Advertisement

Muon Spin Relaxation Studies of Unconventional Superconductors: First-Order Behavior and Comparable Spin-Charge Energy Scales

Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 180)

Abstract

Since the late 1980s, the muon spin rotation and relaxation (\(\mu \)SR) method has been extensively applied to studies of unconventional superconductors, including high-\(T_{c}\) cuprate, ruthenate, FeAs, organic, and heavy-fermion systems. With its unique sensitivity to static magnetic order in both long-range ordered and random spin systems, \(\mu \)SR has played a leading role in determining magnetic phase diagrams and elucidating the evolution from the parent antiferromagnetic state to the superconducting state in these systems. The extremely high sensitivity of \(\mu \)SR to small static magnetic fields allowed studies of time-reversal symmetry breaking in the superconducting state of Sr\({}_{2}\)RuO\({}_{4}\) and several other systems and in the pseudogap region of cuprate systems. \(\mu \)SR measurements of the London penetration depth and the superfluid density led to a unique characterization of the pairing symmetry and energy scales of superconducting charges. In this paper, we review the historical developments and recent progress of \(\mu \)SR studies in unconventional superconductors which revealed, among others, scaling of the superfluid density and \(T_{c}\), comparable spin and charge energy scales, phase separation between superconducting and non-superconducting volumes, and first-order quantum evolution at phase boundaries. We discuss these results in terms of quantum criticality, crossover from Bose Einstein to BCS condensation, and the influence of competing states via inelastic soft modes.

Keywords

Unconventional Superconductors Muon Spin Static Magnetic Order Superfluid Density Cuprate Systems 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The author would like to thank Graeme Luke for collaboration on \(\mu \)SR studies continuing since 1988, all the authors of cited \(\mu \)SR references for their important contributions on studies of unconventional superconductors, and to members of Super-PIRE for collaboration on recent multiprobe studies on FeAs superconductors. This work was supported by US NSF with the individual grant DMR-1105961 and PIRE project OISE-0968226, and by JAEA with the Reimei project.

References

  1. 1.
    R.L. Garwin, L.M. Lederman, M. Weinrich, Observation of the failure of conservation of parity and charge conjugation in meson decays: the magnetic moment of the free muon. Phys. Rev. 105, 1415–1417 (1957)CrossRefADSGoogle Scholar
  2. 2.
    C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes, R.P. Hudson, Experimental test of parity conservation in beta-decay. Phys. Rev. 105, 1413–1415 (1957)CrossRefADSGoogle Scholar
  3. 3.
    J.I. Friedman, V.L. Telegdi, Nuclear emulsion evidence for parity nonconservation in the decay chain \(\pi ^+ - \mu ^+ -\epsilon ^+\). Phys. Rev. 105, 1681–1682 (1957)CrossRefADSGoogle Scholar
  4. 4.
    T.D. Lee, A brief-history of the muon. Hyperfine Interact. 86, 439–453 (1994)CrossRefADSGoogle Scholar
  5. 5.
    For general aspects and historical development of \(\mu \)SR, see Proceedings of twelve international conferences on muon spin rotation / relaxation/ resonance in Hyperfine Interact. 6 (1979); 8 (1981); 17–19 (1984); 31 (1986); 63–65 (1990); 85–87 (1994); 104–106 (1997); Physica B 289–290 (2000); B 326(2003); B 374–375 (2006); B 404 (2009); Physics Procedia 30 (2012)Google Scholar
  6. 6.
    A. Schenck, Muon Spin Rotation Spectroscopy (Hilger, Bristol, 1985)Google Scholar
  7. 7.
    S.L. Lee, S.H. Kilcoyne, and R. Cywinski (ed.), Muon Science: Muons in Physics, Chemistry and Materials, in Proceedings of the Fifty First Scottish Universities Summer School in Physics, St. Andrews, 1998, Inst. of Physics Publishing, Bristol, 1999Google Scholar
  8. 8.
    R.H. Heffner and K. Nagamine (ed.), Special Issue on \(\mu \)SR: muon spin rotation, relaxation or resonance, J. Phys.: Condens. Matter 16 (2004) S4403–S4806Google Scholar
  9. 9.
