Electronic properties of the narrow-band material α-RuCl3

Article abstract of DOI:10.1103/PhysRevB.53.12769

X-ray angle-integrated and ultraviolet angle-resolved photoemission spectra of the low-spin compound t_2g⁵ α-RuCl₃ show that Ru 4d and Cl 3p states contribute to the valence-band structure of this magnetic material. The energy distribution curves measured along the azimuthal directions Γ-M′-π and Γ-K-M using He I radiation indicate an uppermost nearly dispersionless structure of Ru 4d origin, and two dispersive features obtained from Cl 3p-derived bands. The photoemission results, together with the optical and magnetic properties described by ligand-field theory, support the view of localized 4d states forming a very narrow Ru 4d band in the vicinity of the Fermi energy. The main 4d emission structure has been thus assigned to 4d⁴ unscreened hole states, where the band gap corresponds to intersite d-d transitions, and α-RuCl₃ can be classified as a Mott-Hubbard compound in consideration of its electronic and magnetic characteristics. The inconsistency between the photoemission results and the transport properties, describing this material as a conventional band-gap semiconductor, is finally discussed.

Full text of DOI:10.1103/PhysRevB.53.12769

PHYSICAL REVIEW B
VOLUME 53, NUMBER 19
15 MAY 1996-I
Electronic properties of the narrow-band material ␣-RuCl 3
I. Pollini
`
Istituto Nazionale per la Fisica della Materia, Unita di Ricerca di Milano, c/o Dipartimento di Fisica, Via Celoria 16,
20133 Milano, Italy
͑Received 26 July 1995; revised manuscript received 2 January 1996͒
X-ray angle-integrated and ultraviolet angle-resolved photoemission spectra of the low-spin compound t25g
␣-RuCl3 show that Ru 4d and Cl 3p states contribute to the valence-band structure of this magnetic material.
The energy distribution curves measured along the azimuthal directions ⌫-M -⌫ and ⌫-K-M using He I
Ј
radiation indicate an uppermost nearly dispersionless structure of Ru 4d origin, and two dispersive features
obtained from Cl 3p-derived bands. The photoemission results, together with the optical and magnetic prop-
erties described by ligand-field theory, support the view of localized 4d states forming a very narrow Ru 4d
band in the vicinity of the Fermi energy. The main 4d emission structure has been thus assigned to 4d4
unscreened hole states, where the band gap corresponds to intersite d-d transitions, and ␣-RuCl3 can be
classified as a Mott-Hubbard compound in consideration of its electronic and magnetic characteristics. The
inconsistency between the photoemission results and the transport properties, describing this material as a
conventional band-gap semiconductor, is finally discussed.
I. INTRODUCTION
sion spectroscopy as well as in optical spectroscopy. The
most striking difference between the two approaches con-
cerns the magnitude of the conductivity gap. However, as far
as TMO’s are concerned, it seems now more or less accepted
that the ϳ4-eV gap of MnO, FeO, CoO, and NiO arises from
Mott-Hubbard localization of electrons in partly filled d
bands. Recently, it has been suggested that hybridization of
the localized 3d levels and O 2p bands in some TMO’s
͑such as NiO and CuO͒, and halide p bands in some
TMH’s,3,4,9 is of critical importance, and that the insulating
gap is actually of the charge-transfer type ͑CuCl2 , CuBr2 ,
and NiX2) (X ϭ Cl, Br, or I͒. However, despite the apparent
breakdown in band theory that this approach represents, one-
electron models have been successful in correctly determin-
ing the lattice spacings, magnetic moments, and energy gaps,
besides antiferromagnetic ͑AF͒ order.5,6,10,11 Moreover, re-
cent theoretical work5,11,12 has revived the idea that the prin-
cipal origin of the band gap is the inherent AF order: in this
itinerant 3d-electron model of the TMO, the exchange per-
turbation of the one-electron band structure opens a d-d gap.
