Unoccupied electronic states in CaB6 studied by density functional theory and EELS measurements

Article abstract of DOI:10.1103/PhysRevB.69.214419

The electronic structure of CaB₆ has recently attracted great interest because of the discovery that this compound is unexpectedly ferromagnetic and exhibits a surprisingly large thermoelectric effect. We have concentrated on studying the unoccupied electronic states by investigating the boron 1s core-level spectroscopy. Comparison of our data from electron energy-loss spectroscopy with that from x-ray absorption spectroscopy using the total electron yield mode reveals evidence for sample inhomogeneity. The ab initio band structural method has been successfully applied to simulate the overall features found in the boron 1s absorption spectrum. Correlation with the results of a ground state energy-band calculation allows the interpretation of the spectral features in terms of the density of states of the unoccupied conduction band, in particular the identification of a feature associated with hybridization of Ca d orbitals with B p orbitals. This interpretation is confirmed by comparison with similar calculations for related boride systems. However, simulation spectral data cannot be reconciled with high-resolution experimental data at the absorption threshold. The possibility of either the failure of the theoretical method employed to account for many-body effects and/or the need for improved experimental measurements is discussed.

Full text of DOI:10.1103/PhysRevB.69.214419

PHYSICAL REVIEW B 69, 214419 (2004)
Unoccupied electronic states in CaB6 studied by density functional theory and EELS
measurements
Shang-Peng Gao, Jun Jiang, Minghe Cao, Jing Zhu, and Jun Yuan
*
Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
(Received 7 October 2003; revised manuscript received 25 March 2004; published 22 June 2004)
The electronic structure of CaB6 has recently attracted great interest because of the discovery that this
compound is unexpectedly ferromagnetic and exhibits a surprisingly large thermoelectric effect. We have
concentrated on studying the unoccupied electronic states by investigating the boron 1s core-level spectros-
copy. Comparison of our data from electron energy-loss spectroscopy with that from x-ray absorption spec-
troscopy using the total electron yield mode reveals evidence for sample inhomogeneity. The ab initio band
structural method has been successfully applied to simulate the overall features found in the boron 1s absorp-
tion spectrum. Correlation with the results of a ground state energy-band calculation allows the interpretation
of the spectral features in terms of the density of states of the unoccupied conduction band, in particular the
identification of a feature associated with hybridization of Ca d orbitals with B p orbitals. This interpretation
is confirmed by comparison with similar calculations for related boride systems. However, simulation spectral
data cannot be reconciled with high-resolution experimental data at the absorption threshold. The possibility of
either the failure of the theoretical method employed to account for many-body effects and/or the need for
improved experimental measurements is discussed.
DOI: 10.1103/PhysRevB.69.214419
PACS number(s): 75.50.Dd, 71.20.Ϫb, 78.20.Bh
I. INTRODUCTION
the mechanisms involved in n-type thermoelectric conver-
sion depends on a detailed knowledge of the electronic struc-
ture, in particular the nature of the unoccupied density of
states (DOS) at the bottom of the conduction band.
CaB6 consists of a three dimensionally interconnected bo-
ron atom octahedron (B6) network, where each octahedron is
stabilized by two extra electrons provided by the Ca atoms
occupying the interstitial sites in the boron network. It is an
important industrial material and has recently attracted a lot
of interest because of the discovery that this compound ex-
hibits weak high-temperature ferromagnetism1 when doped
by La, a trivalent rare earth element. Similar magnetic effects
The electronic structure of CaB6 has been studied both
experimentally14,15 and theoretically.16–19 Most studies have
concentrated on the occupied states and the possible exis-
tence of a semiconducting gap at the Fermi level. Electronic
structure calculations in the local density approximation
(LDA) for CaB6 yield a semimetallic ground state, with a
small overlap between the valence band and the conduction
band at the X point of the Brillouin zone.16,17 A more sophis-
ticated calculation of the single-particle excitation spectrum
of CaB6 employing the GW approximations,20 based on the
pseudopotential plane wave method, suggests that this com-
pound is a semiconductor, with a rather large band gap of
0.8 eV.18 However, a more recent GW approximation calcu-
lation based on the linear-muffin-tin-orbital (LMTO) method
by Kino et al. shows that electron correlation does not open
a band gap.19 X-ray photoemission spectroscopy has been
used as a probe of the density of states of the occupied va-
lence band, while x-ray absorption spectroscopy (XAS) has
been used as a probe of the unoccupied conduction band
states, both measurements suggesting that stoichiometric
CaB6 is a semiconductor.14 The band structure determined by
angular resolved photoemission spectroscopy (ARPES)
shows a 1 eV energy gap at the X point.14,15 However, the
x-ray absorption data also indicate that the surface of the
crystals used in these studies may have been oxidized.14
Determination of the intrinsic electronic structure of CaB6
is experimentally challenging because of possible inhomoge-
neities in the CaB6 system, particularly in the near surface
layer.10,21 Since both photoemission and x-ray absorption
spectroscopies are broad area techniques and probe only the
near surface region of samples, alternative bulk-sensitive
1
have also been detected in La-doped SrB6 and BaB6 . In
addition, it has been found that the Ca-deficient variant
Ca1−␦B6 is also ferromagnetic.2 In all these compounds, no
conventionally magnetic elements with either a partially
filled d band or f band are present.