    A. Yaouanc, P. Dalmas de Rotier, Muon Spin Rotation, Relaxation, and Resonance : Applications to Condensed Matter (Oxford University Press, Oxford, 2011)Google Scholar
  10. 10.
    J.E. Sonier, MuSR Brochure, http://musr.ca/intro/musr/muSRBrochure.pdf
  11. 11.
    Y.J. Uemura, W.J. Kossler, X.H. Yu, J.R. Kempton, H.S. Chen, D. Opie, C.E. Stronach, D.C. Johnston, M.S. Alvarez, D.P. Goshorn, Antiferromagnetism of La\({}_{2}\)CuO\({}_{4-y}\) studied by muon spin rotation. Phys. Rev. Lett. 59, 1045–1048 (1987)CrossRefADSGoogle Scholar
  12. 12.
    Y.J. Uemura, W.J. Kossler, X.H. Yu, H.E. Schoene, J.R. Kempton, C.E. Stronach, S. Barth, F.N. Gygax, B. Hitti, A. Schenck, C. Baines, W.F. Lankford, Y. Ooniki, T. Komatsubara, Coexisting static magnetic order and superconductivity in CeCu\({}_{2.1}\)Si\({}_{2}\) found by muon spin relaxation. Phys. Rev. B39, 4726–4729 (1989)CrossRefADSGoogle Scholar
  13. 13.
    L.P. Le, A. Keren, G.M. Luke, B.J. Sternlieb, W.D. Wu, Y.J. Uemura, J.H. Brewer, T.M. Riseman, R.V. Upasani, L.Y. Chiang, W. Kang, P.M. Chaikin, T. Csiba, G. Gruner, Muon spin rotation/relaxation studies in (TMTSF)\({}_{2}\)-X compounds. Phys. Rev. B48, 7284–7296 (1993)CrossRefADSGoogle Scholar
  14. 14.
    Y.J. Uemura, Superconductivity: exotic commonalities in phase and mode. Nat. Mater. 8, 253–255 (2009)CrossRefADSGoogle Scholar
  15. 15.
    H. Luetkens, H.-H. Klauss, M. Kraken, F.J. Litterst, T. Dellmann, R. Klingeler, C. Hess, R. Khasanov, A. Amato, C. Baines, M. Kosmala, O.J. Schumann, M. Braden, J. Hamann-Borrero, N. Leps, A. Kondrat, G. Behr, J. Werner, B. Buechner, Electronic phase diagram of the LaO\({}_{1-x}\)F\({}_{x}\)FeAs superconductor. Nat. Mater. 8, 305–309 (2009)CrossRefADSGoogle Scholar
  16. 16.
    S. Sanna, G. Allodi, G. Concas, A.D. Hillier, R. De Renzi, Nanoscopic coexistence of magnetism and superconductivity in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6+x}\) detected by muon spin rotation. Phys. Rev. Lett. 93, 207001 (2004)CrossRefADSGoogle Scholar
  17. 17.
    J. Arvanitidis, K. Papagelis, Y. Takabayashi, T. Takenobu, Y. Iwasa, M.J. Rosseinsky, K. Prassides, Magnetic ordering in the ammoniated alkali fullerides (NH\({}_{3}\))K\({}_{3-x}\)Rb\({}_{x}\)C\({}_{60}\) (x = 2, 3). J. Phys.: Condens. Matter 19, 386235 (2007)ADSGoogle Scholar
  18. 18.
    J.P. Carlo, T. Goko, I.M. Gat-Malureanu, P.L. Russo, A.T. Savici, A.A. Aczel, G.J. MacDougall, J.A. Rodriguez, T.J. Williams, G.M. Luke, C.R. Wiebe, Y. Yoshida, S. Nakatsuji, Y. Maeno, T. Taniguchi, Y.J. Uemura, New magnetic phase diagram of (Sr, Ca)\({}_{2}\)RuO\({}_{4}\). Nat. Mater. 11, 323–328 (2012)CrossRefADSGoogle Scholar
  19. 19.
    S. Nakatsuji, D. Hall, L. Balicas, Z. Fisk, K. Sugahara, M. Yoshioka, Y. Maeno, Heavy-mass fermi liquid near a ferromagnetic instability in layered ruthenates. Phys. Rev. Lett. 90, 137202 (2003)CrossRefADSGoogle Scholar
  20. 20.
