University of Groningen
High energy spectroscopy on vanadium oxides
Pen, Hermen Folken
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1997
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Pen, H. F. (1997). High energy spectroscopy on vanadium oxides: Electronic structure and phase
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Chapter 5
The quasi-one-dimensional vanadium
bronzes
Abstract
We study the electronic structure of the -Mx V2 O5 vanadium bronzes
using XPS, RPES, and XAS. We present O-1s/V-2p core level and valence band spectra of Nax V2 O5 (x = 0:27; 0:33) and Cu0:33V2 O5 single
crystals, and for comparison, of the d 0 insulating compound CaV2 O6 . It
is concluded that the valence of Cu in Cu0:33 V2 O5 is close to 1+, and
that the Na doping in Nax V2 O5 introduces electrons in the V-3d valence
band. The V-3d spectral feature has a low weight near the Fermi level,
due to the strong electron-phonon interaction. Its V-3d character is supported by resonant photoemission, which also shows that the O-2p band
has a considerable V-3d character.
The O-1s and the V-2p absorption edges of Na0:33 V2 O5 show a pronounced linear dichroism. The V-2p edge is described quite well by the
crystal eld multiplet model. However, the broad spectrum and the complicated crystal structure prevent the analysis of the dichroism within
this model. The O-1s edge is compared to the O-p unoccupied density of
states, and its dichroism is explained by the anisotropy in the O-2p{V-3d
hybridization. A band structure calculation shows that the Fermi level
is located in a narrow quasi-one-dimensional band. The calculation predicts Na1=3 V2 O5 to be metallic, in contrast to the observed hopping-like
conductivity. This suggests that the charge carriers are localized, due
to the electron-phonon and/or long-range Coulomb interactions. These
eects, in combination with the anisotropic hybridization, may account
for the low-temperature behaviour of the electrical conductivity.
5.1 Introduction
The -phase vanadium bronzes MxV O (M=Li, Na, K, Cu, Ag) are a series of quasi one-dimensional compounds. This class of materials drew a lot
of attention since Chakraverty connected a linear term in the specic heat of
Na : V O to the presence of V -V singlet pairs, the so-called bipolarons. It
2
0 33
2
5
4+
4+
5
80
Chapter 5. The quasi-one-dimensional vanadium bronzes
Fig. 5.1: Schematic structure
of the -Mx V2 O5 phase (monoclinic, C 2=m). Heavy (light)
markings and circles are centered at y = 1=2 (y = 0). (After Ref.[9].)
c
M2
M3
M4
M1
V3
V2
a
V1
was also suggested that these bipolarons could be precursors to superconductivity [1], but superconducting behaviour has not been reported for the vanadium
bronzes up till now. However, in the Li, Na, Cu and Ag bronzes a structural
phase transition has been observed at temperatures below 200 K [2-4]. It was
shown by V NMR studies that the transition temperature depends on composition and decreases with the reduction of the sodium content in -NaxV O
[5]. X-ray diraction shows that at these temperatures the crystal is slightly
distorted, resulting in a doubling of the unit cell along the b-axis [3]. Together
with magnetic resonance studies [2, 4, 6] this has lead to the attribution of this
phase transition to the formation of bipolarons. At higher temperature, single
V ions and bipolarons coexist.
The rst report on the vanadium bronzes dates already from more than a
century ago [7], but it was not before 1955 that the complicated crystal structure
was determined [8]. The structure of the MxV O - phase is monoclinic and
has a highly anisotropic character, as is shown in Fig. 5.1. There are three
non-equivalent V positions: the V and V atoms are surrounded by distorted
oxygen octahedra and the V atoms by oxygen bipyramids. The distortion of
the octahedra is approximately tetragonal (D h), with one elongated and one
shortened V-O distance; the fourfold rotation axes are in the ac plane. The
oxygen polyhedra are joined by corners and edges and form chains along the
b-axis. This results in the formation of a tunnel-like structure in which metal
atoms M are incorporated. In the Cu and V bronzes, the M ions are randomly
distributed over the M sites. However, two M ions can not occupy neighbouring
M sites, so the occupancy shows a short-range correlation. In the compounds
with x = 1=3, the M ions are completely ordered within each M tunnel.
The one-dimensionality of these compounds is also manifested in their elec51
2
4+
2
1
2
3
4
1
1
5
5
81
5.1. Introduction
Fig. 5.2: Temperature dependence
of the conductivity in Na0:33 V2 O5
parallel and perpendicular to the baxis. The straight lines correspond
to activation energies of 61 meV for
k and 54 meV for ? [*].
tronic properties. The room temperature conductivity of Na : V O along the
b-axis is 110 , cm, , two orders of magnitude larger than the conductivity
perpendicular to the b-axis [10]; its temperature dependence is semiconductorlike. Optical reectivity shows a plasma edge only for light polarized parallel
to the one-dimensional direction [11]. Although it was rst thought that the
anisotropic electronic properties were due to the formation of a one-dimensional
Na-3s conduction band [12], the absence of the NMR Knight shift for M atoms
[13, 14] shows that Na is completely ionized and that the 3s orbitals are empty.
ESR measurements [2, 15] show that most of them are located at the V sites.
This was already expected by Goodenough [16]: using a molecular orbital bonding scheme, he argued that the electrons should enter the V -dyz orbitals (see
also page 82). Later it was found from an analysis of the g-factor measured
by EPR, that at T = 77 K the dyz is indeed the lowest orbital. Another characteristic property is the low mobility [17]: in Na : V O , the Hall mobility
is 1:8 10, m V, s, at 298 K and 9 10, m V, s, at 106 K. In the
Drude model, this would yield a mean free path which is shorter than the interatomic distance, so the electrons are expected to be localized. Furthermore, the
mobility increases with T , suggesting some kind of thermally activated hopping.
The most characteristic property of NaxV O is its one-dimensional conductivity (Fig. 5.2). The conductivity along the b-axis (k ) is about two orders of
magnitude larger than the conductivity perpendicular to it (?). The temperature behaviour of the conductivity is quite complicated: for T ' 80K it can
1
0 33
1
2
5
1
1
H
5
2
1
1
6
2
5
0 33
2
2
1
5
1
82
Chapter 5. The quasi-one-dimensional vanadium bronzes
be described by
/ T , exp(,EA =kB T );
(5.1)
with slightly dierent activation energies E k = 61 meV and E ? = 54 meV for
k and ? [10]. This description holds up to ' 140 K for k and up to ' 210 K
for ?. For T > 140 K, Eq. (5.1) still seems to hold, but with a smaller E k of
1
a
a
a
49 meV [17]. If the charge carriers are localized into small polarons, one would
under certain conditions [18] indeed expect a temperature dependence like in
Eq. (5.1) if the carrier concentration is constant. However, it is not certain
whether one of the required conditions (the optical phonon energy ~! has to
be much larger than kT ) holds in the temperature range of Fig. 5.2 [18].
At low temperature, the conductivity was analysed in another way. Wallis et
al. found that between 18 and 215 K the perpendicular conductivity is very well
described by log ? / T , = , which suggests a two-dimensional variable range
hopping (VRH) conduction. The VRH mechanism describes hopping through
localized orbitals in a random potential, and the conductivity is
0
1 3
/ exp[,(1=T ) = n ];
1 ( +1)
(5.2)
where n is the dimension of the conduction path. For k , the temperature behaviour is more like log ? / T , = , although the t is less good than for ?.
The temperature dependence of k is not in agreement with the VRH model,
which predicts log ? / T , = in one dimension, suggesting an interruption of
the one-dimensional conduction path. In fact the coecient of 1/4 would be
consistent with three-dimensional VRH, but given the strong anisotropy of the
material, Wallis et al. consider this apparent T , = behaviour as accidental.