An explanation for this failure of band theory was first
suggested by Mott,13,14 who brought attention to the impor-
tance of electronic correlation, neglected in a HF approach,
in the case of narrow bands: Mott pointed out that in the
limit where the lattice parameter becomes sufficiently large
that overlap between nearest-neighbor electronic wave func-
tions is negligible, any material must be an insulator. In the
limit of zero-width bands, electrons are localized around
their ion cores, just as core electrons. The existence of a
correlation gap in a simple model, consisting of a single s
band with a ␦-function interaction between electrons, was
then verified by Hubbard.15
The nature of the electronic structure and the origin of the
insulating gap in transition-metal oxides ͑TMO’s͒ and ha-
lides ͑TMH’s͒ has been a controversial subject for many
years.1–6 One-electron band-structure calculations predict
small energy gaps for TMO’s,5,6 and even metallic behavior
both for TMO’s and TMH’s; like Ni dihalides and Cr
trihalides.7 As a matter of fact, transition-metal compounds
͑TMC’s͒ reveal two different types of electronic behavior:
the delocalized regime, as in layer dichalcogenides, and the
localized one, with examples taken frequently from the
TMO’s and TMH’s. The delocalized regime, which is de-
scribed by the independent-electron approximation, adheres
to band-structure calculations very satisfactorily to produce
either metallic behavior or semiconductivity. On the other
hand, localized materials show an insulating behavior,
largely independent of band-structure previsions ͑e.g.,
CrCl3 and Cr2O3 are excellent insulators with partially filled
d bands͒, with the breakdown due to the growth of electron-
electron correlation to produce d electrons essentially
trapped around each TM site. In this case the optical and
magnetic properties are described by ligand-field theory.8
TMH’s are, in general, antiferromagnetic, electrically insu-
lating, ionic compounds presenting layered structures ͑e.g.,
CdCl2 , CdI2 , and BiI3). The halide p bands are fully occu-
pied, the metal s states are empty, and the metal d states are
partially occupied. It is the apparent incompatibility of their
insulating behavior with the partial occupation of the d shell
that makes these materials especially interesting.1,2 Although
attempts at modifying band theory to explain the insulating
behavior have been made, it does not appear likely that a
pure Hartree-Fock ͑HF͒ approach will consistently account
for the electrical behavior of all TMC’s. Two approaches
͑band theory with exchange interaction treated in the
density-functional approximation, and the local cluster
model͒ make clear predictions concerning the structures
which should be observed in direct and inverse photoemis-
Furthermore, TMO’s and TMH’s are ideal subjects for an
investigation of insulating and metallic states, because of the
wide diversity of electrical properties observed in apparently
similar materials: for example, layered CrCl3 and cubic
Cr2O3 are both Mott insulators, while layered RuCl3 is ap-
parently a Mott-Hubbard compound ͑or a not standard semi-
0163-1829/96/53͑19͒/12769͑8͒/$10.00
53
12 769
© 1996 The American Physical Society

12 770
I. POLLINI
53
TABLE I. High-low spin change of the crystal-field parameters
for some 3d and 4d transition-metal compounds. The 4d electrons
present an increase in the crystal-field splitting parameter ⌬CF and
smaller values of the Racah parameter B, ͑h.s. and l.s. means high-
spin and low-spin compounds, respectively͒. Values for CrCl3 and
RuCl3 are taken from Refs. 19 and 18, respectively; those for
MoCl3 and FeCl3 are from Ref. 20.
conductor͒ and cubic RuO2 a metal. A major problem for
these materials is the preparation of good crystals, since most
of them contain important concentrations of random impuri-
ties and lattice defects so that the results of electrical mea-
surements often have little to do with the intrinsic properties
of the material. Most pure, stoichiometric crystalline materi-
als are classified as either metals (10Ϫ6Ͻ␳RTϽ10Ϫ2⍀ cm͒
with a linear increase of the resistivity ␳ with the tempera-
⌬
͑cmϪ1
)
B ͑cmϪ1
)
⌬
CF/B
ture
T
or insulators and semiconductors (103Ͻ␳
RT
CF
Ͻ1017⍀ cm͒ and an exponential decrease with increasing
temperature. Some typical insulators include NiO, TiO2,
CoO, Cr2O3 , and CrCl3, and metals include TiO, CrO2 ,
ReO3 , and RuO2 . Charge-transfer semiconductors are CuO,
CuCl2 , NiCl2 , and NiBr2: holes are light ͑transport in the
anion valence band͒ and electrons are heavy ͑transport in the
d band͒.4,9
3d3 CrCl3 h.s.
4d3 MoCl3 l.s.
3d5 FeCl3 h.s.
4d5 RuCl3 l.s.
13.700
540
410
750
370
25.4
47
18.5
32
19.300
14.000
11.840
due to electrons which move with a bandlike mechanism
within the 4d narrow CF bands with a very low mobility
(0.1Ͻ␮Ͻ1 cm2 V sϪ1) and a high effective mass. The in-
consistency between the photoemission results and transport
properties raises the question whether ␣-RuCl3 is a band or
a Mott compound ͑semiconductor͒. This problem is not new,
as some examples reported in the literature point out: see, for
instance, the case of TMO,5 CoO,22 and TiTe2 .23
In seeking a means of clarifying this point, it seems natu-
ral to turn to photoemission techniques, since they have
played a major role in testing the electronic structure of a
wide variety of materials, including oxides. In principle,
ARP should be able to distinguish between localized and
itinerant ͑bandlike͒ d states by the observation ͑or not͒ of the
energy peak dispersion with the electron wave vector.
Hence the results of an ARP study are presented and dis-
cussed in relation to the known electronic and transport prop-
erties. Further, some considerations concerning the metallic
and insulating behavior of RuO2 ͑Refs. 24–28͒ and RuCl3
materials, where the electrical transport may or not occur in
partially filled d bands, are made by discussing their x-ray
photoemission spectra ͑XPS͒.
In a recent paper,16 the core and valence-band photoemis-
sion ͑PE͒ spectra of layered CrCl3 and ␣-RuCl3 were mea-
sured and discussed. The only difference was a larger width
(ϳ5 eV͒ of the valence band as compared to the core levels,
which reflects the dispersion of the bands. These materials
were classified as Mott-Hubbard ͑MH͒ insulators on the ba-
sis of experimental results obtained by angle-integrated pho-
toemission ͑AIP͒, photoconductivity, and optical spectra.
