Multiscale distribution of oxygen puddles in 1/8 doped YBa2Cu3O6.67

Despite intensive research a physical explanation of high Tc superconductors remains elusive. One reason for this is that these materials have generally a very complex structure making useless theoretical models for a homogeneous system. Little is known on the control of the critical temperature by the space disposition of defects because of lack of suitable experimental probes. X-ray diffraction and neutron scattering experiments used to investigate y oxygen dopants in YBa2Cu3O6+y lack of spatial resolution. Here we report the spatial imaging of dopants distribution inhomogeneity in YBa2Cu3O6.67 using scanning nano X-ray diffraction. By changing the X-ray beam size from 1 micron to 300 nm of diameter, the lattice inhomogeneity increases. The ordered oxygen puddles size distribution vary between 6–8 nm using 1 × 1 μm2 beam, while it is between 5–12 nm with a fat tail using the 300 × 300 nm2 beam. The increased inhomogeneity at the nanoscale points toward a network of superconducting puddles made of ordered oxygen interstitials.

Despite intensive research a physical explanation of high T c superconductors remains elusive. One reason for this is that these materials have generally a very complex structure making useless theoretical models for a homogeneous system. Little is known on the control of the critical temperature by the space disposition of defects because of lack of suitable experimental probes. X-ray diffraction and neutron scattering experiments used to investigate y oxygen dopants in YBa 2 Cu 3 O 61y lack of spatial resolution. Here we report the spatial imaging of dopants distribution inhomogeneity in YBa 2 Cu 3 O 6.67 using scanning nano X-ray diffraction. By changing the X-ray beam size from 1 micron to 300 nm of diameter, the lattice inhomogeneity increases. The ordered oxygen puddles size distribution vary between 6-8 nm using 1 3 1 mm 2 beam, while it is between 5-12 nm with a fat tail using the 300 3 300 nm 2 beam. The increased inhomogeneity at the nanoscale points toward a network of superconducting puddles made of ordered oxygen interstitials. W hile the layered heterostructure at atomic limit is accepted as a universal feature for the lattice of high temperature superconductors, little is known on the control of the critical temperature by the space disposition of defects in the spacer layers [1][2][3][4][5][6][7] . Defects, as mobile oxygen interstitials, can control electronic inhomogeneity [8][9][10][11][12][13][14] and complex multi-scale phase separation [15][16][17][18][19][20][21][22][23][24] . Furthermore, inhomogeneity in the form of stripes have been shown to induce ''shape resonances'' 22,23 in the superconducting gaps in a multiband superconductor 24 , which are type of Fano-Feshbach resonances at a BEC-BCS crossover.
The advances in control of atomic defects and their spatial self-organization is needed for the engineering of new electronic devices at atomic level 11 . Imaging is needed to control defects organization at the nanoscale in novel quantum functional superconducting materials and it is the first step for unveiling the structure-property relation. Several spatial length scales are involved, which creates strongly intermingled defects structures. In high temperature superconductors (HTS), these networks of defects can influence essential properties such as the Fermi surface, pseudogap energy, spin density waves, charge density waves, and even the superconducting critical temperature. The strong tendency towards complex phase separation [14][15][16][17][18][19][20][21][22][23][24] can be used as advantage for developing new electronic devices. In fact, in some circumstances, defects order can be manipulated by scanning tunneling microscopy (STM) 11 , and/or by continuously exposing the sample to a UV or X-ray beam 6,7,10 . Developing techniques for imaging the nanoscale heterogeneity of defects organization is the first step to open new opportunities for their manipulation. YBa 2 Cu 3 O 61y (YBCO) high temperature superconductor is one of the most studied HTS material because of its superconducting transition above the nitrogen liquid evaporation temperature. From high resolution hard Xray diffraction and neutron scattering experiments it is known that the y oxygen dopants form one-dimensional oxygen-compositional stripes that segregate in short-range puddles [25][26][27][28][29][30] but few information exist on their spatial distribution. Here we report a spatial imaging using scanning nano X-ray diffraction [5][6][7][8][9] of the spatial distribution of the puddles made of compositional oxygens stripes (Ortho-VIII puddles) in the basal plane of YBa 2 Cu 3 O 6.67 at hole doping p<1/8 [31][32][33][34] .
