Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x

Abstract

The application of magnetic fields to layered cuprates suppresses their high-temperature superconducting behaviour and reveals competing ground states. In widely studied underdoped YBa₂ Cu₃ O_6+x (YBCO), the microscopic nature of field-induced electronic and structural changes at low temperatures remains unclear. Here we report an X-ray study of the high-field charge density wave (CDW) in YBCO. For hole dopings ∼0.123, we find that a field (B∼10 T) induces additional CDW correlations along the CuO chain (b-direction) only, leading to a three-dimensional (3D) ordered state along this direction at B∼15 T. The CDW signal along the a-direction is also enhanced by field, but does not develop an additional pattern of correlations. Magnetic field modifies the coupling between the CuO₂ bilayers in the YBCO structure, and causes the sudden appearance of the 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high fields, allowing Fermi surface reconstruction, as recently suggested.

ARTICLE

Received 17 Feb 2016 | Accepted 1 Apr 2016 | Published 5 May 2016

J. Chang1, E. Blackburn2, O. Ivashko1, A.T. Holmes3, N.B. Christensen4, M. Hcker5, Ruixing Liang6,7, D.A. Bonn6,7, W.N. Hardy6,7, U. Rtt8, M.v. Zimmermann8, E.M. Forgan2 & S.M. Hayden9

The application of magnetic elds to layered cuprates suppresses their high-temperature superconducting behaviour and reveals competing ground states. In widely studied underdoped YBa2Cu3O6 x (YBCO), the microscopic nature of eld-induced electronic and structural changes at low temperatures remains unclear. Here we report an X-ray study of the high-eld charge density wave (CDW) in YBCO. For hole dopings B0.123, we nd that a eld (BB10 T) induces additional CDW correlations along the CuO chain (b-direction) only, leading to a three-dimensional (3D) ordered state along this direction at BB15 T. The CDW signal along the a-direction is also enhanced by eld, but does not develop an additional pattern of correlations. Magnetic eld modies the coupling between the CuO2 bilayers in the

YBCO structure, and causes the sudden appearance of the 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high elds, allowing Fermi surface reconstruction, as recently suggested.

DOI: 10.1038/ncomms11494 OPEN

Magnetic eld controlled charge density wave coupling in underdoped YBa2Cu3O6 x

1 Physik-Institut, Universitat Zrich, Winterthurerstrasse 190, Zrich CH-8057, Switzerland. 2 School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK. 3 European Spallation Source ERIC, Box 176, Lund SE-221 00, Sweden. 4 Department of Physics, Technical University of Denmark, Kongens Lyngby DK-2800, Denmark. 5 Condensed Matter Physics & Materials Science Department, Brookhaven National Lab, Upton, New York 11973, USA.

6 Department of Physics & Astronomy, University of British Columbia, Vancouver V6T-1Z1, Canada. 7 Canadian Institute for Advanced Research, Toronto M5G-1Z8, Canada. 8 Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany. 9 H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK. Correspondence and requests for materials should be addressed to J.C. (email: mailto:[email protected]

Web End [email protected] ) or to S.M.H. (email:mailto:[email protected]

Web End [email protected] ).

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Charge density wave (CDW) correlations1, that is, periodic modulations of the electronic charge density accompanied by a periodic distortion of the atomic lattice, have

long been known to exist in underdoped La-based cuprate high-temperature superconductors2,3. More recently, it has been found that charge order is a universal property of underdoped high-temperature cuprate superconductors411. CDW correlations appear typically at temperatures well above the superconducting transition temperature Tc. Cooling through

Tc suppresses the CDW and leads to a state, in which the superconducting and CDW order parameters are intertwined and competing1214.

The application of magnetic elds suppresses super-conductivity. In the case of underdoped YBa2Cu3O6 x (YBCO),

a number of changes in electronic properties have been reported in the eld range BE1020 T. For example, new splittings occur in NMR spectra11,15, ultrasound shows anomalies in the elastic constants16 and the thermal Hall effect suggests that there is an electronic reconstruction17. At larger elds, B\25 T a normal state with quantum oscillations (QO)18 and coherent transport along the c axis19 is observed. The existence of QO, combined with a high-eld negative Hall and Seebeck effect, is most easily understood in terms of electron pockets9,2023.