The interpretation of PE spectra becomes more complicated
in compounds that contain open shell ions like transition
metals, and the principal conclusions were that the 3d and
4d states of Cr and Ru atoms and 3p states of Cl contribute
to the formation of the valence band, and that the main
d-band emission is due to crystal-field multiplets of the
dnϪ1 final states.16,17
For MH compounds, the energy gap EG is proportional to
U, the d-d Coulomb interaction which includes exchange
and correlation, and both holes and electrons are heavy since
they move in bands ͑Hubbard bands͒ formed primarily from
d orbitals of the transition-metal ions, and these are narrow
because the ions are relatively far apart. The electrostatic
repulsion between the electrons leads to localization of the
d electrons and a nonconducting state: two typical examples
are CrCl3 ͑Ref. 16͒ and Cr2O3 .17 In a 4d TM compound
͑RuCl3), the situation is rather different from a 3d TM com-
pound ͑CrCl3), since RuCl3 is in the low-spin state. The
4d electrons, being less tightly bound energetically and spa-
tially than the 3d electrons, are more directly exposed to the
ligands, have a greater state mixing with an increase in the
crystal-field ͑CF͒ splitting parameter ⌬CF , and at the same
time they show a smaller value of the Racah parameter B,
which gives a measure of the electron-electron repulsion
within the d shell.8,18–20 In Table I some examples illustrate
the high-low change of these parameters.
II. SAMPLE PREPARATION AND EXPERIMENTAL
PROCEDURE
Crystals of ␣-RuCl3 were grown from the vapor phase by
chemical transport in an open tube reactor. The metal pow-
der reacts at approximately 750 °C with a stream of Cl2 gas,
and crystals are deposited at lower temperature in the growth
zone. The purity of the elements ͑Ru metal powder and
Cl2 gas͒ is greater than 99.9%, and RuCl3 crystals may
present a stoichiometry deviation around 1%, as measured
for the pure compounds. This slight deviation of stoichiom-
etry is too small to be discernable in the photoemission spec-
tra, but can affect the electrical measurements, owing to their
sensitivity to lattice defects and impurities. The crystals
(ϳ25 mm2) are black, lustrous, and very stable with thick-
ness between 10 and 70 ␮m.
␣-RuCl3 has the high-temperature crystal structure of
CrCl3 ͑C32h monoclinic, four formula units per unit cell
above 240 K͒. It belongs to a group of layered transition
metal halides where one hexagonal sheet of atoms ͑Ru͒ is
sandwiched between two hexagonal sheets of chlorine. How-
ever, for RuCl3 two-thirds of the Ru atoms are missing in the
metallic sheet, and the structure of the surface of RuCl3 is
In Ref. 16 it was anticipated that the relative dispersion of
Ru 4d states in the valence band would be less than 0.2 eV,
on the ground of preliminary angle-resolved photoemission
͑ARP͒ measurements, and that the photoconductivity excited
across the d-d energy gap EG could be due to a hopping type
of conduction where the electrons diffuse from one cation
site to the next.
However, this picture does not seem consistent with re-
ported conductivity18,21 and Hall mobility data21 which de-
scribe this material as
a
traditional semiconductor
(␳ RTϳ103⍀ cm͒, where the intrinsic electrical transport is

53
ELECTRONIC PROPERTIES OF THE NARROW-BAND . . .
12 771
identical to that of BiI3. Within a sandwich the bonding is
mainly of ionic character ͑the coordination around the metal
atom is octahedral͒, whereas the van der Waals bonding is
responsible for the stacking between the sandwiches.
␣-RuCl3 is antiferromagnetic below 13 K.16 The rhombohe-
dral unit cell consists of two metal and six halogen atoms.
The three-dimensional Brillouin zone ͑BZ͒, and its related
surface BZ is identical to that of CdCl2-type compounds.
distribution curves were measured along different azimuthal
directions ⌫M, ⌫M , and ⌫K in the BZ.
Ј
The polar angle dependence of the spectra for the ⌫M
Ј
and ⌫K directions has been measured with a normalized
photoemission intensity, and we have calculated the kʈ val-
ues associated with the peak positions on the photoemission
spectra using the equation
1/2
2mEk
The M and M surface symmetry points correspond to in-
Ј
k ϭ
sin␪,
͑1͒
ͩ
ͪ
ʈ
ប2
equivalent directions when the underlying structure is taken
into account. The surface Brillouin zone arises from the
halogen atoms, which are 0.36 nm distant from each other: it
with Ekϭប␻ϪWϪEi , where Ek is the kinetic energy of the
photoelectrons, W the work function, ប␻ the photon energy,
and Ei the energy of the initial state of the transition. The
position of the Fermi level (EF) was determined from the
photoelectron spectrum of gold evaporated on the sample, as
a reference metal. The work function was obtained by sub-
strating the width of the photoelectron energy distribution
͑from zero kinetic energy to EF) from the radiation energy:
the vacuum level was so found at 6.1 eV above the Fermi
level.
follows that ⌫Kϭ12.8 nmϪ1 and ⌫Mϭ11.1 nmϪ1
.