    A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez, A.R. Kortan, Superconductivity at 18 K in potassium-doped C\({}_{60}\). Nature 350, 600–601 (1991)CrossRefADSGoogle Scholar
  21. 21.
    M.J. Rosseinsky, A.P. Ramirez, S.H. Glarum, D.W. Murphy, R.C. Haddon, A.F. Hebard, T.T.M. Palstra, A.R. Kortan, S.M. Zahurak, A.V. Makhija, Superconductivity at 28 K in Rb\({}_{x}\)C\({}_{60}\). Phys. Rev. Lett. 66, 2830–2832 (1991)CrossRefADSGoogle Scholar
  22. 22.
    Y. Takabayashi, A.Y. Ganin, P. Jegli, D. Aron, T. Takano, Y. Iwasa, Y. Ohishi, M. Takata, N. Takeshita, K. Prassides, M.J. Rosseinsky, The disorder-free non-BCS superconductor Cs\({}_{3}\)C\({}_{60}\) emerges from an antiferromagnetic insulator parent state. Science 323, 1585–1590 (2009)CrossRefADSGoogle Scholar
  23. 23.
    A.Y. Ganin, Y. Takabayashi, P. Jeglic, D. Arcon, A. Potocnik, P.J. Baker, Y. Ohishi, M.T. McDonald, M.D. Tzirakis, A. McLennan, G.R. Darling, M. Takata, M.J. Rosseinsky, K. Prassides, Polymorphism control of superconductivity and magnetism in Cs\({}_{3}\)C\({}_{60}\) close to the Mott transition. Nature 466, 221–225 (2010)CrossRefADSGoogle Scholar
  24. 24.
    Y.J. Uemura, B.J. Sternlieb, D.E. Cox, J.H. Brewer, R. Kadono, J.R. Kempton, R.F. Kiefl, S.R. Kreitzman, G.M. Luke, P. Mulhern, T.M. Riseman, D. Ll Williams, W.J. Kossler, X.H. Yu, C.E. Stronach, M.A. Subramanian, J. Goparakrishnan, A.W. Sleight, Absence of magnetic order in (Ba, K)BiO\({}_{3}\). Nature 335, 151–152 (1988)CrossRefADSGoogle Scholar
  25. 25.
    F. von Rohr, A. Schilling, R. Nesper, Ch. Baines, M. Bendele, Conventional superconductivity and charge-density-wave ordering in Ba\({}_{1-x}\)Na\(_{x}\)Ti\({}_{2}\)Sb\({}_{2}\)O, Phys. Rev. B 88 (2013) 140501 (R)Google Scholar
  26. 26.
    Y. Nozaki, K. Nakano, T. Yajima, H. Kageyama, B. Frandsen, L. Liu, S. Cheung, T. Goko, Y.J. Uemura, T.S.J. Munsie, T. Medina, G.M. Luke, J. Munevar, D. Nishio-Hamane, C.M. Brown, Muon spin relaxation and electron/neutron diffraction studies of BaTi\({}_{2}\)(As\({}_{1-x}\)Sb\({}_{x}\))\({}_{2}\)O: Absence of static magnetism and superlattice reflections. Phys. Rev. B 88, 214506 (2013)CrossRefADSGoogle Scholar
  27. 27.
    E. Morosan, H.W. Zandbergen, B.S. Dennis, J.W.G. Bos, Y. Onose, T. Klimczuc, A.P. Ramirez, N.P. Ong, R.J. Cava, Superconductivity in Cu\({}_{x}\)TiSe\({}_{2}\). Nat. Phys. 2, 544–550 (2006)CrossRefGoogle Scholar
  28. 28.
    M. Zaberchik, K. Chashka, L. Patlgan, A. Maniv, Ch. Baines, P. King, A. Kanigel, Possible evidence of a two-gap structure for the Cu\({}_{x}\)TiSe\({}_{2}\) superconductor, Phys. Rev. B 81 (2010) 220505 (R)Google Scholar
  29. 29.