Several theoretical approaches have been proposed to un-
derstand the high-temperature ferromagnetism.1,3–5 For some
of them, the correlation between the electronic band structure
and magnetic properties is crucial. For example, ferromag-
netism has been attributed to a peculiar property of a dilute
electron gas within the framework of carriers in the conduc-
tion band induced by La doping in an otherwise semimetallic
system.6 Alternatively, it has also been suggested that the
ferromagnetism may be associated with a doping-induced
departure from an excitonic ground state.3,5,7 For other ex-
planations, the role of variation in chemical composition (Ca
or B vacancies),2,8,9 defects,8 or impurities10 has been em-
phasized.
Measurements have also shown that both stoichiometric
CaB6 and nonstoichiometric Ca1−␦B6 have large thermoelec-
tric power at room temperature.11,12 The high negative values
of the thermoelectric power for both materials indicate a low
concentration of itinerant n-type charge carriers.11 La- (or Y-)
doped CaB6 is also predicted to be a candidate for an n-type
thermoelectric conversion material.13 The understanding of
0163-1829/2004/69(21)/214419(9)/$22.50
69 214419-1
©2004 The American Physical Society

GAO, JIANG, CAO, ZHU, AND YUAN
PHYSICAL REVIEW B 69, 214419 (2004)
probes for the intrinsic electronic structure of these materials
are highly desirable. As a part of a wide-ranging research
program investigating the origin of its weak ferromagnetism,
we have employed EELS to investigate the chemical and
electronic structural change in CaB6. The B K edge is an
ideal signal for EELS study, as good signal-to-noise ratios
can be easily achieved on account of the high excitation
cross section associated with the low energy loss involved
(188 eV at the B 1s absorption threshold). For our experi-
mental conditions, where small-angle scattering dominates,
the information obtained with EELS is equivalent to that
from XAS, apart from an angular integration factor. With
high-energy electrons propagating through the whole thick-
ness of the thin film sample, EELS is, however, more sensi-
tive to the electronic structure of the bulk material. In con-
junction with high-resolution transmission electron
microscopy (HRTEM), EELS can also reveal spatially re-
solved information about chemical composition and elec-
tronic structure on a nanometer scale, making it a suitable
technique to study CaB6 samples that also contain impurity
phases.
Although the B 1s absorption edges have not been as
extensively studied as C 1s absorption signals, the fine struc-
tures known for several materials show that the B 1s absorp-
tion edges are sensitive to the environment and bonding of
the excited atom.22–29 In order to correlate the fine structure
in the B 1s core-level absorption edge with the electronic
structure in CaB6, we have also carried out simulation of
EELS data. A comparison between the experimental and the-
oretical spectra shows excellent overall agreement, revealing
the effects of Ca hybridization on electron energy-loss near-
edge fine structure (ELNES). The transition into the states
near the Fermi level has also been investigated carefully. A
discrepancy between the theory and experiments indicates
the inadequacy of current single-particle EELS calculations,
as well as the need for better high-resolution experimental
data at the Fermi level.
Chemical analysis by energy dispersive spectrometry con-
firmed that the investigated grains were CaB6. The energy
resolution (measured as the full width at half maximum of
the zero-loss peak) was typically 1.6–1.8 eV. The pre-edge
background was subtracted using a standard power-law
extrapolation30 method. Spectra were deconvolved of mul-
tiple scattering effects using the Fourier-ratio method30, with
the low-loss contribution measured separately.
III. THEORETICAL METHOD
A. Single-particle electronic structure calculation
The B 1 s absorption calculation was based on a plane-
wave pseudopotential method in the framework of density
functional theory31 (DFT) using a generalized gradient ap-
proximation (GGA). The Vanderbilt ultra-soft ionic
pseudopotential32 was employed for the representation of the
atomic cores. The gradient-corrected functional [Perdew-
Wang 1991 (PW91)] exchange-correlation approximation33
was employed, both in the pseudopotential generation and in
the self-consistent band-structure calculations. The calcula-
tion was performed using the experimental lattice constant
͑4.146 Å͒.16 A plane-wave cutoff of 450 eV was used. The
Brillouin zone integration was carried out on an equivalent
Monkhorst-Pack k-point mesh34 with 216 k points used in
the first Brillouin zone for the ground state calculation. The
local basis consisted of the 2s, 2p orbitals for B, and of the
3s, 3p, 3d, and 4s orbitals for the Ca atoms.
The total density of states (TDOS) was obtained directly
from the band structure of the self-consistent calculation.
The band structure calculation was carried out non-self-
consistently for each band line, i.e., a Harris-type calculation,
where the electron density is not updated, using the self-
consistent electron density as an input.
B. Near-edge structure calculation
The electron energy-loss cross section is given by the
Fermi golden rule30
II. EXPERIMENT
2
d2I
4␥2
a02
៝ ៝
q2
͗f͉exp͑iq · r͉͒i͘
=
␦͑E − E − E͒, ͑1͒
f i
ͯ ͯ
͚
CaB6 powder samples were prepared according to the fol-
lowing boron-reduction solid-state reaction:
d⍀dE
f
៝
where q is the wave vector of the momentum transfer during
an electron-energy loss event, a0 is the Bohr atomic radius, ␥
is the relativistic correction factor, and ͉i͘ and ͗f͉ are the
initial and final states respectively, of the excited electron in
the sample.
In the single-particle calculation, all electrons (taking the
total number to be N) are treated as independent, with the
mutual interactions being taken into account through a self-
consistent mean-field potential. Thus the total wave function
can be written as a product of N single-particle wave func-
tions. The initial and the final states involved in a single-
particle excitation (such as for a core electron excitation) can
then be written as
CaO + 7B → CaB6 + BO.
