Resonant inelastic soft-x-ray scattering from valence-band excitations in 3d0compounds
S. M. Butorin*
Department of Physics and Measurements Technology, Linko
¨ping University, S-581 83 Linko
J.-H. Guo, M. Magnuson, and J. Nordgren
Department of Physics, Uppsala University, Box 530, S-751 21 Uppsala, Sweden
~Received 27 September 1996!
Ti and Mn L
x-ray ﬂuorescence spectra of FeTiO3and KMnO4were measured with monochromatic
photon excitation on selected energies across the L2,3 absorption edges. The resulting inelastic x-ray-scattering
structures and their changes with varying excitation energies are interpreted within the framework of a local-
ized, many-body approach based on the Anderson impurity model, where the radiative process is characterized
by transitions to low-energy interionic-charge-transfer excited states. Sweeping the excitation energy through
the metal 2pthreshold enhances the ﬂuorescence transitions to the antibonding states pushed out of the band
of continuous states due to strong metal 3d–ligand 2phybridization and matching the low-photon-energy
satellites in the spectra. Based on the energy position of these charge-transfer satellites with respect to the
recombination peak the effective metal 3d–ligand 2phybridization strength in the ground state of the system
can be estimated directly from the experiment. @S0163-1829~97!04508-6#
One of the important goals of various spectroscopies is to
obtain knowledge about the electronic structure in the
ground state of a system. For strongly electron-correlated
systems such as 3dtransition-metal ~TM!, lanthanide, and
actinide compounds, the electronic structure of a system
without a core hole is often described in terms of low-energy
d-d~or f-f) and charge-transfer excitations. Resonant x-ray
ﬂuorescence spectroscopy ~RXFS!with monochromatic pho-
ton excitation has been shown to be a promising technique
for studies of these types of excitations. Neutral d-dexcita-
tions in MnO ~Ref. 1!and charge-transfer ~CT!excitations in
cerium and uranium compounds2have been successfully
studied in our earlier publications using valence-band RXFS.
In this paper we discuss the application of RXFS to studies
of ligand 2p→metal 3dCT excitations in strongly covalent
These CT excitations are usually described within the
framework of an Anderson impurity model which provides a
satisfactory description of various properties of many sys-
tems with localized states. In this model the 3dstates of a
single TM ion with the on-site Coulomb interaction Uare
treated as a degenerate impurity level coupled by the hybrid-
ization strength Vto the ligand 2pband which is separated
by the CT energy D. The interactions between neighboring
impurities are neglected. It is clear then that the ground state
as well as the character of the band gap in insulators can be
described3in terms of relationships between D,U, and Vas
parameters included in the model Hamiltonian. According to
the 1/Nexpansion theory4the effective value of V2is pro-
portional to the number of 3dholes N(Veff;
NV). This is
the reason for strong hybridization effects in the early TM
compounds where Nis large in addition to large bare hybrid-
ization strength V~3dwave functions are more delocalized
compared to those in late TM’s!. In fact, Veff may be large
enough to dictate the ground-state properties. While for late
TM compounds the character of the band gap and its size
depends on values of Dor U, for early TM compounds the
size of the gap is rather determined by the value of Veff .5
Although the unique sets of the model parameters for dif-
ferent TM compounds can be established only by a consis-
tent description of the whole variety of spectroscopic and
transport properties, the spectroscopic data are often used for
a preliminary estimation of the values of these parameters.
Since CT effects produce so-called CT satellites in x-ray
photoemission, absorption, and bremsstrahlung isochromat
spectra of TM compounds, the set of the model parameters
for the ground state of the system is usually derived by ﬁtting
the energy positions and intensities of CT satellites relative
to the main spectral lines. However, based on ﬁrst-principles
calculations, it has been pointed out6that the TM
3d–ligand 2phybridization strength depends on the 3doc-
cupancy and, furthermore, can be strongly affected by the
presence of a core hole. As a result, Vmay be renormalized
in a different way in different spectroscopic experiments. In
this situation, those spectroscopies are particularly useful
where a set of the ﬁnal states of the spectroscopic process
can be described by the model Hamiltonian which couples
excited states with the ground state itself.