They note the similarity to the conductivity of the quasi-one-dimensional compound K Pt(CN) Br : 3H O (KCP) [19] for which the \interrupted-strand"
model was proposed [20]. According to this model, k is \governed" by ? due
to a break in the conduction path: if a chain is broken, for example due to
impurity potentials, it is necessary for an electron to make a hop perpendicular
to the chain, in order to proceed in the \one-dimensional" direction. In this
model, the ratio k =? is given by T = if the length of the strands is xed [19].
The dependence k / T P = exp(,1=T ) = ts very well to the experimental
data; however, the exponent P = 1:76, much larger than the expected P = 2=3.
This could mean that the average strand length is not constant, but increases
with temperature. Above T = 125 K, the activation energy for k decreases
sharply and k seems no longer limited by ?. This temperature is quite close
to the transition temperature for the bipolaronic state [14]. It is also worth
noting that below 100 K the AC conductivity at 100 GHz along the b is much
larger than the DC conductivity [21]. This is also in agreement with a broken
conduction path, because the break will be less eective for AC than for DC
conductivity.
1 4
1 2
1 4
2
4
03
2
2 3
1 3
83
5.1. Introduction
(a)
O7
Fig. 5.3: Idealized
sublattice chains parallel to the b-axis of the Mx V2 O5 phase: (a)
bipyramidal-site chain; (b) octahedral-site
chain (after Ref.[16]).
O8
O5’
V3
O5
V3’
O8’
b
O7’
O7
z
O8
O5’
V3
y
O5
V3’
O8’
O7’
O3’
x
O2’
V1’
(b)
V2’
O6
O2’
O4
O5
V2
O8
V2’
V1
O2
O6’
O3’
O4’
O2’
O8
V1’
O5’
O6
O3’
V2’
O2’
b
O6’ O
4
V1
O2
O6’
O1’
O5
V2
V2’
O6’
O3
O2’
O3
O2’
V1’
V2’
a/2
Because the crystal structure is complicated, it is good to discuss it in some
more detail, especially in connection to its electronic structure. We will briey
discuss here the explanation of Goodenough [16], who analysed the relation
between the electronic structure and the atomic positions and bond lengths.
To follow his reasoning it is convenient to remodel Fig. 5.1 a little bit. This
is done in Fig. 5.3, which shows an idealized representation of the octahedral
and bipyramidal site chains. The structure of Fig. 5.1 is \stretched" along the
b axis so that all V-O-V bonds along the (010) direction are 180. It is now
possible to introduce a Cartesian coordinate system with the z-axis along (010)
and the x-axis along the V -O -V directions. In this way, the V-O bonds of
the distorted octahedra are approximately along the coordinate axes, so that it
is sensible to speak about V-3d orbitals of t g and eg symmetry.
Goodenough states that the V-O bond lengths, given in Table 5.1, are an
indicator for the multiplicity of the cation-anion bonding. There are three
distinguishable categories: triple (d 1:58 A), double (d 1:80 A) and single
bonds (d 1:89 A). Because the O-2p{V-3d bonding orbitals are completely
lled, the doped electrons will enter the lowest antibonding orbitals, which are
of approximately t g symmetry. The most unstable are the eg orbitals and t g
orbitals that take part in the triple bonds: V -dxy and dzx; V -dxy and dyz ;
V -dxy , dyz , and dzx. Therefore, the doped electrons should necessarily enter
either the V -dyz or the V -dzx orbitals. The latter is expected to be more
2
1
20
2
2
2
1
3
1
2
2
84
Chapter 5. The quasi-one-dimensional vanadium bronzes
V1 -O distances
V1 -O4 1.56 A
V1 -O2 1.89 A
V1 -O5 1.95 A
V1 -O3 2.01 A
V1 -O2 2.32 A
0
V2 -O distances
V2 -O6 1.58 A
V2 -O1 1.80 A
V2 -O3 1.89 A
V2 -O5 2.16 A
V2 -O2 2.34 A
0
V3 -O distances
V3 -O8 1.56 A
V3 -O5 1.78 A
V3 -O7 1.91 A
V3 -O7 2.00 A
V3 -O6 2.68 A
0
Table 5.1: Nearest-neighbour V-O distances for the Nax V O
2
5
phase [8].
unstable because of the strong V -O bond (compared to V -O ), due to the
shorter V -O distance and the V -O -V bond angle of exactly 180. So, the
electrons should preferably occupy the V -dyz orbitals.
Also the hopping process of the V -dyz electrons to another site in the V
array is discussed within the same framework. Direct V -V hopping would
account for the strong anisotropy in the resistivity, but the large V -V separation of 3.36 A is not in agreement with the small activation energy. It is
argued that the hopping should therefore occur via an intermediary V or V
site, and because also the V -V and V -V distances are large, the V-V coupling should be via an intermediate anion. This reasoning is however not clear:
the V states are also directly coupled via the O ions. The V -O -V bond
angles are 151, so quite close to 180, which means that this coupling should
also be quite strong.
Although there are many publications on the vanadium bronzes that discuss
the electronic structure in at least some qualitative way, the number of x-ray
spectroscopic studies on the electronic structure is rather limited. Only x-rayemission (XES) [22] and V-1s x-ray-absorption [23] on Na : V O , and core
level x-ray-photoemission [9] on 0-Cu : V O have been published. In Ref. [9]
the chemical shifts of the V and Cu 2p core levels, which provide information
about the valence of the dierent ions, have been measured for powder 0Cu : V O samples. However, experimental information about the states near
the Fermi level, which determine the electronic properties, has not been obtained
until now.
We performed core level and valence band x-ray-photoemission spectroscopy
(XPS) on single crystals of the vanadium bronzes Cu : V O and NaxV O ,
which gives information on the valence of Cu and V in these materials. To
examine the inuence of Na doping we have studied two dierent compositions
(x = 0:27, 0.33) of the latter compound; also the d insulator CaV O was measured for comparison. In this way, we can verify the current ideas about the Cu
and V valence in these compounds. The main issue of this chapter is however a
combined resonant photoemission (RPES) and x-ray-absorption (XAS) study on
Na : V O single crystals, to probe both occupied and unoccupied states close
to the Fermi level. The nature of the valence band was examined by resonant V2
1
2
1
2
1
1
3
20
1
1
1
10
1
10
1
2
1
2
1
3
20
1
0 33
2
2
5
5
0
2
2
1
5
0 33
0 33
20
1
0 33
0 33
3
5
2
5
2
2
6
5
85
5.2. Core level and valence band XPS
2p and V-3p photoemission, which gives information about its V-3d character.
The results are compared to the V-3d occupied density of states, as obtained
from an LMTO band structure calculation. Furthermore, we have studied the
unoccupied states of Na : V O by means of V-2p and O-1s XAS. We made use
of the linear polarization of the x-rays to examine the linear dichroism, which is
expected from the highly anisotropic properties of this compound. The dichroism at the V-2p edge was determined by the V-3d electron occupation of the
dierent sites and by the energy splitting of the V-3d levels. By a comparison
to crystal eld multiplet calculations, in which dierent ground states can be
simulated, one can try to determine the ground state symmetries and in this
way test the assumptions made about the level ordering [15, 16]. The O-1s edge
probes unoccupied states of O-p character. Because of the strong covalence and
the small inuence of multiplet eects in the nal state, we may expect that the
spectrum is related to the unoccupied O-p projected densities of states. The
polarization dependence, measured with polarization vector either parallel or
perpendicular to the \one-dimensional" (010) direction, will thus give information about the anisotropy in the O-p DOS. The experimental O-1s spectra are
also compared to the results of the band structure calculation.
