Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields

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Science  20 Nov 2015:
Vol. 350, Issue 6263, pp. 949-952
DOI: 10.1126/science.aac6257

Discerning charge patterns in a cuprate

Copper oxides are well known to be able to achieve the order required for superconductivity. They can also achieve another order—one that produces patterns in their charge density. Experiments using nuclear magnetic resonanceand resonant x-ray scattering have both detected this so-called charge density wave (CDW) in yttrium-based cuprates. However, the nature of the CDW appeared to be different in the two types of measurement. Gerber et al. used pulsed magnetic fields of up to 28 T, combined with scattering, to bridge the gap (see the Perspective by Julien). As the magnetic field increased, a two-dimensional CDW gave way to a three-dimensional one.

Science, this issue p. 949; see also p. 914


Charge density wave (CDW) correlations have been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured with x-ray scattering at zero and low fields. We combined a pulsed magnet with an x-ray free-electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields of up to 28 tesla. While the zero-field CDW order, which develops at temperatures below ~150 kelvin, is essentially two dimensional, at lower temperature and beyond 15 tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW appears around the zero-field superconducting transition temperature; in contrast, the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

The universal existence of charge density wave (CDW) correlations in superconducting cuprates (112) raises profound questions regarding the role of charge order: Is it competing or more intimately intertwined with high-temperature superconductivity (HTSC) (1316)? Uncovering the evolution of CDW order upon suppression of HTSC by an external magnetic field provides valuable insight into these issues. One of the most studied cuprate superconductors, YBa2Cu3O6+δ, has become a model material for the study of CDW phenomena in cuprates. Largely two-dimensional (2D), incommensurate CDW order with moderate correlation length has recently been found to coexist with HTSC by using x-ray scattering measurement (7, 8, 17, 18). The temperature and magnetic field dependencies of up to μ0H = 17 T indicate a competition between CDW order and HTSC (8, 17). However, both nuclear magnetic resonance (NMR) (6, 19) and Hall coefficient measurements (20) suggest that there is a distinct, more ordered CDW phase at higher fields and lower temperatures, with an NMR signature that is different than the NMR broadening (21) that correlates with the zero-field CDW. The existence of a phase transition or sharp crossover to a state with a distinct field-induced form of density wave order is also supported by ultrasonic measurements (22). However, there is a discrepancy between NMR (19) and ultrasonic measurements (22) regarding the onset field of this new state, and neither reveal the structure of the CDW at high fields. This calls for high-field x-ray scattering measurements of the CDW phenomenology in superconducting cuprates, which, however, is extremely challenging for existing techniques, especially because the scattering signal is so weak.

To gain insight into this critical question, one needs to introduce a different experimental approach. We performed x-ray scattering at an x-ray free electron laser (FEL) in the presence of pulsed high magnetic fields. The high brilliance of the x-ray FEL (23) enables the measurement of the weak CDW scattering signal with a single x-ray pulse (~50 fs) at the apex of a millisecond magnetic field pulse (24). This approach provides us with the opportunity to probe the CDW signal in YBa2Cu3O6+δ at magnetic fields beyond 17 T, entering a field range comparable with that used in NMR (6, 19, 21), Hall coefficient (20), and ultrasonic measurements (22).

Shown in Fig. 1A is a schematic of how the two pulsed sources—the magnet and the x-ray FEL—were synchronized in order to study the CDW in detwinned, underdoped YBa2Cu3O6.67 (YBCO) with ortho-VIII oxygen order (24). To monitor the field dependence of the CDW, an area detector was used to capture a cut of the kl plane in reciprocal space. The full view of the zero-field diffraction pattern in the vicinity of the CDW position at the zero-field superconducting transition temperature, Tc(H = 0) = 67 K, is shown in Fig. 1B. In this geometry, we observed CDW features centered near (0, 2-q, ±½) with an incommensuration q ~ 0.318 (7, 8, 17, 18). The detected diffraction pattern of the CDW shows that the correlation along the crystallographic c axis is very weak, resulting in a rodlike shape along the l direction. Moreover, we also measured the temperature dependence of the zero-field CDW (Fig. 1C) (24), reproducing earlier reports that the CDW signal is maximal at Tc and suppressed for T < Tc (7, 8, 17, 18), which indicates a competition between CDW order and HTSC.

Fig. 1 Experimental setup and zero-field characterization.

(A) The millisecond pulsed magnetic field and femtosecond x-ray FEL pulses are synchronized to obtain a diffraction pattern from the YBCO single crystal at the maximum magnetic field. The diffraction pattern was recorded by use of a 2D pixel array detector. (B) Zero-field diffraction pattern showing the (0, 2-q, ±½) CDW peaks and the tail of the (0, 2, 0) Bragg peak (δ1= –0.118, δ2 = 0.001, δ3 = 0.021). The sample rotation angle was optimized for the CDW position and not for the (0, 2, 0) Bragg peak (24). (C) The temperature dependence of the CDW peak height near (0, 2-q, ½) measured at the x-ray FEL is shown with red symbols. We have also taken data at synchrotron light sources using hard (blue symbols) and soft (green symbols) x-rays (24), which are shown for comparison. The dashed line is a guide to the eye, and the error bars denote 1 SD as obtained from the peak fitting.

