3·1)
The operator a:v (i=k, /)denotes the creation of an electron in the state (i, v) where
v denotes the combined index to specify both 4/ orbital and spin symmetries (v=l, ... ,
Nf); Uff and V represent the 4/-4/ Coulomb repulsion and the hybridization between
the VB and 4/ states respectively. In the final state of the 3d-XPS and 3d-XAS, we
change E/ to E/- Ufc in order to incorporate the attractive core-hole potential
- Ufc. 54 )
We denote the ground state for the considered system with the energy Eg by
lg>:49),54)
Electron-Electron Correlation, Resonant Photoemission
283
i) When a 3d core electron is excited to a photoelectron state with a (high) kinetic
energy € by absorbing an incident photon of energy w, then the lg> state changes to
the final state of the 3d-XPS noted l/(3d-XPS)> with the energy EA3d-XPS).
ii) When the 3d core electron is excited to the 4/ level, th.e lg> state changes to the
final state l/(3d-XAS)> of the 3d-XAS with the energy Ef(3d-XAS).
iii) When a valence electron (an 0 2P or aCe 4/ electron) is photoexcited, the lg>
state changes to the final state 1/(v-XPS)> of the v-XPS with the energy Ef(v-XPS).
The 3d-XPS spectral amplitude Fsd-xPs(EB) is expressed as a function of the
binding energy EB(EB= w- €, like in § 2) as follows:
(3·2)
with
(3·3)
where r represents the spectral broadening due to the finite life time of the core hole
as well as the experimental resolution. Similarly the 3d-XAS amplitude Fsd-xAs(w) is
expressed as a function of the incident photon energy w as follows:
(3·4)
where lla denotes a given state among the Nrfold degenerate (4/) v state. Next the
v-XPS spectral amplitude Fv-xPs(E) is given, as a function of E=- EB, by:
where Ms is the ratio of the matrix elements for the photoexcitations of a VB electron
and a 4/ electron (Fig. 8). Finally let us just remark that if we use the final states
without core hole, then Eq. (3·4) related to 3d-XAS, also expresses the BIS spectrum,
w being replaced by the energy E €'- w' where €' and w' are the energies of the
incident electron and emitted photon, respectively.
Numerical calculations were carried out by assuming a filled VB defined by the
following dispersion relation:
=
Ek=Ev 0 + W(2k-N-1)/2N,
k=l, 2, ···N,
(3·6)
where W is the VB width. As an approximation, we took the value N to be finite
(discrete VB), but the convergence of the spectrum with N was checked to be
sufficiently good. 46 l In the present calculations we used N=6, Nf=14 and W=3 eV
both for CeOz (§ 3.2.2) and CezOs (§ 3.2.3).
3.2.2. The case of CeOz
In the case of CeOz the spin singlet ground state lg> and the final state
l/(3d-XPS)> are expressed as a linear combination of the following states:
N
Nf
l/0 )= k=l!l=l
II II a.Livacuum),
(3·7)
284
J. C. Parlebas, A. Kotani and S. Tanaka
(3·8)
(3·9)
(3·10)
Let us just comment that l/0 ) corresponds to the system state where the VB is filled
and the 4/ level empty whereas IP.~> and IP~2 > types of states are respectively
through the hybridization V, where -v represents a hole in
coupled with 1/0 ) and IPv>
the VB. The parameter values in the present model are chosen so as to reproduce
satisfactorily the experimental 3d-XPS spectrum of Ce02 (Fig. 9). We obtain: V
=0.76 eV, Uff=10.5 eV, Ufc=12.5 eV, €f- €v 0 =1.6 eV. It is found that the 4/ level
lies close (0.1 eV) above the top of the VB and thus the ground state of Ce02 is a
strongly mixed state between 4/0 and 4P~ configurations with the averaged 4/
electron number nf::::::0.52. For the final state of 3d-XPS, the highest binding energy
peak corresponds to the almost pure 4j0 configuration whereas the lowest and middle
peaks correspond to the state of strongly mixed 4/ 1~ and 4P~2 configurations.
The calculated v-XPS and BIS spectra are shown in Fig. 10 where we assumed Ms
=0.55: 52 > Our results are in good agreement with the following features observed
experimentally by Allen: 38 > The v-XPS of Ce02 has only one broad structure with a
width of 3 to 4 eV. From our calculation, it is found that the v-XPS originates mainly
from the photoexcitation of the ox;ygen VB. Also it is found that the prominent BIS
peak corresponds to the 4P final state, while the weak structure at 13 or 14 eV above
this peak corresponds to the 4P~ final state. 52 >
-·c:
.!!!
::l
.c
t;
.:;:.
v-XPS
[b)
BIS
Ce02
~
"iii
_ v-XPS
BIS
!al
c::
Ill
c
15
20
.l!l
·c:::l
B
.ci
~
V-XPS
(C)
BIS
_g
;::.
"iii
0
25
ENERGY ABOVE EF (eV)
~
0
5
10
15
Fig.IO. Experimental (a) and calculated v-XPS/BIS spectra for Ce02 (b) and Ce20a (c).
tal data are taken from Ref. 38).)
(Experimen-
285
Electron-Electron Correlation, Resonant Photoemission
fN
900
890
880
'hw (eV)
0
Fig. 11. Calculated 3d-XAS (full line) and 3dRXPS (dashed line) for Ce02 as a function of
incident photon energy w. The inset shows the
experimental 3d-XAS spectrum taken from
Ref. 47).
In Fig_ 11, the calculated 3d-XAS
spectrum of Ce02 is shown within the
same parameter values as those previously used in 3d-XPS: agreement with
experiment47 ) (insert of Fig. 11) is quite
satisfactory. For a qualitative discussion of the 3d-XAS result let us adopt
for a while the atomic picture, i.e., N = 1,
and neglect the 4P configuration in the
initial state (as well as the 4/3
configuration in the final state: for a
discussion on the 4/3 configuration effect
see J o and Kotani 49 l). Then we represent the ground state lg> as:
(3·11)
and the final states corresponding to the two peaks of the 3d-XAS spectrum as:
IB(3d-XAS)>=dliP>+d21P!!)
(3·12)
for the lower (highest in amplitude IB) energy peak and
IA(3d-XAS)>= -d21P>+dliP1!_>
(3·13)
for the higher (lowest in amplitude IA) energy peak. The corresponding IB and IA
amplitude are given by: 49 l
IB=Icod1 +J(Nf-1)/Nf c1d2l 2 ,
(3·14)
1A=I-cod2+J(Nf-1)/Nf c1d1l 2 .
