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1 Nanoscale strain-induced pair suppression as a vortex-pinning mechanism in high-temperature superconductors A. Llordés 1, A. Palau 1, J. Gázquez 1,2, M. Coll 1, R. Vlad 1, A. Pomar 1, J.Arbiol 1,3, R.Guzmán 1, S. Ye 1, V. Rouco 1, F. Sandiumenge 1, S. Ricart 1, T. Puig 1, M. Varela 2, D. Chateigner 4, J. Vanacken 5, J. Gutiérrez 5, V. Moshchalkov 5, G. Deutscher 6, C. Magen 7, X. Obradors 1 * 1 Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus de la UAB, Bellaterra, Catalonia, Spain 2 Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 3 Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Catalonia, Spain 4 Laboratoire de Cristallographie et Sciences des Matériaux, CRISMAT, ENSICAEN, IUT-Caen, Université de Caen Basse-Normandie, 6 boulevard Maréchal Juin, Caen Cedex 4, France. 5 INPAC-Institute for Nanoscale Physics and Chemistry, Pulsed Field Group, K.U.Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium 6 School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel 7 Univ. Zaragoza, Inst. Nanociencia Aragon, Zaragoza 50018, Spain NATURE MATERIALS 1

2 A.- Quantitative determination of randomly oriented nanodot fraction The simultaneous out-of-plane measurement of both the diffracted pole from the (00l) epitaxial fraction and the diffraction ring from the randomly oriented fraction has been carried out using a GADDS system provided with a goniometer. These data (Fig. S1a and S1b) have been acquired at the corresponding χ, ω and φ angles to maximize the signal hence ensuring that both the epitaxial and randomly oriented fraction diffract the same counting time. The methodology is based on quantifying the integrated intensity ratio of a single asymmetric reflection from both the epitaxial and random fraction of the secondary MO phase. Given that the same (hkl) reflection is measured, the integrated intensity ratio directly measures the volume fraction ratio, after consideration of the multiplicity and the covered solid angle. The integrated intensity ratio is then as follows, II rrrrrrrr = II eeeeee rrrrrrrr 360 Δχχ 4π eeeeee II eeeeee 8 II pppppppp = vv rrrrrrrr vv eeeeee Equation 1 where χ is the integration range along the ring, which was typically taken as χ =30º, while the integration limits in 2θ for II eeeeee rrrrrrrr were taken as constant to 2θ=1.5º, v rand and v epi are the random and epitaxial volume fractions, respectively. This procedure assumes that the intensity along the ring is uniformly distributed (i.e. no preferred orientation of the MO nanodots), an approximation which has been found to be fairly good applicable through a complete analysis of the oxide texture in YBCO/BZO nanocomposites 1. In the case that several epitaxial orientations exists (BCO and BYTO cases) the measurements need to be performed for each epitaxial orientation and the v rand /v epi ratio (Eq. 1) correspondingly corrected. 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION B.- Inhomogeneous nanostrain determination Size effect in X-ray diffraction patterns is described by the well-known Scherrer formula as follows β = s λ D cosθ V Equation 2 where β s is the integral breadth (at a given 2θ Bragg angle) due to the size effect, λ is the wavelength used in the measurement and D V is the volume-weighted domain size (see Fig. S1c). On the other hand, nanostrain broadening varies with tanθ in the 2θ space according to the equation of Stokes and Wilson (1944) 2 : β = 4 ε tanθ D Equation 3 where β D is the integral breadth due to the distortion effect, λ is the wavelength used in the measurement and ε is the upper limit value of the lattice distortions. Unlike size broadening, strain broadening is not the same for all the reciprocal space points. β D increases with the distance to the origin, thus depending on the reflection order. Therefore, in order to separate both contributions from the overall broadening one considers their different dependencies on the reflection order 3-5 The determination of both size and strain parameters from the analysis of XRD line broadening can be achieved by the so-called Integral Breadth Methods (e.g. Williamson-Hall (WH) plot and Rietveld analysis) which require profile modeling by analytical functions (e.g. pseudo-voigt). Among the Integral Breadth Methods, the socalled Williamson-Hall plot 6 is widely used for its effortlessness though it should be regarded as a semiquantitative method. By contrast, more accurate values are obtained NATURE MATERIALS 3