In a localized many-particle approach, the ﬁnal states of
the TM 3d→2pﬂuorescence process at the TM 2pthreshold
are the ground state ~the electronic recombination peak!and
low-energy excited states ~the energy loss structures!. The
resulting resonant inelastic x-ray-scattering structures have
constant energy losses with respect to the recombination
peak, but exhibit a dispersionlike behavior on the emitted
photon energy scale upon sweeping the excitation energy
across the TM 2pabsorption edge. Similar information can
be obtained from electron-energy-loss ~EELS!and optical
spectroscopies. However, in contrast to all the dipole-
allowed transitions in the EELS and optical-absorption data,
only the TM 3dstates as eigenvalues for the ground state
PHYSICAL REVIEW B 15 FEBRUARY 1997-IVOLUME 55, NUMBER 7
0163-1829/97/55~7!/4242~8!/$10.00 4242 © 1997 The American Physical Society
Hamiltonian are probed in resonant ﬂuorescence spectra via
creation and/or annihilation of a 2phole. This is especially
useful in the case of multicomponent systems such as
FeTiO3and KMnO4, which were used in the present study
as representatives of the 3d0compounds.
These oxides are expected to be highly covalent systems
so that their ground state can be mainly described as a mix-
ture of 3d0,3d
L, and 3d2L2conﬁgurations, where Lstands
for a hole in the ligand 2pband. Regardless, the crystal-ﬁeld
interaction, the multiplet effects, and the contribution of the
3d2L2conﬁguration, the mechanism of the estimation of
Veff from resonant TM 3d→2pspectra can be demonstrated
by writing a simpliﬁed ground-state Hamiltonian
which at the same time describes the ﬁnal state of RXFS.
The diagonalization of this Hamiltonian gives bonding ~the
ground state!and antibonding states between 3d0and 3d1L
conﬁgurations which are separated in energy by
2. For early TM oxides, D!2Veff , and the energy
separation is mainly determined by the value of Veff , so that
the antibonding states will appear in resonant TM 3d→2p
ﬂuorescence spectra at '2Veff below the recombination
peak. The spectral weight for transitions to these antibonding
states in ﬂuorescence spectra can be enhanced by setting the
excitation energy to the TM 2pabsorption CT satellite,
which is in turn the antibonding combinations between
2p53d1and 2p53d2Lconﬁgurations.7Similar resonances of
antibonding states have been observed2,8 in the Ce 4f→3d
ﬂuorescence spectra of covalent CeO2.
The real situation is, however, more complicated, because
of the hybridization effects from the 3d2L2conﬁguration and
because of existing transitions to nonbonding 3d1Land
3d2L2ﬁnal states.9–11 These transitions may have a speciﬁc
resonant behavior upon sweeping the excitation energy
across the TM L2,3 ~2p→3d,4stransitions!absorption
edges, and may depend on the crystal-ﬁeld symmetry which
is actually different in FeTiO3and KMnO4~see Table I!.In
addition, for early TM compounds, the TM 2pspin-orbit
splitting is smaller than or comparable with 2Veff , giving rise
to a signiﬁcant overlap of the structures of the L3and L2
absorption edges7and hence to a mixing of the TM
3d→2p3/2 and 3d→2p1/2 ﬂuorescence at certain excitation
energies. Furthermore, the resonant inelastic x-ray-scattering
structures overlap with those of nonresonant normal ﬂuores-
cence, which occurs due to direct excitations of core elec-
trons to the continuum or due to relaxation of the system
from the core-excited to core-ionized states. The difﬁculty in
quantitatively estimating the contribution of normal ﬂuores-
cence to the near-threshold excitation spectra complicates the
analysis of the shape of resonant ﬂuorescence.
Despite all these complications, we show that the transi-
tion to the antibonding states can be identiﬁed in the TM
~3d,4s→2ptransitions!ﬂuorescence spectra of
FeTiO3and KMnO4recorded at the excitation energies set
near the TM 2pthresholds, and that Veff in the ground state
of these systems can be estimated from this type of experi-
II. EXPERIMENTAL DETAILS
The measurements were performed at the undulator
beamline 7.0 of the Advanced Light Source, Lawrence Ber-
keley Laboratory, with a spherical grating monochromator14
using an end station described in Ref. 15. A high-resolution
grazing-incidence grating spectrometer16 with a two-
dimensional detector was utilized to measure x-ray ﬂuores-
The FeTiO3~ilmenite!sample was a natural crystal ob-
tained from the mineralogical collection of the Mineralogical
Museum at the Uppsala University. The source of the crystal
is Fedde, Norway. The KMnO4sample was a pressed pellet
prepared from 97% material obtained from Aldrich Chemical
The Ti and Mn L
x-ray ﬂuorescence spectra of
FeTiO3and KMnO4were recorded with a spectrometer
resolution of about 0.8 and 0.5 eV, respectively. The inci-
dence angle of the photon beam was about 20° to the sample
surface, and the spectrometer was placed in the horizontal
plane at an angle of 90° with respect to the incident beam.