Fields BE1020 T also cause changes in the CDW order that can be seen by X-ray measurements. Initial experiments5 showed that a magnetic eld causes an enhancement of the diffuse CDW scattering5,8. A recent X-ray free-electron laser experiment24 has shown that a magnetic eld of B\15 T induces a new CDW

Bragg peak, with a propagation vector along the b axis, corresponding to an extended range of ordering along the c axis and an in-phase correlation of the CDW modulation between the neighbouring bilayers.

It is important to determine the nature of the CDW correlations induced by the magnetic eld in YBCO and their relationship to the electronic properties. Of particular interest are the high-eld CDW phase diagram and whether a eld also induces new CDW order propagating along the a axis. We have therefore used hard X-ray scattering measurements to determine the evolution of the CDW correlations, with magnetic elds up to 16.9 T for several doping levels. Here we investigate the CDW for propagation vectors along the crystallographic a- and b-directions, allowing us to extend the pulsed-eld measurements24 and identify new eld-induced anisotropies in the CDW. By measuring the prole of the diffuse CDW scattering as a function of eld, we show that the CDW inter-bilayer coupling along the c axis is strongly eld dependent. We also show that eld-induced changes in the CDW can be associated with many of the anomalies11,1517,25 observed in electronic properties. In particular, the B T phase diagram

has two boundary lines associated with the formation of high-eld CDW order. Our data also provides insight into the likely high-eld structure of the CDW (in the normal state) that is relevant to describe the Fermi surface reconstruction leading to QO.

ResultsCharge density wave order in YBCO. The CDW correlations in the cuprates have propagation vectors with the in-plane components parallel to the CuO bonds and periodicities of 3 4a depending on the system2,3,5,8. YBCO shows a

superposition of modulations localized near the CuO2 bilayers, with basal plane components of their propagation vectors along both a and b: qa (da,0,0) and qb (0,db,0) with correlation

lengths up to xaE70 E20a. Both qa and qb CDWs have ionic displacements perpendicular to the CuO2 bilayers combined with

displacements parallel to these planes, which are p/2 out of phase26. These give rise to scattering along lines in reciprocal space given by QCDW na* mb* cc*qa,b, where n and m

are integers. The distribution of the scattered intensity along c depends on the relative phase of the CDW modulations in the bilayers stacked along the c-direction. In zero magnetic eld, there is weak correlation of phases in neighbouring bilayers and we observe scattered intensity spread out along the c* direction, peaked at cE0.5 0.6. This is illustrated by our X-ray

measurements on YBCO6.67 (P 0.123, Tc 67 K and ortho-VIII

CuO-chain ordering), shown in Fig. 1a,f. Note that the strong scattering around QB(13/8,0,0) in Fig. 1a,b is due the CuO-chain ordering, which does not change with eld, and can be subtracted, as in Fig. 1c,d. By taking cuts through the data, we obtain the intensity of the CDW scattering versus c for the qa and qb positions (Fig. 1e,j).

Field-induced anisotropic CDW correlations. Figure 1 shows that the effect of applying a magnetic eld is very different for two components (qa and qb) of the CDW. For the qa component of the correlations (Fig. 1b), the rod of scattering becomes stronger with no discernible change in the c width or position of the maximum, that is, the correlations simply become stronger. In contrast, for the qb correlations, (Fig. 1i) we see two qualitative changes. First, at BE10 T, the rod of diffuse scattering becomes broader in c and its peak position begins to move to larger c. Second, at BE15 T, a new peak (shaded pink and rst reported in ref. 24) appears centred on c 1, but only for the qb component. The new peak indicates that

the sample has regions, where the CDW modulation is in phase in neighbouring bilayers and is coherent in three spatial directions. These regions would have a typical length along the c axis of xcE47 .

