arXiv:cond-mat/0312622v1 [cond-mat.supr-con] 24 Dec 2003
A 4-unit-cell superstructure in optimally doped YBa2Cu3O6.92superconductor
Zahirul Islam1,∗, X. Liu2, S. K. Sinha2, J. C. Lang1, S. C. Moss3, D. Haskel1, G. Srajer1, P. Wochner4, D. R. Lee1,
D. R. Haeffner1, U. Welp5
1Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439
2Department of Physics, University of California, San Diego, CA 92093
3Department of Physics and Texas Center for Superconductivity and Advanced Materials, University of Houston, TX 77204
4Max-Planck-Institut f¨ ur Metallforschung, 70569 Stuttgart, Germany
5Materials Science Division, Argonne National Laboratory, Argonne, IL 60439
(February 2, 2008)
Using high-energy x-ray diffraction we show that a 4-unit-cell superstructure, q0=?1
the shorter Cu-Cu bonds coexists with superconductivity in optimally doped YBCO. A complex set
of anisotropic atomic displacements on neighboring CuO chain planes, BaO planes, and CuO2planes,
respectively, correlated over ∼3-6 unit cells gives rise to diffuse superlattice peaks. Our observations
are consistent with the presence of Ortho-IV nanodomains containing these displacements.
There have been several experimental indications re-
cently of inhomogeneous phases of various kinds devel-
oping in the high-Tccuprates. These were predicted on
purely electronic considerations , and were given cred-
ibility with the discovery, by neutron scattering, of the
so-called “striped phase” in the low-temperature tetrago-
nal La1.6−xNd0.4SrxCuO4. In this phase the magnetic
periodicity is equal to twice that of the charge. Later
neutron measurements  have revealed incommensurate
spin density waves with a period close to 8 unit cells
along the a axis at optimal doping in the superconduct-
ing phases of La2−xSrxCuO4(LSCO) associated with the
Cu spins in the CuO2 planes, which are enhanced in-
side the vortices induced by an applied magnetic field .
Recent STM measurements  in Bi-2212 reveal a spa-
tial modulation of the local electronic density of states
possibly arising from quasiparticle interference between
states that are nested across the Fermi surface. Very re-
cent Josephson tunneling work suggests a non-uniform
superconducting condensate in LSCO . Inelastic neu-
tron scattering has also revealed the existence of phonon
anomalies at a wavevector q0=(1
a, in both YBa2Cu3O6+x(YBCO) and LSCO
compounds [6,7]. The role of lattice strains in creating
texture has also been discussed recently .
tion, in the YBCO family of compounds, there are O va-
cancies in the CuO chains (except at stoichiometry, i.e.
x=1.0, sligthly beyond the optimum doping), which order
to some degree in well-prepared samples . The phase
diagram of the vacancy ordering on the CuO chains has
been theoretically discussed by De Fontaine and cowork-
ers . While the exact origin of inhomogeneities is be-
ing debated, diffraction studies to understand the nature
of such phases are absolutely necessary.
We have used high-energy synchrotron x-ray scattering
to look for the occurrence of inhomogeneous phases and
lattice modulations in the YBCO family of compounds.
In an underdoped YBCO (x≈0.63) compound we previ-
4,0,0), in reciprocal lat-
ously found modulations with q0= (∼2
short-range order  which coincided with a harmonic
of the so-called Ortho-V phase of O-vacancy ordering on
the Cu-O chains  with a 5-unit-cell repeat along the
a axis. However, the intensities of the diffuse satellites
clearly showed that displacements of atoms in the CuO
chain planes, the CuO2planes and the BaO planes were
involved . This paper describes similar measurements
carried out on an optimally doped YBCO crystal, pos-
sessing on the average 8% of O vacancies on the chains.
We find that a 4-unit cell (Ortho-IV) superstructure,
(Fig. 1), indeed coexists with superconductivity.
4, 0, 0), involving correlated displacements of atoms
(0.01, 0.0)(0.047, 0.0)
FIG. 1. An ideal atomic displacement (arrows) pattern at
∼7 K. All the atoms have been projected on the ac plane.
Note that primary diplacements (δu’s) are along the a axis,
i.e. along the shorter Cu-Cu bond direction. δu’s, (δa,δc) in
units of a and c, of respective atoms are given in parentheses.
δu’s of all other atoms are related by mirror symmetry.
For this study, a high-quality detwinned crystal (∼1
mm×1 mm×130 µm) of optimally doped YBCO (Tc=
91.5 K, ∆Tc ≈ 1 K) was chosen.
twinned crystal allowed us to determine unambiguously
the anisotropy of scattering, the direction of modulation,
and the polarization of atomic displacements, respec-
The use of a de-
tively. The crystal was annealed at 420◦C in flowing pure
O2 for about a week and was stress detwinned in flow-
ing O2 at 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 diffraction studies were performed on the
4ID-D beamline at the Advanced Photon Source. Exper-
imental details can be found elsewhere .
