Four-unit-cell superstructure in the optimally doped YBa2Cu3O6.92 superconductor.
ABSTRACT Diffuse x-ray scattering measurements reveal that the optimally doped YBa2Cu3O6.92 superconductor is intrinsically modulated due to the formation of a kinetically limited 4-unit-cell superlattice, q(0)=(1/4, 0, 0), along the shorter Cu-Cu bonds. The superlattice consists of large anisotropic displacements of Cu, Ba, and O atoms, respectively, which are correlated over approximately 3-6 unit cells in the ab plane, and appears to be consistent with the presence of an O-ordered "ortho-IV" phase. Long-range strains emanating from these modulated regions generate an inhomogeneous lattice which may play a fundamentally important role in the electronic properties of yttrium-barium-copper-oxides.
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ABSTRACT: We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of β=0.18±0.02, γ=1.0±0.1, and α=0.10±0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our simple model. We argue that the nature of the transition in our model is related to surface transitions although our model has no free surface.Physical Review E 09/2010; 82(3 Pt 1):031115. · 2.31 Impact Factor
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ABSTRACT: A simple phenomenological model for the relationship between structure and composition of the high Tc cuprates is presented. The model is based on two simple crystal chemistry principles: unit cell doping and charge balance within unit cells. These principles are inspired by key experimental observations of how the materials accommodate large deviations from stoichiometry. Consistent explanations for significant HTSC properties can be explained without any additional assumptions while retaining valuable insight for geometric interpretation. Combining these two chemical principles with a review of Crystal Field Theory (CFT) or Ligand Field Theory (LFT), it becomes clear that the two oxidation states in the conduction planes (typically d8 and d9) belong to the most strongly divergent d-levels as a function of deformation from regular octahedral coordination. This observation offers a link to a range of coupling effects relating vibrations and spin waves through application of Hund’s rules. An indication of this model’s capacity to predict physical properties for HTSC is provided and will be elaborated in subsequent publications. Simple criteria for the relationship between structure and composition in HTSC systems may guide chemical syntheses within new material systems.Physica C Superconductivity 06/2012; 476:32–47. · 0.72 Impact Factor
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ABSTRACT: We report x-ray diffuse scattering studies of the iron chalcogenide Fe1+xTe as a function of doping and temperature for x=0.03, 0.08, and 0.12. In all cases, remarkably strong, characteristic diffuse scattering is observed. This scattering extends throughout the Brillouin zone and exhibits a nonmonotonic decay away from the fundamental Bragg peaks, with a peaklike structure at a reduced q≈(0.3,0,0.6). We interpret this scattering as Huang diffuse scattering resulting from distortions induced by the interaction between the excess Fe and the FeTe layers. The form of the scattering indicates that this interaction is strong and extends a number of unit cells away from the interstitial Fe site. Further, the diffuse scattering shows a sudden decrease on cooling through the structural and magnetic phase transition, reflecting the first-order change of the electronic structure of FeTe.Physical Review B 05/2011; 83(18). · 3.66 Impact Factor
Four-Unit-Cell Superstructure in the Optimally Doped YBa2Cu3O6:92Superconductor
Zahirul Islam,1,*X. Liu,2S.K. Sinha,2J.C. Lang,1S.C. Moss,3D. Haskel,1G. Srajer,1P.Wochner,4D.R. Lee,1
D.R. Haeffner,1and U.Welp5
1Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
2Department of Physics, University of California, San Diego, California 92093, USA
3Department of Physics and Texas Center for Superconductivity and Advanced Materials, University of Houston,
Houston, Texas 77204, USA
4Max-Planck-Institut fu ¨r Metallforschung, 70569 Stuttgart, Germany
5Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
(Received 23 December 2003; published 7 October 2004)
Diffuse x-ray scattering measurements reveal that the optimally doped YBa2Cu3O6:92superconductor
is intrinsically modulated due to the formation of a kinetically limited 4-unit-cell superlattice, q0?