4 with the Rietveld analysis using the Stokes deconvolution to correct the instrumental affects. WH plot is based on the direct summation of both size and strain effects and the separation of both effects is carried out graphically. However this method assumes that the broadening is fully Lorentzian or fully Gaussian which is unlikely to occur in practice. In addition, WH plot is not useful if the peak broadening is (hkl)-dependent because in that case the determination of the anisotropic size and strain parameters would require the measurement of several orders of different reflections, which is not straightforward in epitaxial films. Nevertheless, anisotropic size-strain parameters can be obtained by XRD pattern modelling using the so-called Popa approach 7 implemented in the Rietveld method. In the Popa approach the size and strain parameters are developed into spherical harmonics from the Gaussian and Lorentzian contribution breadths. We used the Delft Model 8,which is an Integral Breadth-based method, to model the isotropic peak broadening. Then, anisotropic size and strain parameters are modelled with the so-called Popa rules 7, which are based on convergent series of symmetrised spherical harmonics, the coefficients of which being also fitting parameters. The measured diffraction lines were: (002), (003), (004), (005), (006), (007), (008), (009), (113), (103)/(013), (123/213), (303)/(033), (109)/(019), (119) and (129)/(219). Fig. S1g-h presents some of the (00l) and (hkl) diffraction peaks measured though HRDRX of a pure YBCO film. Although the diffraction lines were measured independently, the refinement was carried out simultaneously for all the peaks ((00l) and (hkl)). Blue dots correspond to the experimental data and the solid black line is the fitted profile resultant of applying an isotropic model (Fig. S1g), or an anisotropic one (Fig. S1h). It is remarkable that the peak broadening depends on the (hkl) line, 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION increasing with the sample tilting χ, i.e. broader peaks as moving away from the film normal towards the film plane. Consequently, in that case the best fit was obtained when applying the Popa rules (Fig. S1h). Fig. S1g and S1h show as an example the fitting qualities of a (303) reflection through isotropic and anisotropic models where it becomes clear that only anisotropic strain can describe properly the experimental results. C- TEM and STEM measurements For the electron microscopy analyses, we combined several techniques. On one hand we used the powerful high angular annular dark field (HAADF) or Z-contrast scanning transmission electron microscopy (STEM) technique which allows to obtain atomic resolution images (resolution below 0.1 nm) with chemical contrast, as the intensity in the micrographs is approximately proportional to Z 2. This technique allowed us to clearly observe the formation of intergrowths in the YBCO matrix near the embedded nanodots. In order to accurately measure the strain we used the peak pair analysis (PPA) algorithm 9 applied to Z-contrast images. Briefly, the process consists in three steps. First, a Bragg filter is applied to the original image by selecting two main reflections in Fourier space. This will reduce noise in the image and smooth the image around the peaks. Then the intensity maxima are automatically located. The software searches for pairs of peaks that have a relative distance and direction using two different basis vectors in the Bragg filtering image stage. The result is a grid obtained from this set of pairs. Finally, a reference area in an unstrained area is defined. The displacement field, and hence the strain field, can be evaluated in terms of the selected reference structure in the image. In our case, we chose NATURE MATERIALS 5