The synthesis was carried out using spectra-pure CaO and B
at 1450°C under an Ar atmosphere. X-ray diffraction
showed that the resulting compound was single phase, and
measurement by a vibration magnetometer at room tempera-
ture showed that the compound was ferromagnetic, with a
saturation moment of 2.29 emu/mol. Sintered samples were
either ion beam thinned or simply crushed between glass
plates to produce electron beam transparent specimens.
Electron energy-loss spectroscopy was performed in a
JEOL 2010F transmission electron microscope operating at
200 kV with a thermally assisted field-emission gun. The B
1 s core-level absorption spectra were obtained with an en-
ergy dispersion of 0.3 eV per channel, with a nearly parallel
electron beam, with a spectrometer collection semiangle of
3.4 mrad, and with the microscope in diffraction mode.
͉i͘ = ͉Nth͉͘N − 1͘, ͉f͘ = ͉N*th͉͘N − 1͘,
͑2͒
where the Nth electron is directly excited by the external
perturbation associated by the passage of fast electrons. The
214419-2

UNOCCUPIED ELECTRONIC STATES IN CaB6…
PHYSICAL REVIEW B 69, 214419 (2004)
initial and final states in Eq. (1) can then be replaced by the
initial and final states, respectively, of the excited (Nth) elec-
tron, as provided by the single-particle calculation.
Strictly speaking, the one-electron eigenvalues derived
from the Kohn-Sham density functional theory cannot for-
mally be interpreted as quasiparticle energies. In practice,
however, the band structures resulting from such calculations
have been found to be very useful in interpreting the electron
spectroscopy of solids.35 We have adopted a similar compu-
tational approach, bearing in mind this limitation, particu-
larly with regard to the inability to fully take into account the
many-body interactions.
projection radius for the B 1s core-level spectroscopy calcu-
lation was chosen as 0.26 Å. The energy dependence of the
radial matrix element is ignored in our approach, but it usu-
ally has only a very small effect.37.
C. Core-hole effect
The core-hole effect35–40 arises because an additional at-
tractive potential emerges during the excitation process, due
to an inadequate screening of the nuclear charge after the
removal of an excited electron from the core level. To model
the excited atom in which the hole is localized, a pseudopo-
tential for excited states was specially constructed by reduc-
ing the occupation of the core level (the 1s state for the B 1s
absorption calculation) of the reference configuration by one,
i.e., using a 1s12s22p2 atomic reference configuration for bo-
ron. To minimize the mutual interaction of excited centers in
the nearest cells, a supercell containing 2ϫ2ϫ2 primitive
cells was constructed in which only one atom was excited.
The minimum distance between neighboring excited atoms
was 0.83 nm; this was found to be large enough to avoid
interactions between excited centers located in neighboring
supercells. A plane-wave cutoff of 360 eV was used. This
value is slightly lower than that used for the ground state
calculation, in order to reduce the calculation overhead. The
effect on convergence of PDOS features has been carefully
tested. For the supercell calculation, 64 k points were used
for the first Brillion zone.
For small-angle scattering, the dipole transition dominates
and the transition matrix can be approximated as
៝ ៝
៝ ៝
͗f͉exp͑iq · r͉i͘ Ϸ i͗f͉q · r͉i͘.
͑3͒
As we are dealing with an inner-shell excitation, the initial
state of the excited electron can be approximated by the
atomic equivalents with well-defined orbital angular momen-
tum quantum numbers. The angular integrals in the matrix
element calculation then lead to the dipole selection rule
⌬l= ±1 for the accessible final state. The radial integrals are
determined by the radial overlap between the core and the
conduction-band wave functions. The core-level spectra are
normally considered therefore to be proportional to the site-
and angular-momentum-projected density of the final states
of the excited electron. In the present work, we have used the
local partial density of states (PDOS) of the pseudopotential
single-particle calculation to interpret the near-edge fine
structure for CaB6. The radial projections were approximated
IV. RESULTS
as ͗⌿͉S͉␾ ͘; thus, one-electron wave functions were pro-
atom
A. Electronic structure of CaB6
jected onto the core atomic orbital ͑␾ ͒ at the site of the
atom
excited atom. Note that S is a Hermitian overlap operator,
taking care of the ultrasoft nature of the pseudopotential
employed.32 We have mimicked the effect of the radial ma-
trix element by choosing the projection-sphere radius S␣ be
similar to the radial extension of the core-state wave function
involved.36 Taillefumier et al.37 calculated the Si d and O p
DOS using an integration sphere of 0.4 Å radius; the result-
ing PDOS’s were similar to the result from a direct matrix
element calculation. In our case, projected-sphere radii of
0.13 Å, 0.26 Å, 0.53 Å, and 1.15 Å have been tested to
check the influence of the choice of cutoff radius on the
projected local DOS. All of these projected-sphere radii are
larger than the probable radius of the B 1s core orbital of
0.11 Å. The value of the radial function of the B 1s core
state decreases to one-tenth of the maximum value at 0.59 Å,
and to 1% at 0.94 Å. The projected local DOS results were
similar, except for the case of 1.15 Å, indicating that the
calculated PDOS is insensitive to the size of the cutoff radius
when this radius is small. Our calculation, employing a
1.15 Å cutoff radius, produces a reasonable number of the
total occupied electrons and was used to produce the total
DOS and the partial DOS. However, the integration volume
obtained using this value is much larger than the spatial ex-
tent of the B 1s orbital, and the corresponding cross-section
calculation shows an overestimation of absorption intensities
for the low excitation energy compared to the results for
0.13 Å, 0.26 Å, and 0.53 Å. In the following results, the
The calculated band structure of CaB6 is shown in Fig.