FIG. 2. (a-d) Raw data showing [H, 0, 0] scans for several
integer values of K and L=0. Satellite peaks correspond to
q0 = (1
4, 0 ,0). Vertical lines (displaced along H for clarity)
compare the observed (black) and calculated (red) intensities
corrected for geometric factors; (e) [H, 0, 0] scans with high
values (odd/even) of K relative to H showing the absence of
q0 satellites above background; (f) Contour plot of diffuse
intensity at 7 K around (4, 0, 0) Bragg peak; diagonal dashed
lines indicate [±1,±1,0] directions; (g) Line scans at different
T showing how TDS overwhelms HDS above ∼200 K; (h)
Contour of diffuse intensity at 300 K. Red line in (f) and (h)
indicates where the linescans displayed in (g) were taken.
Figs. 2(a)-(d) show several a-axis [H, 0, 0] scans nor-
mal to the Cu-O-Cu chain direction for different integer
values of K taken at ∼7 K. Broad satellite peaks corre-
sponding to q0=?1
peaks, (h,k,0), when h and k have mixed parity. When h
and k have the same parity strong thermal diffuse scatter-
ing (TDS), however, overwhelms the superlattice peaks.
The intensity of the peak at Q=G+q0(G is a recipro-
cal lattice vector) is ∼450 photons/second which is some
∼106orders-of-magnitude weaker than that of a Bragg
peak. The width in the a* direction of q0 satellites is
much larger than the resolution, indicating a very short
correlation range (ξa∼ 3a, using Scherrer formula )
along the a axis. The use of a detwinned crystal made it
unambiguous that the modulation vector is q0=?1
4,0,0?are clearly visible near Bragg
3(b)) corresponds to larger correlation length (ξb∼ 6b),
while modulations of the intensity which extend along
the c∗axis through the satellite peak as shown in Fig.
3(c) indicate correlations only between neighboring Cu-O
chain planes, BaO planes, and CuO2planes (Fig. 1), re-
spectively, as obtained from Fourier transform (Patterson
function) of these intensity patterns (this is very similar
to the results found in the underdoped system ).
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
“bowtie”-shape Huang diffuse scattering (HDS) pattern
with lobes extending along the four [±1, ±1, 0] di-
rections.The two superlattice peaks at (4±1
can be discerned, although they are not completely re-
solved. A set of linescans through the diffuse lobes at
several temperatures is shown in Fig. 2(g). Whereas at
low temperature two broad peaks corresponding to two
lobes are clearly visible, on increasing T the peaks be-
come indiscernible from the rapidly growing TDS above
∼200 K. Room-temperature pattern of diffuse scatter-
ing (Fig. 2(h)) is nearly identical to TDS around (4,
0, 0) calculated using elastic constants of YBCO (not
shown). Earlier x-ray studies  of tetragonal system
YBa2(Cu0.955Al0.045)3O7 showed that HDS arises from
shear distortions due to long-wave fluctuations of O con-
centrations in the chains along a and b axes. It is pos-
sible that the O stoichiometry in the CuO chains is non-
uniform on submicron scales due to the formation of de-
fective short-range O-ordered domains discussed below.
A 4-unit-cell periodic (Ortho-IV) phase is expected
near O stoichiometry of 6.75  (i.e. one out of ev-
ery four CuO chains has no O atoms denoted by ?1101?)
whereas in optimally doped material the stoichiometry is
6.92 (i.e. approximately one out of every ten CuO chains
has vacancies). There are two ways to explain the for-
mation of ?1101? structure near optimum doping. If O
concentration is nonuniform within the CuO-chain planes
then vacancies tend to phase separate within the forma-
tion range of the Ortho-IV phase . Secondly, if the
long-range Coulomb interactions among distant-neighbor
vacancies are not negligible then the ?1101? phase can be
stable even near the optimal doping with dilute concen-
tration of vacancies. In both cases, however, the ordering
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 (δu’s).First, a strong intensity asym-
metry between the +q0 and -q0 satellites is observed
around all Bragg points. A strong asymmetry can oc-
cur if δu’s are large , or as a result of destructive in-
terference between diffuse scattering due to disorder and
displacive modulation  as found in quasi-1D charge
density wave systems [16,17]. Secondly, for a given satel-
4,0?. The width in the b-axis direction (Fig
4, 0, 0)
lite at (h,k,0)+q0 the intensity is either very strong or
weak when h and k have the same or mixed parity, re-
spectively.This implies out-of-phase displacements of
the dominant scatterers. Thirdly, no second harmonic
(2q0) satellites were observed indicating essentially a si-
nusoidal modulation. Finally, scans (Fig. 2(e)) such as
[H, -5, 0] (H ∈ [0.1 − 0.9]) found no superlattice peaks
suggesting the absence of any δu ? b associated with the
q0 modulation. We performed calculations without as-
suming any displacements to be small in the presence of
an Ortho-IV phase in the CuO-chain plane.