    R.S. Hayano, Y.J. Uemura, J. Imazato, N. Nishida, T. Yamazaki, R. Kubo, Zero- and low-field spin relaxation studied by positive muon. Phys. Rev. B20, 850–859 (1979)CrossRefADSGoogle Scholar
  30. 30.
    R.H. Heffner, J.L. Smith, J.O. Willis, P. Birrer, C. Baines, F.N. Gygax, B. Hitti, E. Lippelt, H.R. Ott, A. Schenck, E.A. Knetsch, J.A. Mydosh, D.E. MacLaughlin, New phase diagram for (U, Th)Be\({}_{13}\): a muon-spin-resonance and H\({}_{C1}\) study. Phys. Rev. Lett. 65, 2816–2819 (1990)CrossRefADSGoogle Scholar
  31. 31.
    G.M. Luke, A. Keren, L.P. Le, W.D. Wu, Y.J. Uemura, D.A. Bonn, L. Taillefer, J.D. Garrett, Muon spin relaxation in UPt\({}_{3}\). Phys. Rev. Lett. 71, 1466–1469 (1993)CrossRefADSGoogle Scholar
  32. 32.
    Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J.G. Bednorz, F. Lichtenberg, Superconductivity in a layered perovskite without copper. Nature 372, 532–534 (1994)CrossRefADSGoogle Scholar
  33. 33.
    G.M. Luke, Y. Fudamoto, K.M. Kojima, M.L. Larkin, J. Merrin, B. Nachumi, Y.J. Uemura, Y. Maeno, Z.Q. Mao, Y. Mori, H. Nakamura, M. Sigrist, Time-reversal symmetry breaking superconductivity in Sr\({}_{2}\)RuO\({}_{4}\). Nature 394, 558–561 (1998)CrossRefADSGoogle Scholar
  34. 34.
    K. Ishida, H. Mukuda, Y. Kitaoka, K. Asayama, Z.Q. Mao, Y. Mori, Y. Maeno, Spin-triplet superconductivity in Sr\(_2\)RuO\(_4\) identified by O-17 Knight shift, Nature 394 658–660 (1998)Google Scholar
  35. 35.
    K. Ishida, Y. Kitaoka, K. Asayama, S. Ikeda, S. Nishizaki, Y. Maeno, K. Yoshida, T. Fujita, Anisotropic pairing in superconducting Sr\({}_{2}\)RuO\({}_{4}\): Ru NMR and NQR studies. Phys. Rev. B 56, R505–R508 (1997)Google Scholar
  36. 36.
    A.P. Mackenzie, Y. Maeno, The superconductivity of Sr\({}_{2}\)RuO\({}_{4}\) and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003)CrossRefADSGoogle Scholar
  37. 37.
    J. Xia, Y. Maeno, P.T. Beyersdorf, M.M. Fejer, A. Kapitulnik, High resolution polar kerr effect measurements of Sr\({}_{2}\)RuO\({}_{4}\): evidence for broken time-reversal symmetry in the superconducting state. Phys. Rev. Lett. 97, 167002 (2006)CrossRefADSGoogle Scholar
  38. 38.
    Y. Aoki, A. Tsuchiya, T. Kanayama, S.R. Saha, H. Sugawara, H. Sato, W. Higemoto, A. Koda, K. Ohishi, K. Nishiyama, R. Kadono, Time-reversal symmetry-breaking superconductivity in heavy-fermion PrOs\({}_{4}\)Sb\({}_{12}\) detected by muon-spin relaxation. Phys. Rev. Lett. 91, 067003 (2003)CrossRefADSGoogle Scholar
  39. 39.
    A. Maisuradze, W. Schnelle, R. Khasanov, R. Gumeniuk, M. Nicklas, H. Rosner, A. Leithe-Jasper, Yu. Grin, A. Amato, P. Thalmeier, Evidence for time-reversal symmetry breaking in superconducting PrPt\({}_{4}\)Ge\({}_{12}\). Phys. Rev. B 82, 024524 (2010)CrossRefADSGoogle Scholar
  40. 40.
    A.D. Hillier, J. Quintanilla, R. Cywinski, Evidence for time-reversal symmetry breaking in the noncentrosymmetric superconductor LaNiC\({}_{2}\). Phys. Rev. Lett. 102, 117007 (2009)CrossRefADSGoogle Scholar
  41. 41.