Cu, Ba, and O atoms, respectively, which are correlated over ?3–6 unit cells in the ab plane, and
appears to be consistent with the presence of an O-ordered ‘‘ortho-IV’’ phase. Long-range strains
emanating from these modulated regions generate an inhomogeneous lattice which may play a
fundamentally important role in the electronic properties of yttrium-barium-copper-oxides.
4;0;0?, along the shorter Cu-Cu bonds. The superlattice consists of large anisotropic displacements of
DOI: 10.1103/PhysRevLett.93.157008PACS numbers: 74.72.Bk, 61.10.Eq, 74.25.–q
There is mounting evidence that the cuprate supercon-
ductors are intrinsically inhomogeneous, even in the
superconducting (SC) phase. The driving force for such
inhomogeneities may well be electronic instabilities ,
or elastic strain , or a combination of these. Further-
more, in the case of the YBa2Cu3O6?x(YBCO) system,
the oxygen vacancies in the Cu-O chains tend to form
superstructures which order  well above the SC tran-
sition temperatures according to the scheme proposed by
de Fontaineandco-workers. InthisLetter,we describe
diffuse x-ray scattering data which yield a quantitative
description of how large-amplitude atomic displacements
modulated with a 4-unit-cell periodicity (q0? ?1
form coherent regions of kinetically limited imperfect
order in the optimally doped YBa2Cu3O6:92supercon-
ductor. Long-range strain fields emanating from these
regions create an intrinsically inhomogeneous lattice
which manifests itself below ?200 K due to the re-
duction in the thermal diffuse scattering (TDS). These
properties persist in the SC phase and appear to be
universal to the YBCO compounds . These findings
are of great importance in several respects. Theoretical
work  has shown how inhomogeneous electronic
phases on different length scales can arise due to
elasticity-driven lattice deformations, and how such de-
formations can suppress superconductivity and modulate
the electronic density of states. Furthermore, locally
modulated regions can act as resonant electron scattering
centers, affecting transport and susceptibility properties
, while strains, as in the twin boundaries, can pin
vortices . According to other theoretical work ,
dopants or vacancies may locally nucleate highly anhar-
monic lattice modulations around them (‘‘breather
modes’’) which can affect the SC order parameter.
Thus, a treatment of the superconductivity in terms of a
single homogeneous phase in these materials appears
We have previously found in an underdoped YBCO
(x ? 0:63)compoundshort-rangeorderedsuperstructures
 with a periodicity, q0? ??2
harmonic of the so-called ‘‘ortho-V’’ phase of O-vacancy
ordering on the Cu-O chains . However, the intensities
of the diffuse satellites clearly showed that displacements
of atoms in the Cu-O chain planes, the CuO2planes, and
the BaO planes were involved . Here we show that at
optimal doping, short-range ordered modulated regions,
atoms (Fig. 1), indeed coexist with superconductivity.
Identical modulations were also observed in a twinned
crystal. Since the data in the detwinned crystal are not
complicated by contributions from twin domains, we
focus on the detwinned crystal in this Letter.
For this study, a high-quality detwinned crystal
(?1 mm ? 1 mm ? 130 ?m) of optimally doped YBCO
(Tc? 91:5 K, ?Tc? 1 K) was chosen. The crystal was
annealed at 420?C in flowing pure O2for about a week
and was stress detwinned in flowing O2at the same
temperature. Polarization-sensitive optical microscopy
showed the presence of a single twin domain. The crystal
mosaic was ?0:03?.The c axis was perpendicular to the
large crystal facet. High-energy (36 keV) x-ray diffrac-
tion studies were performed on the 4ID-D beam line at
the Advanced Photon Source. Experimental details can
be found elsewhere .
