INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 15 (2002) 1–7
PII: S0953-2048(02)27889-6
Lattice fluctuations and inhomogeneous
charge states of high Tc superconductors
N L Saini1, H Oyanagi2, Ziyu Wu1,3 and A Bianconi1
1
Unitá INFM and Dipartimento di Fisica, Università di Roma ‘La Sapienza’, 00185 Roma,
Italy
2
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba
Central 2, 1-1-4 Umezono, Tsukuba, Ibaraki 305, Japan
3
Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy
of Sciences, P O Box 918, Beijing 100039, People’s Republic of China
Received 15 August 2001, in final form 7 January 2002
Published March 2002
Online at stacks.iop.org/SUST/15/1
Abstract
We have used x-ray absorption spectroscopy as a tool to study instantaneous
local lattice distortions of the CuO2 plane in high Tc superconductors and we
have investigated the inhomogeneous charge states of these materials. The
temperature-dependent Cu K-edge extended x-ray absorption fine structure
(EXAFS) has been used to determine the correlated Debye–Waller factor of
the Cu–O bonds, measuring local lattice fluctuations. The Debye–Waller
factor of the Cu–O bonds shows an order-parameter-like behaviour across
the charge stripe ordering temperature. The EXAFS results are supported by
a temperature-dependent Cu K-edge x-ray absorption near edge structure
(XANES) revealing a particular change in the local lattice displacements at
the charge stripe ordering. The experimental Cu K-edge XANES results are
well reproduced by full multiple scattering calculations including different
distortions of the CuO2 plane showing particular lattice displacements which
are consistent with the EXAFS results. The particular distortion mode as a
response function to the charge stripe ordering has been discussed with
several examples. The results are consistent with an inhomogeneous charge
distribution in the high Tc cuprates suggesting an intimate relationship
between the charge stripe ordering, local lattice fluctuations and high Tc
superconductivity in the cuprates.
1. Introduction
Perovskite superconductors are layered materials with CuO2
planes, separated by insulating rock-salt oxide layers. The
importance of the CuO2 planes has created major interest in
studying the electronic and structural characteristics of this
sublattice, since the discovery of high Tc superconductivity
in the cuprates. Recently, research in this field has entered
a new phase where a collective role of lattice, charge and
spin excitations is becoming recognized [1–3]. Indeed recent
developments in materials science and advanced experimental
tools have allowed us to uncover the fact that the electronic
ground state of the cuprates is more complex than previously
considered. Indeed the electron–lattice interaction in hightransition temperature superconductors, which has generally
been overlooked in the past, plays an important role in
describing the basic character of these materials. In fact it
0953-2048/02/000001+07$30.00
is hard to understand the normal and superconducting state
properties by simply considering a doped two-dimensional
antiferromagnetic CuO2 plane with only spin and charge
fluctuations. Even though no consensus has been reached
on the pairing ingredients, experiments are converging on the
importance of lattice excitations. As an example, a recent
photoemission study, probing electron dynamics, velocity
and scattering rate in different families of copper oxide
superconductors, has shown key features which cannot be
explained by any other process than a coupling of the electrons
with the lattice displacements involving movement of the
oxygen atoms [4].
On the other hand, there are now several experiments to
support the emerging view that the electronic ground state of
these materials is inhomogeneous with charge stripe ordering;
this is one of the main themes of recent debate [1–3]. Several
experiments probing different characteristics related with
© 2002 IOP Publishing Ltd Printed in the UK
1
N L Saini et al
charge, spin and lattice dynamics are found to be consistent
with the stripe phases in these materials [4–27]. The stripe
phases are now widely observed in closely related structures
such as insulating nickelates [28] and manganites [29–33].
Among cuprates, the La2CuO4 family of superconductors has
been one of the most popular to study the inhomogeneous
charge transport and charge stripe ordering by a variety of
experimental techniques [5, 6, 10–13, 16, 19–21, 23, 26, 27].
