MAGNETISM AND SUPERCONDUCTIVITY
TWO-DIMENSIONAL GEOMETRY OF SPIN EXCITATIONS IN THE HIGH-
TRANSITION-TEMPERATURE SUPERCONDUCTOR YBa2Cu3O6.85
V. Hinkov1, S. Pailhès2, P. Bourges2, Y. Sidis2, A. Ivanov3, A. Kulakov1, C. T. Lin1, D. P. Chen1,
C. Bernhard1 and B. Keimer1
1 Max-Planck-Institut für Festkörperforschung, 70569 Stuttgart, Germany
2 Laboratoire Léon Brillouin, CEA-CNRS, CEA-Saclay, 91191 Gif-sur-Yvette, France
3 Institut Laue-Langevin, 156X, 38042 Grenoble cedex 9, France
The fundamental building block of the copper
oxide superconductors is a Cu4O4 square plaquette.
In most of these materials, the plaquettes are
slightly distorted and form a rectangular lattice. An
influential theory of high temperature
superconductivity predicts that
dimensional lattice is intrinsically unstable towards
a “striped” state with one-dimensional spin and
charge order [1,2]. Static stripe order has indeed
been reported in specific layered copper oxides in
which superconductivity is suppressed, but the
theory also predicts phases in which robust
superconductivity coexists microscopically with
liquid-crystal-like stripe order. The liquid-crystal
order parameter is expected to align itself
preferentially along one of the axes of the
rectangular lattice, generating a quasi-one-
dimensional pattern in scattering experiments .
Testing this prediction requires “untwinned”
specimens in which the orientation of the
rectangular lattice is maintained throughout the
entire volume. However, almost all neutron
experiments thus far reported have been carried out
on fully ‘twinned’ crystals with equal proportions
of micrometre-scale twin domains in which the
rectangular Cu4O4 plaquettes are rotated by 90°
with respect to one another. Because the scattering
pattern from such crystals consists of equal
contributions from both twin domains, even
perfectly one-dimensional spin
generate a fourfold symmetric pattern, so that they
cannot be discriminated from microscopically two-
dimensional fluctuations. The results of previous
neutron scattering experiments on partially
detwinned YBa2Cu3O6+x crystals have been
interpreted as evidence of a one-dimensional
character of the magnetic fluctuations .
However, owing to significant contributions from
the minority domain, the full geometry of the
excitation spectrum has remained unclear.
Using neutron scattering from a mosaic of fully
untwinned, nearly optimally doped YBa2Cu3O6.85
crystals , we have resolved this issue. Scans
through the (200) and (020) Bragg reflections of
the YBa2Cu3O6.85 array reveal a bulk population
ratio between majority and minority twin domains
of about 95:5 (Fig. 1b) .This is one order of
magnitude larger than in previous experiments.
The contribution of the minority domain to the
magnetic scattering pattern is thus negligible in our
Figure 1. Layout of the reciprocal lattice and magnetic
spectral weight of YBa2Cu3O6.85. a) In-plane
projection of the YBa2Cu3O6.85 reciprocal lattice
indicating the trajectories of the constant-energy scans
shown in Fig. 2.. b) Longitudinal elastic scans through
the (2, 0, 0) and (0, 2, 0) crystallographic Bragg
reflections, demonstrating a twin domain population
ratio of (95:5). C) Intrinsic magnetic spectral weight at
35 meV (see text).
Figure 2 shows magnetic neutron scattering data
from this crystal array. The overall features of the
neutron cross-section are in good agreement with
prior work on twinned crystals. The observed
magnetic excitations are incommensurate (Fig 2)
around the in-plane wave vector QAF =(0.5, 1.5).
The incommensurate excitation branches disperse
towards QAF with increasing excitation energy
(Fig. 2), and they merge at 41 meV, giving rise to
the ‘resonance peak’.
The new aspect of this work is the determination of
the in-plane geometry of the spin excitations.
Figure 2c–j shows representative scans from a
MAGNETISM AND SUPERCONDUCTIVITY Download full-text
comprehensive map of the spin fluctuation spectral
weight at ħω=35 meV. More limited data sets were
also taken at ħω= 33 and 37 (not shown), and 38
meV (Fig. 2a,b). The most important observation is
that well-defined incommensurate peaks are
present in scans along both a* and b* (Fig. 2a-d).
This demonstrates the intrinsic two-dimensional
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 Mook, H. A., Dai, P., Dogan, F. & Hunt, R. D. One-dimensional nature of the magnetic fluctuations in
YBa2Cu3O6.6. Nature 404, 729-731 (2000).
 Hinkov, V. et al. One Two-dimensional geometry of spin excitations in the high-transition-temperature
superconductor YBa2Cu3O6+x. Nature 430, 650-653 (2004).
 Onufrieva, F. & Pfeuty, P. Spin dynamics of a two-dimensional metal in a superconducting state: Application to the
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nature of the spin excitations. To extract the
magnetic spectral weight from the experimentally
numerically convoluted an anisotropic damped
harmonic oscillator cross-section
spectrometer resolution function. The computed
profiles, shown as solid lines in Fig. 2, provide
excellent descriptions of the experimental data. We
find that the locus of maximum spin fluctuation
spectral weight approximately forms a circle in
momentum space, in agreement with its two-
dimensional geometry. However, the damping and
amplitude along the circle are modulated in a one-
dimensional fashion. The intrinsic magnetic
spectral weight at 35meV extracted from this
analysis is depicted in Fig. 1c. The strength of this
modulation also depends strongly on the excitation
Which models can describe the observed one-
dimensional amplitude and width anisotropy? i)
Theories based on a one-dimensional, rigid array
of stripes predict a 100% intensity anisotropy and
cannot account for the two-dimensional scattering
pattern. The map of the magnetic intensity at
35meV does, however, bear a resemblance to the
scattering pattern generated by a nematic liquid
crystal close to a nematic-to-smectic critical point
. In this scenario, the structural anisotropy
between the a and b axes may act as an aligning
field for the nematic director.
ii) Prior Fermi-liquid-based theoretical scenarios
for the spin dynamics of YBa2Cu3O6+x had only
considered independent CuO2 layers, ignoring a
possible influence of the b-axis-oriented CuO
chains . Their impact (via an orthorhombic
anisotropy) on the spin dynamics has to be
assessed in quantitative calculations. Other factors,
such as proximity to a ‘Pomeranchuk’ instability of
the Fermi surface , may also contribute to the
anisotropy of the spin dynamics.
profiles, we have
Figure 2. Constant-energy scans along the
trajectories indicated in Fig. 1a. The excitation
energies are ħω= 38 meV (a, b) and 35 meV (c–j).
The wave vector Q = (H, K,1.7) is given in
reciprocal lattice units, r.l.u.. We show subtractions
of the intensities at T = 10 K (<<Tc) and T = 100 K
(>Tc). The data in panels c, d and i, j were taken in
two different Brillouin zones with exchanged
resolution conditions. The observed anisotropy
between a* and b* is thus not due to resolution