Structure of the three-dimensional CDW order. We measured the intensity of the new three-dimensional (3D) CDW order in 14 different Brillouin zones. These data (Supplementary Note 3; Supplementary Table 1 and 2) are consistent with the high-eld CDW structure of an individual bilayer being unchanged from that determined at zero eld26. Both low- and high-eld structures break the mirror symmetry of a bilayer, but in the high-eld structure (Fig. 2a,d), the atomic displacements in adjacent bilayers are in phase. Thus, the high-eld order has qb (0,db,0); however, its structure yields zero CDW intensity for

c 0 and nonzero for c 1 positions, as we observe

(Supplementary Fig. 4). The relationship between the CDW structures at low and high eld is to be expected, since the coupling between the two CuO2 planes in a bilayer will be stronger than coupling with another bilayer. For the other basal plane direction, no CDW signal was found at q (da,0,0) or

(da,0,1) for Br16.9 T (Fig. 3c).

The phase diagram and 3D CDW precursor correlations. The c-dependent proles in Fig. 1e,j contain information about the correlation between the phases of the CDW modulation in the bilayers stacked along the c axis. For B 0, the broad cE0.5 0.6

peaks in Fig. 1e,j for qa and qb indicate that the CDW phase is weakly anti-correlated between neighbouring bilayers. On increasing the eld above BE10 T, the c-prole of the qb correlations evolves. The onset of this evolution can be seen as an increase in the intensity of the scattering at (0,4-db,1), see Fig. 4c, signalling the introduction of new c axis correlations. This change is accompanied by a growth of correlations along the b axis, as shown by the increase in the correlation length xb,c 1 measured by the peak width of scans parallel to b* through the (0,4-db,1)

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Figure 1 | Charge density wave correlations induced by a magnetic eld in YBa2Cu3O6.67. A magnetic eld applied along the c axis introduces new CDW correlations propagating along both CuO bond directions a and b in the CuO2 planes. (a,b,fi) Raw X-ray scattering intensity data for the (h,0,c) (a,b) and (0,k,c) (fi) planes for magnetic elds 0rBr16.5 T. Strong features in (a,b) are due to CuO chain scattering. (c,d) Field-induced scattering for (h,0,c).

(e,j) CDW intensity along lines Q na* mb*qa,b cc* isolated from data such as (a,b,fi). The CDW intensity has been isolated by tting peaks due to

the CDW and other structural features to a series of h- or k-cuts through data such as (a,b,fi). CDWs propagating along the a axis (ae) within individual bilayers become stronger without changing phase relationship with neighbouring bilayers. Those propagating along b axis (fj) become in phase with neighbouring bilayers, which changes the prole in c. The shaded areas in (j) show: weakly anti-correlated CDW (grey); 3D CDW precursor correlations (blue); and 3D CDW order (red). Error bars are s.d.s determined by counting statistics. We describe reciprocal space as Q ha* kb* cc*, where Ideally

mod (a*) 2p/a, a 3.81 , b 3.87 and c 11.72 .

position (Fig. 4e). We describe this state as 3D CDW precursor correlations. The onset temperature TE65 K of the precursor correlations at high eld (B 16.5 T) may be determined from

the increase in xb,c 1 and the scattering intensity at the (0,4-db,1)

position (Fig. 4c,e). This allows us to designate a region of the B T phase diagram (Fig. 5).

At higher elds, B\15 T, a peak (shaded pink in Fig. 1j) develops abruptly in the c-prole at c 1. The abrupt onset of

the peak signals a rapid growth of the c axis correlation length xc (Fig. 4d,e). The growth of correlations in one spatial direction followed by growth in a second direction is typical of systems, with anisotropic coupling. Another CDW system that shows this behaviour27 is NbSe3. Large correlated regions develop rst in planes, where the order parameter is most strongly coupled. These act to amplify the coupling in the remaining direction. In case of YBCO6.67, the in-plane correlation length continues to grow down to low temperatures with xb,c 1 80b 310

(at B10 K and 16.5 T). The c axis correlation length, however, saturates with xc,c 1 47 at TE30 K. All these changes

together signal the transition to a new phase (see Fig. 5 pink region), which we label 3D CDW order identied with a phase transition also seen in ultrasound16 and thermal Hall effect17 measurements. At the lowest temperatures, Tt25 K, we observe (Fig. 4a) a suppression of the 3D CDW peak intensity signalling a

competition between the superconducting and 3D CDW order parameters.