A popular example is the La1.48Sr0.12Nd0.4CuO4 system
[17, 19–21] in which the static charge stripe order has been
observed.
Recently it has been found that the elastic strain ε [34]
due to the lattice mismatch between the bcc CuO2 and the fcc
rock-salt sublattices plays a key role in the stripe formation
and their dynamics and in the high Tc superconductivity.
The superconducting stripes (superstripes) appear to form
for a microstrain larger than a critical value (εc) and the
superconductivity shows up near this critical value [34]. The
La2CuO4 system has a microstrain larger than the critical
microstrain εc and the charge stripe order is expected to
be comparatively less dynamic. All these experiments have
suggested that the inhomogeneous electronic ground state with
charge stripe ordering could provide the right key to unlock
the puzzle of high Tc superconductivity [1–3].
X-ray absorption spectroscopy (XAS) has been vital
to explore the inhomogeneous charge dynamics of high
Tc materials, supported by high brilliance and polarized
x-ray synchrotron radiation sources allowing us to obtain
directional information around a selective site. The technical
developments in the field have made it possible to obtain the
pair distribution function (PDF) with greater resolution, and
have allowed a solution of the local lattice displacements in
the CuO2 sublattice of the cuprates. Direct evidence for the
Q2-type of distortions in the CuO2 plane has been provided by
polarized Cu K-edge extended x-ray absorption fine structure
(EXAFS) data [35–37].
The Cu K-edge absorption spectroscopy is a fast
(∼10−15 s) and local (∼5–6 Å) tool [38] and is ideally
suited to probing local and instantaneous lattice fluctuations
in complex systems such as high Tc superconductors. Here
we have exploited the Cu K-edge absorption spectroscopy
to study the inhomogeneous structure of the CuO2 plane in
high Tc cuprates. The temperature-dependent distribution
of the local lattice distortions (dynamic and static) are
measured by the correlated Debye–Waller factor of the Cu–O
bond lengths using EXAFS, revealing an order-parameterlike change across the charge stripe ordering temperature.
The x-ray absorption near edge structure (XANES) spectra,
measuring instantaneous local geometry, show an abrupt
change in the temperature-dependent spectral weight at the
charge stripe ordering temperature. The XANES spectra
for different distortions have been simulated by full multiple
scattering (MS) calculations in order to explore the nature of
the geometrical displacements. The temperature-dependent
Cu K-edge measurements have been performed on several
systems to probe the lattice fluctuations across the charge stripe
ordering in these materials. On the basis of the experimental
outcome, we argue that the particular local lattice displacement
is a response function to the charge stripe ordering in the
cuprate superconductors. The results are consistent with an
inhomogeneous charge state of the high Tc cuprates.
2
2. Experimental and calculation details
Cu K-edge XANES measurements were performed at the
beamline BM29 at the European Synchrotron Radiation
Facility (ESRF), Grenoble, and the BL13B of the Photon
Factory, Tsukuba. At the BM29 the synchrotron radiation
emitted by a Bending magnet source at the 6 GeV ESRF
storage ring was monochromatized by a double-crystal Si(311)
monochromator. For temperature-dependent measurements
at the BM29 the samples were mounted in a closed cycle
two stage He cryostat. The Cu K α fluorescence yield (FY)
off the samples was collected using a 13 element Ge solidstate detector system to measure the absorption signal. At
the BL13B the synchrotron radiation emitted by a 27 pole
wiggler source at the 2.5 GeV Photon Factory storage ring was
monochromatized by a double-crystal Si(111) and sagittally
focused on the sample. The samples were mounted in a closed
cycle refrigerator placed on a Huber 420 goniometer. The
spectra were recorded by detecting the fluorescence photons
using a 19 element Ge x-ray detector array. The temperatures
were controlled and monitored within an accuracy of ±1 K.
The emphasis was given to measuring the spectra with a high
signal-to-noise ratio and several scans were collected to limit
the noise level to the order of 10−4. Standard procedure was
used to extract the EXAFS signal and corrected for the x-ray
fluorescence self-absorption before the analysis [38]. Further
details on the experiments and data analysis can be found in
our earlier publications on cuprates and related systems [6, 30,
35–37].