0 33
2
5
5.2 Core level and valence band XPS
Experimental
XPS measurements were carried out using monochromatized Al K radiation
(1486.6 eV). The pressure in the UHV chamber was 2 10, Pa. The overall resolution was about 0.6 eV for the core level spectra and 0.7 eV for the
valence bands. The binding energy was calibrated by measuring the 4f = line
of a sputter-cleaned Au foil. The samples were glued to an aluminium sample
holder and their edges were covered with graphite to make electrical contact.
To obtain clean surfaces, the samples were cleaved by the post method: a small
aluminium block was glued on top of the sample, and knocked o in the UHV
chamber using a wobble stick. The preferred cleavage plane of the V bronzes
is (001), but the surfaces of the cleaved samples appeared not completely at
when looking at it through a light microscope. The cleanliness of the samples was ensured by monitoring the intensity of the C-1s line. The samples
of CaV O and the V bronzes appeared very clean immediately after cleaving.
The Cu : V O samples showed some residual contamination after cleaving,
which was largely removed by scraping with a diamond le. Not surprisingly,
the CaV O samples showed charging eects, in the form of a kinetic energy
shift of the photoelectrons. The charging could be removed only partially using
a ood gun. Therefore, the spectra were aligned by the C-1s core lines which
appear some hours after cleaving. With this alignment, also the O-1s and O-2s
lines coincide.
8
7 2
2
6
0 33
2
2
6
5
86
Chapter 5. The quasi-one-dimensional vanadium bronzes
Fig. 5.4: X-ray
photoemission
spectra of the Cu0:33 V2 O5 Cu2p3=2 core level.
Cu-2p core level x-ray-photoemission spectroscopy
The Cu and V ions in Cux V O can, in principle, take dierent valences. In
order to determine the Cu valence, we measured the Cu-2p = core level spectrum, which is expected to be strongly inuenced by the oxidation state of the
Cu ions. First, one expects a chemical shift towards higher binding energy upon
going from 1+ to 2+ valence: for example, the Cu and Cu 2p = core line of
CuO (Cu ) is at 933.2 eV and that of Cu O (Cu ) is at 932.4 eV [24]. Second, the contribution of Cu shows a pronounced satellite. The CuO satellite
is due do 2p 3d and 2p 3d L (L=ligand hole) nal states; for Cu , only a
2p 3d nal state is possible. In CuO, the satellite binding energy is at about
9 eV higher than the main peak, and the intensity is comparable.
In Fig. 5.4 the Cu-2p = XP spectrum of Cu : V O is shown. At 931.2 eV,
a single pronounced peak is observed; because of the low binding energy it is
attributed to Cu . The two weak features around 934.5 eV (A) and 942 eV (B)
could be assigned to the main peak and the satellite of Cu . However, this
assignment is problematic, because of the large dierence between the \satellite"
and the \main" peak, and also because of the relatively large intensity of the
\satellite". Another possibility is that peak A is due to interatomic screening
eects; for NiO and CuO it has been shown that these give rise to satellites a
few eV above the main line [25]. Extrinsic losses could be the origin of feature
B: other strong core lines show also satellites at 10 eV above the main line.
The conclusion that the Cu ions mainly have a 1+ valence state is in agreement with ESR measurements [26]. Also an XPS study has been reported on
the copper vanadium bronzes. This dealt however with a compound somewhat
dierent from the one studied here, namely the 0 phase, in which the Cu ions
1 Also Cu O shows a satellite (at 945 eV) due to states involving the sp conduction
2
2
5
3 2
2+
2+
2+
5
5
9
5
+
1+
2
1
+
10
10
3 2
0 33
2
5
+
2+
band; this one is however very weak.
3 2
87
5.2. Core level and valence band XPS
Fig. 5.5: Upper panel: X-ray photoemission spectra of the O-1s and V-2p core levels
of the vanadium bronzes and CaV2 O6 . Lower panel: Deconvolution of the Nax V2 O5
spectra into V4+ and V5+ contributions.
occupy the M sites instead of the M sites. The XPS data on an x = 0:40 powder sample indicated a mixed valence state. In the Cu-2p = core level spectrum
two peaks, with a splitting of 2.6 eV were observed; the one at higher binding
energy, with a relative intensity of 60%, was attributed to Cu , and the other
one to Cu . With some precaution, we would like to note that this remarkably
dierent result may not be related to the dierent crystal structure of the and
0 phases, but to surface oxidation of the 0-phase powder samples This would
yield XP spectra that are not representative for the bulk material.
3
1
3 2
2+
1+
O-1s and V-2p core level x-ray-photoemission spectroscopy
The upper panel of Fig. 5.5 shows the combined O-1s/V-2p XP spectra of
Cu : V O , CaV O , Na : V O , and Na : V O . The O-1s core lines of the
0 33
2
5
2
6
0 27
2
5
0 33
2
5
V bronzes are wider (1.5 eV versus 1.2 eV) and more asymmetric than those of
CaV O . The asymmetry is due to the electrons in the valence band, introduced
by the Na doping. The broadening can be intrinsic: the many inequivalent
2
6
88
Chapter 5. The quasi-one-dimensional vanadium bronzes
crystallographic sites in the bronzes and the randomness in the Na distribution
will both lead to variation in the Madelung potential at the V sites. Also
extrinsic broadening can be present: before leaving the solid the photoelectron
can lose energy due to e.g. plasmon excitations.
The V-2p = peaks of NaxV O show a pronounced shoulder at 516 eV. It
is absent in the CaV O spectrum and the intensity is larger for x = 0:33 than
for x = 0:27. Therefore, this feature is clearly related to the Na doping, and
it is attributed to the presence of V ions. The lower binding energy of the
V feature is related to a larger nal state screening, due to the V-3d valence
electron. The V-2p = peak of Cux V O shows a similar spectral weight around
516 eV. However, the feature is broader than for the samples containing Na;
this might be due to a lesser sample quality, indicated by the contamination
from N and C, which was present after cleaving. Also the additional scraping,
which was necessary to remove this contamination, could lead to defects and
thus a less well dened sample surface.
One may think of quantifying the eect of doping by making a deconvolution of the V and V contributions by using some curve tting technique.
However, this is not possible, because of the large overlap between the 5+ and
4+ peaks. The best we can do to examine the doping eect more quantitatively
is to make a decomposition by calculating the dierence spectra of the x = 0:27
and x = 0:33 samples. For these two spectra, the dierence in broadening is
probably quite small. If we presuppose that the spectra consist of V and V
contributions, with weights 1 , x=2 and x=2, respectively, we can even make a
deconvolution into these two contributions, as shown in the lower panel of Fig.
5.5. The width of the \V " V-2p lines is larger than for CaV O . This could
be due to the same eects that also causes the broadening in the O-1s peaks,
in particular the dierences in Madelung potential. In CaV O (and in V O ,
which also has narrow V-2p lines [27]) all V ions occupy equivalent symmetry
(Wycko) positions.
Also the \V " contribution to the O-1s part of the spectrum shows a shift
to lower energy. This could be related to a less positive Madelung potential due
to the presence of the V ions. On the other hand, the extra Na ions will
tend to make the Madelung more positive, but this eect is probably smaller
because the Na ions are at a larger distance from the O ions. Also the screening
eect can contribute: because the O ions may hybridize less with V than with
V ions because of the V on-site Coulomb repulsion, the charge on the O ions
can increase.
The small hump at 533 eV is only present in the samples containing sodium.
It is due to electrons of 954 eV kinetic energy, emitted in the Na KL L Auger
process. The strongest Na KLL Auger line appears at 994 eV kinetic energy,
corresponding to 493 eV binding energy. The contribution of Na KLL Auger
in the 510{530 eV binding energy range is very weak and does not inuence the
analysis of the O-1s/V-2p lines.