Previous X-ray5,8 and NMR25 measurements on YBCO6.67 have shown that the weak anti-phase (c 1/2) CDW correlations

appear at TE150 K. Further NMR anomalies in the form of line splittings11,15 are observed at TE65 K for B 28.5 T and at

BE10 T for T 2 K. These anomalies that are displayed on Fig. 5

appear to coincide with the onset of the 3D precursor correlations reported here. The fact that NMR sees similar transitions shows that the 3D CDW precursor correlations we observe are static on timescales t\0.1 ms. Correlations that are static25 and short ranged are necessarily controlled by pinning with quenched disorder playing a role.

Doping dependence. We also studied other dopings of YBCO6 x. For YBCO6.60 with hole doping P 0.11 and ortho-II

oxygen chain structure, a very similar onset eld (Fig. 5) and c axis correlation length xc were found. In YBCO6.51 and YBCO6.75, no 3D order was observed for Br16.9 T (Fig. 3a). However, we do observe the precursor movement of the CDW scattering to higher c implying that this structure is likely to appear at higher elds. Thus, the 3D order is most easily stabilized for doping around p 0.110.12 (Fig. 5b).

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a b c d e

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Figure 2 | Magnetic eld effect on c axis correlations in YBa2Cu3O6.67. (a) Schematic of the CDW modulation in a bilayer26. Arrows represent the displacement of the planar oxygens. Two phases: A (y 0), B (y p) of the modulation are shown. (bd) Representative CDW stacking sequences for

different elds. (b) (B 0) Weakly anti-correlated and (c) (B 16.5 T) short-range three-dimensional (3D) order with correlated regions of size x(c)E4c. (d) Weakly pinned fully 3D coherence (large B). (e) Field-dependent parameters determined from tting data such as Fig. 1j to the Markov model described in Methods: nearest-neighbour coupling (b); next-nearest-neighbour coupling (g); and the proportion of bilayer AA pairs separated by one lattice spacing

PAA1

. Note PBB1 PAA1. Errors are determined from least square tting of model to data.

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Figure 3 | Doping temperature and eld dependence of induced CDW correlations. (a) c-Scans along (0,db,c) for different dopings of YBCO at TE8 K and B 16.9 T showing the eld-induced 3D correlations or lack thereof. (b) Temperature dependence of c-scans along (0,db,c) measured on YBCO6.67 at

B 16.5 T. All curves in (a,b) have been given an arbitrary shift. (c,d) h-Scans through (2-da,0,1) and k-scans through (0,4-db,1) in YBCO6.67 for zero eld

and B 16.5 T. Error bars are s.d.s determined by counting statistics.

DiscussionA feature of the present data is that the c-dependent proles measured along (0,db,c) and their eld evolution (for example,

Figs 1j and 3a,b) cannot be understood as a superposition of broadened peaks centred at c 1/2 and c 1. The change in the

c-dependence of the intensity represents a variation with eld of the stacking of the bilayer CDWs. To interpret these proles, we use a simple statistical approach based on a Markov chain (Methods; Supplementary Note 2) to model possible CDW stacking sequences along the c axis and compute the scattering prole as a function of c. A good description of our data is obtained if we assume that the CDW phase difference between neighbouring bilayers is 0 or p (Supplementary Note 1 and 2;

Supplementary Fig. 2). The parameters in our model are the

nearest- and next-nearest-neighbour couplings b and g, where positive values favour the coupled bilayers having the same phase. At B 0, the model shows that the broad cE0.5 0.6 peaks in

Fig. 1e,j are due to weakly anti-correlated bilayers (Fig. 2b,e). The eld evolution of the c-dependent proles for qb (Fig. 1j), including the formation of the c 1 peak, may be modelled by a

continuous variation of b and g from anti-phase coupling at low eld to same-phase coupling at high eld (Fig. 2e). The sign of b changes near the onset of the 3D order at BE15 T. Thus, we nd that a c axis magnetic eld can control the coupling between the CDWs in neighbouring bilayers. The eld control of the coupling most likely arises through the suppression of superconductivity by eld. Magnetic eld strengthens the correlations along the a axis (Fig. 1e); however, it does not increase correlation lengths.