(3 ·15)
Actually in 3d-XAS, we have two transition processes from the initial state to the
final state, i.e., the F--+ P and / 11!_--+ P1!_ transitions. The two processes interfere with
each other. By the interference effect, IB (constructive interference) becomes much
stronger than IA (destructive interference). For a comparison and discussion with the
metallic case, especially CeRh3, see also Jo and Kotani. 49 )
The final states of 3d-XAS correspond to the intermediate states of 3d-RXPS (see
§ 3.3.2) and RXES (see § 4.2). From comparison between 3d-XAS and 3d-RXPS
some information on the structure of IA(3d-XAS)> and IB(3d-XAS)> can be obtained,
as will be shown in §3.3.2. When we consider the case N =oo, the main peak of
3d-XAS remains to be a discrete bound state, but the satellite consists of a discrete
antibound state and a continuum, as shown in Fig. 19 (§ 4) as the intermediate state
of RXES. When the incident photon energy resonates with the excitation of this
continuum in RXES, we expect to have a peculiar situation where the emitted photon
energy w becomes almost independent of the incident photon energy, as will be shown
in § 4.2.
286
]. C. Parlebas, A. Kotani and S. Tanaka
3.2.3. The case of Ce203
In the limit of vanishing hybridization V, the ground state of Ce203 is given by the
spin doublet state l/1 ) where the VB is completely filled and one 4/ electron, whose
symmetry can be taken as 1/o without loss of generality, is occupied at the Ce site
(Fig. 8):
with
l.fl>
(3·16)
defined before. When V is switched on, IP >is coupled with the state
IP~(k)>
and
IP~(k)>
JN1 1 a}va ~ a}vakvl/0 ) ,
flJ*lJo
(3·17)
is coupled further with the following states:
1Pv
~ a}vakva}v'awl.fl>,
- 2(k, k)>= V/ (Nf - 1 ~Nf - 2) a}va JJ>JJ'(*JJo)
(3·18)
The coupling of IP> with 4/0 and 4P~ configurations is negligible in the ground state,
because their energy difference is large. However in the final state of the 3d-XPS,
IP> couples considerably with IP~(k)> since their energy difference decreases as a
consequence of the effect of the 3d core-hole potential - Ufc. Actually in Ce203, the
mixing between IP> and IPv(k)> (through V) is very large in the presence of the final
state potential (- Ufc), so that the two peaks of the 3d-XPS spectrum in Ce203 oxide
have comparable intensities: The calculated 3d-XPS spectrum is shown by a dashed
curve in Fig. 9(b). The corresponding parameter values are chosen as: V=0.6 eV,
Uff=9.1 eV, Ufc=12.0 eV, e/- €v 0 =2.0 eV which orders of magnitude are very
similar to the case of Ce02, pointing out that the difference between the two systems
is not so much a question of parameter values but rather a question of differing
ground states (and therefore final states). Our theoretical result is also in good
agreement with experimental data 38 >'53 > (Fig. 9(a)).
In the v-XPS spectrum of Ce203 (Fig. 10), two peaks show up both experimentally
and theoretically, 52 > corresponding to the VB photoemission and 4/-electron
photoemission (whereas Ce02 had a broad structure, which was mainly composed of
the photoemission of the VB). The theoretical result of Fig. 10(c) was obtained using
Ms=0.41. Actually Ce203 has one 4/ electron in the ground state, and therefore there
is a remarkable 4/ electron emission peak. This was not the case in Ce02, where the
number of 4/ electron is small in the ground state and thus the emission of 4/ electron
is much weaker than the emission of the VB.
In BIS, Ce203 has one peak (see our calculated spectrum in Fig. 10) which is
composed of the 4P final state (whereas Ce02 had two peaks corresponding to 4/ 1 and
4P~ final states respectively). As already mentioned, the ground state of Ce203 has
little 4P~ component so that the 4/3~ component in the BIS final states is very small
and there is no peak. The weak structure (called Bin Fig. 10(a)) about 14 eV above
the prominent peak in the experimental BIS spectrum may be a structure of the
conduction band. Quite differently the ground state of Ce02 is composed of the 4/0
Electron-Electron Correlation, Resonant Photoemission
287
and 4P!!._ configurations, so the BIS has the 4P and 4P!!._ peaks.
3.3.
Resonant photoemission in Ce compounds
Most of the RXPS measurements of Ce based systems have so far been made on
Ce metal and metallic Ce compounds. 36>' 37 > On the opposite, for Ce02 and Ce203
insulating compounds, as far as we know, there is only one experimental observation
of the constant-initial state (CIS) spectra by Allen38> (Fig. 12). In this subsection,
using the results obtained in the preceding subsection 3.2, we review the theoretical
analysis of RXPS in Ce insulating oxides and compare with the available data of
Allen.
3.3.1. Formulation of 3d or 4d-RXPS
By absorbing an incident photon of energy w, a core d -electron can be excited to
the 4/ state, while a valence electron (4/-electron or VB-electron) can be excited to
a photoelectron state with kinetic energy €. These processes are described by the
following Hamiltonian45 >' 49 >' 17>
(3·20)
where
(3·21)
(3·22)
In Eq. (3·20), Hv represents the excitation from the 4/ or the VB states to a
photoelectron state and He represents the transition from the core state to the 4/
state. We assume that the dipole transition matrix elements, Mv, Mf and Me are real
constants. Then the intermediate state with a core hole is changed to final states
through Auger (Coster-Kronig) transitions expressed by
(3· 23)
where we assume that VA is a real constant. In these Hamiltonians we did not write
explicitly the second quantization operators of photoelectron and core electrons. We
calculate the RXPS amplitude /(w, EB) in the form:
(3·24)
(3·25)
where HM=H given by Eq. (3·1) in the initial and final states and
(3·26)
in the intermediate state lm>. In the T-matrix of Eq. (3·24) we take into account the
lowest order term of HR and the terms to all orders of HA. Once again we describe
the spectral broadening due to electron life-time and the experimental resolution by
288
]. C. Parlebas, A. Kotani and S. Tanaka
r in the Lorentzian function L(x ). Also in the present calculation, we neglect, in the
intermediate state, the multiplet structure due to the coupling between 4/ electrons
and that between 4/ electron and the core hole. After some manipulation, it is
possible to rewrite /(w, EB) as: 17 >
/(w,
EB)=~NfM/I<f(v-XPS)I( afvo+ m-~akvo)lu>
+ mm'v
~ <f(v-XPS)Iafvoafvlm>Gmm'(am'- i,8m•)l 2
(3·27)
where Ms=Mv/Mf and Gmm' is derived from:
(3·28)
with
Ec
representing a core electron energy and:
(3·29)
am
_·,a _Me VA ( I t I >+
z m- M f
m afv g
VA~ <miHAI/')(/'IHvlu>
Mf E'f'
"'-' (1) +Eg - € ' - E f' + ZT}
·
(3·30)
Some basic wave functions like lu>, 1/(v-XPS)> have already been mentioned in§ 3.2.1.
