1. Michela Fratini Dipartimento di Fisica Università degli studi di Roma “La Sapienza” 6th INTERNATIONAL CONFERENCE OF THE STRIPES SERIES STRIPES 08 Quantum Phenomena in Complex Matter CRITICAL OPALESCENCE IN SUPEROXYGENATED La 2 CuO 4+y Erice, July 26-August 1, 2008

2. OUTLINE We have investigated the ordering of interstitial oxygen (iO) in superoxigenated La 2 CuO 4 Method: synchrotron x-ray micro-diffraction as a probe to detect microscopic phase separation giving self-organized electronic textures Evidence for : 1. The coexistence of ordered and disordered domains 2. The order to disorder phase transition at 330K 3. The statistical distribution of the size of ordered domains shows a power law distribution indicating critical opalescence near a critical point These results open the way to control and manipulate the phase separation for new functional devices

3. HIGH T c SUPERCONDUCTORS: SHOW A COMMON STRUCTURE MgB 2 Cuprates ROFeAs The nanoscale architecture: The lamellar Structure

4. PHASE DIAGRAM OF CUPRATES: 12 3 Critical point for structural phase transition from LTT to LTO

5. STRUCTURE OF La 2 CuO 4+y a = 5.3462±0.0006 alfa = 89.969± 0.026 b = 5.3866±0.0004 beta = 90.014 ± 0.020 c = 13.2039 ± 0.0026 gamma = 89.979 ± 0.010 Space group=Fmmm The cuprate perovskite La 2 CuO 4 is formed by bcc CuO 2 monolayers intercalated by fcc rocksalt LaO bilayers with a periodicity of 1.3 nanometers. The oxygen dopants in the LaO planes are mobile above 200 K Interstitial oxygen

6. PHASE COEXISTING OF SUPERCONDUCTIVITY AND MAGNETIC ORDER (Savici et al. Phys. Lett. 95 157001 (2005)) High Tc superconductor Lee et al. Phys. Rev. B 60 3643 (1999 ) The system shows a coexistence between superconducting and magnetic domains below 41K Tc=41K

7. The existence of an ordered phase of interstitial oxygen has been detected at room temperature OXYGEN ORDERED PHASE q 2 =0.09 a* +0.25 b*+0.50 c* X-ray diffraction pattern with: higher harmonics and narrow lines indicates Domains of 3D commensurate ordered oxygen dopants

8. Interstitial oxygen ordering T=300-350K a)Hysteresis cycle of Q 2 phase using a photon flux of 1.5*10 14 photons/cm 2 /s in the range from 300K to 350K. b) Hysteresis cycle of Q 2 phase using a photon flux of 10*10 14 photons/cm 2 /s The result of the x.ray illumination is a reduction of the Hysteresis loop CONTINUOUS FIRST ORDER PHASE TRANSITION

9. PHOTO-INDUCED ORDERING PROCESS AT DIFFERENT TEMPERATURES. Under x-ray illumination the size of the ordered domains increases in the temperature range between 250 K and 300 K. The photo-induced ordering process shows a threshold characteristic of cooperative phenomena.

10. INHOMOGENEOUS phase with the COEXISTENCE of domains of ordered and disordered interstitial oxygen ions Below 350K bubbles of 3D ordered iO’s in a disordered medium What is the spatial distribution of the ordered domains?

11. Space-resolved X-ray diffraction based upon a beam size of ~ 1 µm METHOD specialises in the delivery of the microfocused X-ray beam Photon sources in the range 12/13 Kev The focussed beam is defined by a pinhole of 5 micron diameter

12. OXYGEN ORDERING PHASE The large orthorhombicity makes easy identify the twinning of the crystal domains and to index the superstructure peaks. q2= (0.09; 0; 0.50) q2 (0;0.25; 0.50) 006 peak in the diffraction pattern We have done a mesh of the whole sample, with a beam size of about 1 micron, after locating q2, present in this oxide cuprate at room temperature around the bragg peak (0,0,6).

13. MICROMAPPING SUPEROXYGENATED SAMPLE T c =41 K Mean Intensity =1.7233 The colours dots show the intensity of the q2 superstructure due to interstitial oxygen ordering The figure shows the intensity on 5000 diffraction superstructure spots due to charge ordered domains

14. STATISTICAL DISTRIBUTION OF THE Q2 PHASE Mean Intensity =1.7233 in SUPEROXYGENATED SAMPLE γ = 1.7 ξ = 2.6

15. MICROMAPPING SAMPLE with INTERMEDIATE OXYGEN CONTENT Y (1 pixel=4.9 micron) X (1 pixel=20.3 micron) T c = 32 K and 41 K Mean Intensity =1.5752

16. STATISTICAL DISTRIBUTION OF THE Q2 PHASE in SAMPLE with INTERMEDIATE OXYGEN CONTENT. γ = 1.7 ξ = 1.5 Mean Intensity = 1.5752 RANK

17. MICROMAPPING IN A SAMPLE with LOW OXYGEN CONTENT Y (1 pixel=4.9 micron) X (1 pixel=20.3 micron) T c =12K and 36K Mean Intensity =1.0954

18. STATISTICAL DISTRIBUTION OF THE Q2 PHASE IN SAMPLE with LOW OXYGEN CONCENTRATION DOPING. γ = 1.7 ξ = 1.1 Mean Intensity =1.0954 RANK

19. CONCLUSIONS The proximity to a quantum critical point determines the critical opalescence with a power law distribution of the size of oxygen ordered domains This is supported by the scale invariance This result is assigned to the criticality of the system being close to the tricritical point identified in the phase diagram (T c, doping and chemical pressure) This conclusion is supported by the photoinduced phase transition near the critical point.

20. Finally I would like to thank my collaborators Alessandra Vittorini-Orgeas Nicola Poccia Ginestra Bianconi Luisa Barba (Elettra) Manfred Burghammer (ESRF) Gaetano Campi