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Figure 4 | Evolution of charge density wave correlation lengths and intensities with magnetic eld and temperature in YBa2Cu3O6.67. (a) Intensity of

the 3D CDW peak extracted from c-scans through Q (0,4-db,c) versus temperature at elds as indicated. (b,c) Total CDW intensity determined from

k-scans (open circles) and 3D CDW peak intensity determined from c-scans (closed squares) through the (0,4-db,1) position. (d,e) Correlation lengths xb,c 1, xc,c1, xb,c1/2 determined from the resolution-corrected peak widths (s x 1) of scans through (0,4-db,1), (0,4-db,1) and (0,4-db,1/2) positions,

respectively. The saturation of xc,c1 47 and xb,c

1/2B100 is likely related to disorder even though it has been shown that xb,c1/2 is insensitive to

oxygen disorder34. Error bars are s.d.s of the t parameters described in the Methods.

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35

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10

5

0 0 50 100 150

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Figure 5 | Phase diagram of YBa2Cu3O6 x. The pink shaded areas represent the regions where short-range 3D CDW order exists. Grey bands indicate the

regions where growing 3D CDW precursor correlations are observed. (a) Temperature-magnetic eld phase diagram. (b) Doping-magnetic eld phase diagram. Solid red square points indicate the onset of a 3D CDW order with qb (0,db,0) determined from the variation of the xc,c1 correlation length and

the intensity of the 3D peak (Fig. 4). Triangles are the Fermi surface reconstruction onset determined from thermal Hall coefcient17. Solid black squares indicate the onset of growing in-plane CDW correlation lengths (3D precursor correlations) determined from the variation of xb,c1 (Fig. 4d,e). Dashed blue

lines in (a,b) indicate Bc2 line35. Solid black circles in (a,b) are derived from NMR11,15. The vertical black dashed line is the onset of weakly anti-phase CDW correlations (refs 4, 5 and 8). Red circular and triangular points originate from ultrasound16 and thermal Hall effect17 experiments, whereas the red squares are the eld onset of qb (0,db,0) found by X-ray diffraction.

Doping (p)

Possible explanations for this difference in behaviour include the inuence of the CuO chains promoting the b axis modulations or the chains pinning the a axis CDW modulations.

We conclude that the appearance of 3D CDW order corresponds to the onset of new c axis electronic coherence and hence electronic reconstruction. This is supported by thermal

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Table 1 | YBCO samples investigated in this study.

x in YBCO Oxygen ordering Doping level p Tc (K) Bc (T) nb (b) nc (c)6.51 o-II 0.096 59 416.9

6.60 o-II 0.11 61.8 15.30.35 48 4.56.67 o-VIII 0.123 67 14.50.5 80 46.75 o-III 0.132 74 416.9

YBCO, YBa Cu O .

The correlation length x and x of the (0,d ,0) CDW order at the highest measured elds and lowest temperature are given in units of the lattice parameters b 3.87\AA() and c 11.7 .

Hall conductivity measurements17 that demonstrate Fermi surface reconstruction at the same eld (Fig. 5a). At highest elds investigated, B 16.9 T, the structure of the CDW within

individual bilayers involves the same breaking of mirror symmetry observed at zero eld26, which has been posited to lead to Fermi surface reconstruction28,29.