In particular high quality untwined single crystals of YBCO with doping set at 6.67 corresponding to 1/8 holes per Cu site in the Y(CuO 2 ) 2 bilayer, have become available in these last years 26 . These new crystals have allowed the identification of the Fermi surface reconstruction with the appearance of a new electron-pocket 32 , the anomalous Nerst effect 32 , the proximity to a critical hole doping regime 33 , the unusual magnetic orders 34 and broken symmetries 35 . Although the observation of all these effects is certainly due to the high quality of the samples, understanding the disposition in real space of the YBCO structural components could be a difficult task, as we may expect form the variety of its oxygen phases in the phase diagram [26][27][28][29] . Of course, as the oxygen ions and the charged vacancies order, a corresponding charge density wave (CWD) and orbital density wave are generated as well.
The key result of this experiment is to unveil the intrinsic inhomogeneity of oxygen puddles distribution. We have recorded images with different spatial resolution by changing the X-ray beam size from 1 micron to 300 nm of diameter. The Ortho-VIII puddles size normal distribution is in the range 6-8 nm for the 1 3 1 mm 2 beam while it is much broader (in the range 5-12 nm) with a fat tail using the 300 3 300 nm 2 beam. The increased inhomogeneity at the nanoscale points toward an intrinsic granular complexity of puddles at 1/8 doping. This is confirmed by the correlation lengths of the spatial correlation function of the maps that show a dramatic reduction decreasing the beam size.

Results
Synchrotron radiation x-ray diffraction shows the high quality of the YBa 2 Cu 3 O 6.67 single crystal with P4/m spatial symmetry, unit cell dimensions a 5 3.807(11) Å , b 5 3.864(12) Å , c 5 11.52(2) Å and volume of 169.5(8) Å 3 . The diffuse streaks of the superlattice reflections have no well-defined peaks along l and the streaks shown in Fig. 1A and B provide direct evidence for nanoscale puddles in the basal a-b plane with Ortho-VIII modulation with a substantial disorder in the stacking of full and empty chains along the c direction. The nanoscale size of Ortho-VIII puddles embedded in a disordered medium is shown as pictorial view in Fig. 1C representing the basal Cu-O plane of YBCO. The Ortho-VIII puddles are made of alternated 5 filled and 3 empty oxygen wires every 8 rows. The number of oxygen ions per unit in the puddles is 6.625 5 6.5 1 0.125 that gives exactly 1/8 holes per Cu site in the Y(CuO 2 ) 2 bi-layers with Cu 21 ions in the chains of the basal plane. Since the average oxygen concentration is 6.67 5 6.5 1 1/6 the hole doping in the disordered background is larger than 1/8.
In order to understand the real space disposition of the Ortho-VIII puddles, and to avoid the transmission electron microscopy (TEM) complications due to electron beam damage of the sample, we have used scanning micro/nano X-ray diffraction (mXRD/nXRD) developed at the ID13 beam-line of the European Synchrotron Radiation Facility in Grenoble (France) (see supplementary info). mXRD and nXRD techniques have been already successfully applied on La214 5-7 , Bi2212 8 cuprates and on iron-based superconductors 9 . In this work by scanning micro areas, this technique gives a mixed information of the k-and r-space of the bulk structure inhomogeneities and it has never been applied on a YBa 2 Cu 3 O 6.67 single crystal. A 1 3 1 mm 2 and 300 3 300 nm 2 beam size, have been employed for our measurements at room temperature.
The integrated intensity of the observed superstructure in Fig. 2A and the peak position of satellites in different spot of the crystal are quite homogenous, q ortho-VIII 5 0.625 with a standard deviation of 0.001. This indicates that the nanoscale oxygen puddles have the Ortho-VIII periodicity and confirms the high quality of the crystal. On the contrary, the FWHM along a* (Fig. 2B) and along c* (Fig. 2C) of diffraction profiles, measured at each point (x,y) of the sample reached by the x-y translator with micron resolution, clearly show a spatial variation. The diffraction profiles (Fig. 2D, 2E) show the position dependence of the domain size, derived from the measured full width half maximum (FWHM) of the superstructure reflections via standard methods of diffraction. The spatial variation of the domain size in the a and c crystallographic directions is showed for three spots of the sample corresponding respectively to a narrow, average and a broad superstructure reflection. Although the micro Xray diffraction profiles give a rough picture on the size variations of the Ortho-VIII puddles, three spots cannot give enough information to construct a real space image of the organization of the Ortho-VIII puddles.