2
3 2
2
5
6
4+
4+
2
3 2
5+
5
4+
5+
5+
2
2
4+
6
6
2
4+
4+
+
4+
5+
1
23
5
89
5.2. Core level and valence band XPS
Fig. 5.6: X-ray photoemission spectra of the valence bands of (a) Cu :
0 33
Na0:33 V2 O5 , (c) Na0:27 V2 O5 , and (d) CaV2 O6 .
V2 O5 , (b)
Valence band x-ray-photoemission spectroscopy
Figure 5.6 shows valence band spectra of Cu : V O , Na : V O , Na : V O ,
and CaV O up to 27 eV binding energy. The peaks at 25 and 21 eV are due
to Ca-3p and O-2s electrons, respectively. The valence band region of CaV O
extends from 3 to 8 eV and is of mainly O-2p character. A similar band is
observed for the V bronzes; in addition, a narrow feature appears close to the
Fermi energy. For NaxV O , it is attributed to electrons doped into the V-3d
band. The intensity change is almost proportional to the doping concentration:
the ratio of the integrated d-band spectral weights (after subtracting a constant
background and normalizing to the intensity of the O-2s band) is 1:25 0:03,
in good agreement with the ratio of the Na concentration, 0:33=0:27 = 1:23.
The peak at 2 eV in Cu : V O is due to Cu-3d electrons and is relatively
narrow. The peak position is in agreement with the 1+ valence state; if Cu
would be 2+, one would again expect a double peak structure similar to that
in the valence band of Cu O. Here, a low-energy feature is due to a d L nal
state, and the 3d nal state is at much higher binding energy ( 12 eV) due to
the strong Coulomb repulsion between the two Cu holes in the 3d nal state.
Also, the low-energy feature in CuO is much broader than in Cu O ( 4 eV
against 2 eV), due to multiplet coupling and charge transfer screening in the
nal state. So also from the narrowness of the Cu-3d peak it is more likely that
Cu is in a 1+ valence state.
0 33
2
2
5
0 33
2
5
0 27
2
5
6
2
2
5
0 33
8
2
5
9
2
8
2
6
90
Chapter 5. The quasi-one-dimensional vanadium bronzes
5.3 (Resonant) photoemission
Experimental
The RPES experiments were carried out at the soft-x-ray beam line of the
ASTRID synchrotron in Arhus, Denmark (3p edge), and at the AT&T Bell
Laboratories \Dragon" high-resolution soft-x-ray beam line [28] at the National
Synchrotron Light Source, Brookhaven (2p edge, and at 110 eV photon energy).
The UHV chamber base pressure was 2 10, Pa in Brookhaven and 5 10,
Pa in Arhus. The overall resolution was 0.3 eV for the spectra taken around the
3p edge, 0.5 eV at the 2p edge, and 0.15 eV for the ~! = 110 eV spectrum. The
binding energy was calibrated for the 3p spectra by measuring the Fermi cuto
in the ~! = 40 eV photoemission spectrum of a sputter-cleaned Ag sample, and
for the 2p spectra by aligning the O-2s line in the o-resonance spectrum to
that of the XP spectrum.
The Dragon monochromator produces a substantial amount of second order
light which aects the photoemission spectra. In RPES, the second order light
is always a problem one has to cope with: at resonance, electrons emitted from
the particular core level by the second order light will have about the same
kinetic energy as valence band electrons emitted by the rst order light. The
2p spectra were corrected by subtracting the appropriately shifted ~! = 544 eV
spectrum; at this photon energy, the second order contributions from the O-1s
and V-2p core lines are just shifted above the Fermi energy of the rst order
spectrum. In the 3p spectra, the contribution of second order light turned out
to be negligibly small.
8
9
High resolution valence band photoemission spectroscopy
Figure 5.7 shows the valence band photoemission spectrum of Na : V O at
110 eV photon energy; this energy is a compromise between resolution and
photon ux. Although it reveals no essential new information compared to
the valence band XPS, the cross sections are dierent, and the resolution is
considerably better (0.15 eV versus 0.7 eV). With the higher resolution it becomes more clear that the spectral intensity at E is extremely small. (The
slightly decreasing background above E might be due completely to second
order light). The spectrum is compared to the occupied broadened DOS of an
LMTO band structure calculation (for details, see Section 5.5), which is shifted
rigidly by 0.7 eV towards higher binding energy. With this shift, the peak
positions match very well.
The low spectral weight (or: the shift of spectral weight to higher binding energy) is an interesting problem, also in connection to the spectra of the
metallic d compounds as discussed in Chapter 6. One might think that the
low spectral weight is due to the one-dimensionality of the system. In a one0 33
F
F
1
2
5
91
5.3. (Resonant) photoemission
Fig. 5.7: Valence band photoemission spectrum (dots) of Na :
0 33 V2 O5 , taken at ~! =
110 eV. The spectrum is compared to the occupied total DOS (solid line), shifted
towards higher binding energy by 0.7 eV. For ease of comparison, the DOS is also
shown after broadening with a Gaussian line shape.
dimensional conductor, the spectral weight at E could be strongly suppressed.
In the Tomonaga-Luttinger model [29], which describes the behaviour of a onedimensional correlated metal, all degrees of freedom are collective (i.e. plasmonlike). There are no quasi-particle elementary excitations like in a normal Fermiliquid, and consequently there is no Fermi edge in the photoemission spectrum.
However, although NaxV O has one-dimensional properties, it is not metallic; the charge carrier are localized, probably in the form of small polarons.
This suggests a large electron-phonon interaction (neglected in the TomonagaLuttinger model) which can also be important for the photoemission spectrum.
What is more, the observed photoemission line shape of NaxV O is quite
similar to that of other lightly doped band insulating transition metal oxides
(three-dimensional La ,xSrxTiO [30] and SrTiO ,x [31], quasi-two-dimensional
V O ,x [32]). Also the quasi-one-dimensional Na : V O can be considered to
belong to this class, if we think of it as a V O host lattice slightly doped by
Na. In this light, the dimensionality of the system seems less important to the
spectral shape when comparing dierent lightly doped early transition metal
oxides.
The broadness of the V-3d feature has been discussed earlier by Egdell et
al. [33] in a PES study on La ,x Srx VO , who attributed it to strong electronphonon interactions, related to the strong polarization of the lattice by the
valence electrons. The broadening mechanism is a manifestation of the FranckCondon eect (see also Section 2.1), well known from molecular spectroscopy.
When an electron is photoemitted, the polarization cloud that it was carrying
F
2
5
2
1
2
3
3
5
0 33
2
1
3
5
2
5
5
92
Chapter 5. The quasi-one-dimensional vanadium bronzes
along with it, is left behind. This is clearly a non-equilibrium state, and the
lattice will relax, but on a time scale much larger than that of the photoemission
process. The PES intensity close to E (related to the \undressed" electron,
corresponding to the \0-0" peak of Fig. 2.1) will be strongly suppressed, and the
spectrum will peak around the relaxation energy, which should be considered,
according to Koopmans' theorem, as the binding energy of the electron.
Figure 5.7 shows that the binding energy of the 3d electrons in Na : V O
is about 0.7 eV. The binding energy of an electron due to polarization can be
estimated using an argument originally proposed by Landau [34], using simple
electrostatics. Consider the electron as a conducting sphere with radius r that
is introduced in a polarizable medium from an innite distance. This will cause
a displacement eld D which is zero inside the sphere and jDj = e=(4 r ) for
r > r [35]. The electric eld ER = D, and the energy needed to move the
charge into the medium is (1/2) D EdV = 1=(8 r ). In the solid, the eld
of a moving electron is screened due the polarization of the other electrons, and
this screening is associated with a dielectric constant (! = 1). However, if
the electron is localized, the dielectric constant (! = 0) is larger because now
also the slowly moving ion cores are able to contribute to the screening. So if
the electron localizes, it gains an energy 1=(8 r )[1=(1) , 1=(0)] relative
to the delocalized electron. Of course, although the electron is \trapped" now
in a potential well, it will still have a kinetic energy in its new ground state.