The intensity of measured spectra were normalized to the
photon ﬂux. For energy calibration, the V Ll,
transitions!and Mn L
ﬂuorescence lines of the pure met-
als were used as a reference. In order to determine the exci-
tation energies, absorption spectra at the Ti and Mn 2pedges
were measured at the 90° incidence angle by means of total
electron yield and with monochromator resolutions set to
about 0.2 and 0.4 eV, respectively. The x-ray ﬂuorescence
and absorption spectra were brought to a common energy
scale using the elastic peak in the ﬂuorescence spectra re-
corded at the excitation energy set below the absorption
edge. During x-ray ﬂuorescence measurements, the resolu-
tion of the monochromator was about 1.5 eV for KMnO4,
and about 0.5 eV for FeTiO3.
Upon irradiation with x rays, KMnO4gradually decom-
poses with time to compounds with lower oxidation state of
manganese. This can be seen as a transformation of the
L2,3 absorption spectrum of Mn71into that of Mn41.By
measuring x-ray-absorption spectra in the total electron yield
mode, the decomposition rate of KMnO4was studied and
the appropriate periodicity for changing the beam position on
the sample was determined. Prior to x-ray ﬂuorescence mea-
surements the sample surface was scraped, and then the po-
sition of the beam on the sample was changed every 3 min in
order to avoid its decomposition.
Self-absorption is known to affect the shape of ﬂuores-
cence spectra when there is an overlap in energy between the
ﬂuorescence and absorption spectra. Assuming a ﬂat sample
surface and regarding the geometry of our experiment, the
observed intensity is given by
TABLE I. The site symmetry and average metal-oxygen dis-
tance ~in units of Å!in studied compounds.
Compound Symmetry TM2O distance Reference
55 4243RESONANT INELASTIC SOFT-X-RAY SCATTERING . . .
where I0is the unperturbed decay intensity, and
out are the absorption coefﬁcients for the incident and out-
going radiation. We derive the values of these coefﬁcients at
the TM 2pthreshold by normalizing the TM L2,3 absorption
spectra to known values17 below and above the correspond-
ing absorption edges. Based on this procedure the self-
absorption losses are estimated to be less than 15% for all the
III. RESULTS AND DISCUSSION
1. Resonant ﬂuorescence
The Ti L
x-ray ﬂuorescence spectra of FeTiO3re-
corded at different excitation energies near the Ti 2pthresh-
old are displayed in Fig. 1. The resonant part of the Ti
3d→2pﬂuorescence ~hereafter we disregard a contribution
of weak 2p–4stransitions in both x-ray-absorption and ﬂuo-
rescence spectra!exhibits dispersionlike behavior upon
sweeping the excitation energy across the Ti L2,3 absorption
edges, while nonresonant normal ﬂuorescence appears at
constant energy of emitted photons. For an excitation energy
of 458.2 eV, where a contribution of nonresonant normal
ﬂuorescence is expected to be small, one can see that the
spectral structures extend to more than 22 eV below the re-
combination peak. Different structures resonate in a different
way with varying excitation energies. These spectra are in
contrast to what one could expect for purely tetravalent Ti ~a
single line due to the 2p63d0→2p53d1→2p63d0
excitation-deexcitation process!, thus indicating a high de-
gree of covalency of chemical bonds and the signiﬁcance of
theO2p→Ti 3dCT in FeTiO3.
The resonant x-ray ﬂuorescence process for a covalent
3d0compound is shown schematically in Fig. 2, where only
the two lowest electronic conﬁgurations for intermediate and
ﬁnal states are included for simplicity. As a result of strong
TM 3d2O2phybridization in the ground and intermediate
states of this process, there are radiative transitions to the
ﬁnal states which are the bonding ~the ground state!, non-
bonding, and antibonding states between 3d0and 3d1Lcon-
ﬁgurations. The nonbonding states are of the 3d1Lcharacter,
and are not directly coupled to the 3d0state, but transitions
to these states become possible through the intermediate
state. The split-off antibonding state pushed out of 3d1Lcon-
tinuous states by large Vcreates a low-photon-energy CT
satellite in resonant ﬂuorescence spectra.