Methods

Experimental details. Our experiments used 98.5 keV hard X-ray synchrotron radiation from the PETRA III storage ring at DESY, Hamburg, Germany. A 17 T horizontal cryomagnet30 was installed at the P07 beamline. Access to the (h,0,c) and (0,k,c) scattering planes was obtained by aligning either the ac axes or the bc axes horizontally, with the c axis approximately along the magnetic eld and beam direction. The samples were glued to a pure aluminium plate on which was mounted a Cernox thermometer for measurement and control of temperature. With the high intensities of PETRA III, a small amount of beam heating of the sample was observed. By observing the effect of changes in beam heating (controlled by known attenuation) on the measured temperature of the 3D phase transition, we determined the effect of the beam on the sample temperature near40 K. The sample heating at other temperatures was determined using the Cernox thermometer and a model of the heat ow from the sample to the aluminium plate. We estimate that there is an absolute uncertainty in our temperature determination of 2 K. The relative temperature uncertainty is smaller than this.

Four YBCO crystals with different in-planar doping and different oxygen chain structure were studied (Table 1). Except for the YBCO6.60 sample, detailed descriptions of these crystals are found in refs 5,31,32. The YBCO6.60 sample was

studied with the scattering plane dened by (k,k,0) and (0,0,c). This conguration has the advantage that CDW modulations along both a and b axis directions could be accessed without reorienting the sample. The absence of c 0,1 CDW order

along the a axis direction was checked using the (h,0,c) scattering plane.

Data analysis. h- and k-scans, as shown in Fig. 3c,d, are tted with a single Gaussian function on a weakly sloping background. c-scans with a well-dened peak at c 1 (Figs 1j and 3a,b) are tted using a two Gaussian functions. Corre

lation lengths x 1/s are dened by the inverse Gaussian s.d. s s2meas s2R

0:5.

The instrumental resolution sRfor a CDW reectionwas estimated at Bragg reections near to the measured CDW reections. Resolution-corrected correlation lengths are given in Table 1.

Simulation of scattering proles. We use a simple Markov chain model33 of order m 2 to interpret the diffuse and c 1 scattering proles, for example, in

Fig. 1j. A Markov chain is a stochastic series. Here we generate a series of two types of bilayer (A and B) corresponding to the phase of the displacement of the CDW in a given bilayer. We represent the bilayer type at position index i along the c-direction by a stochastic variable xi. This can take either the value xi 1, denoting

bilayer type A, or xi 0 for type B. We create a series of bilayers starting, for

instance, with an A bilayer, followed by a B. The probability P(xi 1) of adding an

A bilayer at position i, preceded by xi 1 and xi 2 , in the series is given by:P xi 1 j xi 1; xi 2

a bxi 1 gxi 2: 1

Clearly, P(xi 0) 1 P(xi 1). Equation (1) is a recipe, using random numbers

to represent the probabilities, to create a series of bilayers with a given amount of correlation built in. Let mA (mB 1 mA) be the fraction of A-type (B-type)

bilayers in the series and PAA1 the proportion of AA bilayer pairs separated by one lattice spacing. We choose a 12 1 b g

so that macroscopically mAmB 12.

A number (NB500) of stochastic series xi (Nsite 100) subject to a given a, b and g

are generated. The corresponding scattered intensity (assuming the single-unit cell structure from ref. 26) for each series is calculated and averaged. b and g are adjusted to give the best t to the data and PAA1 is calculated.

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Acknowledgements

We wish to thank M.H. Julien and L. Taillefer for helpful discussions. This workwas supported by the Engineering and Physical Sciences Research Council (EPSRC) (grant numbers EP/G027161/1, EP/K016709/1 and EP/J015423/1), Danish Agency for Science, Technology and Innovation through DANSCATT and grant number 0602-01982B and the Swiss National Science Foundation grant number BSSGI0-155873.

Author contributions

R.L., D.A.B and W.H. grew and prepared the samples. J.C., E.B., M.H., N.B.C., U.R., M.Z., E.M.F. and S.M.H. conceived and planned the experiments. J.C., E.B., O.I., A.H., M.Z., E.M.F. and S.M.H. carried out the experiments. J.C. and S.M.H. carried out the data analysis and modelling. All co-authors contributed to the manuscript.

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How to cite this article: Chang, J. et al. Magnetic eld controlled charge density wave coupling in underdoped YBa2Cu3O6x. Nat. Commun. 7:11494

doi: 10.1038/ncomms11494 (2016).

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