1(b), and is in overall agreement with other calculated
results.16–19 To facilitate understanding of the overall features
of the band structure, we have also plotted the corresponding
band structure for a “fictitious” B6 cluster framework crystal
(obtained with all the Ca atoms removed from the CaB6 crys-
tal) and for the isostructural compound LaB6. The dominant
features of the band structure, particularly for the valence
band, can be attributed to the electronic states of the three-
dimensionally interconnected B6 clusters. The main effect of
metal atom additions (Ca and La) is to shift the Fermi level
upwards in accordance with the electron counting rule,
where each Ca (La) atom donates 2 (3) electrons to the va-
lence band. However, the dispersion of the “B6”-related band
also changes significantly in addition to the presence of ad-
ditional levels in the conduction band due to Ca or La atoms.
Our DFT-GGA calculation shows that the valence band and
the conduction band are just touching at the X point at the
Fermi level. In comparison, DFT-LDA results16,17 show a
slight band overlap. A GW-approximated band structure
starting from a LDA calculation performed with a plane
wave basis and using norm-conserving pseudopotentials has
suggested that CaB6 is a semiconductor with a band gap of
0.8 eV.18 Another GW calculation using LMTO wave func-
tions as inputs, however, shows no such gap.19 These con-
flicting results indicate that the details of the band structure
near the Fermi level are clearly very sensitive to the way that
214419-3

GAO, JIANG, CAO, ZHU, AND YUAN
PHYSICAL REVIEW B 69, 214419 (2004)
FIG. 1. The single-particle electronic band structure for a fictitious octahedron B6 crystal (a), CaB6 (b), and LaB6 (c) calculated using the
pseudopotential plane-wave method.
the many-body correction41 is introduced. Nevertheless,
throughout the Brillouin zone, the band dispersion in our
DFT-GGA calculation is similar to that of the reported DFT-
LDA and GW data. Thus, the electronic state relative to
ground state properties may still be interpreted by our DFT-
GGA pseudopotential plane wave calculation, particularly
for states away from the Fermi levels, even though the band
gap as a many-body property may not be well reproduced in
the present single-particle ground state calculation.
The total and partial DOS profiles of CaB6 are shown in
Fig. 2. As we are primarily interested in the fine structure of
the B 1s core-level absorption spectrum, we have plotted the
DOS profile with a 0.4 eV broadening, in order to obtain an
overview. The total DOS is given in panel (a), showing that
the Fermi level is located in a region of low density of states,
with the additional electrons occupying the strongly dis-
persed conduction band (see Fig. 1). The valence bands are
mainly composed of the boron orbitals, as shown in panel (b)
for boron s and in panel (c) for boron p symmetry-projected
DOS. The nature of the site and angular-momentum projec-
tions is different in the conduction band region, where a
prominent peak in the calcium 3d PDOS exists as shown in
panel (f). The Ca s and p PDOS do not make any important
contribution over the energy range concerned; to show them,
they have been enlarged 30 times in panels (d) and (e). The
valence states with Ca p-like PDOS are mainly localized at a
deep energy range, about 22 eV below the Fermi level (2p
semicore state), and a few eV above the Fermi level. A com-
parison with the TDOS of the fictitious “B6” compound is
shown in Fig. 3, where the valence band DOS resembles that
of CaB6, in agreement with our analysis of Fig. 1. This simi-
larity shows that the Ca atom plays mainly an ionic role,
with charge transfer from its s, p, and d states. However,
hybridization of boron p orbitals with its empty 3d states
does have some influence on the structure of the density of
states near the Fermi level, as the mixing of the two are
significant over this energy range. This behavior is different
from other semimetallic systems where the states near the
Fermi level are dominated by one angular symmetry compo-
nent (e.g., pz in graphite), and may be responsible for the
observed sensitivity of the calculations to the different meth-
ods of incorporating the many-body perturbations19.
In discussing the possible intrinsic mechanisms of ferro-
magnetism in CaB6, it is important to know the Fermi level
FIG. 2. The total density of states (TDOS) curve for CaB6 (a)
and the symmetry-projected density of states for the boron atomic
site (b) and (c), and for the calcium atomic site (d)–(f).
FIG. 3. Total density of states (TDOS) for the fictitious B6 oc-
tahedral crystal (lower panel) compared with that for CaB6 (upper
panel).
214419-4

UNOCCUPIED ELECTRONIC STATES IN CaB6…
PHYSICAL REVIEW B 69, 214419 (2004)
separation. The dominant peak c in the spectra is modified
both in its energy position and in its shape by the core-hole
interaction. At high energies, the width of the peak d is only
slightly adjusted, and the shape of the peak e remains un-
changed.
C. Experimental result and comparison
The experimental spectrum in Fig. 4(III) is taken from an
area within a single CaB6 grain to minimize the contribution
from intergranular phases with different chemistry (a detailed
microstructural investigation will be reported elsewhere).
The shape of the spectrum is very similar to that reported by
Hoffmann et al.25 A careful examination of spectra taken
from different regions of the specimen shows, however, that
the relative intensity of the experimental peak b sometimes
varies. For previously published XAS experimental spectra14
[reproduced as a dashed line in Fig. 4(III)] obtained using the
total electron yield method (TEY), a sharp peak appears at a
similar energy. This peak has been attributed to surface bo-
ron oxide.14 This shows that although XAS is more bulk-
sensitive than photoemission experiments, the influence of
surface contamination and from intergranular phases can still
have a significant effect on x-ray absorption spectra taken
from a large surface area. The close resemblance between the
energy position of the sharp peak in the TEY spectra and of
the intensity-varying peak b suggests that these peaks may be
of the same origin. The comparatively weaker signal seen in
the EELS data suggests that this peak is a surface effect.