We first discuss the temperature dependence of the CDW at μ0H = 20 T. The (0, 2-q, l) CDW signal is shown in Fig. 2A at both 0 and 20 T. There is no field-induced change of the CDW at Tc, which is consistent with earlier results (8). With decreasing temperature (T < Tc), the CDW signal becomes sharper along the k direction and more intense than at zero field. This indicates that as the magnetic field suppresses superconductivity, the CDW order is enhanced (Fig. 2B). Surprisingly, as shown in the 2D difference map I20TI0T (Fig. 2A, bottom) the field-induced enhancement is most dramatic at l ~ 1, rather than at l ~ ½ where the zero-field CDW signal is maximal (7, 8, 17, 18). This observation indicates that a different kind of CDW correlation emerges around Tc(0)—well below the zero-field CDW onset temperature (Fig. 1C). As shown in Fig. 2C, the temperature dependence of the field-induced CDW is consistent with that of the CDW signatures inferred from NMR measurements (6), implying that both share the same origin.

Fig. 2 Temperature dependence of the CDW order at μ0H = 20 T.

(A) Top and bottom show the evolution of the projected (0, 2-q, ½) CDW peak profile along the k direction and the difference map of the diffraction pattern between μ0H = 0 and 20 T, respectively, at representative temperatures of T = 67, 40, and 10 K. Positions are given in reciprocal lattice units (r.l.u.). Solid lines are Gaussian fits to the data with a second-order polynomial background. (B) Temperature dependence of the peak height from the projected CDW profiles at 0 and 20 T. (C) Peak height of the projected CDW profiles near l ~ 1 as a function of temperature. The projected CDW profiles [inset, traces offset by 10 counts (cts)] are obtained from the 2D difference map by integrating near l ~ 1, as indicated in (A). As a comparison, NMR data taken from (6) are superimposed. Dashed lines are guides to the eye. Error bars correspond to 1 SD.

Next, we explored the field-induced enhancement of CDW order at T = 10 K. The diffraction patterns at μ0H = 0 – 25 T are shown in Fig. 3A, top. The projected intensities at both l ~ ½ and l ~1 are depicted in Fig. 3A, bottom, integrated over the ranges of l indicated in Fig. 3A, right. Up to μ0H = 15 T, the intensities of the CDW order at both l ~ ½ and l ~ 1 are similar. Above 15 T, however, the intensity at (0, 2-q, ~1) continues to grow strongly, whereas it saturates at (0, 2-q, ~½) (Fig. 3B). This was confirmed in an equivalent CDW region (0, 2+q, 1) (Fig. 4) (24), where we were able to follow the enhancement of CDW intensity at l = 1 up to our maximum field, μ0H = 28 T. Furthermore, the in-plane correlation lengths ξk at l ~ ½ and l ~ 1 start to diverge from each other at μ0H ~ 15 T (Fig. 3C), which is suggestive of a transition; ξk at l ~ 1 increases for μ0H > 15 T, whereas ξk at l ~ ½ saturates or is slightly suppressed. As discussed in (24), the estimated correlation length at the highest magnetic fields may be limited by the instrument resolution. Nevertheless, the distinct field dependence of the CDW intensity and the correlation length confirm that the CDW order at l ~ 1 is different from that at l ~ ½, and that both CDW orders coexist at high magnetic fields. In particular, the onset of the field-induced CDW (l ~ 1) above 15 T is consistent with NMR results in which the line-splitting signature of CDW order is absent at low fields (6, 19) and the ultrasonic measurements (22). Unfortunately, because of the relatively coarse field interval in Fig. 3, it is difficult to precisely determine the value of the onset field (Fig. 3, B and C, shaded area) or to distinguish whether the field-induced CDW emerges in a phase-transition or a crossover.

Fig. 3 Field dependence of the CDW order at T = 10 K.

(A) CDW diffraction pattern (top) and projected CDW peak profiles (bottom) near l ~ ½ and l ~ 1, obtained through integration of the signal in the windows indicated on the image, in the field range μ0H = 0 – 25 T. Features due to ice condensation on the sample surface that do not overlap with the CDW signal were subtracted from the diffraction patterns (24). Solid lines are Gaussian fits to the data with a second-order polynomial background. (B) Peak height of the projected CDW profile near l ~ ½ and l ~ 1 as a function of H. Data taken in an equivalent CDW region (0, 2+q, 1), shown in Fig. 4, are superimposed by normalizing the values at 20 T. (C) H dependence of the in-plane correlation length ξk = 1/σk deduced from Gaussian fits (σk is the Gaussian SD) to the projected CDW profile shown in (A) as well as Fig. 4C. Values of ξk have not been corrected for the instrument resolution and, therefore, represent lower bounds. The gray shaded area denotes the onset region of the l ~ 1 CDW component, and dashed lines are guides to the eye. Error bars correspond to 1 SD.