This energy is given by the virial theorem [36], which states that in the ground
state the average kinetic energy is equal to half of the average potential energy.
Thus, the net binding energy is
1 , 1 ):
E = 161 r ( (1
(5.3)
) (0)
The approximation used here is very rough, a better way is to calculate the
polarization of the nearby atoms explicitly and use the continuum approximation for the more distant atoms. However, the obtained expression gives an
idea of the order of magnitude of the polaron radius. Substituting E = 0:7 eV,
(1) = 4:5 [11], and assuming that (0) is large enough to be neglected in
Eq. (5.3), we nd r = 3:6 A. So the peak maximum can be understood if we
assume that the polaron is small, i.e. comparable to the size of the unit cell.
The polaron binding energy is much larger than the activation energy for
electrical conductivity, which is about 60 meV. The latter energy should however
be related to the lowest possible electron removal and addition states (the \0-0"
peaks). In the ideal case, that is, if no disorder is present, the activation energy
can even be zero. This is not surprising: although the electron is bound by its
polarization cloud, the binding energy does not depend on the particular site
that is occupied, and the conduction occurs by tunneling. Indeed, the Holstein
model [37] which describes conduction of small polarons, predicts tunneling
behaviour at low T . In this regime, the polaron is not localized, but it moves
F
0 33
2
p
0
p
0
0 p
0 p
p
0 p
p
p
2
5
93
5.3. (Resonant) photoemission
in a conduction band with a renormalized (reduced) width due to the electronphonon interaction.
Recently, Fujimori et al. [32] pointed out that for V O , and NaxV O the
binding energy of the V-3d photoemission peak is much larger than the activation energy for conduction, while the Holstein model predicts a dierence of only
a factor of two [38]. This discrepancy was attributed to the neglect of long-range
electron-phonon interactions in the Holstein model. Another possibility could
be that the \Holstein" activation energy is indeed large ( 0:35 eV' 4 10 K)
so that the polaron should be described in the low-temperature (tunneling)
regime of the Holstein model. The localized character of the carriers, as suggested by the activated conductivity, may now be related to impurities. Because
the polaron bandwidth is very small, the randomness of the impurity potential
is likely to disturb the coherent polaron motion. In this situation, the conductivity would be determined by variable range hopping [39]; this is indeed
observed, at least at low temperatures (Ref. [10], see also Section 5.5).
2
5
2
5
3
Vanadium 2p resonant photoemission spectroscopy
Figure 5.8 shows the valence band photoemission spectra of Na : V O on
scanning through the V-2p absorption edge. The inset shows the V-2p x-ray
absorption spectrum and the small circles correspond to the photon energies at
which the photoemission spectra were taken. The dots and the thick solid lines
are the spectra before and after correction for the second order contribution.
Because this procedure implies some arbitrariness (e.g. the change in O-1s and
V-2p cross section on going from ~! = 1088 eV to lower photon energy is not
accounted for), also the \raw" data are shown.
From Fig. 5.8 it is clear that both the feature near E and the broad band
around 5 eV binding energy are strongly enhanced on scanning the photon
energy through the V-2p = absorption edge. The maximum intensity coincides
with the maximum in the V-2p = absorption spectrum (see Fig. 5.10). The
enhancement of the O-2p band indicates a large amount of V-3d character in this
band, i.e. a strong O-2p{V-3d hybridization. The O-2p{V-3d bonding states
have a higher binding energy than the non-bonding O-2p states. At resonance,
only the photoemission intensity of bonding states is enhanced, resulting in a
clearly visible shift of the peak maximum to higher binding energy.
Another important eect is the appearance of \incoherent" LV V Auger
emission in the spectrum. The intensity of this broad peak increases also at
resonance; because the kinetic energy of the Auger electrons does not depend
on the photon energy, the peak maximum shifts in the subsequent PE spectra,
as indicated by the dashed line in Fig. 5.8. Weinelt et al. [40] found that in the
2p RPES of Ni there are dierent distinguishable energy ranges for which the
spectrum shows either RPE or Auger-like behaviour. Fig. 5.8 indicates however
that for Na : V O these ranges are not well separated; the RPE and Auger
0 33
F
3 2
3 2
0 33
2
5
2
5
94
Chapter 5. The quasi-one-dimensional vanadium bronzes
Fig. 5.8: Resonant photoemission spectra of Na :
V2 O5 at the V-2p edge. The dots
are the raw data; the removal of second order contribution results in the spectra
represented by the solid lines.
0 33
intensity seem to increase simultaneously.
Due to the strong Auger emission it is not possible to make a quantitative
estimation of the amount of V-3d character in the O-2p band. However, we can
make a comparison to the calculated partial V-3d density of states, as indicated
by the thin lines in Fig. 5.8. Like in Fig. 5.7, the DOS is shifted 0.7 eV towards
higher binding energy. The smooth line shape shows the DOS broadened by a
Gaussian, to ease a comparison with the experimental spectrum. Considering
the Auger background, the agreement between theory and experiment is quite
good. The band structure calculation supports the conclusion that the high
binding energy side of the O-2p band consists of the O-2p{V-3d bonding states.
The intensity near E arises from the occupied O-2p{V-3d antibonding states.
F
Vanadium 3p resonant photoemission spectroscopy
Figure 5.9 shows the V-3p resonant photoemission spectra of Na : V O . The
0 33
2
5
inset shows the constant initial state (CIS) spectra of the three important features. The Auger emission appears to be less pronounced than at the 2p edge.
95
5.3. (Resonant) photoemission
Fig. 5.9: Vanadium 3p resonant photoemission spectra of Na :
0 33
shows the constant initial state spectra of the peaks A, B and C.
V2 O5 . The inset
On the other hand, the resonance is also much weaker here, due to the smaller
cross section for exciting a 3p core electron [41].
For several reasons, the analysis of the resonance eect is much less straightforward than for the 2p edge. In the rst place, the resonance is small compared
to the variation in the O-2p atomic cross section. The smaller kinetic energy of
the photoelectrons for 3p RPES also causes complications, because the electron
wavelength is of the order of the lattice spacing. This can lead to interference
eects between emission from O and V atoms. Also, the nal state is less freeelectron like because it is still aected by the periodic potential of the crystal.
Other eects that make an interpretation of the 3p RPES less straightforward
are: the relatively small spin-orbit splitting (compared to the energy spread of
the intermediate states) and the smaller core hole life time.
Nevertheless, the changes with photon energy are quite similar to those
observed in 2p RPES; this can be seen best from the CIS spectra. Feature A,
connected with the antibonding O-2p{V-3d states, shows the largest relative
enhancement at resonance. Feature B, related to non-bonding O-2p states,
shows the smallest resonance, and feature C, which is due to the bonding O2p{V-3d states, is in between.
96
Chapter 5. The quasi-one-dimensional vanadium bronzes
5.4 Polarization-dependent XAS
Experimental
The XAS measurements were also carried out at the \Dragon" beam line in
Brookhaven. In this experiment, the energy resolution of the monochromator
was approximately 0.15 eV. The energy scale was calibrated using NiO, for
which the O-1s white line energy is known accurately from high energy electron
energy loss spectroscopy experiments [42]. The base pressure in the measuring
chamber was 2 10, Pa. The x-ray-absorption was measured in the total
electron yield mode. The spectra were normalized to the absorption intensities
at 510 and 528 eV, after subtraction of a constant background (approximately
20% of the maximum absorption). Both the one-dimensional b-axis and the polarization vector of the incoming x-rays were within the cleavage plane. Because
the cleavage plane is (001), all spectra could be taken at normal incidence. The
angle between the one-dimensional axis and the polarization vector was varied
by rotating the sample holder.