Figures 2(a)–2(d) show several a-axis H-scans normal
to the Cu-O-Cu chain direction for different integer val-
ues of K taken at ?7 K. Broad satellite peaks in the
diffuse scattering corresponding to q0? ?1
clearly visible near Bragg peaks ?h;k;0?: when h and k
have mixed parity, the structure factor including TDS is
5;0;0?, coincident with a
4;0;0?, involving correlated displacements of
VOLUME 93, NUMBER 15
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2004 The American Physical Society157008-1
weak. The intensity of the peak at Q ? G ? q0(G is a
reciprocal lattice vector) is some ?106orders of magni-
tude weaker than that of the (4, 0, 0) Bragg peak. The
width in the a? direction of q0satellites is much larger
than the resolution, indicating a very short correlation
range (?a? 3a, using Scherrer formula ) along the a
axis. The use of a detwinned crystal made it unambigu-
ous that the modulation vector is q0? ?1
responds to longer correlation length ??b? 6b?, while
modulations of the intensity which extend along the c?
axis through the satellite peak as shown in Fig. 3(c) in-
dicate correlations only between neighboring Cu-O chain
planes, BaO planes, and CuO2planes (Fig. 1), respec-
tively, as obtained from Fourier transform (Patterson
function) of these intensity patterns (similar to the results
found in the underdoped systems ).
In addition, significant lattice-strain effects are present
in this material. A 2-dimensional scan around (4, 0, 0), as
shown in Fig. 2(f), reveals a strongly anisotropic ‘‘bow-
tie’’ -shape Huang diffuse scattering (HDS) pattern, with
lobes extending along the four [?1, ?1, 0] directions,
which require the existence of long-range strain fields
generated by the modulated regions. The two superlattice
peaks at (4 ?1
scans through the diffuse lobes at several temperatures is
shown in Fig. 2(g). Whereas at low T two broad peaks
corresponding to two lobes are clearly visible, on increas-
ing T the peaks become indiscernible from the rapidly
growing TDS above ?200 K.The room-temperature dif-
fuse scattering [Fig. 2(h)] is nearly identical to the calcu-
latedTDS(not shown)around(4,0,0). Earlier x-ray stud-
ies  of tetragonal system YBa2?Cu0:955Al0:045?3O7
showed that HDS arises from shear distortions due to
long-wave fluctuations of O concentrations in the chains
along the a and b axes. It is possible that the O stoichi-
4;0;0? and not
4;0?. The width in the b-axis direction [Fig. 3(b)] cor-
4, 0, 0) are barely discernible. A set of line
FIG. 2 (color).
and L ? 0. Satellite peaks are due to q0? ?1
lines (displaced along H for clarity) compare the observed
(black) and calculated (red) intensities corrected for geometric
factors; (e) H-scans with high values (odd/even) of K relative to
H; (f) Contours of diffuse intensity at 7 K around (4, 0, 0)
Bragg peak; (g) Line scans at different T showing how TDS
overwhelms HDS above ?200 K; (h) Contours of diffuse
intensity at 300 K. Line scans in (g) were taken along the
red line in (f) and (h).
(a)-(d) H-scans for several integer values of K
(0.01, 0.0)(0.047, 0.0)
at ?7 K. All the atoms have been projected on the ac plane.
Note that primary displacements (?u’s) are along the a axis,
i.e., along the shorter Cu-Cu bond direction. ?u’s, ??a;?c? in
units of a and c, of respective atoms are given in parentheses.
?u’s of all other atoms are related by mirror symmetry.
An ideal atomic displacement (arrows) pattern
(b) K-scans through the (5.25, 0, 0) peak. Lines in (a) and
(b) are fits (see text). (c) Intensity modulations along c? of the
same peak. Note that the oscillation amplitude grows on
decreasing T. Different T’s are shown with unique colors (b).