6 as basis vectors the vectors connecting the cations (Y and Ba), and as the reference area the bottom right area of the micrograph, the farthest part from intergrowths. Fig. S2a displays the Z-contrast STEM image (also shown in Fig.4a) with a green square corresponding to the smaller area where strain is here analyzed in more detail. The red arrows signal two intergrowths. Fig. S2b shows the grid details obtained from the reference basis. The strain component ε yy is shown in Fig. S2c and Fig. S2d is a superposition of the image shown in Fig. S2b with the ε yy map. Here the intergrowth appears as a highly strained area and hence saturated (white colour). As it is observed, ε yy shows well defined ripples along the c-axis which are due to the fact that in YBCO the Ba-Ba spacing is greater than the Ba-Y spacing, therefore, the perovskite block containing the Cu-O chains (between Ba planes) looks like a tensile area (red regions) and the perovskite blocks between Ba-Y as a compressive area (green colour). The distortion generated by the intergrowth in the neighbouring perovskite blocks is evident in ε yy at distances as far as 2-3 nm. Additional evidence of the disorder generated in the YBCO matrix by the nanodots with incoherent interfaces is provided by conventional TEM images. First, it is to be noticed that nanodots have a different shape aspect when they are non-coherent (quasi-spheres), as compared to those exhibiting cube on cube epitaxy (platelets) (see Fig. S3a and Fig. S4a for YO and Fig.S4c-d for YBTO). This is in agreement with the fact that the spherical nanodots have nucleated homogeneously within a quasi-amorphous environment (the nanocrystalline precursors to YBCO) and hence an isotropic mean value of interfacial energy determines the shape of the first stable nuclei When the nucleation occurs at the YBCO interface faceting occurs as a consequence of the epitaxial growth and the smaller interfacial energy σ i which leads to a flat shape of the nanoparticle On the other hand, comparison of the YBCO matrix orientation in 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION both cases in the YBCO-YO nanocomposite shows that non-coherent nanodots induce further disorder in the YBCO lattice. For instance, a YO nanodot rotated by 7º (Fig. S3b) induces YBCO rotations around it of 3º (Fig. S3c), while no such effect is observed in epitaxial nanodots (Fig. S4b). Fig. S5 displays an additional example of a conventional Z-contrast image with a randomly oriented BZO nanodot evidencing that intergrowths are generated at incoherent interfaces. In conclusion, therefore, we have provided evidence that non-coherent interfaces and highly mismatched interfaces are more efficient than low misfit epitaxial interfaces in generating disorder within the YBCO lattice. We have also recorded plan view bright field TEM images of YBCO/BZO nanocomposites taken with the diffraction vectors g=200 and g=110 (Fig. S6a-b). These micrographs reveal the high degree of disorder induced in the YBCO lattice by the non coherent interfaces with the BZO nanodots (marked with red arrows). Twin boundaries, with a close separation (20-40 nm), exhibit strong bending when they interact with the strain fields surrounding the nanodots, the dislocation loops and intergrowths which are difficult to sort out unambiguously due to the strong global lattice bending. Interaction of dislocation loops, and in-plane partial dislocations surrounding the intergrowths, with the twin boundaries in YBCO has been previously described and the details of their shape depend on processing issues 20,21. Finally, we have recorded plan view STEM images of YBCO/BZO nanocomposites taken along the [001] zone axis. These images allowed us to estimate the size of the intergrowths generated around the BZO nanoparticles. Fig. S7a is a high resolution Z- contrast image of a YBCO/BZO interface where an Y248 intergrowth has been identified. The bottom part of the image shows a differentiated contrast due to the superposition of the YBCO and the Y248 phases. The boundary of the intergrowth can NATURE MATERIALS 7

8 then be easily identified, as seen in Fig. S7b, which shows a Fast Fourier filtered image of marked zone in Fig.S7a. Following the track of the intergrowth s boundary one can set its limits and estimate its projected size, as shown in Fig. S7c marked in yellow. References 1 Llordés, A. et al. to be published. 2 Stokes, A. R. & Wilson, A. J. C. A method of calculating the integral breadths of Debye-Scherrer lines: Generalization to non-cubic crystals. P Camb Philos Soc 40, , (1944). 3 Klug, H. P. & Alexander, L. E. X-Ray Diffraction Procedures For Polycrystalline and Amorphous Materials. (John Wiley and Sons, Inc., 1974). 4 Snyder, R. L. Defect and Microstructure Analysis by Diffraction. (Oxford Science Publications, 1999). 5 Sutton, A. P. Interfaces in Crystalline Materials. (Oxford University Press Inc., 1995). 6 Williamson, G. K. & Hall, W. H. X-ray line broadening from filed aluminium and wolfram Acta Metallurgica 1, 22-31, (1953). 7 Popa, N. C. The (hkl) dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement. J. Appl. Crystallogr. 31, , (1998). 8 Dekeijser, T. H., Mittemeijer, E. J. & Rozendaal, H. C. F. The Determination of Crystallite-Size and Lattice-Strain Parameters in Conjunction with the Profile- Refinement Method for the Determination of Crystal-Structures. J. Appl. Crystallogr. 16, , (1983). 8 NATURE MATERIALS

9 SUPPLEMENTARY INFORMATION 9 Galindo, P. L. et al. The Peak Pairs algorithm for strain mapping from HRTEM images. Ultramicroscopy 107, , (2007). 10 Lewis, B. & Anderson, J. C. Nucleation and growth of thin films. (Academic Press, 1978). 11 Chen, H. et al. Nucleation and growth rate influence on microstructure and critical currents of TFA-YBa 2 Cu 3 O 7 under low-pressure conditions. J Mater Res 25, , (2010). 12 Puig, T. et al. Vortex pinning in chemical solution nanostructured YBCO films. Superconductor Science & Technology 21, , (2008). 13 Gutiérrez, J. et al. Strong isotropic flux pinning in solution-derived YBa 2 Cu 3 O 7-x nanocomposite superconductor films. Nat. Mater. 6, , (2007). 14 Teichert, C. Self-organization of nanostructures in semiconductor heteroepitaxy. Phys. Rep.-Rev. Sec. Phys. Lett. 365, , (2002). 15 Gibert, M., Garcia, A., Puig, T. & Obradors, X. Thermodynamic stability analysis of isometric and elongated epitaxial Ce 1-x Gd x O 2-y nanostructures on perovskite substrates. Phys Rev B 82, , (2010). 16 Abellán, P. et al. Interaction between solution derived BaZrO 3 nanodot interfacial templates and YBa 2 Cu 3 O 7 films leading to enhanced critical currents. Acta Materialia 59, , (2011). 17 Figueras, J. et al. Multidirectional in-plane linear correlated disorder pinning of vortices in YBa 2 Cu 3 O 7. Superconductor Science & Technology 21, , (2008). 18 Plain, J., Puig, T., Sandiumenge, F., Obradors, X. & Rabier, J. Microstructural influence on critical currents and irreversibility line in melt-textured NATURE MATERIALS 9