In order to identify the spectral structures corresponding
to different ﬁnal states, we plotted the Ti L
FeTiO3in Fig. 3 as energy-loss spectra relative to the energy
of the recombination peak. Despite the overlap between the
resonant x-ray inelastic scattering structures and a nonreso-
nant normal ﬂuorescence line which moves toward low en-
ergies upon increasing the excitation energy, some tentative
assignments for the loss structures can be made. The struc-
tures appearing in the energy range between 211 and 24eV
can be attributed to the transitions to nonbonding 3d1L
states. The split-off antibonding satellite, schematically
shown in Fig. 2, is found to be located at about 214.5 eV.
The loss structures at lower energies can be assigned to tran-
sitions to nonbonding 3d2L2states.
The transition rates to different ﬁnal states, and conse-
quently, the intensities of different energy-loss features, de-
pend on the character of the intermediate states which are
represented by the Ti L2,3 absorption spectrum. Within the
ligand-ﬁeld model the main four absorption peaks were as-
cribed to the 2p63d0→2p53d1transitions of the Ti41ion to
the states of t2g~peaks at 458.2 and 463.7 eV!and eg~460.5
and 466.0 eV!symmetry,18 regardless of some distortion of
FIG. 1. The Ti L2,3 x-ray absorption and resonant Ti L
ﬂuorescence spectra of FeTiO3. The arrows on the absorption spec-
trum indicate excitation energies used for ﬂuorescence spectra.
FIG. 2. A schematic representation of the resonant TM
3d→2px-ray ﬂuorescence process for 3d0compounds. The en-
ergy levels which are labeled with electronic conﬁgurations corre-
spond to the average multiplet energies of these conﬁgurations in
the limit of V→0. The shaded rectangles represent the nonbonding
states for the 3d1Land 2p53d2Lconﬁgurations.
BUTORIN, GUO, MAGNUSON, AND NORDGREN
the octachedral crystal-ﬁeld symmetry in FeTiO3.12 In order
to describe the Ti L
spectra of this compound, however,
high covalency of the chemical bonds and CT effects should
be taken into account in the description of the Ti L2,3 absorp-
tion spectrum. Using conﬁguration interaction cluster calcu-
lations, Okada and Kotani7reproduced both the main struc-
tures and high-energy satellites in Ti L2,3 absorption for the
local Ohsymmetry around the Ti ion. They assigned weak
absorption satellites at about 471.5 and 477 eV to the CT
satellites, which are the antibonding combinations between
2p53d1and 2p53d2Lconﬁgurations. The large broadening
of main L2peaks compared to those of L3was shown to be
due to a contribution of transitions to the 2p53d2Lstates.
Recent measurements on CeO2~Refs. 2 and 8!revealed a
resonant enhancement of the CT satellite ~antibonding state
between 4f0and 4 f1Lconﬁgurations!in the resonant Ce
4f→3dx-ray ﬂuorescence spectra when the excitation en-
ergy was set to the Ce 3dabsorption satellite ~antibonding
combination between 3d94f1and 3d94f2Lconﬁgurations!.
Therefore, one can expect similar resonant behavior for the
CT satellite in the resonant Ti 3d→2pﬂuorescence of
FeTiO3. Indeed, for the excitation energy set to the Ti L2,3
absorption satellite at 471.7 eV, there is an enhancement in
the ﬂuorescence weight at about 14.5 eV below the recom-
bination peak, as one can see from the comparison between
the 471.7 and 490.0-eV-excited Ti L
spectra ~Fig. 1!. This
resonance helps to determine the energy of the split-off an-
tibonding state between the 3d0and 3d1Lconﬁgurations ~see
Fig. 2!, and in turn indicates the O 2p→Ti 3dCT character
of the absorption satellite. In light of this, the other proposed
mechanisms to explain the existence of the absorption satel-
lite such as intraligand 2p→3sexcitations19,20 or O
2p→Ti 4sshake-up21 appear to be less probable. The en-
ergy loss of 14.5 eV for the CT satellites in ﬂuorescence
spectra of FeTiO3indicates that the value of Veff in the
ground state of this oxide is more than 7 eV.
When the excitation energy is set to the t2gand egpeaks
in the Ti L3edge, the most intense structures in the energy-
loss spectra of FeTiO3~Fig. 3!appear at 27.5 and 210 eV,
respectively, so that the 2.5-eV energy difference between
them matches the ligand-ﬁeld splitting in this compound es-
timated from the O 1sx-ray-absorption spectra.22 This sug-
gests that the transitions to nonbonding 3d1Lﬁnal states of
the resonant ﬂuorescence process depend on the symmetry of
the core-excited states, unless the observed intense structures
are strongly affected by the nonresonant normal ﬂuorescence
contribution. For an excitation energy of 466.0 eV, the shape
of the Ti L
spectrum ~Fig. 3!in the energy range between
211 and 24 eV resembles that of the valence band in isos-
From optical-absorption measurements the band gap in
MgTiO3was estimated to be 3.7 eV,24 while the ﬁrst energy-
loss structure in the resonant Ti L
spectra of FeTiO3~Fig.