The calculations were carried out based on the oneelectron full MS theory [39–42]. We have used the Mattheiss
prescription [43] to construct the cluster electronic density
and the Coulomb part of the potential by superposition of
neutral atomic charge densities obtained from the Clementi–
Roetti tables [44]. In order to simulate the charge relaxation
around the core hole in the photoabsorber of atomic number Z,
we have used the screened Z + 1 approximation (final state
rule) [45], which consists in taking the orbitals of the Z + 1
atom and in constructing the final state charge density using
the excited configuration of the photoabsorber with the core
electron promoted to a valence orbital.
For the exchange-correlation part of the potential, we
have used the energy and position-dependent complex Hedin–
Lundquist (H–L) self energy (r, E) as illustrated by Tyson
et al [46]. The imaginary part of the H–L potential gives
the amplitude attenuation of the excited photoelectronic wave
due to extrinsic inelastic losses, and automatically takes into
account the photoelectron mean free path in the excited final
state. The calculated spectra are further convoluted with a
Lorentzian function with a full width tot ∼ 2.5 eV to account
for the core hole lifetime [47] and the experimental resolution.
We have chosen the muffin-tin radii according to the criterion
of Norman [48], allowing a 10% overlap between contiguous
spheres to simulate the atomic bond. In our experience, the
non-muffin-tin potentials could improve slightly the agreement
between experiment and theoretical calculations, however in
many cases the muffin-tin approximation gives the same results
as the non-muffin-tin approach [49]. The use of overlapping
spheres in a highly symmetric system (as in our case) gives
a good agreement with 10% overlap. The calculations were
Lattice fluctuations and inhomogeneous charge states of high Tc superconductors
0.004
Cu-O
100
20
σ 2CuO (Å2 )
|FT(χ(k)*k2)|
100
Cu-La(Nd,Sr)
Cu-O-Cu
20
0.003
0.002
0.001
0
0
2
4
6
R (Å)
8
10
12
Figure 1. Fourier tranform of the EXAFS spectra (multiplied by k2)
recorded on the La1.48Nd0.4Sr0.12CuO4 system (raw data). The inset
shows an enlargement of the main peaks representing Cu–O, Cu–La
(Nd, Sr) and Cu–O–Cu scattering.
made for a convergent cluster containing 101 atoms, which
covers a radius of ∼7 Å around the photoabsorbing Cu.
3. Results and discussion
We have studied several cuprates that are found to show charge
stripe ordering in the CuO2 plane. A widely discussed example
is La1.48Sr0.12Nd0.4CuO4 (LNS) [20] and hence we start our
discussion with this model compound. A well-characterized
single crystal of LNS, grown by the travelling solvent floating
zone (TFSZ) method was used for the measurements. Fourier
transforms (FTs) of the EXAFS spectra (multiplied by k2)
recorded in the in-plane geometry of the LNS at representative
temperatures is shown in figure 1. The FT represents the global
atomic distribution of nearest neighbours around the absorbing
Cu atom in the LNS system. The FT in figure 1 represents
raw experimental data and shows the standard peaks. The main
peaks are shown enlarged in the inset and are denoted by Cu–O,
Cu–La(Nd, Sr) and Cu–O–Cu representing respectively the
scattering of the ejected photoelectron at the Cu site with the
in-plane oxygen atoms (at ∼1.88 Å), La (Nd,Sr) atoms (sitting
at ∼3.2 Å and 45◦ from the direction of the photoelectron) and
a direct MS with the next Cu atom (at ∼3.8 Å), across the
in-plane oxygen. The peaks in the FT do not represent the
real atomic distances and the position should be corrected
for the photoelectron back-scattering phase shifts to find the
quantitative value to the atomic positions with respect to the
central Cu. The high signal-to-noise ratio in the data can
be judged from the FT (one hardly expects any true signal
above ∼9 Å, and above this range the FT amplitude gives an
idea of the noise in the data). The FT amplitude of the Cu–
La(Nd, Sr) and Cu–O–Cu peaks increases with decreasing
temperature (inset). It is clear from the raw data (figure 1) that
the amplitude of the Cu–O FT amplitude at 20 K is decreased
instead of the expected increase, indicating anomalous local
lattice displacements at low temperature.