3.3.2.
3d and 4d-RXPS in Ce02
The total cross section F3d·RXPs(w) of 3d-RXPS is given by summing over the
binding energies:
F3d-RXPs(w)=
1:""dEB!(w, EB),
(3·31)
where /(w, EB) is given by Eq. (3·27). In the photon energy region of 3d-RXPS, the
effect of the interference is small and the value of Ms is also very small. Therefore,
we disregard the interference and put Ms=O, then we obtain
D
r
3d-RXPS
(
)-
(1)
-
V: 2M2~~~ ~ <!(4/-XPS)Iafvaf!l'lm><mla}v"lu> 12
A
c "'-'
"'-'
"'-'
f
m uu'u"
E m - w - E u-ZJ.·,..,m
'
(3·32)
li>J.J'
where lm> are intermediate states, and Em and Fm are their energy and damping,
respectively. It is important to note that 1/(v-XPS)> is here reduced to I/(4/-XPS)>
and that the intermediate state lm> is given by the previously considered l/(3d-XAS)>,
i.e., lm> corresponds to the final state 3d-XAS process (3d 104r->3d 94/n+ 1). Then, as
already stated in general, by Coster-Kronig transition, one 4/ electron makes a
transition into the 3d core hole whereas another 4/ electron is excited as a
photoelectron of energy € (3d 94r+l ..... 3d 104r- 1+ €). Since two 4/ electrons are
removed in the Coster-Kronig transition, the transition only occurs through the 4P!!..
component of the intermediate state. Therefore, the 3d-RXPS plays a role of
extracting the weight of 4Pv configuration [(d2? in Eq. (3·12) and (d1)2 in Eq. (3·13)]
Electron-Electron Correlation, Resonant Photoemission
289
from //(3d-XAS)>. In the 3d-XAS spectrum of CeOz [Fig. 11 and Eqs. (3 ·12) and
(3·13)], both final states /B(3d-XAS)>
and /A(3d-XAS)> are strongly mixed
(d)
states between the 4/1 and 4/2!!._
-15 -10 -5 0 5
Photon Energy (eV)
~ 10
configurations. The Coster-Kronig
transition, therefore, occurs for incident
J!!
photon
energies corresponding to both
·c
:J
the
lower
(B) and higher (A) energy
.0
a
peaks of 3d-XAS. Thus F3d-RxPs(w) in
~
·~
CeOz is expected to have a hump (see
~ 1---.Y
dotted curve of Fig. 11) near the higher
100
125
energy peak of the 3d-XAS in addition
PHOTON ENERGV(eV)
to a main resonance peak near the low
Fig. 12. Experimental (a) and theoretical ((b) and
energy peak of 3d -XAS. Unfortunate(c)) 4d-RXPS (CIS curves) for Ce02 and Ce20a.
ly, there is no experimental data on the
(Experimental data are taken from Ref. 38).)
3d-RXPS
of CeOz with good resolution.
In (b) the dashed line is for q=l and the solid
It is expected that the present theoretkal
line for q= -1.
prediction for CeOz will be confirmed by
future experimental measurements of the 3d-RXPS spectra with sufficient resolution.
The latter improvement can be attained by the high photon flux from improved
synchrotron radiation sources (see for example Refs. 56) and 57)).
For the 4d-RXPS of CeOz, experimental CIS data 381 are shown in Fig.12(a), where
the binding energy is taken in the oxygen VB region. The observed resonant enhancement suggests a considerable mixing of 4/ states with the 0 2P states. A theoretical calculation of the CIS spectra was made by Nakano 551 on the basis of Eqs. (3·27)
~(3·30) and with some simplifying assumptions. He approximately put am-ifJm in
Eq. (3·27) in the form
~
§
.ti
./ \\
,
~...
',_ ... ------
1
(3·33)
where q corresponds to the so-called Fano's q-factor and is expressed as
q
= VAMc +A_
Mfr
r·
(3·34)
Here, Llmm' and Ymm' in Eq. (3·29) are assumed to be diagonal and independent of the
suffix m, and they are written as L1 and r, respectively.
The calculated CIS spectra (for the center of the VB) are shown in Fig. 12(b),
where rand q are taken to be r=2 eV and q=1 or -1 (respectively dashed and solid
lines) and the same set of SIAM parameter values as in § 3.2.2 is used. The calculated
resonant enhancement (especially for q= -1) seems to be consistent with the experimental data. This implies that the mixing between 4/ and VB states, as well as the
value of Ms=0.55, was taken reasonably in our calculation in § 3.2.2.
3.3.3. 4d-RXPS in Cez03 and comparison with CeF3
Next we summarize a theoretical analysis 161 '581 for the 4d-RXPS and more precise-
290
]. C. Parlebas, A. Kotani and S. Tanaka
ly the CIS spectrum in Cez03. In the experimental energy distribution curve (EDC) of
Cez03 (Fig. 10), we can see two peaks with 3 eV of separation. From the data (Fig.
12(a)), the higher energy peak of v-XPS, which is named "Cez03 Ce 4!" in Fig. 12(a),
is very strongly enhanced at the 4d-threshold (about 120 eV) but the lower energy
peak of v-XPS, which is named "Cez03 0 2P", is not very much enhanced. The
calculated CIS spectra 17> are shown in Fig. 12(c), where Eqs. (3·27) ~(3·30) are solved
with Ms=0.41, p VA 2 =0.05 eV and (Mc/Mf)2/p=3.2 eV and without the approximation
of Eq. (3·33). The higher energy peak of v-XPS comes mainly from 4/ electron
excitation so that the resonant enhancement is very large. The lower energy peak of
v-XPS comes mainly from the VB excitation and the resonant enhancement is small.