To solve this issue, we have collected 10000 images of mXRD diffraction patterns, scanning the sample with a 1 micron step along both the real space direction x-y (a-c plane). Fig. 3A and Fig. 3B show the maps of the Ortho-VIII domain size along a* and along c*. Although the color bar of the maps extends from dark blue to dark red and is associated to 5 nm to 12 nm sizes respectively, actually the observed color are green and yellow, which indicate a smooth variation of the puddles size in the system within a range of 6.5 nm to 8.5 nm. The average size of this interval is in agreement with the average size of the Ortho-VIII puddles investigated with hard X-ray diffraction at ELETTRA using a 200 3 200 mm 2 beamsize. To test if the observed size variation of the Ortho-VIII puddles is an intrinsic aspect of the YBCO system or it is a sample dependent property, we have increased the spatial resolution of the X-ray beam, by diminishing the beam size and performed the same experiment in a similar area. Using a monochromatic X-ray beam of photon energy  www.nature.com/scientificreports 14 KeV (DE/E 5 10 24 ), the beam has been focused by Kirkpatrick Baez (KB) mirrors down to a 300 nm spot size on the sample (full width at half maximum). We collected other 20000 diffraction images in the reflection geometry using a Fast Readout Low Noise charged coupled device (FReLoN CCD) detector. We constructed the 2D maps from the collected nXRD diffraction patterns, each one for a different spatial x-y position (a-c plane) of the sample. Figure 3C and 3D show respectively the 2D plots of the domains size variation along a and c crystallographic directions. Visual inspection of the maps show a more inhomogeneous spatial distribution of the Ortho-VIII puddles respect that measured delivering a 1 3 1 mm 2 beam on the sample (mXRD case). Here the color extends from dark blue to dark red, respectively associated to 5 and 12 nm. The broad distribution of sizes shown in the map indicates an intrinsic and incommensurate nanoscopic order in the system. In addition, the heterogeneous granular structure of the dopants, unveiled by the employ of a nanobeam, shows the relevance of the spatial resolution of the probe on the sample. Statistical analysis is used to quantify the size distributions of the Ortho-VIII puddles as seen by scanning micro and nano X-ray diffraction experiments. Figure 4A shows the probability density function (PDF) of the Ortho-VIII puddles sizes along the crystallographic a-axis, observed using a beam of 1 mm and 300 nm of diameter. The distribution of the puddles is nearly symmetric as seen with a resolution of 1 micron while with 300 nm X-ray beam it shows a remarkable asymmetric fat tail, although the average value of 7.5 6 0.2 nm is comparable. Figure 4B shows the probability density function of the Ortho-VIII puddles sizes along the c crystallographic direction. Also in the size of the puddles in the transversal direction from the CuO 2 planes is nearly symmetric however the distribution of sizes measured by the 300 nm nXRD probe, shows a remarkable fat tail. Also in this case the maps obtained by mXRD and the nXRD are in agreement for the average size of domains which is 8.0 6 0.2 nm. The standard deviation is 0.4 nm for the 1 micron X-ray probe and 0.6 nm for the 300 nm X-ray probe. The fat tails, observed in the maps, have been quantified by the evaluation of the higher statistical  Tab. 1). Similar situation is evidenced evaluating the fourth statistical moment, the Kurtosis k, that is an indication of the distribution sharpness respect to the Gaussian shape that has k 50. Like is summarized in Tab. 1 k a 5 0.61 and k c 5 0.64 for the Ortho-VIII domain size measured by nXRD and k a 5 0.03 and k c 5 0.05 for mXRD results. In all the cases, the Skewness and the Kurtosis parameters, result to deviate from the Gaussian distribution characteristic 0 values. The more symmetric distribution observed by the mXRD can be easily explained by the fact that the X-ray beam probes a sample volume of the order of mm 3 , since the effective X-ray penetration depth is in the micron range, that contains about 10 6 puddles, on the contrary using the nXRD the number of Ortho-VIII puddles decreases by a factor higher than 10. Although the number of 10 5 puddles, in each illuminated spot of the nXRD, is still quite large, it allows to unveil the fat tails of the Ortho-VIII puddles quite clearly.
Looking at the distance-dependent intensity correlations in Fig. 4C and 4D measured with a 1 micron and 300 nm X-ray beam, it is clear that along both the directions a* and c* the size of the beam unveils different level of spatial organization. Although the G(r) measured by mXRD and nXRD show that the spatial correlations are more extended out-of-plane than in-plane, the G(r) appears different by comparing the result from different beam sizes. For the domain sizes distribution along the a directions, the correlation length of 22 micron measured by mXRD, is reduced of about the half (to 11 micron) using a 300 nm X-ray beam (nXRD). Along the c directions, the reduction is even more dramatic, in fact, from about 25 micron measured with the 1 micron X-ray beam, the correlation length of the scanned area with a 300 nm X-ray beam is 5 micron.