VOLUME 93, NUMBER 15
PH YSICA LR EVI EWL ET T ERS
8 OCTOBER 2004
ometry in the Cu-O chains is nonuniform in the defective
short-range O-ordered domains discussed below.We note
that similar HDS is also observed in optimally doped and
underdoped twinned compounds eliminating the possi-
bility that the HDS is due to stress detwinning of the
A 4-unit-cell periodic (ortho-IV) phase is expected
near O stoichiometry of 6.75  (i.e., one out of every
four Cu-O chains has no O atoms denoted by h1101i)
whereas in optimally doped material, the stoichiometry
is 6.92 (i.e., approximately one out of 12 Cu-O chains has
vacancies).There aretwowaysto explaintheformation of
h1101i structure near optimum doping. If the O concen-
tration is nonuniform within the Cu-O-chain planes, then
vacancies tend to phase separate within the formation
range of the ortho-IV phase . Secondly, if the long-
range Coulomb interactions among distant-neighbor va-
cancies are not negligible, then the h1101i phase can be
stable even near the optimal doping with a dilute con-
centration of vacancies. In both cases, however, the order-
ing will be short ranged and imperfect, leading to
significant lattice strains responsible for HDS.
Next, we note some general features of our data which
were used to narrow down possible models of atomic
displacements (?u’s). First, a strong intensity asymmetry
Bragg points. A strong asymmetry can occur if ?u’s are
large , or as a result of destructive interference be-
tween diffuse scattering due to disorder and displacive
modulation  as found in quasi-1D charge density
wave systems [13,14]. Second, for a given satellite at
?h;k;0? ? q0the intensity is either weak or very strong
when h and k have the same or mixed parity, respectively.
This implies out-of-phase displacements of the dominant
scatterers. Third, no second harmonic (2q0) satellites
were observed, indicating essentially a sinusoidal modu-
lation. Finally, scans [Fig. 2(e)] such as [H, -5, 0] (H 2
?0:1 ? 0:9?) found no superlattice peaks suggesting the
absence of any ?u k b associated with the q0modulation.
We performed calculations without assuming any dis-
placements to be small in the presence of an ortho-IV
phase in the Cu-O-chain plane.
Since the satellite appears at a commensurate wave
vector, we can adopt a supercell model to calculate the
integrated intensity using
where the displacement relative to an average lattice site
(Rn) of the n-th atom is ?un, fn?Q? and e?Wn?Q?are the
form factors and Debye-Waller factors (DWFs), respec-
tively. The expression above is for integrated intensity of
the satellites regardless of peak widths. Although the
extraction of intensities is difficult, since the satellites
are sharper than TDS and HDS, and located away from
Bragg peaks, it is possible to represent the satellites at the
lowest T using a Gaussian above some monotonic back-
ground with errors in intensities varying ?15%–35%
depending on background modeling. A least-squares pro-
cedure was performed taking these errors into account to
fit the intensities of 45 satellite peaks and the intensity
modulation of the (5.25, 0, 0) peak along c?.Vertical bars
in Figs. 2(a)–2(d) indicate that there is good agreement
between the calculated (red) and observed (black) inten-
sities within experimental uncertainties for the resultant
model shown in Fig. 1. Like the Ba and Cu atoms, both
chain (O(1)) and plane oxygen atoms (O(2) and O(3)) are
displaced primarily along the a axis. Although there may
be small displacements along the c axis as well, we are
more certain of them in the case of Ba. Our error esti-
mates are ?10%–15% for Ba and Cu ?u’s, and ?15 ?
25% for O atoms, respectively.While the model obtained
may not be perfect, it does account for all the systematics
of the data. Furthermore, it portrays a pattern of displace-
ments similar to that of ortho-V phase in an underdoped
YBCO obtained from first-principles electronic calcula-
tions . In our case, however, the periodicity is 4a
Figure 3(a) shows H-scans through a superlattice peak
at several temperatures. It is clear from these scans that as
T is increased, the intensity of the q0peak decreases
relative to the TDS emanating from (5, 0, 0). Intensity
modulation of (5.25, 0, 0) peak presented in Fig. 3(c)
shows that while the mean intensity of the oscillations
falls with decreasing T due to the reduction of TDS, the
oscillation amplitude of every other peak about the mean
grows. In order to get more quantitative information as a
function of temperature we fitted  a combination of a
Lorentzian (TDS), a Gaussian, and a constant term to the
H-scans [Fig. 3(a)]. K-scans shown in Fig. 3(b) are well
represented by a combination of three Gaussian line
profiles and a constant term to account for the back-
ground. Note that both HDS and TDS contribute to the
broad lobes. Since the peak widths and positions do not
change with T, only the peak heights and the constant
term (i.e., four parameters all together) were needed to fit
the entire data. Figure 4(a) shows the T-dependence of the
fitted intensity for (5.25, 0, 0) peak. Although keeping
positions and widths constant may introduce some sys-
FIG. 4 (color).