Comparison with the B K-edge spectra of boron oxide44 sug-
gests that it may be caused by an oxidized phase either in the
surface or at the intergranular layer. Overall, we believe that
the high energy EELS result is much more representative of
the bulk property of CaB6 than data obtained using the XAS-
TEY method.
FIG. 4. Calculated ELNES without inclusion (panel I), and with
inclusion (panel II) of the core-hole effect; both are convolved with
a Lorentz function of a width of 1.3 eV. The experimental ELNES
(panel III) has a width mainly caused by a combination of the
instrumental resolution limit ͑1.6–1.8 eV͒ and lifetime broadening.
The XAS-TEY spectrum from Ref. 14 is reproduced in panel III
(short dashed line).
shift associated with electron or hole doping of the CaB6
parent compounds either from La doping1 or as the result of
a Ca deficiency.2 This has been simulated using a supercell
model with 56 atoms (including 8 Ca atoms). A 0.45 eV shift
can be identified after removing one electron, translating into
a 3.2 eV shift per electron per primitive cell. For example, a
1% Ca deficiency in the sample could induce a shift of
0.06 eV at the Fermi level.
B. Simulation of B K-edge electron energy-loss spectrum
The ELNES data calculated including the core-hole effect
give a better overall agreement with the experimental
ELNES data than the simulation using the ground state cal-
culation only [Figs. 4(I) and 4(II)]. Both calculations cor-
rectly reproduce the five main peaks found in the experimen-
tal spectrum, but the relative intensities from the core-hole
simulation are in particularly good agreement with the ex-
periments. The main discrepancy between the core-hole
simulation and the experimental result is the splitting of peak
b in the simulated result in the energy region corresponding
to peak b in the experimental spectrum. This discrepancy
may be due to the possible presence of the unavoidable sur-
face oxide layer. Another difference between the simulated
and experimental data is the apparent “shrinking” in the en-
ergy scale near the Fermi level, i.e., the energy separation
between peak a and peak c. The distance in the core-hole
calculation result ͑ϳ9 eV͒ is smaller than that found in the
experimental spectrum ͑ϳ9.6 eV͒. A detailed comparison of
the relative peak positions in Figs. 4(I) and 4(II) reveals that
inclusion of core-hole effects results in a downshift of all
peaks to lower energies with respect to the Fermi level,
though the amount of shift is different for each peak, being
most significant for peaks within 25 eV from the Fermi level.
A similar difference in the apparent energy scaling can also
Figure 4 compares the experimental and calculated EL-
NES of the B K-edges of CaB6, for calculations using the
ground state information only [Fig. 4(I)], and including the
core-hole effects [Fig. 4(II)]. To facilitate comparison with
the experimental spectrum [Fig. 4(III)], the calculated spec-
tra have been convolved with a Lorentz function of a fixed
width of 1.3 eV. This width is chosen so as to avoid showing
excessive detail, but that the resolution of the theoretical
spectra is still slightly better than the experimental result,
such that no fine feature may be overlooked. In practice, the
lifetime broadening may vary with the excitation energy;42,43
this modification is not included in Fig. 4. We have labeled
the main peaks alphabetically, as shown in Fig. 4. The core-
hole calculation and experimental spectra are aligned accord-
ing to the energies of peaks labeled c and d. The theoretical
calculated spectra with and without core-hole effects, Figs.
4(I) and 4(II), are aligned with respect to the Fermi level,
which was set to zero (shown on the upper energy scale of
the figure). It is clear that the presence of the core hole in-
duces a general transfer of spectral-weight from the high-loss
region to the absorption threshold. However, no additional
peak features are induced. The relative intensities of the
peaks labeled a and b are enhanced, and have a decreased
214419-5

GAO, JIANG, CAO, ZHU, AND YUAN
PHYSICAL REVIEW B 69, 214419 (2004)
ization between Ca and B orbitals is not very strong. Careful
analysis shows two distinct differences. A clear difference
near the absorption edge can be found. The presence of a
distinct pre-edge peak a in the spectrum for the “B6” crystal
is the result of the Fermi level shifting into the top of the
valence band, which has a high density of states energy re-
gion with a major contribution from the boron p-symmetry
states. The other difference is the absence of peak b for the
fictitious B6 structure. Coupled with the fact that Ca d com-
ponents make a bigger contribution to the total density of
states for the same energy region, this reinforces our conclu-
sion that peak b found in the calculated CaB6 absorption
spectrum is due to hybridization of B p-symmetry states with
the above-mentioned Ca d components. Thus, feature b is
intrinsically related to the presence of Ca in the compounds.
FIG. 5. The simulated B K-edge ELNES for the fictitious B6
octahedron (lower panel) compared with that for CaB6 (upper
panel).
B. Fine structure at the absorption threshold
So far, we have shown that an ab initio calculation for the
B 1s absorption spectrum can give a reasonably good agree-
ment with the experimental spectra for an energy resolution
of the order of 1 eV. For many core-level absorption pro-
cesses, this resolution is adequate, as the spectral resolution
is fundamentally limited by the finite lifetime of the core
hole produced during the excitation process. However, for
light elements such as boron, the core-hole lifetime can be
very long,22,23 allowing us to study the electronic structure in
much finer detail. In this study, we are also interested in the
electronic states near the Fermi level because they figure
prominently in the discussion of possible mechanisms for
intrinsic ferromagnetism1,4,5 as well as for thermoelectric
effects.11–13 Until now, these states have been studied by
photoemission experiments for the occupied states, and by
XAS for the unoccupied states. Core-level absorption spec-
troscopy using EELS is potentially a more bulk-sensitive
technique. Our experimental electron energy-loss data lack,
however, the necessary resolution for such studies. For the
time being, we therefore compare our theoretically derived
results with the currently available x-ray absorption data.