    A.D. Hillier, J. Quintanilla, B. Mazidian, J.F. Annett, R. Cywinski, Nonunitary triplet pairing in the centrosymmetric superconductor LaNiGa\({}_{2}\). Phys. Rev. Lett. 109, 097001 (2012)CrossRefADSGoogle Scholar
  42. 42.
    P.K. Biswas, H. Luetkens, 1, T. Neupert, T. Sturzer, C. Baines, G. Pascua, A.P. Schnyder, M.H. Fischer, J. Goryo, M. R. Lees, H. Maeter, F. Bruckner, H.-H. Klauss, M. Nicklas, P.J. Baker, A.D. Hillier, M. Sigrist, A. Amato, D. Johrendt, Evidence for superconductivity with broken time-reversal symmetry in locally noncentrosymmetric SrPtAs. Phys. Rev. B 87, 180503(R) (2013)Google Scholar
  43. 43.
    A.A. Aczel, T.J. Williams, T. Goko, J.P. Carlo, W. Yu, Y.J. Uemura, T. Klimczuk, J.D. Thompson, R.J. Cava, G.M. Luke, Muon spin rotation/relaxation measurements of the noncentrosymmetric superconductor Mg\({}_{10}\)Ir\({}_{19}\)B\({}_{16}\). Phys. Rev. B 82, 024520 (2010)CrossRefADSGoogle Scholar
  44. 44.
    V.K. Anand, A.D. Hillier, D.T. Adroja, A.M. Strydom, H. Michor, K.A. McEwen, B.D. Rainford, Specific heat and \(\mu \)SR study on the noncentrosymmetric superconductor LaRhSi\({}_{3}\). Phys. Rev. B 83, 064522 (2011)CrossRefADSGoogle Scholar
  45. 45.
    P.K. Biswas, A.D. Hillier, M.R. Lees, DMcK Paul, Comparative study of the centrosymmetric and noncentrosymmetric superconducting phases of Re\({}_{3}\)W using muon spin spectroscopy and heat capacity measurements. Phys. Rev. B 85, 134505 (2012)CrossRefADSGoogle Scholar
  46. 46.
    T. Goko, Y. Ando, M. Kriener, G. Gu, B. Frandsen, Y.J. Uemura et al., unpublished workGoogle Scholar
  47. 47.
    B. Fauque, Y. Sidis, V. Hinkov, S. Pailhes, C.T. Lin, X. Chaud, P. Bourges, Magnetic order in the pseudogap phase of high-T\({}_{c}\) superconductors. Phys. Rev. Lett. 96, 197001 (2006)CrossRefADSGoogle Scholar
  48. 48.
    H.A. Mook, Y. Sidis, B. Fauqu, V. Baldent, P. Bourges, Observation of magnetic order in a superconducting YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.6}\) single crystal using polarized neutron scattering, Phys. Rev. B 78 (2008) 020506 (R)Google Scholar
  49. 49.
    Y. Li, V. Baledent, N. Barisic, Y. Cho, B. Fauque, Y. Sidis, G. Yu, X. Zhao, P. Bourges, M. Greven, Unusual magnetic order in the pseudogap region of the superconductor HgBa\({}_{2}\)CuO\(_{4+\delta }\). Nature 455, 372–375 (2008)CrossRefADSGoogle Scholar
  50. 50.
    C.M. Varma, Non-fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 14554–14580 (1997)CrossRefADSGoogle Scholar
  51. 51.
    C.M. Varma, Theory of the pseudogap state of the cuprates. Phys. Rev. B 73, 155113 (2006)CrossRefADSGoogle Scholar
  52. 52.
    R.F. Kiefl, J.H. Brewer, I. Affleck, J.F. Carolan, P. Dosanjh, W.N. Hardy, T. Hsu, R. Kadono, J.R. Kempton, S.R. Kreitzman, Q. Li, A.H. O’Reilly, T.M. Riseman, P.W. Schleger, P. Stamp, Hu Zhou, L.P. Le, G.M. Luke, B.J. Sternlieb, Y.J. Uemura, H.R. Hart, K.W. Ley, Search for anomalous internal magnetic fields in high-T\(_{c}\) superconductors as evidence for broken time reversal symmetry. Phys. Rev. Lett. 64, 2082–2085 (1990)CrossRefADSGoogle Scholar
  53. 53.
