1. Negative Oxygen Isotope Effect on the Static Spin Stripe Order in La 1.875 Ba 0.125 CuO 4 Z. Guguchia, 1 R. Khasanov, 2 M. Bendele, 1 E. Pomjakushina, 3 K. Conder, 3 A. Shengelaya, 4 and H. Keller 1 1 Physik-Institut der Universität Zürich, Switzerland 2 Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, Switzerland 3 Laboratory for Developments and Methods, Paul Scherrer Institute, Switzerland 4 Department of Physics, Tbilisi State University, Georgia Tbilisi State University

2. Zurab Guguchia Physik-Institut der Universität Zürich, Switzerland Laboratory for Muon Spin Spectroscopy, Paul-Scherrer Institut, Switzerland Negative Oxygen Isotope Effect on the Static Spin Stripe Order in La 1.875 Ba 0.125 CuO 4

3. Thank you! Markus Bendele Hugo Keller Laboratory for Muon Spin Spectroscopy (PSI) Rustem Khasanov Laboratory for Developments and Methods (PSI) Ekaterina Pomjakushina Kazimierz Conder Alexander Shengelaya Tbilisi State University

4. Outline Introduction  Stripe phase in cuprates.  Isotope effects.  Muon Spin Rotation (µSR) technique. Results  Oxygen Isotope Effect (OIE) on superconductivity in LBCO-1/8.  OIE on the static spin stripe order in LBCO-1/8.  Pressure effects in LBCO-1/8. Conclusions

5. Superconductivity in La 2-x Ba x CuO 4 Moodenbaugh et al, Phys. Rev. B 38, 4596 (1988). Axe et al, Phys. Rev. Lett. 62, 2751 (1989). Hücker et al, Phys. Rev. B 83, 104506 (2011).

6. Experimental evidence for static stripes in La 1.48 Nd 0.4 Sr 0.12 CuO 4 Neutron Scattering Tranquada et al, Nature (London) 375, 561 (1995). Guguchia, PhD thesis,University of Zürich (2013). Real space Spin order Charge order M. Vojta, Adv. Phys. 58, 699 (2009) and references therein. T. Wu et. al., Nature 477, 191 (2011).

7. Central issues in Cuprates  What is microscopic origin of the stripe formation? The stripe phase may be caused by electronic and/or electron-lattice interaction.  Do stripes promote or inhibit superconductivity? Zaanen and Gunnarson Phys. Rev. B 40, 7391 (1989). White and Scalapino, PRL 80, 1272 (1998). Emery and Kivelson, Physica C 209, 597 (1993). M. Vojta, Adv. Phys. 58, 699 (2009). Do they contain all ingredients required for stripe formation?

8. Superconductivity in La 2-x Ba x CuO 4 Moodenbaugh et al, Phys. Rev. B 38, 4596 (1988). 0.11 < x ≤ 0.13 Axe et al, Phys. Rev. Lett. 62, 2751 (1989). Hücker et al, Phys. Rev. B 83, 104506 (2011).

9. Experimental evidence for static stripes: Neutron Scattering Tranquada et al, Nature (London) 375, 561 (1995). Zaanen and Gunnarson, PRB 40, 7391 (1989). White and Scalapino, PRL 80, 1272 (1998). La 1.48 Nd 0.4 Sr 0.12 CuO 4 Momentum space Real space Spin peaks Charge peaks

10. Central issues in Cuprates  What is microscopic origin of the stripe formation?  Do stripes promote or inhibit superconductivity?

11. Early stripe predictions Zaanen and Gunnarson Phys. Rev. B 40, 7391 (1989) Hubbard model Mean-field solution White and Scalapino, PRL 80, 1272 (1998) t-J model Density matrix renormalization group

12. Alternative: Frustrated Phase Separation Löw, Emery, Fabricius, and Kivelson, PRL 72, 1918 (1994) Competing interactions result in striped and checkerboard phases Analysis of t-J model by Emery and Kivelson: Holes tend to phase separate! t-J model lacks long-range part of Coulomb interaction Long-range Coulomb repulsion frustrates phase separation

13. Holes in an AF : Why Do Stripes Occur? PHASE SEPARATION Coulomb Interactions Kinetic Energy Frustration STRIPES Emery and Kivelson Physica C 209, 597 (1993). The investigated models do not contain all ingredients required for stripe formation!

14. Stripe order in La 1.875 Ba 0.125 CuO 4 M. Hücker et al., Phys. Rev. B 83, 104506 (2011). Z. Guguchia et al., New Journal of Physics 15, 093005 (2013). Maisuradze and Guguchia, University of Zurich.

15. V sc (0) + V m (0) ≈ 1 Superconductivity and magnetism are competing order parameters. Phase diagrams Z. Guguchia et al., New Journal of Physics 15, 093005 (2013).

16. Diamond anvil cell for high-pressure magnetization measurements Maisuradze and Guguchia, University of Zurich.

17. Superconducting properties of La 1.875 Ba 0.125 CuO 4 Z. Guguchia et al., New Journal of Physics 15, 093005 (2013).

18. Hücker et al, PRL 104, 057004 (2010).

19. Double wall piston-cylinder type of cell made of MP35N material for µSR under pressure Andreica, Ph.D. thesis, IPP/ETH-Zürich, (2001).