10 YBa 2 Cu 3 O 7-x reannealed at high oxygen pressure. Phys Rev B 65, , (2002). 19 Rabier, J., Tall, P. D. & Denanot, M. F. On the Dissociation of Dislocations in YBa 2 Cu 3 O 7-d. Philos Mag A 67, , (1993). 20 Puig, T. et al. High oxygen pressure generation of flux-pinning centers in melttextured YBa2Cu3O7. Appl Phys Lett 75, , (1999). 21 Sandiumenge, F., Puig, T., Rabier, J., Plain, J. & Obradors, X. Optimization of flux pinning in bulk melt textured superconductors: Bringing dislocations under control. Adv Mater 12, 375, (2000). 10 NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION Figures Fig S1a χ=0º [110] BaCeO 3 // [001] LAO Fig S1b (003) YBCO (200) BaCeO 3 (103) YBCO [001] BaCeO 3 // χ= 45º [001] LAO (102) YBCO Fig S1c YBCO (004) Y 2 O 3 (400) YBCO (005) nanostrain % BZO YO BCO BYTO Fig S1d [Np] (mol %) Fig S1e Intensity (counts) ω YBCO(005) (º) 1.2 BZO YO BYTO Fig S1f 0.4 ω ( ) [Np] (mol %) NATURE MATERIALS 11

12 (g) Fig S1g-h (006) (123) (303) (h) χ (006) (123) (303) Figure S1. X-ray diffraction analysis of the nanodot size and microstrain analysis of the YBCO lattice in the nanocomposites. a-b, 2D-XRD images centered at the (110) Bragg reflections of the BCO and BZO epitaxial nanodots allowing the quantification of the fraction of randomly oriented nanodots. The orientation of the two epitaxial fractions for BCO are (00l)BCO//(001)YBCO and (01l)BCO//(001)YBCO and for BZO (001)[100]BZO//(001)[010]YBCO. c, Conventional θ-2θ X-ray diffraction pattern showing the (h00) peaks of YO and (00l) of YBCO for a nanocomposite with 10 mol.% YO.. d, Influence of the randomly oriented nanodots on the YBCO vertical nanostrain in the nanocomposites (BZO, YO, BCO and BYTO) as determined with Williamnson Hall plots. e-f, Rocking curves of (005) diffraction peaks for YBCO/BZO and YBCO/YO nanocomposites (15 % mol) and dependence of ω with the nanodot concentration in the YBCO/BZO and YBCO/BYTO nanocomposite series. g-h, Rietveld refinement analysis of some of the symmetric and asymmetric YBCO in a YBCO/BZO 10 mol % nanocomposite film. The refinement in (g) was carried out considering an isotropic strain model whereas an anisotropic one was applied in (h). The improvement of profile quality is clearly evidenced in the case of asymmetric reflections. 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION Fig S2 (a) (b) (c) (d) ε yy c-axis -10 % 0 % 10 % Figure S2. Peak pairs analysis of strain in the very onset of the intergrowth, where the partial dislocation is located. a, Z-contrast image where two intergrowths are indicated by red arrows. The green square is the region where the strain maps were generated. b. Grid obtained by peak pairs analysis from the squared region in Fig. a. The dotted red square indicates the region of the image taken as reference. c and d show the calculated ε yy map and its superposition with the image displayed in b. NATURE MATERIALS 13