XAS data for CaB6, collected using the TEY method, are
known to be very surface sensitive and suffer from a large
contribution from surface oxides. For our comparison, we
have instead used XAS data collected using a partial fluores-
cence yield (PFY) method,14 in which the signal is generated
over relatively large depths within the sample, and hence is
relatively less surface sensitive. These data are reproduced in
Fig. 6(a) for easier comparison with our calculated result
near the Fermi level. To account for the fine structure re-
vealed by the high-resolution PFY data, the calculation is
broadened only to 0.2 eV for this narrow energy range.
Whether this high spectral resolution is necessary for evalu-
ating high excitation features in the absorption spectrum re-
mains an open question for this compound.
be found in the B K-edge simulation of cubic BN.39
Overall, the core-hole calculation shows a good one-to-
one correspondence between ground state information, such
as the PDOS, and the spectral features in the B K-edge spec-
trum. It is still possible therefore to study the nature of the
unoccupied states in CaB6 using B 1s absorption spectros-
copy, as long as the influence of the core hole is properly
taken into account.
V. DISCUSSION
A. Spectral signature of Ca-B hybridization
The comparison of the electronic density of states of CaB6
and B6 (Fig. 3) reveals a relatively large difference in their
unoccupied density of states. The biggest difference is
mainly located at 4 eV above the Fermi level and is attrib-
uted to Ca d orbitals in CaB6. There is a corresponding peak
in the B 2p symmetry-projected DOS, indicating that there
exists a certain degree of hybridization. This peak is labeled
as b in the ground state ELNES simulation results (Fig. 4).
This feature is also observed in the calculation taking into
account the core-hole effect. Thus, we can identify the spec-
tral feature b in the simulation as a signature of Ca-B hybrid-
ization. The difference in the nature of the density of states at
the bottom of the conduction band in the two compounds
demonstrates that the bottom of the conduction band in CaB6
is quite complex, involving hybridization of both B and Ca
orbitals. This also means that one cannot strictly interpret the
spectral change in Ca1−␦B6 using a rigid band approach.
Given the importance of the core-hole effect in modifying
the appearance of the B 1s core-level spectra in CaB6 (Fig.
4), we have also simulated the B K edge of the fictitious B6
octahedron, employing the same method used for CaB6. The
result is given in Fig. 5 (lower panel), together with the
calculated B K-edge spectrum of CaB6 for easy comparison.
Given that this comparison is designed to probe the unoccu-
pied states, it is surprising to see a large similarity in the B 1s
core-level excitation between CaB6 and “B6,” as the Ca d
orbitals make a strong contribution in CaB6 and as this con-
tribution is absent in B6. This similarity means that hybrid-
In general, we expect the lifetime of the quasiparticles to
change with the excitation energy.42,43 However, the precise
energy dependence of this change is usually unknown. Ini-
tially we concentrate on the spectral details near the absorp-
tion threshold, where we may assume that the change is un-
important. Subsequently, we also try several other
214419-6

UNOCCUPIED ELECTRONIC STATES IN CaB6…
PHYSICAL REVIEW B 69, 214419 (2004)
FIG. 7. Comparison of the theoretical and experimental spectra
for the near-edge features of the B 1s absorption spectra for CaB6
(a) and for LaB6 (b). Data are presented in their first derivative
forms to highlight the extra feature predicted by the theoretical
spectra for CaB6, and the consistency of the peaks found in the
theoretical and experimental spectra for LaB6.
FIG. 6. Comparison of the theoretical and experimental spectra
for the near-edge features at the threshold of the B 1s absorption for
CaB6 (a) and for LaB6 (b). The high-resolution experimental spectra
are reproduced from Refs. 14 and 45, which were obtained using
the partial florescence yield (PFY) method.
phenomenological models of the energy dependence of the
lifetime over this narrow energy range to test its influence on
the spectral appearance.
LaB6, a comparison between the experimental and theoreti-
cal derivatives of the x-ray absorption spectra reveals an ad-
ditional peak near the Fermi level in the theoretical spectrum
for CaB6, which is absent in the experimental spectra.
In both the CaB6 and LaB6 cases, the relative intensities
of the experimental peaks are not particularly well repro-
duced by the simulations. One possible reason may be ex-
perimental, as the PFY detection method of soft-x-ray ab-
sorption suffers from possible saturation effects caused by
self-absorption of the emerging x-ray fluorescence. This can
cause a nonlinearity in the detection of the intense peaks in
the absorption spectra (the so-called saturation effect46,47). In
addition to possible false peaks due to the experimental
noise, and to suppression of high intensity peaks resulting
from possible saturation in fluorescence measurements, an-
other important reason for the difference may be that the
energy-dependent lifetime effects of the inelastic photoex-
cited electrons vary dramatically near the threshold and that
such effects cannot reproduced as the many-body interac-
tions are not entirely included in the calculation.48
Although the theoretical spectrum obtained using the
single-particle core-hole calculation fits the experimental re-
sult reasonably well over a wide energy region at an energy
resolution of the order of 1 eV, the comparison between the
calculated and experimental results in Fig. 6(a) suggests that
the present spectral simulation does not reproduce the ex-
perimental spectral features near the Fermi level at the finer
0.2 eV scale. The PFY spectrum for CaB6 shows a weak
steplike threshold onset, whereas the single-particle calcula-
tion shows a gradual rise from the Fermi level. The theoret-
ical and experimental spectra have been aligned according to
the peaks indicated in Fig. 6(a). This alignment may not be
entirely justified, because it is hard to identify a one-to-one
correspondence for the features in the two spectra. Neverthe-
less, the discrepancy in spectral shape is independent of the
peak identification.