8
Linear dichroism
Figure 5.10 shows the combined V-2p and O-1s x-ray-absorption spectra of
Na : V O for polarizations along the (100) and the (010) crystal axes, i.e.
perpendicular and parallel to the one-dimensional direction. Both edges show
a pronounced polarization dependence; we will discuss them now separately.
The V-2p x-ray-absorption spectra are mainly determined by on-site V 2p !
3d transitions. The main splitting into the L (2p = ) and L (2p = ) edge is
due to the strong spin-orbit interaction of the 2p core hole. Furthermore, the
spectrum is very sensitive to the symmetry of the V ion ground state. The
transition metal 2p edges are often interpreted by comparison to crystal eld
multiplet calculations; for a d ground state, the calculation is particularly
simple, because d-d Coulomb and exchange interactions are not present even in
the nal state. With a crystal eld of OH symmetry, the core hole spin orbit
coupling and the core-hole{d-electron Coulomb-exchange interaction, seven nal
states are possible. The calculation of 2p absorption edges of d compounds in
OH symmetry has been discussed extensively by de Groot et al. [43].
0 33
2
5
2
1 2
3
3 2
0
0
Vanadium 2p x-ray-absorption spectroscopy
In Fig. 5.11, the \isotropic" experimental spectrum (somewhat articially, the
spectrum with k b plus two times the spectrum with ? b) is compared
to a crystal eld multiplet calculation in OH symmetry. A d ground state is
assumed, i.e. the inuence of doping is neglected for simplicity. To obtain the
best t, a crystal eld parameter 10Dq = 1:4 eV was used, and the p-d Slater
integrals were reduced to 50% of the Hartree-Fock values. The theoretical line
0
97
5.4. Polarization-dependent XAS
Fig. 5.10: Polarization-dependent V-2p and O-1s absorption edges of Na :
V2 O5 .
The dashed line is for polarization parallel to the one-dimensional b-axis, the solid
line is for perpendicular polarization.
0 33
shape, obtained by convoluting the transition probabilities by a Gaussian and a
Lorentzian to account for the experimental resolution and lifetime broadening,
is in good agreement with the experimental spectrum: almost all experimental
features coincide with sticks representing the calculated transitions. Only the
small shoulder at 513.8 eV is not in the theoretical spectrum: this feature is
probably due to the presence of d ions. In the L edge, no separate features can
be distinguished. However, the two dierent L nal states in the calculation
cause an asymmetry in the line shape, which is also present in the experimental
spectrum. The calculated spectrum in OH symmetry already gives a good
agreement with experiment. However, the choice of the broadening parameters
greatly inuences the simulated line shape, which causes uncertainty in the
values for 10Dq and the p-d Slater integral reduction.
The linear dichroism is due to a crystal eld with a symmetry lower than
OH . The VO octahedra are distorted, and have one very short V-O distance
(1.56{1.58 A), while the distance of the opposite V-O pair is much longer (2.32{
2.68 A). Therefore, the crystal eld is of approximately D h symmetry, resulting
1
2
2
6
4
98
Chapter 5. The quasi-one-dimensional vanadium bronzes
Fig. 5.11: V-2p
absorption
edge of Na0:33 V2 O5 , compared to an crystal eld multiplet calculation in OH crystal
eld symmetry.
in dierent absorption spectra for x-rays polarized parallel or perpendicular to
the tetragonal axis. The VO units are oriented in dierent directions, but the
tetragonal axes are all in the ac plane. For a single VO unit, we expect therefore
a dichroism for polarization vectors along the a and b direction. Unfortunately,
an analysis of the dichroism by the crystal eld multiplet model turned out to
be impossible, even with the assumption of a D h symmetry. The inuence of
the d ions can not be neglected now: the dichroism is stronger than for the d ,
and the dierence spectra for both d and d show fast oscillations. Therefore,
small variations in the parameters cause large changes in the spectra. With
the many parameters to t (dierence in d and d screening energy, Slater
integrals, crystal eld, lifetime broadening) it is therefore impossible to make a
unique choice.
Although the theoretical description of the V-2p linear dichroism is thus
problematic due to the complicated crystal structure of Na : V O , the result
for the \isotropic" spectra in Fig. 5.11 is very reasonable. This suggests that
despite the strong covalence, reected in the large reduction of the p-d Slater
integrals, the crystal eld multiplet theory is still applicable. This is quite
contradictory to the conclusions of Goering et al. [44] for V-2p XAS on V O
and V O . They argue that the linear dichroism in both the O-1s and the V-2p
edge is explained by band structure eects. The agreement between the O-1s
edge and the O-2p DOS in these experiments is indeed quite good, concerning
both peak positions and the polarization-dependent intensity. However, the
peak positions at the V-2p edge are certainly not well reproduced by the V-3d
DOS, if we take Fig. 5.11 as a reference. Also the number of peaks is not
correctly described. It is very likely that also these V-2p spectra are strongly
inuenced by the Coulomb interaction between the core hole and the valence
electrons; this eect could easily account for the larger number of peaks in the
experimental spectrum, and also for the energy shifts. Note that the observed
6
6
4
1
0
0
1
0
1
0 33
2
5
2
6
13
5
99
5.4. Polarization-dependent XAS
correlations between the polarization dependence and the anisotropy in the DOS
are certainly not coincidental, because the peaks in the d crystal eld multiplet
spectrum can still be related to the symmetry of the V-3d states [43], just like
in the DOS.
0
Oxygen 1s x-ray-absorption spectroscopy
For the O-1s edge, it is more likely that band structure eects are important,
due to the less localized nal state. Because of the dipole selection rules and the
local character of the x-ray-absorption process, the O-1s XAS spectrum probes
unoccupied states of oxygen p character. We will concentrate on the intensity
in the near-edge region, between 528 and 534 eV. The near-edge absorption is
attributed to states with mainly V-3d character, hybridized with O-2p states.
The higher energy features are due to states of mixed V-4sp/O-2p character.
Figure 5.12 shows the O-1s x-ray-absorption spectra for polarization angles
between 0 ( k b) and 90 ( ? b) As a check, also the spectra for 180 and
270 were measured, and they turned out to be virtually identical to those for
0 and 90, respectively. The angular dependence can be described very well by
I (E; ) = I (E; = 0 ) cos () + I (E; = 90) sin ();
(5.4)
which is a sign of the good sample quality. (Surface contamination could also
cause a false \dichroism", because the rotation centre of the sample and the
beam spot do not match perfectly. This means that for dierent rotation angles also slightly dierent parts of the sample are probed, which would lead to
changes in the spectra if the sample is contaminated. However, the resulting
periodicity would have been 360 instead of 180.) The inset of Fig. 5.12 shows
the intensity of the 529 eV peak for dierent polarization angles. The squares
represent the experimental intensities and the dotted line is the best t for an
angular dependence like in Eq. (5.4).
Because of the extended nature of the O-2p orbitals, the O-1s spectrum can
be associated with the O-p-projected, unoccupied densities of states. Also, the
V-3d band is almost empty; therefore, multiplet eects are expected to have a
negligible inuence on the spectrum. For light polarized along the z-axis, the
dipole selection rules require that M = 0, so that only transitions to states of
pz character are allowed. Thus by changing the polarization angle, we are able
to probe the anisotropy in the band structure.