Owing to the surface sensitivity of ultraviolet-
photoelectron spectroscopy ͑UPS͒ photoemission, the
samples were peeled in the 10Ϫ8-Pa range, and the quality of
the basal plane was controlled by low-energy electron dif-
fraction ͑LEED͒. Since the LEED diagrams do not discrimi-
nate between M and M , a careful examination was made of
Ј
the absolute PE intensity vs the polar angle in order to
specify the different crystallographic orientations. The ⌫M
and ⌫M directions were identified as follows: going from a
Ј
metal atom along the ⌫M direction the first-neighbor ligand
III. RESULTS AND DISCUSSION
lies under the ⌫M line, whereas in the ⌫M direction it lies
Ј
Figure 1 presents the UPS and XPS valence-band spectra
of ␣-RuCl3, and the XPS spectrum of the metallic compound
RuO2 (4d4). The PE spectra of RuCl3 are formed by three
resolved bands originating from the Ru 4d and Cl 3p states:
the metal 4d band and Cl 3p bands are still separated, al-
though some metal-chlorine hybridization is present. The
symmetry attributions follow from the strong increase of the
photoemission intensity from the Ru 4d electrons relative to
the signal strength from the Cl 3p electrons in going from
UPS to XPS data. This effect is due to the strong dependence
of the valence-band photoionization cross sections with the
increase of the photon energy.17 The comparison with the
RuO2 PE spectrum shows that in this compound the 4d4
final-state structure is displaced from a Fermi energy of
about 0.6 eV. The experimental density of states is in good
agreement with the theoretical density-of-states curves.24,27
The calculated DOS curves20 show that the metal-oxygen
covalency-overlap interactions determine the width of the
valence and conduction bands. In particular, most of the 4d
bandwidth arises from the overlap interactions of the t2g and
eg orbitals with the oxygen 2s-2p states; the Fermi level
falls at the lower part of the 4d band, in the t2g manifold.
Thus the Ru 4d states broaden into a dispersive, partly filled
band, where metallic conduction is possible. The electron
transport properties are then explainable in terms of normal
behavior, as described by the Boltzmann equation.28 In me-
tallic RuO2 the screening in the final state is more effective
than in nonmetallic RuCl3 , therefore it is not surprising that
the peak in the 4d4 structure in RuCl3 is found around 1 eV
͑XPS͒ as compared to 0.6 eV in RuO2 . The entire Cl 3p
band exhibits a full width at half maximum ͑FWHM͒ of
about 5 eV, while the Ru 4d peak has a broadening of 1.5 eV
in XPS and 1.0 eV in UPS spectra. The dominant source of
the linewidth in d levels is most probably hybridization
broadening; that is, the effect of hybridizing the 4d hole
orbitals with anion 3p orbitals, whose energies are spread
over a considerable bandwidth ͑about 5 eV according to Fig.
above the ⌫M line.
Ј
XPS experiments were performed with a Vacuum Gen-
erators ESCALAB MKII system, equipped with a mono-
chromatized Al K␣ x-ray source (ប␻ϭ1486.6 eV͒: the an-
gular acceptance of photoelectrons is so large that in the final
state the wave vector k of the photoelectrons is smeared out
over a large part of the whole BZ. There is a second effect:
for electromagnetic radiation of 1.5 keV, the photon wave
vector is relatively large, ␬Ӎ0.7 ÅϪ1, and therefore one no
longer has a vertical transition. This adds to averaging over
the BZ. In experiments using a polycrystalline sample, the
XPS spectrum, therefore, reproduces the density of states
͑DOS͒ of the material, in which contributions from electrons
with different angular momenta are weighted differently be-
cause of their different photoelectric cross sections. In ex-
periments with single crystals, this XPS density of states is
further modulated with an angular projection factor. How-
ever, although experience has shown that, in general, single-
crystal experiments on pure materials do not give much more
detailed information than experiments with polycrystalline
samples, in the case of RuCl3 XPS spectra measured on
single crystals have exhibited a structure unnoticed in previ-
ous works.16 The total instrumental resolution was about 1
eV.
In the UPS ͑ultraviolet photoelectron spectroscopy͒ re-
gime, the spectra are dominated by direct ͑vertical͒ transi-
tions in the reduced zone scheme. In an experiment with a
single-crystal sample, one investigates direct transitions with
well-defined k vectors. This then provides a method to map
the band structure E(k). The spectra were obtained in an
ultrahigh vacuum system (10Ϫ10-mbar range͒ with an hemi-
spherical energy analyzer by using a He discharge lamp
͑He I, ប␻ϭ21.2 eV͒. The photon beam had an incidence
angle ␣iϭ45° with respect to the normal at the sample sur-
face. The energy resolution was about 150 meV, and the
acceptance angle was Ϯ1°. The polar angle ␪ of emission
was incremented by 5° steps from 0° to 80°. The energy

12 772
I. POLLINI
53
FIG. 2. Mott-Hubbard energy-level diagram for an unfilled d
band in a solid as a function of the inverse lattice parameter. The
separation at 1/aϭ0 is U, the Coulomb repulsion between two
electrons of opposite spins simultaneously located in Wannier states
centered on the same ion core. The two energy levels broaden with
increasing 1/a, and their separation is the energy gap Eg , the acti-
vation energy for conduction. In the zero bandwidth limit, the Bloch
energies T0 are separated by U.