From this result, we confirm that our choice of parameter values, especially Ms, is
reasonable and the ground state of Cez03 is in the almost CeH state. The agreement
with experiment is improved further by taking account of the energy-dependence of
Mv and Mf as shown by Okada and Kotani. 58 >
Before closing this section we present, for comparison, the 4d-RXPS results
obtained in CeF3. According to recent experimental observations, 59 > let us first recall
that v-XPS spectra in Ce-halides, especia]ly CeF3 compounds, have the two-peak
structure like in Cez03. Then one of the peaks is also strongly enhanced, while the
other is weakly enhanced at the 4d-4/ excitation threshold of the 4d-RXPS experiment. The observed EDC for CeF3 is shown in Fig. 13(a); as can be seen from the
experimental difference curve between the Fano maximum and the Fano minimum,
the lower EB peak originates almost from the /-electron emission, while the higher EB
one originates from the valence band (halogen P-band) emission. Calculated EDC
and CIS results 58 > are given in Figs. 13(b) and (c) are in good agreement with
Fig. 13(a). Here the parameter values of p VA 2 =0.05 eV, (Mc/Mf)2/p=3.2 eV and Ms
=0.55 are used and the energy-dependence of Mv and Mf are taken into account. The
SIAM parameter values are taken to be E/-Ev 0 =4.0 eV, V=0.5 eV, Uff=9 eV, Ufc
=12 eV and W=2.5 eV. Similarly to Cez03, the ground state of RXPS in CeF3 is
again (almost) of / 1 configuration; then
the intermediate state is of / 2
CeF3
-tv=120.5e\l
····1>/=114 e\1
-·-·Difference
configuration. The origin of double
peak feature in the EDC both in Cez03
and CeF3 is ascribed to the bonding and
antibonding state between / 0 and / 1
15
10
5
0
Binding energy (eV)
configurations in the final state. To
what extent both configurations mix
-FanoMax.
---.fanoMin.
with each other depends on the considPhoton energy (eV)
ered material and is closely related to
the transfer energy from the valence
band to the 4/ level, i.e., E/- Ev 0 • This
15
10
5
0
quantity is much larger in CeF3 (4 eV) as
Binding energy (eV)
compared
to Cez03 (2 e V), so that the
Fig. 13. Experimental (a) and theoretical (b) EDC
mixing
is
very
weak in CeF3.
curves for CeFa. (Experimental data are taken
J\A"'
/\7\if~bl
~~jl\.
from Ref. 58).); (c) shows the corresponding
calculated CIS curve.
Electron-Electron Correlation, Resonant Photoemission
§ 4.
291
X-ray emission in rare-earth compounds
Section 4 presents a theory of XES (§ 4.1) corresponding to the Ce 5p~ 3d
electronic transition 19 > in insulating Ce compounds (CeF3 and Ce02) as well as a theory
of RXES 60 > (§ 4.2) which is applied in the previously considered case under the
condition that incident photon energy Q resonates with the Ce 3d ~41 initial excitation energy. The spectra are calculated within essentially the same impurity Anderson model as in § 3.
4.1.
Ce
sp~3d
XES in CeFs and Ce02
First we discuss the Ce 5p~3d XES in CeF3. We consider the situation where a
3d core electron is excited to a high energy ionization continuum by absorbing a
monochromatic incident X-ray with energy Q, as shown in Fig. 14(a). Then, the 4/
level E/ is pulled down by the attractive core-hole potential - Ufc(3d), and a 5P core
electron makes a transition to the 3d level by emitting an X-ray photon with energy
w (see Fig. 14(b)). In the final state, we have a 5P core hole (Fig. 14(c)), so that the
core-hole potential is switched from - Ufc(3d) to - Ufc(5p).
The Ce ion in the ground state of CeF3 is trivalent with an almost pure 4/1
configuration, because the charge transfer energy between 4P and 4F!:!__
configurations, E/- Ev 0 + Uff, is much larger than the hybridization V, where !:!__
represents a hole in the F 2P valence band with a typical energy - Ev 0, and Uff is the
Coulomb interaction between 4/ electrons. When a 3d core hole is created, on the
other hand, the charge transfer energy decreases by Ufc(3d) and becomes comparable
with V, so that the Ce 4/ state relaxes from the 4P configuration to mixed states
between 4/ 1 and 4F!:!__ configurations. This relaxation is denoted hereafter by the
valence-mixing relaxation. At the same time, the 3d core hole decays by the lifetime
relaxation, which is mainly caused by the Auger transition. It is interesting to study
initial
(8)
intermediate
<bl
final
(C)
Fig. 14. 4/-> 3d XES process in CeFs, described by a second order optical process within a schematic
electronic band ;;tructure.
292
J. C. Parlebas, A. Kotani and S. Tanaka
the interplay between the valence-mixing relaxation and the lifetime relaxation in the
Ce 5p--+ 3d XES.
The Hamiltonian of our system is given by
+ uff :l! a}vafva}v'afv'- {Ufc(3d)[1- aJda3d] + Ufc(5p)[1- aJpasp]} :l!a}vafv ,
JJ>JJ'
J)
(4·1)
where we have also written 3d and 5p core states explicitly, and this model is a
straightforward extention of the SIAM to the system with two core levels.
In contrast to the 3d-RXPS process treated in § 3.3, the 3d core electron is not
excited to the 4/ state but to the high energy continuum in the present XES process.
In calculating the XES spectrum S(w), however, it is still essential to treat the whole
process as a coherent second order optical process, since the characteristic time of the
valence-mixing relaxation is comparable with that of the lifetime relaxation; in other
words, the hybridization strength V is comparable with the 3d core hole damping
F(3d) due mainly to the Auger transition lifetime. The XES is expressed, in a
similar way to the derivation of Eq. (3·32), by
S(w)= (dE:l!l:l!
p
i
;
<j/aJdasp/i><i/a3d/g> 12
F(5p)/;r
E;+E-Eg-Q-iF(3d) (Q+Eg-w-E-E;) 2 +F(5p) 2
'
(4·2)
where /g) is the ground state of H with energy Eg, /i> and /j) are intermediate and
final states (i.e., the eigenstates of H with 3d and 5P core holes, respectively) with
energies E; and E;, respectively. The energy € represents the high energy ionization
continuum and F(5p) represents the lifetime broadening of the 5p core level, as well
as the spectral resolution. The spectrum S(w) is calculated by numerically diagonalizing the Hamiltonian H for a finite system where the energies of the valence band are
expressed as Eq. (3 · 6) and in the sub-space spanned by the basis states given by Eqs.
(3·16)~(3·19). It is to be noted that the state //0 ) in Eqs. (3·16)~(3·19) is now given
by
/0>= IT~ alvaJpaJd/vacuum),
/! >=
0
{
a3dl o;~lv=l (intermediate state)
asp/ O> .
(final state)
(for ground state)
(4 ·3)
In Fig. 15, we show the calculated result of S(w) with the solid curve, where the
parameter values are taken as €f 0 - Ev 0 =4.0 eV, V=0.53 eV, Uff=8.0 eV, Ufc(3d)
=11.3 eV, Ufc(5p)=3.75 eV, W=3.0 eV, F(3d)=0.75 eV and F(5p)=l.O eV. These
values are consistent with the analysis of the 3d-XPS, the v-XPS and its renonance
enhancement (see § 3.3.3). The calculated spectrum exhibits two prominent peaks
and a weak shoulder, and these features are in fairly good agreement with experimental data by Hayasi et al., 61 > which is shown in the inset of Fig. 15. In order to see the
origin of these spectral structures, the total-energy-level scheme is shown in Fig. 16.