Discussion
We have shown that the intrinsic granular organization of mobile oxygen defects can be unveiled by scaling the size of the X-ray beam in the specific case of YBa 2 Cu 3 O 6.67 single crystal. If we were seeing a narrowing in the size distributions and a broadening in the correlation length of the puddles, this would have mean that the inhomogeneity observed with the 1 micron beam was due to the sample preparation procedure. Instead, what we measure is a broader and asymmetric distribution of the puddles sizes which show a range of 5-12 nm and a shorter correlation length both along a and c-direction, by scaling the X-ray beam from 1 micron to 300 nm. So far, the defects self-organization and the related nanoscale phase separation controlled by thermal treatments have been well established in high temperature superconductors, like super-oxygenated La 2 CuO 41y [5][6][7] , Bi 2 Sr 2 CaCuO 81y 8 and electron doped iron-chalcogenides 9 . Therefore, the present results support the idea that each high temperature superconductor displays different and specific realizations of a granular and spatially inhomogeneous lattice, controlled by misfit strain [36][37][38] . Moreover, high temperature superconductivity resists to the complex lattice broken symmetry that is the characteristic feature of the superstripes scenario 39,40 . These results show that also broken symmetry observed in the pseu dogap phase 35 could be triggered by a lattice broken symmetry in nanoscale grains and in the domain walls at the interface between the nano-puddles.
We have investigated the spatial arrangement of Ortho-VIII puddles in YBa 2 Cu 3 O 6.67 , using scanning micro and nano X-ray diffraction for measuring superstructure reflections with unprecedented real space resolution up to 300 nm. Nevertheless the crystal is clearly of high quality, intrinsic inhomogeneities are found in the Ortho-VIII puddles size distributions. In particular, comparing maps obtained from measurements at different spatial scale (1 3 1 mm 2 vs. 300 3 300 nm 2 ), we are able to show how the inhomogeneities appears more clearly at smaller scale, indicating such local structural inhomogeneities as an intrinsic property in these materials.

Methods
The high-quality untwined YBCO crystals were grown in a nonreactive BaZrO 3 crucible from high-purity starting materials 26 . The oxygen content was set at y 5 0.67. The hole concentration (doping) p 5 0.12 was determined from the c-axis lattice constant. The diamagnetic response across the superconductive transition of the YBa 2 Cu 3 O 6.67 single crystal has been characterized by means of the Vibrating Sample Magnetometer (VSM) option in a Physical Properties Measurement System (PPMS 6000) from Quantum Design (see supplementary info). After cooling down the sample from room temperature to 10 K in zero applied field (Zero Field Cooling, ZFC) the diamagnetic response upon application of H 5 20 Oe has been observed during the warm up across the transition, spanning the 10 K to 80 K temperature range at a rate of 0.5 K/min K. The superconducting transition temperature results to be T c 5 66 K. To study the superlattice reflections due to the oxygen ions (Oi) ordering in the basal plane Ortho-VIII superstructure we performed x-ray diffraction measurements in transmission geometry at the XRD1 beamline of ELETTRA in Trieste (Italy) (see supplementary info) with an energy of 20 KeV and a 200 3 200 mm 2 beamsize. We recorded the x-rays scattered by the sample in the a*b* diffraction plane using a charged coupled device (CCD) and results are in agreement with the hard X-ray diffraction data 26 . Scanning micro/nano X-ray diffraction patterns were collected in the reflection geometry with a CCD that records the X-rays scattered from the sample in the a*c* diffraction plane, showing the Ortho-VIII oxygen chains superlattices q Ortho-VIII (a*) 5 (3/8,k,0) and q Ortho-VIII (a*) 5 (5/8,k,0). Table 1 | Statistical moments of the Ortho-VIII domain size PDF along a and c direction. PDFs are calculated from the intensity maps measured by mXRD (beamsize of 1 3 1 mm 2 ) and nXRD (beamsize of 300 3 300 nm 2 ). Both PDFs from mXRD and nXRD show compatible mean values, but variance increased a lot going from the first to second case. The third and the fourth statistical moments deviate from the nominal 0 value for a Gaussian distribution. In particular it is evident that the Skewness and Kurtosis parameters increase a lot decreasing the dimension of the incident beam. In addition, the coherence length j, calculated from G(r), is shown in the last row, going from micro-beam to nanobeam it shows a dramatic reduction indicating the intrinsic inhomogeneity of cuprates