14 Fig S3 a-c (a) (b) 7.7º YBCO B YBCO A YBCO A vs Y 2 O 3 Y 2 O 3 (c) 3.2º [010] YBCO YBCO A vs YBCO B Figure S3. TEM image of the local microstructure in a YBCO/Y 2 O 3 nanocomposite in the region near a incoherent nanodot. a-c a, HRTEM micrograph obtained on a spherical non-coherent YO nanodot. b, Comparison of the rotation angle between the YBCO matrix and the YO nanodot growth planes by superposing the green and red Power Spectra obtained in areas around YBCO A and YO labels in a, respectively. c, Comparison of the rotation angle between the YBCO matrix in the regions A and B by superposing corresponding power spectra. 14 NATURE MATERIALS

15 SUPPLEMENTARY INFORMATION (a) Fig S4 a-b (b) YBCO Y 2 O 3 (002) [110] Y 2 O 3 [010] YBCO (c) Fig S4 c-d (d) (003) YBCO YBCO (220) BYTO BYTO(-2-20) YBCO [010] BYTO BYTO BYTO YBCO Figure S4. TEM images of the local microstructure in YBCO/Y 2 O 3 and YBCO/BYTO nanocomposites. a-d. a, HRTEM micrograph obtained in a region near a flat coherent epitaxial YO nanodot embedded in the YBCO matrix. b, Comparison of the rotation angle between the YBCO matrix and the YO nanodot growth planes by superposing the Power spectra obtained in the red and green squared areas in a. No misorientation of the YBCO lattice is detected versus that of YO. c-d, HRTEM micrograph of a YBCO/BYTO (10 % mol) nanocomposite where a randomly oriented BYTO nanodot within the YBCO matrix is observed, c, (see the power spectra at the inset) and two BYTO nanodots grown at the substrate interface and having the orientation [100]BYTO//[100]YBCO are shown d. NATURE MATERIALS 15

16 Fig S5 BZO YBCO 2 nm Figure S5. STEM image of a YBCO/BZO nanocomposite with 16 % mol BZO displaying a non coherent interface. High resolution Z-contrast image show the noncoherent interface between an embedded BZO nanodot and the YBCO matrix. The darker stripes correspond to intergrowths. 16 NATURE MATERIALS

17 SUPPLEMENTARY INFORMATION (a) Fig S6 a-b (b) g=200 g=110 g=11 0 Figure S6. Bright field TEM plan view micrographs (g=200 and g=110) of a YBCO/BZO nanocomposite. a-b. TEM images obtained in a YBCO/BZO nanocomposite with a 13 % mol BZO content. The corresponding g vector used to obtain the micrographs is indicated in the figures. Some of the BZO nanodots, identified through the Moirée patterns, have been pointed by red arrows. The dislocation substructure and the twin boundaries are seen to be strongly bended within the (001) plane due to the strain associated to the BZO nanodots. NATURE MATERIALS 17

18 (a) BZO Fig S7 a-b [100] YBCO [010] YBCO YBCO (c) YBCO BZO YBCO + Y248 (b) YBCO + Y248 b Figure S7. STEM plan view micrographs obtained along the [001] axis of a YBCO/BZO nanocomposite with a 13 % mol BZO content. a-c. a, shows a high resolution Z-contrast image of the interface between an embedded BZO nanodot and the YBCO matrix. A Y248 intergrowth has been identified thanks to the fact that the two parts of the structure on either side of the fault are laterally shifted over b/2, and in result the image presents different contrast bellow the intergrowth s boundary. b, a magnified Fast Fourier filtered image of the red squared region in a. The schematics of the [001] projection of both they248 and the YBCO phases are also included and superposed to the imaged structure. c, lower magnification Z-contrast image where two intergrowth s boundaries were identified and highlighted in yellow. 18 NATURE MATERIALS

19 SUPPLEMENTARY INFORMATION (a) 10 8 Fp Fig S8 a-d (b) 25 7% BZO 10% BZO 20 F p (GN/m 3 ) 6 4 Fp aniso Fp iso F p (GN/m 3 ) Fp iso Fp 2 5 Fp aniso (c) F p (GN/m 2 ) µ 0 H (T) Fp aniso Fp iso Fp µ 0 H (T) µ 0 H (T) (d) 20% YO 6 6% BYTO F p (GN/m 3 ) Fp iso Fp aniso Fp µ 0 H (T) 8 6 Fig S8 e BZO YO BCO BYTO γ eff [Np] (mol %) Figure S8. Pinning forces and effective pinning anisotropy of the nanocomposites. a-d, Separation of the isotropic and anisotropic pinning force components measured at 77 K in a series of nanocomposites with the indicated compositions. e, Dependence of the effective mass anisotropy with the concentration of random nanodots in the different series of nanocomposites. NATURE MATERIALS 19