3!is already observed at about 2.5 eV below recombination
peak. A comparison of these spectra with those of rutile
TiO2~Ref. 25!~Fig. 4!clearly indicates the existence of
additional states in the O22→Ti41CT gap of FeTiO 3. For
TiO2, this gap, determined as an energy difference between
the recombination peak and the onset of the intense struc-
tures at low energies, is about 3.0 eV, which is in agreement
with optical data for this oxide.26 In order to show the origin
FIG. 3. The resonant Ti L
x-ray ﬂuorescence spectra of
FeTiO3~dots!, plotted as energy-loss spectra, relative to the energy
of the recombination peak which is set at 0 eV, and the diffuse
reﬂectance spectrum of FeTiO3~solid line!taken from Ref. 27.
FIG. 4. The resonant Ti L
x-ray ﬂuorescence spectra of
FeTiO3~dots!and TiO2plotted as energy-loss spectra.
55 4245RESONANT INELASTIC SOFT-X-RAY SCATTERING . . .
of the in-O22→Ti41CT-gap states in FeTiO 3, we plotted
the diffuse reﬂectance spectrum27 of this compound in Fig. 3.
The spectrum exhibits two strong optical-absorption peaks at
about 21.2 and 22.4 eV, which were attributed in Ref. 27 to
the t2g→egtransition of Fe21and to the Fe21→Ti 41CT,
respectively. The molecular-orbital calculations performed
for the ~FeTiO10)142cluster28 ~a pair of edge-sharing octa-
hedra containing Fe21and Ti41ions, respectively!support
these assignments, thus indicating some Fe-Ti bonding.
Since the Fe21→Ti41CT excitations can be as well probed
in the resonant Ti L
spectra, the structure at about 2.5 eV
below the recombination peak in these spectra can, therefore,
have Fe21→Ti41CT character. Alternatively, this structure
may be interpreted in terms of d-dand CT excitations of
Ti31as a result of possible oxygen vacancies.
2. Nonresonant normal ﬂuorescence
The existence of nonresonant normal ﬂuorescence at ex-
citation energies set to the TM 2pabsorption edge is usually
considered to be due to direct core-electron excitations to the
continuum or due to the Coster-Kronig process. In this case,
the intermediate state is a core-ionized state for the system.
The energy for the onset of continuum states in FeTiO3
can be determined as the energy difference between the Ti
2plevel and the bottom of the conduction band, and can be
estimated from a combination of Ti 2pphotoemission,
valence-band photoemission, and optical spectroscopies. In
order to disregard a contribution of the Fe 3dstates in the
valence and conduction bands, one can use valence-band
photoemission ~the top of the valence band at 23.5 eV!~Ref.
29!and optical data ~the band gap is 3.7 eV!~Ref. 24!for
isostructural MgTiO3. Taking the Ti 2p3/2 binding energy in
FeTiO3to be 459.0 eV ~Ref. 30!, one then ﬁnds that the
onset of the continuum is at 459.023.513.75459.2 eV, i.e.,
about 1 eV above the t2gpeak in the Ti L3absorption edge.
The existence of the prominent 451-eV structure in the
458.2-eV-excited Ti L
spectrum ~as well as in the 460.5-
eV-excited spectrum; see Fig. 1!at the emitted photon en-
ergy close to that for nonresonant normal ﬂuorescence sug-
gests that there might be a relaxation of the system into a
core-ionized state in the intermediate state of the ﬂuores-
cence process, thus resulting in normal ﬂuorescence decay.