Electron-Electron Correlation, Resonant Photoemission
293
<utc<5P),rl3d))
/
0
=(3.75,0. 75)eV
(3.75,1.25)eV
W(eV)
Fig. 15. Calculated results of XES in CeF. for the
parameter values listed in the text especially
F(3d)=0.75 eV. The dashed curve corre·
sponds to F(3d)=1.25 eV. The inset shows
the experimental result of Ref. 61).
initial
intermediate
final
Fig. 16. Total level scheme of XES in CeF.: The
four paths 1 ~4 correspond to the structures
1 ~4 in Fig. 15.
The ground state of CeF3 is in the almost pure 4P configuration, but in the intermediate state the energy difference between 4/1 and 4P!!_ configurations becomes very
small by the effect of the core-hole potential - Ufc(3d), and these configurations are
mixed strongly by the hybridization V. In the final state with the 5P hole, the
hybridization between 4P and 4P!!.. configurations becomes much smaller because
Ufc(5p) is much smaller than Ufc(3d). There are four different paths, through which
we can go from the initial state to the final state, as numbered by 1 ~4 in Fig. 16.
From Eq. (4 · 2), it is found that the integral over E has main contributions from c
~Q+ Eu- E, and E~Q+ Eu-w- Ej, which means that S(w) has maximum values at
w~E;- Ej. Therefore, the XES structures 1 ~4 in Fig. 15 originate from the paths
1 ~4 in Fig. 16, respectively, while the contributions from the paths 2 and 3, overlap
each other to form a single XES peak. The paths 1 and 3 have the transition
probability l<ila3d/g)/ 2 much larger than the paths 2 and 4, and the paths 1 and 2 have
/<j/aJdaspli>/ 2 much larger than the paths 3 and 4, as easily seen from the character of
/g), li> and /j). Thus the XES intensity corresponding to each path increases in the
order paths 4, 3, 2, 1.
When we calculate the XES with varying F(3d), we find that the relative intensity
between two main peaks (or between the features (1, 4) and (2, 3)) changes as F(3d)
changes. As an example, we show the result for F(3d)=1.25 eV with the dashed
curve in Fig. 15, and compare it with the solid curve for F(3d)=0.75. The relative
intensity of the higher energy peak (or the features (1, 4)) which comes from the 4P
final state increases with increasing F(3d). This can be explained by the competition
between the valence-mixing relaxation by V and the lifetime relaxation by F(3d) in
the intermediate state. The ground state of CeF3 is in the 4/1 configuration, but when
a 3d core hole is created the 4P configuration starts to hybridize with the 4P!!_
294
]. C. Par!ebas, A. Kotani and S. Tanaka
configuration. If F(3d) > V, however, the valence-mixing relaxation is prevented by
the short lifetime of the intermediate state, and thus the relative weight of the 4P final
state to 4P!!._ one increases with increasing F(3d).
This effect of F(3d) on XES can also be explained by the quantum mechanical
interference effect in the coherent second order optical process. In the integrand of
Eq. (4·2), the factor describing the second order transition from lg> to lj> can be
written as
(4·4)
The second term of the right-hand side of Eq. (4·4) represents the quantum
mechanical interference. If we disregard this term, the relative intensity among the
features 1 ~4 does not depend on the value of F(3d). When we take into account this
interference term, it can be shown that the paths 1 and 4 interfere constructively while
the paths 2 and 3 interfere destructively. Furthermore, this interference effect
becomes larger as F(3d) increases (the interference term is negligibly smaller than
the first term in the limit of vanishing F(3d)). Therefore, the relative intensity of
(1, 4) to (2, 3) increases with increasing F(3d). This is the most interesting feature of
XES in comparison with XPS and XAS. Since XPS and XAS are first order processes, they are free from such a quantum mechanical interference effect.
Next we calculate the 5p~3d XES for CeOz. The basis states are taken in the
forms of Eqs. (3·7)~(3·10), where l/0 ) is given by Eq. (4·3). We use the same
parameter values as those used before in the calculation of 3d-XPS, 3d-XAS and
RXPS. The total level scheme is shown in Fig. 17. In the ground state of CeOz the
4/0 configuration is strongly hybridized with the 4P!!._ configuration so that the
average 4/ electron number is about 0.5. In the intermediate state, 4P!!._ and 4Pv 2
Ce02
c~
(UfC15pJ,rl3dl)
(3.75,1.5) IN
fO-~'
initial
intermediate
final
Fig. 17. Total level scheme of XES in Ce02.
Fig. 18. Calculated results of XES in Ce02 for
various values of the parameters ( Ufc(5p),
r(3d)).
295
Electron-Electron Correlation, Resonant Photoemission
configurations are strongly hybridized. Therefore, there are many different paths
from initial to final states. The calculated result of XES is shown in Fig. 18, where
we changed the values of Ufc(5p) and T(3d) as parameters. We find complicated
XES structures, which correspond to many different paths from initial to final states.
There has been no experimental data to be compared with the calculated result. It
is desirable that the calculated XES structures are confirmed by high-resolution XES
experiments.
4.2.
Resonant X-ray emzsszon
We consider the Ce 5p---3d XES in CeOz under the condition that the incident
photon energy Q resonates with the Ce 3d ---41 excitation energy. The total-energylevel scheme is shown in Fig. 19. The ground state of CeOz is a strongly mixed state
between 4/0 and 4P!:!. configurations, as shown before. In order to make explicit that
the valence hole !:!_ is a continuous energy state over the valence band width W, we
show hatched rectangles in Fig. 19. In the intermediate state, a 3d core electron is
excited to the 4/ state, so that we have strongly mixed states between 4P and 4P!:!_
configurations. In the final state, the mixing between P and P!:!. configurations
decreases because Ufc(5p) is weaker than
Ufc(3d). It is to be noted that the 4/ O(eV) = -3
configurations in intermediate and final
states are similar to those of CeFa under
the high-energy excitation (see Fig. 16).
-5
Keeping this in mind, we describe the
ground state by the basis states of Eqs.
(3·7)~(3·10) and the intermediate and
-7
final states by the basis states of Eqs.
(3·16)~(3·19). In this case, the symmetry
~.A.
of the photocreated 4/ electron corresponds to /.loin Eqs. (3·16)~(3·19).
The resonant X-ray emission spectrum (RXES) is given by
A.
-1~•1110
-13
X
1/5
A..
5p4f2l!
4--+-~---
initial
mtermediate
final
Fig. 19. Total energy level scheme of the 5p-->3d
RXES in Ce02.
-30
-20
-10
0
10
CsJ (eV)
Fig. 20. Calculated results of the 5p-->3d RXES in
Ce02 for various values of the incident photon
energy Q.