In Fig. 5.13 the experimental spectra for light polarized perpendicular and
parallel to the b direction are compared to the corresponding density of states. In
the near-edge region two features are present. The lower energy peak increases
in intensity on changing from perpendicular to parallel polarization, while the
peak at higher energy decreases. The calculation describes this polarization
dependence quite well. Qualitatively, we can explain the observed changes by
the orientation of the short V-O bonds in the MxV O - structure. These bonds
2
2
2
5
100
Chapter 5. The quasi-one-dimensional vanadium bronzes
Fig. 5.12: O-1s absorption edge of Na :
0 33 V2 O5 for dierent polarization angles. The
polarization vector is in the (001) plane, and the angle is taken with respect to the
(010) direction. The inset shows the intensity of the 529 eV peak, integrated in a
0.4 eV interval around the maximum.
101
5.5. Band structure calculation
Fig. 5.13: O-1s absorption edge
of Na0:33 V2 O5 , with polarization
parallel to the a and b axes. The
spectra are compared to the O-2p
densities of states, projected for
the 2p orbitals along these axes.
correspond to the more antibonding V-3d{O-2p states, which appear at higher
energy in the spectrum. Because all the short V-O bonds are in the ac plane,
the O-2p states involved are mainly of px and py symmetry, and transitions to
these states are forbidden for z-polarized light.
The calculated splitting between the peaks is too large: about 3 eV, instead
of 2 eV experimentally. This is probably due to the presence of the core hole in
the x-ray-absorption nal state. As was shown in Fig. 2.2, the eect of the core
hole potential is basically a redistribution of spectral weight towards lower
energy; for increasing , the spectrum evolves into a narrow peak at the band
minimum. This eect is larger for the broader eg band, because the t g band
is already quite narrow. The redistribution of spectral weight can explain also
the relatively large intensity of the t g peak, compared to the calculation. The
similarities and dierences between calculation and experiment are comparable
to those found for V O [44]: here, the polarization dependence is also described
well, and the calculated intensity of the lowest energy peak is also too low.
c
c
2
2
2
5
5.5 Band structure calculation
A band structure calculation on Na = V O was performed using the linearized
mun-tin orbital (LMTO) method [45] within the local density approximation.
The basis set for the valence electrons consisted of 3d-, 4s-, and 4p-like basis
functions for V; 3s-, 3p-, and 3d-like for Na; 2s- or 3s-, 2p- and 3d-like for O. It
turned out to be necessary to treat the 2s states of the oxygen atoms involved
in the very short V-O bonds (d < 1:6 A) as valence states. For the densities
1 3
2
5
102
Chapter 5. The quasi-one-dimensional vanadium bronzes
7
6
5
Energy (eV)
4
3
2
1
0
Γ
X
Z M
Fig. 5.14: V-3d band structure of Na :
0 33
a quasi-one-dimensional band.
A
V2 O5 . The Fermi level at zero energy is in
of states calculation, 128 k-points in the irreducible part of the Brillouin zone
(BZ) were used (256 points in the entire BZ). The unit cell in this calculation is
NaV O , which diers from the real crystal structure in the sense that disorder
between the dierent Na tunnels is not considered.
Figure 5.14 shows the band structure between -0.5 and 7 eV, which has predominantly V-3d character, along the high symmetry points of the monoclinic
Brillouin zone (Fig. 5.15). The O-2p band is between -7.5 and -2.0 eV (For clarity, it is not shown in Fig. 5.14: if there is one band structure that deserves the
name \spaghetti", it is this O-2p band). The Fermi level falls in a very narrow
band, which is almost threefold degenerate. The band is quasi-one-dimensional,
with dispersion only along the (0 ) direction in reciprocal space, which corresponds with waves in the (010) direction in real space. This direction is followed
from ,(000) to Z (0 ) and from M ( ) to A(00), and the dispersion along
these two lines is very similar. Along directions perpendicular to ,Z , such as
,A and ,X (0 ), the dispersion is much smaller. Note that X is not an \ocial" point of high symmetry of the monoclinic BZ [46]; it is chosen because the
,X direction is approximately perpendicular to both ,A and ,Z . Now that
the band structure is plotted in this way, it seems plausible that the low-energy
6
15
11
22
11
22
11
22
111
222
1
2
103
5.5. Band structure calculation
kz
Z
Fig. 5.15: The Brillouin zone
of the base-centered monoclinic Bravais lattice. , = (000);
A = ( 12 00); Z = (0 21 12 ); M = ( 12 12 12 ); X = (0 12 12 ).
S
1 gS
3S
2
,
X J
J J kx
1
2 g2
J
J
J
M
J
J
J
J
J
J
, 1 g1
2
A
J
J
J
J
J J
ky
band is really quasi-one-dimensional, i.e. that the dispersion is small along all
directions perpendicular to ,Z .
To get a better understanding of the origin of the quasi-one-dimensional
band, we will make a projection of its site- and orbital-projected characters.
For this purpose, the coordinate system is put with the x-axis along the V -O V0 direction and the z-axis along the (010) direction, following the convention
of Goodenough [16]. It turns out that the band has almost completely dyz
and dzx character. The projections for the dyz and dzx orbitals at the dierent
V sites are shown in Fig. 5.16 as \fat bands". The fat bands for the other
symmetries (dxy , dx2,y2 , and d z2,r2 ) are not drawn, because their contribution
is very small: on the energy scale of Fig. 5.16, they look like single lines.
Of the six orbital projections in Fig. 5.16, three give clearly the most important contribution: V -dyz , V -dzx, and V -dyz . From Fig. 5.3 we see that these
are exactly the orbitals that have their lobes in the planes perpendicular to the
shortest V-O bonds. The O-2p-V-3d interaction resulting from these bonds is
thus strong enough to push all antibonding O-2p-V-3d orbitals up to higher energies. Now we know the orbital character of the band, the one-dimensionality
becomes also clear if we look again at Fig. 5.3: only along the (010) direction
there are chains of V and O, with all bond angles close to 180. This direction
shows therefore by far the largest dispersion: V-O-V hopping occurs relatively
easily because there is an O-2p orbital that has overlap with the V orbitals on
both sites. (From Table 1.1 we see that this is py for the dyz orbitals, and px for
the dzx orbitals.)
At rst sight, the periodicity of the low-energy band seems not in agreement
with its quasi-one-dimensional character. In a one dimensional tight-binding
s band, the energy dispersion E (k) is proportional to cos(ka), where a is the
lattice constant. This means that the distance from , to the Brillouin zone
boundary, which is at k = =a, covers half a period of the cosine. However,
Fig. 5.14 shows that ,Z covers a full period. This apparent discrepancy is due
to the particular symmetry of the crystal. The Bravais lattice is base centered
monoclinic, and its Brillouin zone is twice as large as the monoclinic primitive
2
2
3
1
2
3
1
104
Chapter 5. The quasi-one-dimensional vanadium bronzes
Brillouin zone [46]. (This is comparable to the dierence between cubic face
centered and cubic primitive Bravais lattices.) Consequently, the Brillouin zone
boundary on the kz axis is at kz = 2=b, where b is a lattice constant of the
monoclinic cell. If we would only consider the one-dimensional V-O chains,
without looking at the symmetry of the crystal, we would also choose a lattice
constant b. However, for a one-dimensional chain, the rst zone boundary is
now at kz = =b and the second at kz = 2=b, which explains the \full period"
dispersion along ,Z .