20. High pressure µSR experiments on La 1.875 Ba 0.125 CuO 4 Z. Guguchia et al., New Journal of Physics 15, 093005 (2013).

21. High pressure µSR experiments on La 1.875 Ba 0.125 CuO 4 T LTT = 0 Z. Guguchia et al., New Journal of Physics 15, 093005 (2013).

22. Conventional superconductivity Electron-phonon interaction BCS: Isotope effect: Ranges from 0.2-0.5 in elemental metals Weak coupling BCS predicts a value of  = 0.5 C.A. Reynolds et. al., Phys. Rev. 78, 487 (1950). E. Maxwell, Phys. Rev. 78, 477 (1950). J. Bardeen et. al., Phys. Rev. 108, 1175 (1957).

23. Unconventional Oxygen Isotope effects (OIE’s) in cuprates J. Hofer et. al., PRL 84, 4192 (2000). K.A. Müller, J. Phys. Condens. Matter 19, 251002 (2007). H. Keller et. al., Materials today 11, 9 (2008). Shengelaya et. al, PRL 83, 24 (1999). Khasanov et. al., PRL 101, 077001 (2008). Lanzara et. al., J. Phys. Condens. Matter 11, L541 (1999). Rubio Temprano et. al., PRL 84, 1990 (2000). Zhech et. al., Nature 371, 681–683, 1994.

24. Isotope effect on T c near 1/8 M.K. Crawford et. al., Science 250, 1390 (1990). G.M. Zhao et. al., J. Phys.: Condens. Matter 10, 9055 (1998). J.P. Franck et. al., PRL 71, 283 (1993). J. Hofer et. al., PRL 84, 4192 (2000). B. Batlogg et. al., PRL 59, 912 (1987). G.Y. Wang et. al., PRB 75, 212503 (2007).

25. TRIUMF http://neutron.magnet.fsu.edu/muon_relax.html Muon-spin rotation (μSR) technique

26. Courtesy of H. Luetkens homogeneous amplitude → magnetic volume fraction frequency → average local magnetic field Damping → magnetic field distribution / magnetic fluctuations time (  s) μSR in magnetic materials inhomogeneous

27. Magnetization experiments Tranquada et. al., PRB 78, 174529 (2008). Li et. al., PRL 99, 067001 (2007). Z. Guguchia et al., New Journal of Physics 15, 093005 (2013). Z. Guguchia et al., Phys. Rev. Lett. (2014).

28. Magnetization experiments Tranquada et. al., PRB 78, 174529 (2008). Li et. al., PRL 99, 067001 (2007).

29. Isotope effect on T c in La 1.875 Ba 0.125 CuO 4 Z. Guguchia et al., Phys. Rev. Lett. (2014).

30. Oxygen Isotope effect on T so Z. Guguchia et al., Phys. Rev. Lett. (2014).

31. Oxygen Isotope effect on T so Z. Guguchia et al., Phys. Rev. Lett. (2014).

32. G.M. Luke et. al., Physica C 185-9, 1175 (1991). B. Nachumi et. al., PRB 58, 8760 (1998). Oxygen Isotope effect on T so Z. Guguchia et al., Phys. Rev. Lett. (2014).

33. +

34. OIE effect on T so and magnetic fraction V m Z. Guguchia et al., Phys. Rev. Lett. (2014).

35. Summary of the OIE studies on La 1.875 Ba 0.125 CuO 4 Give evidence for stripe-lattice coupling in cuprates. Superconductivity and stripe order are competing phenomena.

36. Pressure experiments with SQUID and µSR Z. Guguchia et al., New Journal of Physics 15, 093005 (2013). SQUID (Maisuradze and Guguchia) µSR ( R. Khasanov )

37. Pressure effect on static spin-stripe order in La 1.875 Ba 0.125 CuO 4 V sc (0) + V m (0) ≈ 1 Z. Guguchia et al., New Journal of Physics 15, 093005 (2013).

38. LTT structural phase under pressure Hücker et al, PRL 104, 057004 (2010).

39. Pressure effect on the isotope effect inLBCO-1/8

40. Conclusions  Large negative OIE’s were observed on T so and V m in La 2-x Ba x CuO 4 (x = 1/8).  Oxygen-isotope shifts of T c and T SO are sign reversed. Stripe order and superconductivity are competing orders.  The electron-lattice interaction is involved in the stripe formation and is a crucial factor controlling the competition between the stripe order and superconductivity.  A purely electronic mechanism can not explain the present isotope and pressure experiments!

41. Thank you very much for your attention! Thank you very much for your attention!

43. Superconducting properties of La 1.875 Ba 0.125 CuO 4 Diamond anvil cell for high- pressure measurements. Dr. A. Maisuradze, University of Zurich.

45. M. Hücker et. al., PRL 104, 057004 (2010).

46. B. Nachumi et. al., PRB 58, 8760 (1998).

48. T LTO→LTT ≈ 50 K T HTT→LTO ≈ 200 K

49. La 2-x Ba x CuO 4 La 1.8-x Eu 0.2 Sr x CuO 4 G.M. Luke et. al., Physica C 185-189, 1175-1176 (1991). M. Hücker et. al., Physica C 460-462, 170(2007). LTT LTO