The intensity calculations were performed using
where the displacement relative to an average lattice site
(Rn) of the n-th atom is δun, fn(Q) and e−Wn(Q)are the
form factors and Debye-Waller factors (DWFs), respec-
tively. The summation was carried out only over Cu, O,
and Ba atoms in the 4×1×1 supercell (Fig. 1). The ex-
pression above is for integrated intensity of the satellites
regardless of peak widths. The extraction of integrated
intensity from the experimental data at ∼7 K, however,
was difficult due to the presence of TDS and HDS. Nev-
ertheless, since the satellite peaks are sharper than TDS
and HDS, and located away from Bragg peaks, it is pos-
sible to model the satellites at the lowest T using a Gaus-
sian above some monotonic background. We found that
extracted intensities for the strong peaks varied ∼15-20%
(∼35% for the weak peaks) depending on how the back-
ground scattering was modeled. A least-squares proce-
dure was performed taking these errors and the general
considerations discussed above into account to fit the in-
tensities of 45 peaks within the [H, K, 0] zone and the in-
tensity modulation of the (5.25, 0, 0) peak along c*. We
kept the displacements symmetric about the Cu(1)-O(4)-
Cu(2) and CuO mirror planes centered on the O-vacancy
inside a supercell. Vertical bars in Figs. 2(a)-(d) indicate
that there is good agreement between the calculated (red)
and observed (black) intensities within experimental un-
certainties. The model obtained from fitting is shown in
Fig. 1. While the dominant contributions come from dis-
placements of Ba and Cu atoms, both chain (O(1)) and
plane oxygen atoms (O(2) and O(3)) are displaced signif-
icantly. Note that the displacements are 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 estimates are ∼ 10−15% for Ba
and Cu δu’s, and ∼ 15 − 25% for O atoms, respectively.
While the model obtained may not be perfect given the
difficulty of extracting accurate intensities, it does ac-
count for all the systematics of the data. Furthermore,
it portrays a pattern of displacements similar to that of
Ortho-V phase in an underdoped YBCO obtained from
first-principles electronic calculations . In our case,
however, the periodicity is 4a (Fig. 1) along the a axis.
FIG. 3. (a) [H, 0, 0] scans at several temperatures. Lines
are fits using a combination of a Lorentzian (TDS), a Gaus-
sian (satellite), and a constant term. (b) K scans through
the (5.25, 0, 0) peak. (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).
Fig. 3(a) shows [H, 0, 0] scans through a superlattice
peak at several temperatures. It is clear from these scans
that as T is increased the intensity of the q0 peak de-
creases relative to the TDS emanating from (5,0,0). In
fact, an inspection of the data reveals that the inten-
sity (area under the dome) at 7 K is at least twofold
larger than that at 300 K. 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
about the mean grows. In order to get more quantita-
tive 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, one for the central satel-
lite peak and two for the broad lobes, respectively, and
a constant term to account for the background which is
predominantly made up of TDS. 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. Fig. 4(a)
shows the T-dependence of the fitted intensity for (5.25,
0, 0) peak. Although keeping positions and widths con-
stant may introduce some systematic errors for the cen-
tral satellite, its integrated intensity (width×peak inten-
sity) agrees well with that obtained in fitting the H-scan
as shown in Fig. 4(a). The intensity was also estimated
via the maximum amplitude of the modulation defined as Download full-text
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 ob-
tained from intensity 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 lower temperatures.
FIG. 4. (a) Temperature dependence of (5.25, 0, 0) peak.
(b) T dependence of Fourier amplitudes obtained from inten-
sity modulations shown in Fig. 3(c).
Although the origin of q0can be attributed to Ortho-
IV phase it is puzzling to observe a large increase of
the diffuse peak with decreasing T. Using the displace-
ment model presented above and DWFs for the average
lattice measured on ceramic samples  we estimated
I(300K)≈ 1.2 for the intensity of (5.25, 0, 0) satellite,
which is at odds with the observed ratio of at least ∼2.2.
Since diffusive motion of chain oxygens (O(1)) practi-
cally freezes below ∼ 250 K, the growth of Ortho-IV
patches in size or number seems unlikely. Given that
atomic displacements (Fig. 1) are clearly anharmonic in
these nanoscale patches 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.
In conclusion, we have shown that lattice modulations
with a 4-unit-cell periodicity exist from above room tem-
perature down to the lowest temperatures 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 δu’s (Fig. 1) one may calcu-
late DWFs for the whole crystal and by comparison with
the experimental DWFs  we estimate roughly ∼10-
20% of the crystal contain these patches 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 by the disorder between O atoms and va-
cancies along both a and b axes; strains induced by the
patches is not assumed. However, the coincidence of the
observed periodicity (q0=(1
for charge instabilities in the CuO2planes from measure-
ments on other superconducting cuprates is striking. It
4,0,0)) with values expected
seems clear that in YBCO the electronic structure and
the oxygen vacancies together possess instabilities which
can lead to inhomogeneous phases and local softening of
We have benefitted from our discussions with B. W.
Veal, D. de Fontaine, V. Ozolins and D. Basov. Use of
the Advanced Photon Source is supported by the U.S.
Department of Energy, Office of Science, Office of Basic
Energy Sciences, under Contract No. W-31-109-ENG-38.
SCM thanks the NSF for support on DMR-0099573.
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