Here we focus our attention on the Debye–Waller factors
of the Cu–O pairs, σ 2CuO, that take into account both static and
50
100
150 200
T (K)
250
300
Figure 2. Temperature dependence of the correlated Debye–Waller
factors (symbols) of the Cu–O pairs (σ 2CuO). The expected
temperature dependence of the Debye–Waller factor for a fully
correlated motion of Cu and O, calculated using the Einstein model,
is shown by the lower dotted curve. A constant value of 0.001 45 is
added to guide the temperature dependence of the experimental
Debye–Waller factor (upper dotted curve).
dynamic local lattice distortions. The Debye–Waller factors
of the Cu–O pairs, σ 2CuO, were obtained by analysis of the
EXAFS signal due to the Cu–O bonds, well separated from
the higher shells of other neighbouring atoms. Here the Cu–O
EXAFS signal is due to single scattering and probes the pair
correlation function between Cu and in-plane oxygen. The
EXAFS spectra due to Cu–O were simulated by a standard
least-squares approach using curved wave theory [38]. The
starting parameters were taken from diffraction studies [17].
The temperature dependence of σ 2CuO is shown in figure 2.
Before proceeding, it is worth clarifying that σ 2CuO measures
the correlated displacements between Cu and O and is not the
same as that observed in the diffraction experiments where the
Debye–Waller factor accounts for the mean-square deviation
of a given atom from its average site in the crystal. σ 2CuO
shows an anomalous upturn at ∼60 K. Considering evidence
of stripe ordering in LNS appearing at ∼60 K, provided by
several experimental techniques [11, 17, 20], we assign the
anomalous upturn in σ 2CuO to a charge instability giving charge
stripe ordering in this system. Indeed, the appearance of any
charge density wave-like instability gives rise to an anomalous
change in the Debye–Waller factor, known from studies of
density wave systems [50]. This is also consistent with an
anomalous upturn in σ 2CuO due to a particular local lattice
distortion (the Q2-type of rhombic distortion) in the CuO2
plane that appears at the charge stripe ordering temperature
[6, 35, 36]. Therefore the present result provides a clear
indication that a particular local lattice distortion, revealed
by an anomalous Debye–Waller factor of the Cu–O bonds,
appears in the CuO2 plane at the charge stripe ordering in the
cuprates.
Let us now turn to the XANES results. Figure 3 shows
representative Cu K-edge XANES spectra measured on the
LNS system in the in-plane (E//ab) and out-of-plane (E//c)
polarizations. The XANES spectra show the usual peaks,
which are denoted by standard notations [36] in the polarized
XANES spectra. The main absorption features are denoted by
3
N L Saini et al
0.68
A2
1.6
B1
B2
0.8
A1
E//ab
E//c
0.4
α/α0
R=b1-a1/b1+a1
1.2
0
1.6
A2
0.02
B2
0.01
0.00
0.8
A1
-0.01
0.4
(α/α0) T-(α/α0) 20K
B1
1.2
-0.02
absorption (arb. units)
0
B1
A2
B2
A1
8980
8990
9000
9010
Photon Energy (eV)
Figure 3. Polarized Cu K-edge XANES of the
La1.48Sr0.12Nd0.4CuO4 single crystal measured with E//ab and E//c
at 20 K (upper). Different absorption features have been identified
by the second derivative of the absorption spectra and denoted as A1
and A2 in the E//c spectrum and by B1 and B2 in the E//ab
spectrum. An unpolarized spectrum measured at 20 K on the same
system has been shown (middle) along with a difference spectrum
between a spectrum measured above the charge stripe ordering. A
calculated XANES spectrum for the La2CuO4 (not including the Nd
and Sr in the cluster) is also shown (lower panel) to identify the
natures of different peaks. The absorption peaks are well
reproduced in the calculated spectrum.