C. Comparison with LaB6
To investigate the suitability of our current calculation
method for studying the band structure at the Fermi level, we
have also used an identical procedure to calculate the boron
1s absorption spectrum for LaB6. The PFY spectrum45 of
LaB6 is reproduced for easier comparison with our calculated
result in Fig. 6(b). In contrast to the case for CaB6, there is a
clear one-to-one correspondence of the spectra features over
an energy range of 3 eV at a resolution of 0.2 eV. This cor-
respondence shows that the overall features of the absorption
edge in the metallic LaB6 system can be reasonably well
described by our ab initio single-particle calculation, even at
this fine energy scale.
D. Modeling the energy dependence of the core-hole lifetime
The actual lifetimes are the result of a delicate balance
between localization, density of states, screening, and Fermi-
surface topology.43 So far, the broadening width used for the
theoretical spectra in Figs. 6(a) and 6(b) is assumed to be
constant over the energy range shown. We have attempted to
estimate the effect of the energy-dependent lifetime broaden-
ing on the change in relative peak intensity by looking at the
sensitivity of the spectral change for various assumed energy
dependencies for the excited electrons. The effect of different
energy dependencies is shown in Fig. 8. We found that while
the peak intensity does change, the peak positions and num-
bers in the derivative spectra remain unchanged. We con-
clude therefore that although energy dependent lifetime
broadening is an important factor for simulation of high-
The differences between the experimental and theoretical
results in Fig. 6 can be seen more clearly by looking at the
derivatives of the spectra, as shown in Figs. 7(a) and 7(b). In
contrast to the consistency in peak position and number for
214419-7

GAO, JIANG, CAO, ZHU, AND YUAN
PHYSICAL REVIEW B 69, 214419 (2004)
VI. CONCLUSION
Experimental EELS investigation of the B 1s core-level
spectroscopy has revealed inconsistencies, which may be due
to the ubiquitous oxide at both surfaces and interfaces of
CaB6 grains. The intrinsic part of the B 1s core level spec-
trum is found to be in excellent overall agreement with the
ab initio theoretical simulation that takes into account the
core-hole effect. By studying the ground state electronic
structure, we can identify a specific feature associated with
boron p orbitals hybridized with the Ca d orbitals. This in-
terpretation is confirmed by the results of a simulation of the
fictitious “B6” compound. However, comparison of the high-
resolution simulated spectra and the high-resolution x-ray
absorption spectra for states near the Fermi level shows a
significant discrepancy. This may point to the importance of
correctly accounting for the nature of the many-body inter-
actions for states at the Fermi level in CaB6. The results of
the investigation highlight the need for better experimental
results that can truly reflect bulk intrinsic properties of this
material.
FIG. 8. The effect of different energy dependences of the life-
time effect on the appearance of the near-edge feature at the B 1s
absorption threshold of the compound LaB6: (I) a constant 0.2 eV,
(II) 0.15+0.5E+0.05E2, (III) 0.15+0.2E2, (IV) 0.15+0.2E2 for
EϽ1.0 eV and 1.0 eV for the higher excitation energy. Also shown
are the corresponding spectra in their derivative forms.
resolution spectra, it cannot explain the main discrepancy for
CaB6 between the high-resolution simulation and the XAS-
PFY data.
ACKNOWLEDGMENTS
The simulation work was mainly carried out using the
computer code DACAPO of the CAMP Open Software
Project, Denmark. The research is supported by the National
Key Research and Development Project for Basic Research
(Grant No. 2002CB613500 from the Ministry of Science and
Technology), the National Natural Science Foundation of
China, the Changjiang Scholar Program of Ministry of Edu-
cation and the 985 funding of Tsinghua University. We thank
Professor A. Godfrey for a careful reading of the text.
Alternatively, the discrepancy between the experimental
spectrum and the single-particle core-hole calculation result
for CaB6 may reflect the importance of the many-body inter-
actions, which are not fully taken into account in the present
simulation. This may be related to the controversy over the
existence and the nature of an energy gap in the electronic
states.14,16,18,19 We hope that our work will stimulate more
detailed experimental and theoretical work to settle this
question definitively.
Author to whom correspondence should be addressed. Electronic
address: yuanjun@tsinghua.edu.cn
Fisk, J. Phys.: Condens. Matter 15, 6739 (2003).
13 Y. Imai, M. Mukaida, M. Ueda, and A. Watanabe, Intermetallics
9, 721 (2001).
*
1 D. P. Young, D. Hall, M. E. Torelli, Z. Fisk, J. D. Thomson, H. R.
Ott, S. B. Oseroff, R. G. Goodrich, and R. Zysler, Nature
(London) 397, 412 (1999).
14 J. D. Denlinger, J. A. Clack, J. W. Allen, G.-H Gweon, D. M.
Poirier, C. G. Olson, J. L. Sarrao, A. D. Bianchi, and Z. Fisk,
Phys. Rev. Lett. 89, 157601 (2002).
2 T. Moriwaka, T. Nishioka, and N. K. Sato, J. Phys. Soc. Jpn. 70,
341 (2001).
15 S. Souma, H. Komatsu, T. Takahashi, R. Kaji, T. Sasaki, Y.
Yokoo, and J. Akimitsu, Phys. Rev. Lett. 90, 027202 (2003).