296
]. C. Parlebas, A. Kotani and S. Tanaka
S(Q
'w
)=~I~ (j)aJda5pli><ila}va3dlg>
j
;
E;-Eg-Q-iF(3d)
1
2
r(5p)f;r
(Q+Eg-w-Ej)2+F(5p)2'
(4·5)
where )g> is the ground state of H with energy Eg, li> and )j> are intermediate and
final states with energies E; and EJ, respectively.
In Fig. 20, we show the calculated result of RXES for various values of the
incident photon energy Q, where we choose €v 0 - €3d as the origin of Q, and €5p- €3d as
that of the emitted photon energy w. The parameter values are the same as those
used in the calculation of Fig. 18, and Ufc(5p) and F(3d) are taken to be 3.75 eV and
0.75 eV, respectively. The double peak structures in Fig. 20 correspond to the final
state structures: The higher energy peak (the main peak) and the lower energy peak
(the satellite) correspond to the discrete (mainly 4P character) and the continuous
final state (mainly 4PJ!.. character) in Fig. 19, respectively. On the relationship among
Q, w and the energy Ej of the j-th final state, we note the energy conservation
condition
(4·6)
which holds exactly in the limit of vanishing F(5p). This relation tells us that the
emitted photon energy increases as the incident photon energy increases, and explains
the shift of the XES peaks with varying Q. The dependence of the total intensity
upon Q is given by
(4 ·7)
D(eV)=
-20
cu
-10
(eV)
Fig. 21. The satellite spectrum of the 5p->3d
RXES for various values of the incident photon
energy Q in the vicinity of the resonant region
with the continuous intermediate state. The
dotted line is a guide to the peak positions.
which is proportional to the intensity of
3d-XAS calculated before (see Fig. 11).
Resonant enhancements occur when the
incident photon resonates with the
intermediate eigenstates: The large and
the small enhancements occur at Q
::::::-11 eV (main peak of the 3d-XAS)
and :::::: -6~ -8 eV (satellite of the 3dXAS), respectively. The former and
the latter correspond to the bound state
(bonding state) and the continuous and
anti-bound states (anti-bonding states) in
Fig. 19, respectively.
As shown in Fig. 20, the relative
intensity of the two peaks also changes
significantly as one sweeps the incident
photon energy across the resonant
region. When the incident photon
resonates with the intermediate bound
state (Q:::::: -11 eV), which decays strongly to the discrete final state through the
Electron-Electron Correlatz"on, Resonant Photoemission
297
radiative transition, the main peak corresponding to the discrete final state predominates over the satellite. On the other hand, when the resonant state becomes the
continuous intermediate state (.Q~ -7 eV), which decays strongly to the continuous
final state, the relative intensity of the satellite becomes almost equal to that of the
main peak. When the energy of the incident photon is too large or too small to
resonate with the intermediate state, the main peak predominates over the satellite
while the total intensity becomes quite smalL
A peculiar feature appears in the dependence of the peak position of the satellite
upon Q when the incident photon resonates with the continuous intermediate state.
The satellite does not change its peak position irrespective of the change of Q, as
shown in Fig. 21. A luminescence-like feature appears in the sense that there is no
correlation between the incident and the emitted photon energies.
An essential point of the mechanism giving rise to the luminescence-like feature
can be understood by considering the satellite spectrum in the simplified situation,
where both of the initial and the final hybridizations are neglected. The spectrum of
the 5p~ 3d RXES is given by
S(Q, cv)= ~J<jJaJdaspG(z)a}va3dJg>J 2 o(.Q+ Eg- cv- E;),
(4·8)
1G(z)=z-H
(4·9)
j
where
and
(4 ·10)
In this case eigensta tes in the final state are
Jf>=a}voaspl/ 0 )
(4 ·11)
lk>
(4·12)
and
The satellite spectrum can be easily derived by using Dyson's equation for G:
(4 ·13)
where
(4·15)
298
]. C. Parlebas, A. Kotani and S. Tanaka
and
(4·16)
The satellite spectrum is written by
X
I
1
Q- tf+ iF(3d)- Nr;; 1
V2~ Q-(2cf+ u}-E,.)+ iF(3d)
12'
(4 ·17)
where p(E) represents the density of states of the valence electron. When the incident
photon resonates with the continuous intermediate state, i.e., when
(4 ·18)
the satellite spectrum can be decoupled for Q and m in the limit of F(3d)~o.
Therefore, the peak position of the satellite does not shift from the energy, m=2(Ef
- €f ), even if Q changes within the range of Eq. (4 ·18). Another interpretation of the
mechanism causing the luminescence-like feature can be extracted from the orthogonality relation between the continuous state of the intermediate state and that of the
final state. When the incident photon resonates with a particular state in the continuous intermediate state with energy E, i.e., Q=E- Eu, only the final state with the
same energy E couples with the resonant state through the radiative transition.
From this and the energy conservation relation Eq. (4·6) the emitted photon energy
does not depend on the change of Q within the range (4 ·18). In other words, the
excess energy of Q within the range (4 ·18) is carried away by the valence electron.
For more details on the orthogonality relation, see Ref. 60).
§ 5.
Concluding remarks
In this paper we have reviewed the development in the study of the resonant
photoemission and the X-ray emission in systems with 3d and 4/ electrons.
In § 2, we have recalled that even a simplified 3d 4s hybridized band model can
explain general trends of the 3p-RXPS line shape in both Cu and Ni metals. Using
the assumption of a well-localized two d-hole bound state, we have pointed out that
the 4s-electron screening effect is important in interpreting the RXPS spectra.
According to Penn, 22 J Davis and Feldkamp, 62 J Liebsch, 63 J Treglia et al. 64 J and
Igarashi, 65 J the two d-hole bound state moves translationally with a finite energy
dispersion; however all these authors neglected the effect of s-electrons. From
another point of view developed in § 3, it is expected that the bound state becomes
localized, or almost so, through the s-electron screening around it, as first pointed out
by Kanamori 66 J for alloy problems. Also on the basis of the same hybridized sd band
model, the spin polarization of the RXPS in ferromagnetic nickel has been success-
Electron-Electron Correlation, Resonant Photoemission
299
fully discussed in terms of the incident photon energy. For a more quantitative
description of the photoelectron spectra the theory should be extended to more
realistic 3p, 3d, 4s and 4P states and a more careful treatment of the band hybridization. Also, the theory is extensible to the other 3d transition metals (for experimental spectra see for instance Chandesris et al. 67l). However, Cu and Ni metals are
simpler test cases for studying screening effects, associated with super Coster-Kronig
mechanism, because of the filled or almost filled 3d-shell ground state.