B1 and B2 in the E//ab spectrum and A1 and A2 in the E//c
spectrum.
The unpolarized spectrum is shown in the lower panel of
figure 3. The unpolarized spectrum contains information on
the local and instantaneous displacements in the overall cluster
around the central atom. In fact in complex systems, such as
the high Tc cuprates, the displacements are anisotropic with
doping and temperature and hence the unpolarized spectrum
is a useful tool to obtain important information on the local
and anisotropic geometrical displacements around the selected
site (i.e. Cu). In the lower panel of figure 3, we have shown
a difference between a spectrum measured at a temperature
(80 K) larger than the charge stripe ordering temperature
4
0.66
0.64
0
50
T (K)
100
150
Figure 4. Temperature evolution of the peak intensity ratio R =
(b1 − a1)/(a1 + b1) for the La1.48Sr0.12Nd0.4CuO4. The ratio shows a
clear change across the charge stripe ordering temperature.
(∼60 K) and a spectrum at the lowest temperature measured
in this work (20 K).
The absorption features in the polarized Cu K-edge
XANES spectrum are due to MS of photoelectrons emitted
at the Cu site in the direction of the electric field, and their
physical origin is revealed by MS calculations for La2CuO4.
The calculated spectrum is also displayed in figure 3. For
the La2CuO4 system, a very good agreement is shown for
the experimental features in respect to their energy positions
and relative intensity. The calculations are also in agreement
with those reported by Li et al [51], for La2CuO4. From the
calculated spectrum it is easy to find the origin of different
features observed in the experimental spectrum. The features
A1 and A2 are determined by MS of the ejected photoelectrons
off apical oxygen and La, Nd and Sr atoms while the peak B1
corresponds to MS of the in-plane oxygen and Cu in the CuO2
plane. The peak B2 includes a MS contribution, similar to the
main peak B1 and also contributed by multi-channel effects.
It can be seen that there is a high-energy spectral weight
transfer resulting in positive and negative differences with a
maximum difference of ∼2% of the normalized absorption
(figure 3). On cooling the sample, the spectral weight around
the peak A1 (A2) is decreased with an increase around the peak
B1 (B2). We have plotted the temperature dependence of the
XANES peak intensity ratio R = (b1 − a1)/(b1 + a1) in figure 4.
Here, b1 and a1 represent the intensities of the peaks B1 and
A1 probing high-energy spectral weight transfer from the core
excitations Cu1s → εpz (peak A1) to the Cu1s → εpxy (peak
B1). The ratio R shows a clear increase below the charge stripe
ordering temperature.
We have studied another model system, La1.875Ba0.125CuO4 (LBC125), representing the family of cuprates where
clear evidence for the charge stripe ordering is found. The
temperature-dependent unpolarized Cu K-edge absorption
spectra were used to determine the ratio R = (b1 − a1)/(b1 +
a1). The temperature dependence of R for the LBC125 system
is shown in figure 5. As for the LNS system, a clear increase
of R is observed across the charge stripe ordering temperature
(∼60 K) in the LBC125 system, indicating geometrical
changes in the CuO2 plane at the charge stripe ordering
temperature. This confirms that the ratio R is a good indicator
of charge stripe ordering in the cuprates.
Lattice fluctuations and inhomogeneous charge states of high Tc superconductors
Cu K-edge
Absorption (arb. units)
La1.875Ba 0.125CuO4
R=b1-a1/b1+a1
0.695
0.69
0
50
100
150
To explore the nature of these local displacements around
the Cu atom across the charge stripe ordering, we have made
MS calculations and calculated Cu K-edge XANES spectra
for different distortions. For this purpose we have taken a
simple approach by taking the HgBa2CuO4+δ (Hg1201) system
as a model for the calculations, where the Cu–O plane is
crystallographically flat due to a small mismatch between the
CuO2 planes and the rock-salt oxide layer. In addition the
simple structural unit cell with tetragonal crystal structure
(a ∼ 3.8755 Å; c ∼ 9.4952 Å) [52] provides the added
advantages of simulating different local lattice distortions
and investigating the evolution of the XANES spectrum with
different geometrical displacements.