Figure 5.14 shows that the band structure calculation predicts Na = V O
to be metallic: the Fermi-level is located in the V-3d band. This is in disagreement with the conductivity measurements, which show an activated hopping
conductivity. This dierence could be a result of the shortcomings of the local
density approximation, which does not completely take into account correlation eects. The localization of the electrons can be due to polarization eects
or to the long range Coulomb interaction, which both can be of the order of
the bandwidth. On the other hand, the band structure is expected to give a
quite accurate description of the dierent hybridization interactions. Therefore,
there is certainly a connection between the anisotropy in the calculated 3d-band
dispersion and the one-dimensional character of the actual compound.
It seems that the threefold degeneracy of the lowest band is in disagreement
with the statement of Goodenough that all orbitals taking part in triple bonds
are unoccupied, which leaves only two possible occupied orbitals: V -dyz and V dzx. Figure 5.16 shows however that the lowest bands have also an appreciable
V character. In fact this is quite obvious: although it looks if two V orbitals
(dyz and dzx) take part in a \triple bond" with an O -pz orbital, this is merely
a consequence of the choice of the coordinate system. The short V -O and
V -O bonds are almost parallel with a coordinate axis, but the V -O bond is
not. This is very clear from Fig. 5.1, which shows that the bipyramids are tilted
with respect to the octahedrons. Therefore the single V orbital that strongly
overlaps with O -pz is a linear combination of dyz and dzx, in such a way that
its lobes are perpendicular to the V -O bond direction. This is also reected
in Fig. 5.16: the contribution of the orbitals located on the V (V ) site is of
almost pure dyz (dzx) character; however, for the V site orbitals of both dyz
and dzx symmetry contribute.
We conclude that orbitals located on V , V , and V contribute almost
equally to the one-dimensional band. From the band structure it appears impossible to predict which orbital should have the lowest \on-site" energy. On
the average, V seems to contribute a bit more to the higher energy part of the
band, V to the lower part, and V is in between. This is contradictory to EPR
measurements, which show that the V site is preferably occupied. Note however that the calculated dierences are small, and that correlation eects can
also inuence the on-site energy. For example, polarization screening could be
less eective for V than for V and V , because V is only ve-fold surrounded
1 3
1
3
8
1
6
3
8
3
8
3
8
1
3
1
2
2
3
1
1
3
1
2
3
3
5
2
3
2
2
2
4
105
Energy (eV)
Energy (eV)
Energy (eV)
Energy (eV)
Energy (eV)
Energy (eV)
5.5. Band structure calculation
0.8
V1 yz
0.4
0
-0.4
0.8
V1 zx
0.4
0
-0.4
0.8
V2 yz
0.4
0
-0.4
0.8
V2 zx
0.4
0
-0.4
0.8
V3 yz
0.4
0
-0.4
0.8
V3 zx
0.4
0
-0.4
Γ
X
Z
M
A
Fig. 5.16: Site and orbital projected band structure of the quasi-one-dimensional
band around the Fermi level. The orbital character is reected in the \fatness" of the
band: a 100% contribution corresponds to a \fatness" of 0.2 eV.
by oxygen ions.
Starting from the experimental fact that the V orbital is the lowest, it can be
explained from the band structure that the remaining electrons will preferably
reside at the V sites. The hopping probability for the dyz electron to a V site
is very small: the V -O-V bonds are almost 90, so the hopping goes primarily
via an intermediate O -2py or O -2pz orbital; however, these do not couple to
1
3
2
1
2
2
30
106
Chapter 5. The quasi-one-dimensional vanadium bronzes
the dzx orbital at the V site. The hopping from V to V is more likely: the
V -O -O bond angle is 134, so much larger than 90, and the O -pz has a
considerable overlap with both the V -dyz and the lowest V (t g ) orbitals.
Once an electron is at a V site, it is also likely to hop in the (010) direction
via an O ion to a neighbouring V site, thus contributing to the large conductivity in the (010) direction. In this respect, it is interesting to note again the
peculiar low-temperature behaviour of the conductivity as observed by Wallis
et al. [10]. As discussed already in Section 5.1, they suggested the interruptedstrand model, in which k depends directly on ?, because the one-dimensional
conduction path is broken, and the valence electrons have to make hops perpendicular to the chains in order to proceed. So in Na : V O , an electron in a
V chain that encounters an interruption could proceed in a V chain or|less
likely|a V chain.
It might be possible that interruptions in the V chain are not \extrinsic"
in the form of impurity potentials, but \intrinsic" due to the on-site Coulomb
repulsion. The V sites are about 50% occupied (i.e. d ), so hopping of an
electron along this chain would require d intermediate states. This process
is clearly less favourable than hopping along the V or V chain. What is
more, the V band is of almost pure dyz character: this would mean that in the
intermediate d state, the electrons would have to be in the same spatial orbital,
which even increases the Coulomb repulsion energy. If the temperature is low
and bipolarons are present, the energy cost would be even higher because also
the bipolaronic state has to break down now. The bipolaron is a spin singlet
state, apparently with one \up" and one \down" electron in dyz orbitals on
neighbouring sites, but this state is no longer bound if one extra dyz electron is
present at one of the sites. Indeed, the temperature range for which the k is
limited by ? coincides more or less with the temperature range in which the
bipolarons are formed [10].
2
1
5
1
3
3
5
1
3
2
3
30
7
0 33
2
5
1
3
2
1
1
1
2
2
1
3
2
5.6 Conclusions
The Cu-2p core level spectrum of -Cu : V O shows that the valence of Cu is
close to 1+. The electrons introduced by the Na doping in -NaxV O occupy
the V sites, as is indicated by O-1s/V-2p XPS. The valence band spectra of
these compounds show a 1 eV wide feature close to E ; it is of predominantly
V-3d character, as concluded from resonant photoemission and band structure
calculations. The V-3d spectral feature has a very low weight near the Fermi
level. This is in contrast with the calculated DOS, which predicts NaxV O to
be metallic, with a very small energy spread of the occupied d states. The discrepancy is probably due to the strong electron-phonon coupling, which transfers spectral weight to higher binding energy and which could also lead to the
polaronic nature of the charge carriers.
0 33
2
5
2
5
F
2
5
107
References
The anisotropic nature of Na : V O is studied by x-ray-absorption spectroscopy. Both the O-1s and the V-2p absorption edge show a pronounced
linear dichroism. Despite the strong covalence, the isotropic V-2p absorption
spectrum is described quite well by a crystal eld multiplet calculation in OH
symmetry. Unfortunately, the complicated crystal structure, the broad spectrum, and the large overlap between the d and d spectral features prevent a
detailed analysis of the dichroism at this edge. The O-1s edge is compared to
the O-p unoccupied density of states, obtained from an LMTO band structure
calculation. The dichroism in the O-1s edge is described very well by the O-p
projected densities of states, and can be explained by the anisotropy in the O2p{V-3d hybridization. The band structure also suggests that this anisotropy
is the origin of the one-dimensional properties of NaxV O . It shows that the
Fermi level is located in a 1 eV wide, quasi-one-dimensional band, originating
from the three 3d orbitals at the V , V and V sites that are oriented perpendicular to the short (d < 1:58 A) V-O bonds. The one-dimensional character
of the band arises from the V-O chains along the b direction, in which orbitals
of these types are strongly connected. The calculation predicts Na = V O to
be metallic; this is in contradiction to the experimentally observed hopping-like
conductivity, which suggests that the charge carriers are localized. Nevertheless,
the anisotropic character of the conduction band can probably account for the
low-temperature behaviour of the electrical conductivity. The one-dimensional
conduction path in the V chains can be broken by the formation of bipolarons
in the occupied chains, and the conductivity along the chain direction is limited
by the conductivity perpendicular to the chains.
0 33
2
5
0
1
2
1
2
5
3
1 3
2
5
1
References
[*] Reprinted from Anisotropic conductivity of the vanadium bronze Na0:33 V2 O5
c 1977
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