observes a greater broadening ͑width 1–1.5 eV͒ of the partial
bandwidth due to t2g and eg orbitals, arising from the effec-
tive d-d hopping integrals.2,14
The energy gap, ascribed to d-d transitions, is
EGϭUϪ 12 B ϩB ͒,
͑2͒
͑
1
2
where U is the ͑atomic͒ Coulomb correlation energy, and
B1 and B2 are the widths of the two bands. In Fig. 2 a
Mott-Hubbard energy-level diagram for an unfilled d band in
a solid is illustrated. We see that the separation at 1/aϭ0 is
UϭIϪEA;
͑3͒
FIG. 1. Valence-band structure of paramagnetic ␣-RuCl3: ͑a͒
that is, for many electron atoms U is defined as the energy
required to transfer an electron from one atom to another, so
that U is given by the ionization energy (I) minus the elec-
tron affinity ͑EA͒. With increasing 1/a the two energy levels
are broadened by ion-ion interaction in the solid, and their
separation is the gap energy given by Eq. ͑2͒. It is seen that
for a vanishingly small bandwidth, the band d splits into two
subbands ͑upper and lower Hubbard bands͒ separated by an
energy gap EG of the order of U. Hubbard15 in an approxi-
mate solution found that ordinary band theory predicted cor-
rect electrical behavior in the range where the ratio of the
bandwidths B to U was large,but that near the opposite limit,
when BӶU, the material was indeed a Mott insulator: in the
Hubbard approximation the Mott transition comes at
B/Uϳ1.16 ͑the dashed line in Fig. 2͒. A typical example is
NiO, which for a long time was considered a prototype of a
Mott insulator. Since for Ni2ϩ the atomic limit is Uϭ18 eV
͑Ref. 29͒ and WӍ1–3 eV,30 even with a considerable reduc-
tion of U by solid-state screening the insulating nature of
NiO is understandable in this simple picture.
Angle-resolved photoemission spectrum measured at normal emis-
sion with a He I radiation. ͑b͒ Angle-integrated photoemission spec-
tra measured with Al K␣ radiation. ͑c͒ XPS spectrum of metallic
RuO2 ͑Ref. 21͒. The Fermi level is to be identified with zero bind-
ing energy.
1͒. In the case of the 4d structure observed in UPS/XPS
spectra, one observes a considerable broadening ͑1–1.5 eV͒,
for the bandwidth of the t2g orbitals ͑Frenkel excitons͒ of the
4d4 ligand-field state 3T1 , while typical widths of ligand-
field transitions in the optical spectrum are of the order of
0.1–0.2 eV. Since we are considering the same d states, it is
not at once evident why the hopping of 4d electrons between
neighboring cations should produce widths much larger than
the exciton widths ͑0.1–0.2 eV͒. The reason is that an exci-
ton transfer consists of the excited electron hopping simulta-
neously with the hole from which it was excited. The effec-
tive exciton transfer integrals are of the order of 2t2/U ͑in
the AF phase, but also above TN where short-range order still
occurs͒ rather than t, a typical d-hopping integral. For in-
stance, in NiO or CoO the effective 3d-transfer integral is of
the order of 10Ϫ3 eV, which corresponds to an intrinsic
bandwidth of the order of 10Ϫ2 eV, far smaller than the
observed exciton widths ͑about 0.1 eV͒. In the case of the
4d structure observed in UPS/XPS, there is no such extra
particle-hole factor 2t/U to reduce the hopping contribution
to the widths of the final 4d state in RuCl3: one therefore
A central element in Hubbard’s treatment of correlation
effects and in any discussion of conduction mechanisms in
narrow-band materials is the d-state bandwidth. For
␣-RuCl3 , one finds from PES spectra that the bandwidth is
of the order of 1–1.5 eV in line with the reported widths of
TMO’s ͑Ref. 17͒ and TMH’s.30 In particular, from UPS
spectra one can make an estimation of the Ru

53
ELECTRONIC PROPERTIES OF THE NARROW-BAND . . .
12 773
FIG. 3. Polar spectra of
␣-RuCl3 measured at 300 K.
␣iϭ45° is the photon incidence
angle, and ␪ is the polar angle.
The azimuthal angle corresponds
to the ⌫M ⌫ direction of the sur-
Ј
face Brillouin zone. The experi-
mental band structure E vs Kʈ in
the repeated zone scheme for the
⌫-M -⌫ symmetry direction is
Ј
shown. In the insets the experi-
mental geometry and the surface
and bulk Brillouin zones for the
CdCl2 structure are also shown.
4d-bandwidth B of 0.7–0.8-eV FWHM for the 3T1 final
state. In XPS spectra, B may be estimated at around 1.3–1.4
eV after correction for instrumental resolution. The photo-
conductivity edge, which gives the experimental value of the
photoconductivity gap of the material ͑an energy separation
between the d4 and d6 configurations͒ in a direct way, can be
estimated around 0.7–0.8 eV ͑see Fig. 8 of Ref. 16͒. From
Eq. ͑2͒ one thus obtains a value of U of 1.4–1.6 eV, which
may be slightly reduced, if one makes a proper correction for
hybridization, to 1.2рUр1.4 eV, but it still greater than the
observed 4d-band-width. Moreover, if one compares the ob-
tained value of U, let us say Uϳ1.2 eV, or a still lower
value, like Uϳ0.8–1 eV ͑the value of the photoconductivity
edge͒, with the dispersional part of the 4d band ͑in Figs. 3
and 4͒, one finds that U is greater than five times the band-
width of 0.2 eV ͑see Refs. 4 and 6͒. In the MH model a
nonmetallic behavior is thus expected, without considering a
conventional band gap, and ␣-RuCl3 can be described as a
Mott compound.16
Let us now present an angle-resolved photoemission in-
vestigation of the valence bands of RuCl3. Figures 3 and 4
present angle-resolved spectra for the ⌫M and ⌫K direc-
Ј
tions with energy relative to EF , the Fermi level, and nor-
malized photoemission intensity. The peak positions have
then been plotted with the initial energy origin taken at EF
for the ⌫M and ⌫K directions as a function of the wave
Ј
vector kʈ by means of ͑1͒. The experimental plots E(kʈ)
along the ⌫M and ⌫K orientations are also shown in Figs.