One of the relaxation mechanisms which can occur at the
excitation energies set below the onset of the continuum
states was discussed by de Groot, Ruus, and Elango31 in the
framework of CT. In particular, it has been shown that, when
kcorresponds to an electron in the
continuum!relaxation is impossible, the 2p53d2L
kchannel can be energetically allowed. Consid-
ering a signiﬁcant admixture of the 3d1Lconﬁguration in the
ground state of the system ~the 3d1Lcontribution was esti-
mated to be about 48% from the analysis of different high-
energy spectroscopic data5!, the assumption about the relax-
ation origin of the 451-eV structure in the 458.2-eV-excited
spectrum would be reasonable. However, we believe
that this structure is to a large extent due to resonant ﬂuores-
cence. The main argument that this is not a relaxation is the
shape of the ﬂuorescence spectrum ~Fig. 1!recorded at the
excitation energy of 462.5 eV ~in a dip between L3and L2
absorption lines!. The spectrum exhibits a similar intense
structure at about 7 eV below the recombination peak, while
the excitation energy is set below the 2p1/2→3dmultiplet18
and, hence, no L
normal ﬂuorescence can be observed as a
result of the relaxation process mentioned above. Further-
more, this structure can hardly be attributed to so-called Ra-
man scattering below the Ti L2absorption edge, because
such Raman-scattering spectra are usually quite broad. On
the other hand, 2p53d2Lstates have been shown7to contrib-
ute to the region between the egline of L3and the t2gline of
L2so that the high-energy part of the 462.5-eV-excited Ti
spectrum most likely belongs to resonant ﬂuorescence
as a result of the decay of these states.
At an excitation energy of 490.0 eV, nonresonant normal
ﬂuorescence dominates in Ti L
spectra of FeTiO3. The
main maximum at about 450.5 eV can be assigned mainly to
2p53d1L→2p63d0Ltransitions. The energies of the most
intense transitions can be estimated from simple energetical
considerations. The strongest peak of Ti 2pphotoemission
which has mainly 2p53d1Lcharacter7,9 is located at 459.0
eV.30 Assuming the binding energy of the 3d0Lmaximum to
be about 8 eV, which is similar to what was found for
TiO2from resonant valence-band photoemission data,10,32
we obtain 459.0–8.05451.0 eV as the emission energy for
the intense 2p53d1L→2p63d0Ltransitions. In addition, it
has been shown7,9 that the Ti 2pphotoemission spectrum
contains a signiﬁcant amount of 2p53d2L2component,
which may in principle decay radiatively. Therefore, one can
expect some contribution of 2p53d2L2→2p63d1L2transi-
tions to the normal ﬂuorescence spectrum.
The normal ﬂuorescence structures also originate from so-
called shake-up, shake-off, and 2p1/22p3/23dCoster-Kronig
processes. At high excitation energies a contribution of these
processes to normal ﬂuorescence is mainly determined by
the admixture of the 3d2L2conﬁguration in the ground state
of the system, giving rise to 2p53d1L2→2p63d0L2transi-
tions. At excitation energies set to the 2p1/2 threshold, the
2p1/22p3/23dCoster-Kronig process also leads to
due to the 3d1Land 3d2L2components in the ground state.
An enhancement of normal L
ﬂuorescence due to this
Coster-Kronig decay upon sweeping the excitation energy
across the L2edge is, however, not signiﬁcant, as one can
see in Fig. 1.
1. Resonant ﬂuorescence
For KMnO4, the Mn 2pspin-orbit splitting is comparable
with 2Veff . Therefore, it is difﬁcult to identify charge-
transfer satellites in the Mn L3absorption edge33,34 because
of the overlap of these satellites with Mn L2structures. In
this case, the sensitivity of the radiative decay and the shape
of resonant Mn L
spectra to the character of core-excited,
intermediate states is especially useful. These Mn L
tra of KMnO4recorded at various excitation energies across
the Mn 2pthreshold are displayed in Fig. 5. At excitation
energies set to the Mn L3edge ~640.5 and 644.9 eV!an
overall shape of the Mn L
spectra, consisting of the recom-
bination peak, prominent structure a few eV below it, and
low-energy tail is similar to that of resonant Ti L
FeTiO3, despite differences in the crystal structure of these
compounds.12,13 For the tetrahedral symmetry of the crystal
4246 55BUTORIN, GUO, MAGNUSON, AND NORDGREN
ﬁeld the eg-derived states of the 2p53d1multiplet split to-
ward low energies, so that the main Mn L3and L2absorption
peaks in KMnO4have mostly t2g-like character.33 As in the
case of FeTiO3, the shape of resonant Mn L
KMnO4indicates a strong covalency of the Mn-O chemical
bonds in the latter compound.