    G.J. MacDougall, A.A. Aczel, J.P. Carlo, T. Ito, J. Rodriguez, P.L. Russo, Y.J. Uemura, S. Wakimoto, G.M. Luke, Absence of time reversal symmetry breaking in La\({}_{2-x}\)Sr\({}_{x}\)CuO\({}_{4}\). Phys. Rev. Lett. 101, 017001 (2008)CrossRefADSGoogle Scholar
  54. 54.
    W. Huang, V. Pacradouni, M.P. Kennett, S. Komiya, J.E. Sonier, Precision search for magnetic order in the pseudogap regime of La\({}_{2-x}\)Sr\({}_{x}\)CuO\({}_{4}\) by muon spin relaxation. Phys. Rev. B 85, 104527 (2012)CrossRefADSGoogle Scholar
  55. 55.
    J.E. Sonier, J.H. Brewer, R.F. Kiefl, R.I. Miller, G.D. Morris, C.E. Stronach, J.S. Gardner, S.R. Dunsiger, D.A. Bonn, W.N. Hardy, R. Liang, R.H. Heffner, Anomalous weak magnetism in superconducting YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6+x}\). Science 292, 1692–1695 (2001)CrossRefADSGoogle Scholar
  56. 56.
    J.E. Sonier, V. Pacradouni, S.A. Sabok-Sayr, W.N. Hardy, D.A. Bonn, R. Liang, H.A. Mook, Detection of the unusual magnetic orders in the pseudogap region of a high-temperature superconducting YBa\({}_{2}\)Cu3O\({}_{6.6}\) crystal by muon-spin relaxation. Phys. Rev. Lett. 103, 167002 (2009)CrossRefADSGoogle Scholar
  57. 57.
    S. Strassle, J. Roos, M. Mali, H. Keller, T. Ohno, Lack of evidence for orbital-current effects in the high-temperature Y\({}_{2}\)Ba\({}_{4}\)Cu\({}_{7}\)O\({}_{15-}\) \({}_{\delta }\) superconductor using \(^{89}\)Y nuclear magnetic resonance. Phys. Rev. Lett. 101, 237001 (2008)CrossRefADSGoogle Scholar
  58. 58.
    S. Strassle, B. Graneli, M. Mali, J. Roos, H. Keller, Absence of orbital currents in superconducting YBa\({}_{2}\)Cu\({}_{4}\)O\({}_{8}\) using a Zeeman-perturbed nuclear-quadrupole-resonance technique. Phys. Rev. Lett. 106, 097003 (2011)CrossRefADSGoogle Scholar
  59. 59.
    J. Xia, E. Schemm, G. Deutscher, S.A. Kivelson, D.A. Bonn, W.N. Hardy, R. Liang, W. Siemons, G. Koster, M.M. Fejer, A. Kapitulnik, Polar Kerr-effect measurements of the high-temperature YBa\({}_{2}\)Cu3O\({}_{6+x}\) superconductor: evidence for broken symmetry near the pseudogap temperature. Phys. Rev. Lett. 100, 127002 (2008)CrossRefADSGoogle Scholar
  60. 60.
    H. Karapetyan, M. Hucker, G.D. Gu, J.M. Tranquada, M.M. Fejer, J. Xia, A. Kapitulnik, Magneto-optical measurements of a cascade of transitions in superconducting La\({}_{1.875}\)Ba\({}_{0.125}\)CuO\({}_{4}\) single crystals. Phys. Rev. Lett. 109, 147001 (2012)CrossRefADSGoogle Scholar
  61. 61.
    R.E. Allen, The London-Anderson-Englert-Brout-Higgs-Guralnik-Hagen-Kibble-Weinberg mechanism and Higgs boson reveal the unity and future excitement of physics, arXiv:1306.4061 [hep-ph]
  62. 62.
    J.E. Sonier, J.H. Brewer, R.F. Kiefl, \(\mu \)SR studies of the vortex state in type-II superconductors. Rev. Mod. Phys. 72, 769–811 (2000)CrossRefADSGoogle Scholar
  63. 63.