16 S. Massidda, A. Continenza, T. M. de Pascale, and R. Monnier, Z.
Phys. B: Condens. Matter 102, 83 (1997).
3 S. Murakami, R. Shindou, N. Nagaosa, and A. S. Mishchenko,
Phys. Rev. Lett. 88, 126404 (2002).
4 C. Hotta, H. Fukuyama, and M. Ogata, Phys. Rev. B 65, 184421
(2002).
17 S. Massidda, R. Monnier, and E. Stoll, Eur. Phys. J. B 17, 645
(2000).
5 M. E. Zhitomirsky, T. M. Rice, and V. I. Anisimov, Nature
(London) 402, 251 (1999).
18 H. J. Tromp, P. van Gelderen, P. J. Kelly, G. Brocks, and P. A.
Bobbert, Phys. Rev. Lett. 87, 016401 (2001).
6 D. Ceperley, Nature (London) 397, 386 (1999).
7 M. E. Zhitomirsky and T. M. Rice, Phys. Rev. B 62, 1492 (2000).
8 S. E. Lofland, B. Seaman, K. V. Ramanujachary, N. Hur, and S.
W. Cheong, Phys. Rev. B 67, 020410(R) (2003).
9 R. Monnier and B. Delley, Phys. Rev. Lett. 87, 157204 (2001).
10 T. Mori and S. Otani, Solid State Commun. 123, 287 (2002).
11 K. Giannò, A. V. Sologubenko, H. R. Ott, A. D. Bianchi, and Z.
Fisk, J. Phys.: Condens. Matter 14, 1035 (2002).
12 K. Giannò, A. V. Sologubenko, H. R. Ott, A. D. Bianchi, and Z.
19 H. Kino, F. Aryasetiawan, K. Terakura, and T. Miyake, Phys. Rev.
B 66, 121103 (2002).
20 L. Hedin, Phys. Rev. 139, A796 (1965).
21 C. Meegoda, M. Trenary, T. Mori, and S. Otani, Phys. Rev. B 67,
172410 (2003).
22 M. Terauchi, Y. Kawamata, M. Tanaka, M. Takeda, and K.
Kimura, J. Solid State Chem. 133, 156 (1997).
23 M. Terauchi, Y. Kawamata, M. Tanaka, H. Matsuda, and K.
214419-8

UNOCCUPIED ELECTRONIC STATES IN CaB6…
PHYSICAL REVIEW B 69, 214419 (2004)
Kimura, J. Solid State Chem. 133, 152 (1997).
24 H. K. Schmid, Microsc. Microanal. Microstruct. 6, 99 (1995).
25 K. Hofmann, and R. Gruehn, and B. Albert, Z. Anorg. Allg.
Chem. 628, 2691 (2002).
36 C. Elsässer and S. Köstlmeier, Ultramicroscopy 86, 325 (2001).
37 M. Taillefumier, D. Cabaret, A.-M. Flank, and F. Mauri, Phys.
Rev. B 66, 195107 (2002).
38 S. Köstlmeier and C. Elsässer, Phys. Rev. B 60, 14025 (1999).
39 D. N. Jayawardane, C. J. Pickard, L. M. Brown, and M. C. Payne,
Phys. Rev. B 64, 115107 (2001).
26 K. Hofmann and B. Albert, ChemPhysChem 3, 896 (2002).
27 K. Lie, R. Hoier, and R. Brydson, Phys. Rev. B 61, 1786 (2000).
28 I. Tanaka, H. Araki, M. Yoshiya, T. Mizoguchi, K. Ogasawara,
and H. Adachi, Phys. Rev. B 60, 4944 (1999).
29 S. Suzuki, M. Tomita, and T. Hayashi, J. Phys. Soc. Jpn. 34,
L191 (1995).
40 W.-Y. Ching, S.-D. Mo, and Y. Chen, J. Am. Chem. Soc. 85, 11
(2002).
41 M. S. Hybertsen and S. G. Louie, Phys. Rev. B 34, 5390 (1986).
42 J. E. Müller, O. Jepsen, and J. W. Wilkins, Solid State Commun.
42, 365 (1982).
30 R. Egerton, Electron Energy Loss Spectroscopy in the Electron
Microscope (Plenum, New York, 1996), p. 269 p. 264 , and p.
227.
43 I. Campillo, J. M. Pitarke, A. Rubio, E. Zarate, and P. M. Ech-
enique, Phys. Rev. Lett. 83, 2230 (1999).
31 M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and D. Joan-
nopoulos, Rev. Mod. Phys. 64, 1045 (1992).
44 The B K-edge x-ray spectra provided by Karine Varlot (Wiscon-
sin, USA) was found in the EELS and x-ray spectrum database
32 K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt,
Phys. Rev. B 47, 10142 (1993).
http://www.cemes.fr/˜eelsdb/.
45 J. D. Denlinger, J. W. Allen, and Z. Fisk, http://www-als.lbl.gov/
als/compendium/Abstract Maneger/uploads/01090.pdf
46 R. Nakajima, J. Stöhr, and Y. U. Idzerda, Phys. Rev. B 59, 6421
(1999).
33 J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R.
Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671
(1992).
34 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).
35 P. Rez, J. R. Alvarez, and C. Pickard, Ultramicroscopy 78, 175
(1999).
47 P. Pfalzer, J.-P. Urbach, M. Klemm, S. Horn, M. L. denBoer, A. I.
Frenkel, and J. P. Kirkland, Phys. Rev. B 60, 9335 (1999).
48 A. Soininen, Ph.D. thesis, University of Helsinki, Finland, (2001).
214419-9