In order to see similarities and differences between optical
absorption, electron-energy-loss, and resonant Mn L
tra of KMnO4, we placed all of them on the same energy
scale in Fig. 6. The shape of the resonant part of the Mn
ﬂuorescence within 10 eV below the recombination peak
is somewhat similar to that of optical absorption, although
ﬁne structures in x-ray ﬂuorescence spectra are smeared out
due to a signiﬁcant spread of the excitation energy and due to
experimental broadening from the spectrometer. It is known
that the shape of resonant ﬂuorescence spectra is sensitive to
the width of the excitation energy.37 For KMnO4, this width
~1.5 eV!in x-ray ﬂuorescence measurements was three times
larger than that ~0.5 eV!for FeTiO3. As a result, the insu-
lating gap of KMnO4, which was estimated to be only about
1.6 eV based on transport38 and EELS ~Refs. 35 and 39!data
is completely smeared out in resonant Mn L
Referring to the discussion for FeTiO3, the spectral
weight of resonant Mn L
ﬂuorescence of KMnO4within
;10 eV below the recombination peak can be associated
with transitions to nonbonding 3d1Lstates. The difference in
energy of the prominent structures at 5.5–7 eV below the
recombination peak between the 640.5- and 644.9-eV-
excited ﬂuorescence spectra and between the 649.0- and
655.6-eV-excited spectra is similar to the value of the ligand-
ﬁeld splitting (;1.5 eV!in KMnO4, as determined from O
We ﬁnd the CT satellite ~an antibonding combination be-
tween 3d0and 3d1Lconﬁgurations!in resonant x-ray scat-
tering of KMnO4~Fig. 6!to be located at about 213 eV,
based on resonances which are observed at this energy in the
649.0- and 655.6-eV-excited spectra. Although, for the
former spectrum, this resonance appears at an energy close to
that of normal ﬂuorescence ~see also Fig. 5!, it cannot en-
tirely originate from the normal ﬂuorescence transitions. The
contribution of these transitions to the 649.0-eV-excited
spectrum is expected to be small based on the analysis of the
nonradiative decay for the same excitation energy. The nor-
mal Auger line, a counterpart of the normal ﬂuorescence
decay, is fairly weak in the corresponding resonant photo-
emission spectrum of KMnO4.34
The enhancement of the spectral weight at about 213 eV
in the 655.6-eV-excited Mn L
spectrum of KMnO4~Fig.
6!cannot be caused by the 2p1/22p3/23dCoster-Kronig pro-
cess, which becomes possible at excitation energies set to the
L2edge. As for FeTiO3this process can give rise only to
and, thus, is expected to enhance the nonresonantlike,
FIG. 5. The Mn L2,3 x-ray absorption and resonant Mn L
x-ray ﬂuorescence spectra of KMnO4. The arrows on the absorption
spectrum indicate excitation energies used for ﬂuorescence spectra. FIG. 6. The resonant Mn L
x-ray ﬂuorescence spectra of
KMnO4plotted as energy-loss spectra, relative to the energy of the
recombination peak which is set at 0 eV, and the electron-energy-
loss spectrum of KMnO4~Ref. 35!recorded at the primary electron
energy of 25 eV. The optical-absorption spectrum of an aqueous
solution of KMnO4is taken from Ref. 36.
55 4247RESONANT INELASTIC SOFT-X-RAY SCATTERING . . .
line. Since the 3d1L1conﬁguration is likely to be
dominant in the ground state of KMnO4, the 2p1/22p3/23d
Coster-Kronig decay with excitation at the Mn 2p1/2 thresh-
old should lead to a spectral weight enhancement in the
photon-energy range of the main nonresonantlike L
(;637.6 eV on the photon-energy scale!which corresponds
mainly to 2p53d1L1→2p63d0L1transitions ~see below!.A
further argument against the Coster-Kronig origin of the
structure at 213 eV in the 655.6-eV-excited Mn L
trum ~Fig. 6!comes from the analysis of the shape of this
spectrum between 210 and 0 eV. If the 2p53d2Land
2p53d3L2components of the intermediate state decayed
mostly through the Coster-Kronig process then the intensity
of the 3d1Lstructure at 27 eV would be strongly suppressed
with respect to that of the recombination peak. The corre-
sponding Mn L
spectrum, however, shows the opposite
behavior: the 3d1Lstructure is intense, and the recombina-
tion peak is weak. Thus, taking into account the arguments
discussed above, the resonances 213 eV in the 649.0-eV-
and 655.6-eV-excited spectra ~Fig. 6!can be regarded as a
manifestation of the CT satellite, which is an antibonding
combination between 3d0and 3d1Lconﬁgurations.