Figure 6 shows Cu K-edge XANES measured at room
temperature on a powder sample of Hg1201 superconductor,
along with a calculated spectrum using the MS theory. The
real-space MS of the photoelectrons is excited from the Cu 1s
states to the cluster of atoms within a radius of ∼7 Å from
the central Cu. The features observed in the experimental
spectrum could be satisfactorily reproduced not only with
respect to the relative intensities, but also in energy separations.
The calculations were extended to a distorted CuO2 plane
considering a particular rhombic distortion where two oxygen
atoms move away and two move closer, as observed in the
cuprates [6, 36]. The evolution of the absorption differences
with an increasing quantity of the rhombically distorted sites
(Q2-type rhombic distortion), with respect to the undistorted
CuO2 plane, is shown in figure 6. It is clear from the
calculated absorption differences that the Q2-type of rhombic
distortion introduces the spectral weight transfer, as observed
in the experimental spectra below the charge stripe ordering
temperature. Thus the results of the calculations are consistent
with the experimental findings, suggesting that the observed
weight transfer is due to an octahedral distortion where one
of the Cu–O–Cu directions becomes elongated [6], observable
only when the amplitude of the lattice fluctuations becomes
larger than the amplitude of thermal fluctuations. This rhombic
distortion has been previously determined by polarized Cu Kedge EXAFS on the La2CuO4 system [6] and was later found
to be common to the CuO2 plane of other high Tc cuprates
Experiment
A1
MS
0.06
0.003
0.05
0.002
0.04
0.001
0.03
0
0.02
10% Q2
20% Q2
0.01
40% Q2
0
-10
-5
0
5
10 15
Energy (eV)
∆α
Figure 5. Temperature evolution of the peak intensity ratio R =
(b1 − a1)/(a1 + b1) for the La1.875Ba0.125CuO4. As for
La1.48Sr0.12Nd0.4CuO4, the ratio shows a clear change across the
charge stripe ordering temperature.
α
T(K)
Hg1201
B1
-0.001
-0.002
20
-0.003
25
Figure 6. Calculated absorption spectrum for Hg1201 is compared
with an experimental Cu K-edge XANES measured on the same
system (upper). The calculated absorption is plotted along with
absorption differences with respect to the calculated spectra
considering the variable quantity of distorted sites (Q2-type of
rhombic distortion). The rhombic distortion is at the origin of the
spectral weight transfer between peaks A1 and B1.
[6, 35–37]. Indeed this is the Q2 mode of the Jahn–Teller
distortion [53], which appears at the same temperature
where the system shows charge stripe ordering. This
was demonstrated by combined EXAFS and diffraction
experiments [35].
Returning to figures 4 and 5, showing the anomalous
change in the ratio R = (b1 − a1)/(b1 + a1), we can state that
the Q2-type of rhombic distortions of the CuO2 plane could
be considered a suitable response function of the charge stripe
ordering parameter in the cuprates. It is worth stating that, even
if the temperature-dependent upturn of R at the charge stripe
ordering is different, with different magnitude, the change is
clear. The differences of R in different systems are due to
different strains on the CuO2 plane [1–3] because of different
substitutional disorder (rock-salt blocks are different).