In § 3, we have discussed the 3d- and 4d-RXPS for Ce oxides with the single
Impurity Anderson Model (SIAM), consistently with the other spectroscopies. For
more quantitative calculation of the 4d-RXPS, the theory should be extended by
taking into account the intraatomic multiplet effect which originates from the Coulomb and exchange interactions and the spin-orbit coupling. In this connection, the
interplay between the intraatomic multiplet effect and the interatomic hybridization
has recently been studied in detail for the 4d -XAS in CeOz and other Ce
compounds. 68 l· 69 l It is desirable that the same type of theory would be applied to the
analysis of the 4d-RXPS. In addition to the RXPS for transition metals and rareearth compounds, extensive theoretical studies of RXPS have recently been made for
transition metal compounds and the new series of high Tc Cu based superconductors,
with the use of the SIAM or of a cluster model. Because of space limits, we have not
reviewed on these various "d" based compounds. For these studies, the reader can
refer to the papers by Davis, 3 l Fujimori and Minamj/l lgarashi,7ll Okada and KotanVl
Gunnarsson et ai.,72l and Ghijsen et aJ.13 l
In § 4, we have studied the Ce 5p~ 3d XES and RXES in insulating Ce compounds
with the SIAM. The theory can be extended to XES caused by other electronic
transitions; Tanaka et aJ.1 4 l calculated the 4/~3d XES is La and Ce compounds, and
showed that the spectral features are very sensitive to the differences in the 4/
electron populations in these materials, because the 4/ electron participates directly
in the radiative process. Two more interesting extensions of the theory will be the
4!~4d XES and the 3d~2p RXES following the 2p~5d excitation in rare-earth
compounds. The former will strongly reflect the intraatomic multiplet effect, as well
as the interatomic hybridization effect, and the latter will be sensitive to the Coulomb
interaction between 5d and 4/ electrons, which is expected to play an important role
in the final state of 2p-XAS, as pointed out by Jo and Kotani. 75 l Experimental
observations of these XES spectra are new interesting fields in future by using
synchrotron radiation sources with high brightness.
In addition to these XES measurements, we would like to propose, as another
interesting XES experiment, the coincidence spectroscopy of XES and XPS. We
have shown in § 4 that the Ce 5p~3d XES for CeOz should exhibit complicated
structures because of the contribution of many different paths (see Fig. 17) overlapping each other. If we measure the coincidence between Ce 3d-XPS and Ce 5p~3d
XES for CeOz the contributions from different intermediate states consisting of / 0 , / 1!:!._
and P!:!._2 configurations can be separated out, because the intermediate states of the
XES are the same as the final states of the XPS. Furthermore, the coincidence
experiment provides us with information on the quantum-mechanical interference
effect of the coherent second-order process. As shown in § 4, the interference effect
300
]. C. Parlebas, A. Kotani and S. Tanaka
gives important contribution to XES, for instance to the Ce 5p--> 3d XES for CeF3.
The interference occurs between second order processes with different intermediate
states. However, if we measure the coincidence between XES and XPS, the intermediate states (the final states of XPS) are restricted, so that the interference effect
should be suppressed.
Finally it is to be mentioned that some theoretical and experimental studies of
XES have recently been made for high- Tc oxide superconductors76 >'77 > to obtain information complementary to XPS and XAS.
Acknowledgements
It is our pleasure to dedicate this paper to Professor Junjiro Kanamori on the
occasion of his sixtieth birthday. Especially one of the coauthors (JCP) is grateful to
him for the common work done at Osaka University on the resonant photoemission in
copper and nickel metals which has also been the starting point of a long and fruitful
French-Japanese collaboration in this field. Also we would like to thank Professor
T. Jo, Dr. K. Okada, Dr. Y. Kayanuma, Dr. T. Nakano and Mr. H. Ogasawara for
valuable discussions and collaborations. This work is partially supported by the
International Joint Research Project from the JSPS, the France-Japan Scientific
Collaboration Program between CNRS and JSPS, and the Grant-in-Aid for Scientific
Research from the Ministry of Education, Science and Culture in Japan.
References
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
Core-level Spectroscopy in Condensed Systems, ed.]. Kanamori and A. Kotani (Springer Verlag, 1988).
C. Guillot, Y. Ballu, ]. Paigne, ]. Lecante, K. P. Gain, P. Thiry, Y. Petroff and L. M. Falicov, Phys. Rev.
Lett. 39 (1977), 1632.
For a review see, L. C. Davis, ]. Appl. Phys. 59 (1986), R25.
K. Okada and A. Kotani, ]. Phys. Soc. Jpn. 58 (1989), 1095.
]. Igarashi, in Ref. 1), p. 175.
]. C. Parlebas, Phys. Status Solidi(b) 160 (1990), 11.
A. Kotani, T. ]o and]. C. Parlebas, Adv. Phys. 37 (1988), 37.
C. Bonnelle and R. C. Karnatak, ]. de Phys. 32-C4 (1971), 230.
T. M. Zimkina, V. A. Fomichev and S. A. Gribovskii, Sov. Phys. -Solid State 15 (1974), 1786.
P. M. Motais, E. Belin and C. Bonnelle, Phys. Rev. B30 (1984), 4399.
K. Ichikawa, A. Nisawa and K. Tsutsumi, Phys. Rev. B34 (1986), 6690.
M. Okusawa, K. Ichikawa, A. Aita and K. Tsutsumi, Phys. Rev. B35 (1987), 478.
]. Friedel, Nuovo Cim. Suppl. 7 (1958), 287.
P. W. Anderson, Phys. Rev. 124 (1961), 41.
0. Gunnarsson and T. C. Li, Phys. Rev. B36 (1987), 9488.
T. Nakano, K. Okada and A. Kotani,]. Phys. Soc. Jpn. 57 (1988), 655.
Y. Kayanuma and A. Kotani, in Ref. 1), p. 72.
S. Tanaka, H. Ogasawara, Y. Kayanuma and A. Kotani,]. Phys. Soc. Jpn. 58 (1989), 1087.
S. Hi.ifner and G. K. Wertheim, Phys. Lett. 51A (1975), 299.
P. C. Kemeney and N. ]. Schevchik, Solid State Commun. 17 (1975), 255.
]. Kanamori, Prog. Theor. Phys. 30 (1963), 275.
D. R. Penn, Phys. Rev. Lett. 42 (1979), 921.
A. Liebsch, Phys. Rev. Lett. 43 (1979), 1421.
F. ]. Himpsel, ]. A. Knapp and D. E. Eastman, Phys. Rev. B19 (1979), 2919.
Electron-Electron Correlation, Resonant Photoemission
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
301
]. Barth, G. Karkoffen and C. Kunz, Phys. Lett. 74A (1979), 360.