For KMnO4, this satellite, as well as the one correspond-
ing to transitions to the nonbonding 3d2L2states, have
smaller energy losses with respect to the recombination peak
than those for FeTiO3~13 eV versus 14.5 eV for the former
satellite, and 18 eV versus 22 eV for the latter one!. The
observed energy differences can be tentatively explained by
a difference in the value of Dbetween these compounds. D
is expected to be smaller in KMnO4due to the higher oxi-
dation state for TM and, hence, higher covalency of TM-O
chemical bonds than those in FeTiO3. For oxides of tetrava-
lent Ti such as TiO2and SrTiO3, the values of Dand U,
estimated from the analysis of various high-energy spectro-
scopic data5,10 are 4.0 and 4.5 eV, respectively. Assuming
Uto be the same in KMnO4and taking Veff57.0 eV, one
can roughly estimate the value of Din this compound by
diagonalizing a simpliﬁed Hamiltonian so that its eigenval-
ues match the energies of the resonant ﬂuorescence struc-
tures associated with transitions to both nonbonding and an-
tibonding states between different electronic conﬁgurations
with respect to the recombination peak. This gives about 2
eV for the value of Din KMnO4.
2. Nonresonant normal ﬂuorescence
In KMnO4the chemical potential is located close to the
bottom of the conduction band.35 Therefore, the onset of the
continuum states in the Mn 2pabsorption spectrum of this
compound can be expected to be at about 645.5 eV based on
the same value for the Mn 2p3/2 binding energy as deter-
mined from core-level x-ray-photoemission spectroscopy.34
Indeed, the appearance of the normal Auger line, correspond-
ing to the decay from the core-ionized state, was detected in
resonant photoemission spectra of KMnO4only at excitation
energies higher than 645.5 eV.34 Accurate quantitative esti-
mations of the contribution of normal ﬂuorescence into Mn
spectra excited at different excitation energies near the
Mn 2pthreshold are, however, hampered due to an overlap
of structures belonging to normal ﬂuorescence with resonant
inelastic x-ray-scattering structures.
For an excitation energy of 716.5 eV, normal ﬂuorescence
dominates in the Mn L
spectrum of KMnO4. The spec-
trum is similar to those obtained earlier40,41 on samples
cooled with liquid nitrogen using x-ray tubes as a source of
the radiation. Expecting the main Mn 2p3/2 photoemission
line to have largely 2p53d1Lcharacter, and based on the
energy difference between this peak (;645.5 eV!and the
3d0Lmaximum (;7.5 eV!in resonant Mn 3d
photoemission,36 one can assign the main peak (;647.6 eV!
in the normal Mn L
ﬂuorescence spectra to
2p53d1L1→2p63d0L1transitions. This peak is accompa-
nied by a high-energy shoulder which is more pronounced
than that in the normal ﬂuorescence spectra of FeTiO3. Since
the 3d2L2and 2p53d2L2admixtures in the ground and in-
termediate states of the ﬂuorescence process should be larger
in KMnO4compared to those in FeTiO3, this may be the
reason for the increase in the intensity of the shoulder as a
result, for example, of 2p53d2L2→2p63d1L2transitions.
To summarize, the TM L
x-ray ﬂuorescence spectra of
FeTiO3and KMnO4recorded at excitation energies set in
the vicinity of the TM 2pthreshold exhibit features which
suggest the validity of the localized, many-body description
of the resonant TM 3d→2pﬂuorescence process in these
compounds. In particular, speciﬁc spectral changes with
varying excitation energies can be explained based on the
Anderson impurity model, so that resulting inelastic x-ray-
scattering spectra are associated with transitions to the low-
energy interionic CT-excited states. The corresponding
analysis of these spectra gives the estimates for the value of
TM 3d-O 2phybridization strength used in a set of model
parameters to describe the ground state of the studied sys-
At the same time, the existence of the large spectral
weight in all the recorded ﬂuorescence spectra at the photon
energies close to that of normal L
ﬂuorescence may be an
indication of partial relaxation to the core-ionized state in the
intermediate state of the resonant ﬂuorescence process as a
result of a signiﬁcant degree of the 3ddelocalization in the
We would like to thank Dr. P. Nysten for providing the
FeTiO3crystal. S.M.B. acknowledges fellowship support
from the NFR ~the Swedish Natural Science Research Coun-
cil!. This work was supported by NFR and Go
son Foundation for Research in Natural Sciences and Medi-
cine. The experiments at ALS were also supported by the
director, Ofﬁce of Energy Research, Ofﬁce of Basic Energy
Science, Material Science Division of the U.S. Department
of Energy, under Contract No. DE-AC03-76SF00098.
4248 55BUTORIN, GUO, MAGNUSON, AND NORDGREN
*Also at MAX-lab, University of Lund, Box 118, S-221 00 Lund,
Sweden. On leave from the Institute of Metal Physics, Ekaterin-
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55 4249RESONANT INELASTIC SOFT-X-RAY SCATTERING . . .