Ј
3 and 4, respectively. One can see that the experimental band
structure extends across the first BZ, entering the second BZ
along the ⌫K and ⌫M symmetry lines.
Ј
Three prominent features have been identified and labeled
FIG. 4. Polar spectra of
␣-RuCl3 at Tϳ300 K with
␣iϭ45°. The azimuthal angle
was now chosen to correspond
to the ⌫KM direction of the
surface Brillouin zone. The ex-
perimental band structure E vs
Kʈ in the repeated zone scheme
for the ⌫-K-M symmetry di-
rection is shown.

12 774
I. POLLINI
53
that photoemission satellites, which are due to multielectron
effects involving the transition metal d and ligand p states,
have been observed in Ni oxides and halides,3,4 and also in
CoO ͑Ref. 22͒ and MnO.31 In all cases resonant photoemis-
sion has suggested that the satellite bands observed in the
valence-band photoemission spectra of these compounds are
due to 3dnϪ1 final states, and that the main emission features
are due to ligand-to-3d charge-transfer final states. It was
also pointed out31 that the satellite peaks are generally ob-
served in transition-metal compounds which cannot be de-
scribed by ligand-field theory. As recalled, in the valence-
band photoemission of ␣-RuCl3 no satellite peak occurs, and
only the 4d main structure is observed. While the absence of
satellites seems to support the idea that the PES spectra of
this compounds can be interpreted within a ligand-field pic-
ture, it further indicates that exchange and correlation effects
͑which are observed in final excited states created by the
photoexcitation of the one-electron wave functions of the
initial states͒, as given by the value of U, should not be very
strong in ␣-RuCl3: in fact we have obtained 1.2рUр1.4
eV, to be compared with 6 eVрUр9 eV in NiO.4,32
The final part of Sec. III concerns the discussion of the
electrical and optical properties of this material, which is
characterized by a narrow band in the vicinity of the Fermi
energy. For such materials ͓e.g., CrCl3 ,7 Ni halides,4–6,9 or
NiO ͑Refs. 4 and 5͔͒, both electronic correlation and the
electron-phonon coupling ͑small polarons͒ should be consid-
ered explicitly.14,33–36
as A, B, and C. The intensity of peak A is weaker than that
of peaks B and C, in contrast to what is observed in XPS
and, for this reason, peak A is attributed to the d states of Ru
atoms. The second and third peaks (B and C) arise from the
3p states of chlorine. The first p band (B) shows a clear
dispersion which is not attenuated at high angles. Along
⌫M ͑Fig. 3͒, the B band is symmetrical with respect to the
Ј
M point, and reaches the ⌫ point of the second BZ at high
Ј
angles. The second p band (C), which also has dispersion,
does not follow the symmetry of the BZ. The extrapolation at
constant binding energy of the C band along ⌫K reaches
point M at an energy near 6 eV, corresponding to the binding
energy at the M point ͑Fig. 4͒.
Ј
Feature A, about 0.75 eV below the Fermi level, shows a
very weak dispersion, less than 0.2 eV across the entire Bril-
louin zone. We think that this dispersionless band near EF ,
observed by a surface-sensitive technique, is a true feature of
bulk RuCl3 . It is possible that the observed localization only
occurs for Ru 4d electrons at the surface; however, for a
surface state we expect appreciable changes with photon en-
ergy or a contaminated surface, which we did not observe.
One can learn many interesting things from the results pre-
sented in Figs. 3 and 4. First of all, they show that the fun-
damental difference between Ru 4d and Cl 3p lies in their
energy bandwidths. The bandwidth for the chlorine bands is
about 2 eV, while that of the Ru 4d band is about 0.2 eV.
For the 4d band we obtain a ratio U/Wdу7: this ratio,
greater than unity, seems to indicate that the one-electron
picture should not give a proper description of the d states
͑see, for example, the band calculation for 3d bands in Cr
and Ni halides made in Ref. 7͒, and that a more localized
model would be a more appropriate approach.22
We interpret these results by assuming that the broad Cl
3p bands provide enough of a degree of freedom for relax-
ation so that the PES experiment measures approximately the
one-electron band structure. On the other hand, the localized
4d band which has stronger correlations, cannot relax during
the measurement, and therefore the final states are excited
states, which can be assigned to 4d4 unscreened holes. The
narrowing of the dispersional part of the Ru 4d band is thus
believed to be due to d-level correlation effects. If this de-
scription of the electronic properties of ␣-RuCl3 is valid, it
also appears that the material investigated here does not
seem to be a conventional band-gap semiconductor.
Thus, coming back to Fig. 1, where the comparison of the
XPS valence-band spectrum of ␣-RuCl3 with that of metal-
lic RuO2 is shown, one can say that, although the XPS spec-
trum of RuCl3 is very similar, the Fermi level is not inside
the t2g manifold and the compound is not a metal; in addi-
tion, the covalency-overlap interactions do not seem strong
enough for the formation of itinerant ͑bandlike͒ 4d states.
This also seems to be confirmed by the results of ARP spec-
tra, which show almost dispersionless Ru 4d bands along
important symmetry lines. These data suggest that the 4d
states remain quite localized, and that electronic conduction
in the 4d narrow band is not possible because of the pres-
ence of the correlation gap, which prevents the material from
becoming metallic.