M. Iwan, F. ]. Himpsel and D. E. Eastman, Phys. Rev. Lett. 43 (1979), 1829.
U. Fano, Phys. Rev. 124 (1961), 1866.
R. Clauberg, W. Gudat, E. Kisker, E. Kuhlmann and G. M. Rothberg, Phys. Rev. Lett. 47 (1981), 1314.
L. A. Feldkamp and L. C. Davis, Phys. Rev. Lett. 43 (1979), 151.
A. Kotani and Y. Toyozawa, J. Phys. Soc. Jpn. 37 (1974), 912.
]. C. Parlebas, A. Kotani and ]. Kanamori, J. Phys. Soc. Jpn. 51 (1982), 124.
A. Kotani,]. C. Parlebas and]. Kanamori,]. Magn. Magn. Mater. 31·34 (1983), 323.
T. Jo, A. Kotani, ]. C. Parlebas and J. Kanamori, ]. Phys. Soc. Jpn. 52 (1983), 2581.
J. C. Parlebas, A. Kotani and ]. Kanamori, Solid State Commun. 41 (1982), 439.
E. Antonides, E. C. Janse and G. A. Sawatzky, Phys. Rev. B15 (1977), 1669.
]. W. Allen, S. ]. Oh, 0. Gunnarsson, K. Schonhammer, M. B. Maple, M. S. Torikachvili and I. Lindau,
Adv. Phys. 35 (1986), 275.
D. J. Peterman,]. H. Weaver, M. Craft and D. T. Peterson, Phys. Rev. B27 (1983), 808.
J. W. Allen,]. Magn. Magn. Mater. 47&48 (1985), 168.
P. Burroughs, A. Hamnett, A. F. Orchard and G. Thornton, J. Chern. Soc. Dalton Trans. 17 (1976), 1686.
]. C. Fuggle, M. Campagna, Z. Zolnierck, R. Lasser and A. Plateau, Phys. Rev. Lett. 45 (1980), 1587.
E. Beaurepaire, Thesis, Inst. Polytechnique, Nancy-France (1983).
A. Fujimori, Phys. Rev. B28 (1983), 2281, 4489.
E. Wuilloud, B. Delley, W-D Schneider and Y. Baer, Phys. Rev. Lett. 53 (1984), 202.
A. Kotani and ]. C. Parlebas, ]. de Phys. 46 (1985), 77.
]. C. Parlebas and A. Kotani, ]. Appl. Phys. 57 (1985), 3191.
A. Kotani, H. Mizuta, T. Jo and]. C. Parlebas, Solid State Commun. 53 (1985), 805.
G. Kaindl, G. Kalkowski, W. D. Brewer, E. V. Sampathkumaran, F. Holtzberg and A. Schach v.
Wittenau, ]. Magn. Magn. Mater. 47&48 (1985), 181.
W. D. Schneider, B. Delley, E. Wuilloud, J. M. Imer and Y. Baer, Phys. Rev. B32 (1985), 6819.
T. Jo and A. Kotani, J. Phys. Soc. Jpn. 55 (1986), 2457.
T. Jo and A. Kotani, Ref. 1), p. 34.
]. C. Parlebas, T. Nakano and A. Kotani, ]. de Phys. 48 (1987), 1141.
T. Nakano, A. Kotani and J. C. Parlebas, J. Phys. Soc. Jpn. 56 (1987), 2201.
F. Le Normand,]. El Fallah, L. Hilaire, P. Legare, A. Kotani and]. C. Parlebas, Solid State Commun.
71 (1989), 885.
A. Kotani and Y. Toyozawa, ]. Phys. Soc. Jpn. 35 (1973), 1073.
T. Nakano, Thesis, Osaka University (1987).
]. W. Allen, S. ]. Oh, I. Lindau and L. I. Johansson, Phys. Rev. B29 (1984), 5927.
C. Laubschat, E. Weschke, G. Kalkowski and G. Kaindl, Physica Scripta 41 (1990), 124.
K. Okada and A. Kotani, in Ref. 1), p. 64.
A. Fujimori, Japanese Photon Factory Activity Report (1987) Proposal no 86-146.
.S. Tanaka, Y. Kayanuma and A. Kotani,]. Phys. Soc. Jpn. 59 (1990), 1488.
Y. Hayasi, H. Arai and T. Takahashi, unpublished.
L. C. Davis and L. A. Feldkamp, Phys. Rev. B23 (1981), 6239.
A. Liebsch, Phys. Rev. B23 (1981), 5203.
·G. Treglia, F. Ducastelle and D. Spanjaard, ]. de Phys. 43 (1982), 341.
J. Igarashi, ]. Magn. Magn. Mater. 31-34 (1983), 355.
]. Kanamori, Electron Correlation and Magnetism· in Narrow-Band Systems, ed. T. Moriya (Springer
Verlag, 1981), p. 102.
D. Chandesris, ]. Lecante and Y. Petroff, Phys. Rev. B27 (1983), 2630.
T. Jo and A. Kotani, Phys. Rev. B38 (1988), 830.
A. Kotani, H. Ogasawara, K. Okada, B. T. Thole and G. A. Sawatzky, Phys. Rev. B40 (1989), 65.
A. Fujimori and F. Minami, Phys. Rev. B30 (1984), 957.
]. Igarashi, see contribution in the present volume and ]. Phys. Soc. Jpn. 59 (1990), 348, 1868.
G. Gunnarsson, J. W. Allen, 0. Jepsen, T. Fujiwara, 0. K. Andersen, C. G. Olsen, M. B. Maple, J. S. Kang,
L. Z. Liu, ]. H. Park, R. 0. Anderson, W. P. Ellis, R. Liu, ]. T. Markert, Y. Dalichaeuch, Z. X. Shen,
302
73)
74)
75)
76)
77)
]. C. Parlebas, A. Kotani and S. Tanaka
P. A. P. Lindberg, B. 0. Wells, D. S. Dessau, A. Borg, I. Lindau and W. E. Spicer, Phys. Rev. B4l (1990),
4811.
]. Ghijsen, L. H. Tjeng, H. Eskes, G. A. Sawatzky and R. L. Johnson, Phys. Rev. B42 (1990), 2268.
S. Tanaka, Y. Kayanuma and A. Kotani, ]. Phys. Soc. Jpn. 58 (1989), 4626.
T. ]o and A. Kotani, Solid State Commun. 54 (1985), 451.
V. Barnole, ]. M. Mariot, C. F. Hague, C. Michel and B. Raveau, Phys. Rev. B41 (1990), 4262.
A. Kotani and K. Okada, Prog. Theor. Phys. Suppl. No. 101 (1990), 329.