Stripe structure of the CuO
2
plane in Bi
2
Sr
2
CaCu
2
O
8 y
by anomalous x-ray diffraction
A. Bianconi and M. Lusignoli
Dipartimento di Fisica, Universita ` di Roma ‘‘La Sapienza,’’ P. A. Moro 2, 00185 Roma, Italy
N. L. Saini
Istituto Nazionale di Fisica Nucleare, Dipartimento di Fisica, Piazza A. Moro 2, 00185 Roma, Italy
P. Bordet
Laboratoire de Crystallographie, Centre National de la Recherche Scientifique, Avenue des Martyrs, F-38043 Grenoble, France
A
˚
. Kvick
European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble, France
P. G. Radaelli
Institut Laue Langevin, Avenue des Martyrs, F-38043 Grenoble, France
Received 26 February 1996
The modulated structure of the CuO
2
plane in Bi
2
Sr
2
CaCu
2
O
8 +y
superconductor has been solved by Cu
K -edge anomalous x-ray diffraction. The displacement of Cu ions along the c axis shows the largest amplitude
and anharmonic character. The results show flat stripes of CuO
2
lattice of width L =15.5 Å with long Cu-Bi
distances that are separated by stripes of bent CuO
2
plane and shorter Cu-Bi distances. In each CuO
2
bilayer
the flat stripes in a first layer are close to the bent stripes in the second layer, suppressing the electronic
coupling between the two adjacent planes. S0163-18299603929-X
I. INTRODUCTION
In most of the high-T
c
superconductors the local structure
of the CuO
2
lattice deviates from the average crystallo-
graphic structure.
1
Models for mechanisms of pairing in
high-T
c
superconductors based on the coexistence of two
components have been proposed
2–6
where a first component
is made of a gas of itinerant charges while the second one is
made of relatively localized charges. Recently a model has
been proposed
7
where the two components are spatially
separated in a superlattice of undistorted stripes U stripes
alternated with distorted stripes D stripes. In this model the
superconducting phase coexists with a one-dimensional an-
harmonic modulation of the CuO
2
plane.
There is growing evidence that an incommensurate modu-
lation with superstructure vector of the type
q
s
=b*+1/c* in the orthorhombic notation where
b *=1/&d and d is the average Cu-Cu distance is a com-
mon feature of optimally doped cuprate superconductors. It
has been observed in Bi
2
Sr
2
CaCu
2
O
8+
Bi2212 with
0.21 and =1;
8,9
in Bi
2
Sr
2
CuO
6+
Bi2201 with 0.21
and varying from sample to sample in the range
1.6–3;
10–12
in La
2
CuO
4.1
LCO with =0.22 and =3 Ref.
13 or =0.2 and =3;
14
in Tl
2
Ba
2
CaCu
2
O
8
Tl2212Ref.
15 and in Tl
2
Ba
2
Ca
2
Cu
3
O
10
Tl2223,
16
with 0.2; and in
La
2 -x
Sr
x
Cu
2
O
4
LSCO, for x 0.075 with 0.16 and
3.5.
17
Recently a similar superstructure has been seen for
x =0.1, x =0.15 and, much more weakly, in the overdoped
sample x =0.2.
18
The c-axis period changes from one system
to another and it can be assigned to different staging of dop-
ants; on the contrary the in-plane b-axis direction modula-
tion seems to be a common feature. However, the satellite
reflections are often weak and diffused, indicating ordering
over small domains, and better resolved at temperatures
lower than 200–100 K. The best-characterized situation, in
this respect, is that of bismuth-based superconductors,
19
in
which the modulation gives rise to sharp and intense satellite
peaks up to high temperatures.
The modulated structure of the Bi2212 system has been
studied by several groups using electron, x-ray, and neutron-
diffraction techniques.
8,9,19–27
The solution of the anhar-
monic incommensurate superstructure of Bi2212 is at the
limit of the capabilities of diffraction methods, due to the
large number of parameters needed in the structural refine-
ment. Electron diffraction
12
has pointed out that the main
lattice modulation involves the BiO layers. Bi L
3
-edge
anomalous diffraction has shown the distribution of Bi atoms
over Ca and Sr sites.
24
The BiO rocksalt layers form blocks
of undistorted rocksalt lattice U blocks alternated by blocks
of stretched BiO lattice D blocks in the b direction. The
latter are characterized by 1 low Bi density, 2 variation of
the BiO coordination geometry, 3 presence of interstitial
oxygen, and 4 deviations from the stoichiometry. Although
various experiments
8,9,23,25–27
report modulation of the Cu
sublattice mainly along the c axis, the results disagree on the
amplitude and anharmonic character of the modulation.
In the present paper we report a study of the modulation
of the CuO
2
plane in Bi2212 by x-ray anomalous scattering,
taking advantage of tunability of synchrotron radiation.
28
Due to the strong variation of the copper scattering factor
near the Cu K threshold, the technique provides direct and
selective information on the sublattice of copper atoms. Fur-
thermore, the data were collected in a selected region of the
reciprocal space with Bragg reflections of Miller indices
l h k . In this case, the diffracted intensities are mainly
sensitive to displacements along the c axis. As a result the z
PHYSICAL REVIEW B 1 AUGUST 1996-II VOLUME 54, NUMBER 6
54 0163-1829/96/546/43105/$10.00 4310 © 1996 The American Physical Society