peak. (b) T dependence of Fourier amplitudes obtained from
intensity modulations shown in Fig. 3(c).
(a) Temperature dependence of (5.25, 0, 0)
VOLUME 93, NUMBER 15
PH YSICA LR EVI EWL ET T ERS
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tematic errors for the central satellite, its integrated in-
tensity (width ? peak intensity) agrees well with that
obtained in fitting the H-scan as shown in Fig. 4(a).
The intensity was also estimated via the maximum am-
plitude of the modulation defined as I?5:25;0;0?? I?5:25;0;1:8?.
All three cases consistently show that the superlattice
peak decreases nearly linearly with increasing T
[Fig. 4(a)]. If this linear trend continues then the intensity
will extrapolate to zero around ?500 K. Furthermore,
Fig. 4(b) shows Fourier amplitudes obtained from inten-
sity modulations [see Fig. 3(c)], which are a measure of
displacement-displacement correlations as a function of
T. It is clear that both amplitudes also grow stronger at
Although the origin of q0can be attributed to the
ortho-IV phase, it is puzzling to observe a large increase
of the diffuse satellite peak with decreasing T. Using the
displacement model presented above and DWFs for the
average lattice measured on ceramic samples  we esti-
satellite, which is at odds with the observed ratio of at
least ?2:2. Since diffusive motion of chain oxygens
(O(1)) practically freezes below ?250 K, the growth of
ortho-IVregions in size or number seems unlikely. Given
that atomic displacements (Fig. 1) are clearly anharmonic
in these imperfectly ordered nanoscale regions, it appears
that enhanced elastic softening of the lattice takes place
within these regions on lowering T which may account
for the low-T increase of the intensity.
To summarize, lattice modulations with a 4-unit-cell
periodicity exist from above room-temperature down to
the lowest temperature in optimally doped YBCO. These
correspond to local regions in extent ?3–6 unit cells in
the ab plane and less than one unit cell along the c axis.
From the ?u’s (Fig. 1) one may calculate DWFs for the
whole crystal and by comparison with the experimental
DWFs , we estimate roughly ?10%–20% of the crys-
tal contain these modulated regions at the lowest T. At
low temperatures clear evidence of anisotropic strain in
the lattice is provided by anisotropic patterns of HDS
around the Bragg points. This HDS originates with the
strain induced both by the disorder between O atoms and
vacancies along a and b axes and by the presence of
modulated regions; coherent strains induced in the lattice
must also exist.
Our results are suggestive when compared with the
phonon anomalies and extra branches in the vicinity of
from the modulated regions. The formation of ‘‘striped’’
phases and spatial modulations as those in lanthanum and
bismuth-based cuprates [18,19] per se is insufficient to
explain the diffraction effects presented in this Letter. It
appears that in YBCO the electronic structure and the O
vacancies together produce inherently local modulations
which lead to inhomogeneous lattice and local softening
within these modulated regions.
Idiffuse?300 K?? 1:2 for the intensity of (5.25, 0, 0)
4;0;0? observed in YBCO , which may arise
D. de Fontaine was the first to suggest the origin of q0
to be an O-ordered ortho-IV phase [4,15]. We benefitted
from discussions with B.W. Veal, V. Ozolins, and D.
Basov. Use of the Advanced Photon Source is supported
by the U.S. Department of Energy, Office of Basic Energy
Sciences, under Contract No. W-31-109-ENG-38. S.C. M.
thanks the NSF for support on DMR-0099573.
*Email Address: email@example.com
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