1. Muon Spin Rotation (µSR) technique and its applications in superconductivity and magnetism Zurab Guguchia Physik-Institut der Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland Group of Prof. Hugo Keller

2. Outline  Basic principles of the μSR technique  Vortex matter in cuprate superconductors  Multi-band superconductivity in high-temperature superconductors  Magnetism and superconductivity  Low-energy μSR and applications  Conclusions

3. Thank you! University of Zurich in collaboration with: Paul Scherrer Institute (PSI) Laboratory for Muon Spin Spectroscopy Laboratory for Developments and Methods Tbilisi State University Prof. Alexander Shengelaya ETH Zürich IBM Research Laboratory Rüschlikon (Zurich) Max Planck Institute for Solid State Research, Stuttgart EPFL, Lausanne Institute of Low Temperature and Structure research, Poland Brookhaven National Laboratory, Upton NY

4. All experiments presented in this talk were performed at Paul Scherrer Institute, Villigen (Switzerland) Paul Scherrer Institute (PSI) photons muons neutrons

5. Basic principles of the μSR technique

6. PropertyValue Rest mass m μ 105.658 MeV/c 2 206.768 m e 0.1124 m p Charge q+e Spin S1/2 Magnetic moment μ μ 4.836 x 10 -3 μ B 3.183 μ P Gyromagnetic ratio γ μ /2π135.5387 MHz/T Lifetime τ μ 2.197 μs Some properties of the positive muon

8. Muon production and polarised beams Pions as intermediate particles Protons of 600 to 800 MeV kinetic energy interact with protons or neutrons of the nuclei of a light element target to produce pions. Pions are unstable (lifetime 26 ns). They decay into muons (and neutrinos): The muon beam is 100 polarised with S µ antiparallel to P µ. Momentum: P µ =29.79 MeV/c. Kinetic energy: E µ =4.12 MeV.

9. Muon decay and parity violation

10. Muon-spin rotation (μSR) technique S µ (0) B μ = (2π/γ μ ) ν μ

11. TRIUMF http://neutron.magnet.fsu.edu/muon_relax.html Muon-spin rotation (μSR) technique B μ = (2π/γ μ ) ν μ

12.  Implanted nuclear probe: little pertubation to the system, no requirement in the presence of isotopes.  Full polarisation of the probe, including in zero field and at any temperature.  Extremely high sensitivity: detection of decay of (almost) all muons, detection of small magnetic field (large μ).  Only magnetic fields are probed. No sensitivity to electric fields.  Local probe: independent determination of magnetic moment and magnetic volume fraction Advantages of µSR

13. Muons are purely magnetic probes (I = ½, no quadrupolar effects). Local information, interstitial probe complementary to NMR. Large magnetic moment: μ µ = 3.18 µ p = 8.89 µ n sensitive probe. Particularly suitable for: Very weak effects, small moment magnetism ~ 10 -3 µ B /Atom Random magnetism (e.g. spin glasses). Short range order (where neutron scattering is not sensitive). Independent determination of magnetic moment and of magnetic volume fraction. Determination of magnetic/non magnetic/superconducting fractions. Full polarization in zero field, independent of temperature unique measurements without disturbance of the system. Single particle detection extremely high sensitivity. No restrictions in choice of materials to be studied. Fluctuation time window: 10 -5 < x < 10 -11 s.

14. The µSR technique has a unique time window for the study of magnetic flcutuations in materials that is complementary to other experimental techniques.

18. NMRμSR Probenucleus (I = 1/2, 3/2, …)muon μ + (S = 1/2) Magnetic moment2.22 μ N ( 63 Cu, I = 3/2)8.9 μ N Lifetime∞2.2 μs Time window Fluctuation rate 10 -2 - 10 5 Hz10 4 - 10 12 Hz External magnetic fieldyes (NQR no)yes/no RF fieldyesno μSR vs. NMR

19. 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

20. Vortex matter in cuprate superconductors

21. Type I and type II superconductors

23. Flux-line lattice (Abrikosov lattice)

24. B ext Since the muon is a local probe, the  SR relaxation function is given by the weighted sum of all oscillations:  SR  local magnetic field distribution p(B) in the mixed state of a type II sc P(t)

25. μSR time spectra T > T c T < T c

26. μSR technique

27. Gaussian distribution p(B) BSCCO 2212 Determination of the magnetic penetration depth Determination of the magnetic penetration depth second moment of p(B) BSCCO 2212 Bi 2.15 Sr 1.85 CaCu 2 O 8+δ

28. Magnetic penetration depth λ Pümpin et al., Phys. Rev. B 42, 8019 (1990)

29. Melting of the vortex lattice

30. Vortex lattice melting Lee et al., Phys. Rev. Lett. 71, 3862 (1993)

31. Lineshape asymmetry parameter α “skewness parameter”

32. Vortex lattice melting Lee et al., Phys. Rev. Lett. 71, 3862 (1993)

33. Magnetic phase diagram of BSCCO (2212) µ 0 H ext (mT) Aegerter et al., Phys. Rev. B 54, R15661 (1996)

34. Magnetic phase diagram of BSCCO (2212) µ 0 H ext (mT)

35. Crossover field B cr Aegerter et al., Phys. Rev. B 54, R15661 (1996)

36. Crossover field B cr B cr (mT)

37. Multi-band superconductivity in high-temperature superconductors

38. Nb-doped SrTiO 3 is the first superconductor where two gaps were observed! Nb-doped SrTiO 3 is the first superconductor where two gaps were observed!