The electrical conductivity measured in the paramagnetic
phase of ␣-RuCl3 , shown in Fig. 2 of Ref. 18, shows a
temperature dependence typical of
a
semiconductor
(␳RTϳ2ϫ103⍀ cm͒ with an activation energy around 0.1
eV below 300 K, and about 0.5 eV above 400 K, for the
crystallographic directions parallel and perpendicular to the
c axis. The fact that deviations from linearity occur above
400 K indicates that the lower activation energy may not be
due to an intrinsic process. It is also worthwhile noting that
the thermal activation energy for conduction above 400 K
corresponds to an energy gap of about 1 eV very close to the
value obtained in photoconductivity.16 Hall-effect measure-
ments performed in the layers perpendicular to the c axis in
the 180–320-K range have been also reported.21 The sign of
Hall coefficient indicates electron conduction in the tempera-
ture region studied: the temperature dependence of the Hall
mobility ␮ varies as TϪ2.3, and its value is 0.1Ͻ␮Ͻ1
cm2 V sϪ1. The decrease of the electron mobility indicates,
according to Ref. 21, that the electrons ͑holes͒ move in the
conduction ͑valence͒ band, derived from the 4d5 crystal-
field split levels with bandwidths about 0.1–0.2 eV, and
separately by an energy gap EGϳ0.3 eV. As a matter of fact,
crystal-field excitations between single-ion 4d5 spectral lev-
els appear as a discrete structure in the absorption spectrum18
observed below the outset of the strong 3p-4d absorption
edge of the electrical dipole-allowed charge-transfer transi-
tions observed around 4 eV ͑see Fig. 9 of Ref. 16͒.
The absorption coefficient is of the order of 104 –105
cmϪ1 over 1 eV, where a photoconductivity tail is observed,
while two small peaks at 0.3 and 0.5 eV are measured with
absorption coefficients of the order of 103 cmϪ1. The ab-
sorption observed in the range 0.1–3 eV has been assigned to
ligand-field transitions in terms of the Tanabe-Sugano dia-
A last comment abut the absence of photoemission satel-
lites in the PES data also seems important. It is well known

53
ELECTRONIC PROPERTIES OF THE NARROW-BAND . . .
12 775
jority carriers are electrons.21 This picture, which does not
seem unreasonable, seems to indicate a smaller screening of
the intra-atomic Coulomb repulsion, and that the low-spin
compound is approaching the delocalization boundary.38,39 In
this sense consideration of the electronic absorption in the
energy region over 3 eV, reported in the reflectance spectrum
of Fig. 11 of Ref. 16, seems interesting. The ‘‘extra’’ absorp-
tion, observed in reflectance, between the first 1-eV spin-
allowed d-d transition ͑which in this material may approach
delocalization through a covalency relaxation mechanism͒
and the first parity-allowed charge-transfer p-d transition
around 4 eV, consists of broad bands of slightly higher ex-
tinction coefficients than the accompanying ligand-field type,
overlapping to produce long, relatively unstructured absorp-
tion and a photoconductivity tail. The photocurrent, due to
the excitation of electron-hole pairs in the MH bands,
steadily increases up to 2.5–3 eV and is observed in the
region where the extra absorption occurs. On decreasing cor-
relation one must progressively move towards a one-electron
band description, passing through a region where the two
descriptions ͑ligand field vs one-electron band picture͒ must
be merged. This extra absorption may thus be considered as
an indication for delocalized d-d ligand-field transitions
rather than intersite hopping transitions, which seem to occur
most likely in strongly hybridized, low-spin compounds.
Thus, although this magnetic material can be described by
means of a localized model of the grounds of its spectro-
scopic, electronic, and magnetic features, the room-
temperature transport properties, if they are not of extrinsic
origin ͑tentatively ruled out by Refs. 18 and 21͒, seem to
indicate a more conventional approach based on a band
model. One should conclude that the theory of either photo-
emission or layered TMH’s ͑or both͒ is poorly understood.
The implication is that one should be cautious in making
deep interpretations when the general phenomenology is in
part contradictory ͑i.e., inconsistency between photoemission
results and transport properties͒ and incomplete. For a better
understanding of these materials with open 4d or 5d shells,
further investigations, both theoretically ͑band or localized
model calculations͒ and experimentally ͑new transport mea-
surements on pure, stoichiometric, carefully checked crys-
tals, and perhaps resonant photoemission with a synchrotron
source͒, seem necessary and are called for.
gram for the d5 configuration,8 with a value of the crystal-
field splitting parameter ⌬CFϭ1.4–1.5 eV for the low-spin
configuration ͑see Table I͒. While the low-energy weak
peaks at 0.28 and 0.53 eV have been assigned to spin-
6
4
forbidden transitions (2T2→ A1 and 2T1→ A1), the first
strong absorption peak at the 1.18- and 2.08-eV bands have
2
been attributed to spin-allowed transitions (2T2→ A2 ,2T1
2
2
and T2→ T2 ,2A1).