Figure 7 shows another example, La1.94Sr0.06CuO4,
an underdoped superconductor. Again, the ratio R shows
an anomalous increase below ∼110 K. Recently, the
La1.94Sr0.06CuO4 system was used as a model compound to
explore the oxygen isotope effect on the charge stripe ordering
temperature [54]. The charge stripe ordering temperature was
found to change from 110(±10) K to 170 (±10) K while
substituting 18O in place of 16O in La1.94Sr0.06CuO4. The result,
showing an isotope shift of ∼60 K, not only suggests a large
change in the local structure of the CuO2 plane due to isotope
substitution but also provides direct evidence of the important
role of local lattice displacements in charge stripe ordering
phenomena.
5
N L Saini et al
0.64
R=b1-a1/b1+a 1
La1.94Sr 0.06CuO4
0.63
0.62
0
50
100
150
200
T(K)
Figure 7. Temperature evolution of the peak intensity ratio R =
(b1 − a1)/(a1 + b1) for La1.94Sr0.06CuO4. The ratio shows an abrupt
change below ∼110 K reflecting charge stripe ordering in the
system below this temperature.
150
T(K)
100
50
0
Acknowledgments
0.05
0.1
0.15
0.2
0.25
Hole doping
Figure 8. Doping dependence of the charge stripe ordering
temperature obtained by the jump of the XANES peak intensity
ratio R (squares) plotted with that obtained by the wipeout fraction
of Cu NQR (circles). The open circles correspond to the data for
La2−xSrxCuO4 [11] while the closed circles represent data obtained
for the La1.6−xSrxNd0.4CuO4 system [11].
In figure 8 we have plotted the charge stripe ordering
temperature (defined by the abrupt local geometrical change
as reflected by the anomalous increase of the XANES peak
intensity ratio R) as a function of the hole concentration
in La-based cuprate superconductors. This temperature has
been compared with that obtained by the wipeout fraction
of Cu NQR [11, 20]. The temperatures for charge stripe
ordering, obtained by the two techniques, agree quite well in
the underdoped regime within the experimental uncertainties.
The temperature also agrees well with that determined by other
techniques [20]. A detailed discussion of the phase diagram
of the charge stripe ordering in different cuprates will be
presented elsewhere.
In summary, we have reported evidence in the local
structural fluctuations supporting the inhomogeneous charge
6
distribution in cuprate superconductors. We have used
Cu K-edge EXAFS and XANES spectroscopies to explore
local lattice fluctuations associated with charge stripe ordering
in the cuprates. We find an order-parameter-like change
in the instantaneous local lattice fluctuations across the
charge stripe ordering temperature, revealed by an anomalous
increase in the correlated Debye–Waller factor of the Cu–O
pairs. On the other hand, Cu K-edge XANES measurements,
measuring geometrical changes, show a particular evolution of
temperature-dependent XANES peak intensities with an orderparameter-like change in the anisotropic and instantaneous
local displacements around Cu, across the charge stripe
ordering. The MS calculations of different distortions suggest
that the abrupt change in the spectral weight transfer, reflected
by the XANES peak intensities, is due to the appearance of
the Q2-type of Jahn–Teller distortions at the charge stripe
ordering. On the basis of studying the model systems, we have
argued that the Q2-type of displacements across the charge
stripe ordering could be considered to be a response function.
In addition to providing a new response function, the results
construct clear evidence for the importance of electron–lattice
interactions in the charge stripe ordering. Moreover, a large
isotope effect on the charge stripe ordering [54] and pseudogap
temperature [55] suggest that the electron–lattice interaction
is an important ingredient for the high Tc in doped cuprates,
and there appears to be an intimate relationship between the
charge stripe ordering, local lattice fluctuations and high Tc
superconductivity. Here, the local strain in the electronically
active CuO2 plane, ε, controls the local lattice fluctuations
and the superconducting and normal state phenomena of the
perovskite superconductors [34].
This work is supported by ‘Istituto Nazionale di Fisica della
Materia’ (INFM) and ‘Progetto 5% Superconduttività of
Consiglio Nazionale delle Ricerche’(CNR). One of us (ZYW)
was supported by the Hundred Talent Research Programme of
the Chinese Academy of Sciences.
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7
Queries
(1) Author: Please provide page numbers for references [1],
[3] and [44].