39. Nature 377, 133 (1995) Two-gap superconductivity in cuprates?

40. T-dependence of sc carrier density and sc gap

41. Low temperature dependence of magnetic penetration depth reflects symmetry of superconducting gap function

43. Two-gap superconductivity in single-crystal La 1.83 Sr 0.7 CuO 4 Khasanov R, Shengelaya A et al., Phys. Rev. Lett. 75, 060505 (2007) Keller, Bussmann-Holder & Müller, Materials Today 11, 38 (2008) d-wave symmetry (≈ 70%) Δ 1 d (0) ≈ 8 meV s-wave symmetry (≈ 30%) Δ 1 s (0) ≈ 1.6 meV

44. Two-gap superconductivity in Ba 1-x Rb x Fe 2 As 2 (T c =37 K) Guguchia et al., Phys. Rev. B 84, 094513 (2011). Δ 0,1 =1.1(3) meV, Δ 0,2 =7.5(2) meV, ω = 0.15(3).  SR V. B. Zabolotnyy et al., Nature 457, 569 (2009).

45. Magnetism and superconductivity

46. Magnetic structure of EuFe 2 As 2 at 2.5 K Y.Xiao et al., PRB 80, 174424 (2009). Raffius et al., J. Phys. Chem. Solids 54, 13 (1993). T AFM (Eu 2+ ) = 19 K AFe 2 As 2 (A=Ba,Sr,Ca,Eu) T SDW (Fe) = 190 K Eu 2+ 4f 7, S = 7/2

47. Phase diagram of EuFe 2 (As 1-x P x ) 2 Z. Guguchia et. al., Phys. Rev. B 83, 144516 (2011). Z. Guguchia, A. Shengelaya et. al., arXiv:1205.0212v1. Y. Xiao et al., PRB 80, 174424 (2009). T AFM (Eu 2+ ) = 19 K T SDW (Fe) = 190 K

48. E. Wiesenmayer et. al., PRL 107, 237001 (2011). X. F. Wang et al., New J. Phys. 11, 045003 (2009). Phase diagram of Ba 1-x K x Fe 2 As 2

49. Z. Guguchia et. al., arXiv:1205.0212v1. Temperature-pressure phase diagram for EuFe 2 (As 0.88 P 0.12 ) 2

50. Superconductivity in AFe 2-x Co x As 2 (Ba,Eu) X. F. Wang et al., New J. Phys. 11, 045003 (2009). Y. He et al., J. Phys.: Condens. Matter 22, 235701 (2010).

51. An electronic phase diagram of EuFe 2 (As 1-x P x ) 2 H. S. Jeevan et al., arXiv:1011.4481v2

52. Phase diagram of SmFeAsO 1-x F x (1111 family) Drew et al., Nature Mater. 8, 310 (2009)

53. Phase diagram of FeSe 1-x Bendele et al., Phys. Rev. Lett. 104, 087003 (2010)

54. Low-energy μSR and applications

55. Low-energy  SR at the Paul Scherrer Institute E. Morenzoni et al., J. Appl. Phys. 81, 3340 (1997)

56. Depth dependent µSR measurements Jackson et al., Phys. Rev. Lett. 84, 4958 (2000)

57. More precise: use known implantation profile Jackson et al., Phys. Rev. Lett. 84, 4958 (2000)

58. Direct measurement of the magnetic penetration depth  SR experiment  magnetic field probability distribution p(B) at the muon site  p(B)  B(z)  SR experiment  magnetic field probability distribution p(B) at the muon site  p(B)  B(z) Jackson et al., Phys. Rev. Lett. 84, 4958 (2000)      

59. Direct measurement of λ in a YBa 2 Cu 3 O 7-  film

60. SSS’ S S ++ LE  SR study of multilayer structures S: La 1.84 Sr 0.16 O 4 T c ≈ 32 K d = 46 nm S’: La 1.94 Sr 0.06 O 4 T c ’ ≤ 5 K d = 46 nm S: La 1.84 Sr 0.16 O 4 T c ≈ 32 K d = 46 nm S’: La 1.94 Sr 0.06 O 4 T c ’ ≤ 5 K d = 46 nm Morenzoni et al., Nature Communications, DOI: 10.1038/ncomms1273

61. LE  SR study of multilayer structures Morenzoni et al., Nature Communications, DOI: 10.1038/ncomms1273 SS’S S’

62. LE  SR study of multilayer structures Morenzoni et al., Nature Communications, DOI: 10.1038/ncomms1273

63. Conclusions  The positive muon is a powerful and unique tool to explore the microscopic magnetic properties of novel superconductors and related magnetic systems  μSR has demonstrared to provide important information on high-temperature superconductors, which are hardly obtained by any other experimental technique, such as neutron scattering, magnetization studies etc.  However, in any case complementary experimental techniques have to be applied to disentangle the complexity of novel superconductors such as the cuprates and the recently discovered iron-based superconductors

64. Thank you very much for your attention!

65. Question 1: How the distance between the vortices depends on the applied magnetic field in case of square/hexagonal lattice? Question 2: Magnetic field at the centre of the vortex can be calculated as follows: Derive the formula for the energy corresponding to the unit volume of the vortex. dd

66. Question 3: Why the scenario (a) is preferable for the system? Question 4: What was the first experiment which confirmed the presence of the superconducting gap? (a)(b)

67. The muon as an elementary particle Discovered in 1936 by Anderson and Neddermeyer who studied cosmic radiations.

70. GPS and LTF µSR in silver in a magnetic field of 10mT measured at the GPS facility instrument in conventional and in MORE mode. Insert: Reduced asymmetry plot for the first 2µs in MORE mode (function fitted for t > 0.4µs).

72. Melting of ice

74. Melting of the vortex lattice