Table I reports the high-low spin change of the crystal-
field parameter for some typical 3d and 4d transition-metal
compounds.18–20 An increase results in the ratio ⌬CF /B
when one considers a low-spin compound in which one
moves to the right on a Tanabe-Sugano diagram.8 In such
conditions, for four-, five-, six-, and seven-electron systems
and octahedral coordination, 4d and 5d electrons no longer
follow the Hund spin alignment with promotion to eg states,
and favor double occupation of the t2g states. The absence of
eg electrons in RuCl3 gives a value of ⌬CF below that of
FeCl3 , though the ⌬ CF /B ratio still remains larger in the
4d compound.18
However, crystal-field excitations between localized
states involve no transport of charge and should not contrib-
ute to electrical conductivity. As previously recalled, elec-
trons are essentially localized in the narrow t2g band ͑a band-
width of about 0.2–0.3 eV͒ and cannot move, even if the
band is not full, for the energy cost of transferring a 4d
electron to an adjacent site. The transport properties of the
material18,21 thus seem in contrast with the recent classifica-
tion of RuCl3 as a MH insulator, based on PES results: that
is, is ␣-RuCl3 a band or Mott semiconductor?
If we accept a localized description of the valence-band
d electrons, there is little reason to expect that the
3d-electron wave vector be conserved in the photoemission
process; hence the Ru 4d profile in ARP spectra is expected
to be unchanged with the electron wave vector, and just vary
in intensity following the photoemission cross section. The
experimental bandwidth of feature A assigned to Ru 4d
states show a very small dispersion (р0.2 eV͒, less than the
one-electron bands. If the narrowing of the cation 4d band
can be considered a result of the d-level correlation effect,
then we are left with a MH insulator, and it is not easy to
explain its semiconductivity in the case of a pure, stoichio-
metric material.
On the other hand, one may consider that the weak dis-
persion of feature A observed in the photoemission spectra
can be due to a small hybridization with ligand 3p orbitals,
which can delocalize the 4d states to some extent, thereby
making them describable within the band picture ͑different
from the result of the ground-state calculations͒. Thus the
weak dispersion of the Ru 4d structure could have this ori-
gin, no different from the ͑stronger͒ dispersion effect ob-
served in the 3d band of NiI2 .37 In the latter compound, a
charge-transfer semiconductor, the observed transport pro-
cess is then explained by hole conduction in the ligand I
5p band,9,37 and by polaronic conduction in the 3d band.14
Thus, if one insists in explaining the electrical properties of
RuCl3 by means of a band picture model, one must claim
that the partially hybridized 4d states are not to be too local-
ized, and that either carrier ͑electrons and holes͒ is moving in
these states of large effective mass and with very low Hall
mobility. The Hall measurement then specifies that the ma-
IV. CONCLUSIONS
A recent study of the electronic properties of the low-spin
compound t52g ␣-RuCl3 suggested that this material may be
classified as a Mott-Hubbard insulator. This was not an evi-
dent result for a 4d compound, since the larger d orbitals
imply smaller correlation U and larger bandwidth B param-
eters, weakening the Mott tendency for many 4d and 5d
cations. The less corelike nature of the 4d orbitals, mani-
fested in more hybridization, is evidenced by a larger crystal-
field parameter ⌬CFӍ1.5 eV and smaller Racah parameter
(Bϭ370 cmϪ1), due to both larger average radii and in-
creased covalency.
Photoelectron spectroscopy has been used in order to de-
termine the energy separation of the localized Ru 4d states
from the Cl 3p bands, and their dispersion curves in the
Brillouin zone. Angle-integrated and -resolved photoemis-

12 776
I. POLLINI
53
sion, together with photoconductivity, give an estimation of
the Coulomb correlation energy Uϭ1.4–1.6 eV. It is found
that the Ru 4d states, separated by 2 eV from the top of the
valence-band 3p states, do not disperse more than Ϯ0.1 eV
across the entire Brillouin zone. It is believed that the ob-
served lack of dispersion is evidence of localized 4d elec-
trons. In line with a Mott-Hubbard model, valid for
U/WdϾ1, it is found that the estimated ratio for ␣-RuCl3 is
у7 and, therefore, it is believed that a localized picture may
be a more appropriate approach for the description of its
electronic, optical, and magnetic properties.
However, this description seems contradictory with the
transport properties describing the material as a conventional
band-gap semiconductor. In addition, one-electron band cal-
culations are not known for ␣-RuCl3, and from a comparison
with the XPS spectrum of RuO2, which is bandlike, one can-
not rule out a priori a standard band picture for 4d states
owing to the strong similarity of the spectra. Thus, although
one cannot exclude a band conduction for the description of
the electrical properties of this compound approaching the
delocalization boundary, in consideration of its optical and
magnetic characteristics and angle-resolved photoemission
results one can also regard it as an unconventional
semiconductor39 in the Mott sense. The apparent inconsis-
tency between photoemission and transport results may be
understood by considering that photoemission investigates
the multielectron excited-state system under relaxation cor-
rections greater than the relevant bandwidth (4d band͒,
while transport measurements study the ground-state behav-
ior of the system. In photoelectron spectra of Mott materials
the multiplet structure of d states is observed, which is char-
acteristic of the final-state electron count, not the initial
state.17,32 In conclusion we suggest that for ␣-RuCl3 the ap-
pellation ‘‘Mott insulator’’ is more informative in regard to
the transport and magnetic characteristics of this material
than the label of ‘‘band-gap semiconductor’’ attributed to it
in the literature.
ACKNOWLEDGMENTS
The photoemission measurements have been performed at
the University of Toulose, Solid State Physics Laboratory, as
a part of an international cooperation research program. I
thank B. Carricaburu and R. Mamy for experimental work
and critical comments on the whole subject.
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