Fig. 4 Three-dimensional CDW order at μ0H > 20 T.

(A and B) CDW diffraction pattern near (0, 2+q, l) at μ0H = 20 and 28 T. (C and D) Projected CDW peak profiles along the k and l direction within the regions indicated in (B). Gaussian fits to the data with a linear background (solid lines) and taking into account the measurement accuracy, reveal that the field-induced CDW peak is centered at k = 2.318(10) and l = 1.00(2).

Data shown in Fig. 3 motivate scrutiny of the field-induced CDW in the l ~ 1 region at the highest accessible magnetic field of 28 T. Given our experimental configuration (24), a larger l range is accessible near l = 1 by monitoring the equivalent CDW reflection near (0, 2+q, l), rather than near (0, 2-q, ~1). As shown in Fig. 4, A and B, the CDW diffraction pattern at 28 T becomes sharper not only along the k direction (Fig. 3C) but also along the l direction (perpendicular to the CuO2 planes). This indicates that CDW correlations along the c axis are enhanced—ξl = 34(4) and 50(2) Å at 20 and 28 T, respectively, where the numbers in parentheses are the error bars—concomitant with roughly a threefold increase of the peak height. Even though these values of ξl are lower bounds, because they have not been corrected for the instrument resolution (24) they are considerably larger than that of the zero-field CDW (ξl ~ 7 Å) (8), indicating that the field-induced CDW at l = 1 is much more correlated in all three dimensions than is the zero-field CDW. Furthermore, as shown in Fig. 4, C and D, the CDW peak positions are identical at 20 and 28 T. There has been speculation that the in-plane component of the CDW Q vector may shift and lock in to a commensurate value at high magnetic fields (25). However, within our experimental resolution the field-induced in-plane components of the Q vector [h = 0.00(1), k = 0.318(10)] are identical to that of the zero-field CDW.

A field-induced spin density wave (SDW) has been observed in La2-xSrxCuO4 at weaker fields ~6 T, which is also peaked at integer l owing to an alignment of SDW patches, associated with the vortex cores (26). However, the emergence of field-induced CDW order at l = 1 is unlikely to be caused by the alignment of CDW regions that are associated with vortices (2). This is because at magnetic fields beyond 20 T, the distance between vortices, if still present, would be less than ~100 Å in the CuO2 plane (27), which is already smaller than the in-plane CDW correlation length at these field strengths (Fig. 3C).

There are implications of the observed field-induced 3D CDW at l = 1. First, its emergence at high fields and low temperatures implies a boundary that separates the phase diagram into different CDW regions, as also suggested by ultrasonic (22) and NMR measurements (19). Second, given that a field-dependence of the CDW order is only observed below Tc(0) (Fig. 2), we infer that the enhancement is related to the suppression of superconductivity. Thus, the growth of the CDW peak intensity in fields up to 28 T suggests that superconducting correlations may exist beyond the upper critical field that was deduced from transport measurements (28, 29). Third, our observations shed light on quantum oscillation results, which have been interpreted as evidence for the existence of small electron pockets in the “nodal” region of the Brillouin zone (4, 5, 30). It is plausible that the Fermi surface is reconstructed by the stronger field-induced CDW at l = 1, rather than the shorter-range correlated one at l ~ ½ (31). Last, the relation between the zero-field and field-induced CDW is puzzling. On the one hand, they seem unrelated because they exhibit distinct temperature and field dependences, as well as a different ordering perpendicular to the CuO2 planes. On the other hand, they must be somehow related because they feature the same in-plane CDW incommensuration q. Thus, our results reveal a rich CDW phenomenology in cuprates, which is not a simple competition with HTSC.

Supplementary Materials

Materials and Methods

Figs. S1 to S5

References (3235)

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: We thank J. Hastings, J. Defever, D. Damiani, G. Curie, and V. Borzenet for technical assistance in developing the scattering setup. Discussions with C. Mielke are acknowledged. This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. X-ray FEL studies were carried out at the Linac Coherent Light Source, a Directorate of SLAC and an Office of Science User Facility operated for the DOE, Office of Science by Stanford University. Soft and hard x-ray scattering studies were carried out at the Stanford Synchrotron Radiation Lightsource, a Directorate of SLAC and an Office of Science User Facility operated for the DOE, Office of Science by Stanford University. Hard x-ray scattering studies were also conducted at the Advanced Photon Source, supported by the DOE, Office of Science, Office of Basic Energy Sciences under contract DE-AC02-06CH11357. S.G. acknowledges partial support by the Swiss National Science Foundation under fellowship P2EZP2_148737. H.N. acknowledges the support by Grants-in-Aid for Scientific Research (KAKENHI) 23224009, International Collaboration Center–Institute for Materials Research, and MD-program. Materials development was supported by the Natural Sciences and Engineering Research Council and by the Canadian Institute for Advanced Research.

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