    L.P. Le, G.M. Luke, B.J. Sternlieb, W.D. Wu, Y.J. Uemura, J.H. Brewer, T.M. Riseman, C.E. Stronach, G. Saito, H. Yamochi, H.H. Wang, A.M. Kini, K.D. Carlson, J.M. Williams, \(\mu \)SR measurement of magnetic penetration depth in organic superconductors (BEDT-TTF)\({}_{2}\)-X: X=Cu(NCS)\({}_{2}\) and Cu[N(CN)\({}_{2}\)]Br. Phys. Rev. Lett. 68, 1923–1926 (1992)CrossRefADSGoogle Scholar
  64. 64.
    K. Izawa, H. Yamaguchi, T. Sasaki, Y. Matsuda, Superconducting gap structure of \(\kappa \)-(BEDT-TTF)\(_{2}\)Cu(NCS)\(_{2}\) probed by thermal conductivity tensor. Phys. Rev. Lett. 88, 027002 (2002)CrossRefADSGoogle Scholar
  65. 65.
    W.N. Hardy, D.A. Bonn, D.C. Morgan, R.X. Liang, K. Zhang, Precision measurements of the temperature dependence of \(\lambda \) in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\): Strong evidence for nodes in the gap function. Phys. Rev. Lett. 70, 3999–4002 (1993)CrossRefADSGoogle Scholar
  66. 66.
    J.E. Sonier, R.F. Kiefl, J.H. Brewer, D.A. Bonn, J.F. Carolan, K.H. Chow, P. Dosanjh, N. Hardy, R.X. Liang, W.A. MacFarlane, P. Mendels, G.D. Morris, T.M. Riseman, J.W. Schneider, New muon-spin-rotation measurement of the temperature dependence of the magnetic penetration depth in YBa\({}_{2}\)Cu\({}_{3}\)0\({}_{6.95}\). Phys. Rev. Lett. 72, 744–747 (1994)CrossRefADSGoogle Scholar
  67. 67.
    C.C. Tsuei, J.R. Kirtley, Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000)CrossRefADSGoogle Scholar
  68. 68.
    D.J. Van Harlingen, Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors: evidence for d\({}_{x}\) \({}^{2}\) \({}_{-}\) \({}_{y}\) \({}^{2}\) symmetry. Rev. Mod. Phys. 67, 515–535 (1995)CrossRefADSGoogle Scholar
  69. 69.
    A. Damascelli, Z. Hussain, Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003)CrossRefADSGoogle Scholar
  70. 70.
    K. McElroy, R.W. Simmonds, J.E. Hoffman, D.-H. Lee, J. Orenstein, H. Eisaki, S. Uchida, J.C. Davis, Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi\({}_{2}\)Sr\({}_{2}\)CaCu\({}_{2}\)O\({}_{8+}\) \({}_{\delta }\). Nature 422, 592–596 (2003)CrossRefADSGoogle Scholar
  71. 71.
    R. Khasanov, S. Strassle, D. Di Castro, T. Masui, S. Miyasaka, S. Tajima, A. Bussmann-Holder, H. Keller, Multiple gap symmetries for the order parameter of Cuprate superconductors from penetration depth measurements. Phys. Rev. Lett. 99, 237601 (2007)CrossRefADSGoogle Scholar
  72. 72.
    see, for example, R. Khasanov, D.V. Evtushinsky, A. Amato, H.-H. Klauss, H. Luetkens, Ch. Niedermayer, B. Buchner, G.L. Sun, C.T. Lin, J.T. Park, D.S. Inosov, V. Hinkov, Two-Gap Superconductivity in \(Ba_{1-x} K_{x} Fe_{2} As_{2}:\) A Complementary Study of the Magnetic Penetration Depth by Muon-Spin Rotation and Angle-Resolved Photoemission, Phys. Rev. Lett. 102 (2009) 187005. Google Scholar
  73. 73.
    Y.J. Uemura, V.J. Emery, A.R. Moodenbaugh, M. Suenaga, D.C. Johnston, A.J. Jacobson, J.T. Lewandowski, J.H. Brewer, R.F. Kiefl, S.R. Kreitzman, G.M. Luke, T.M. Riseman, C.E. Stronach, W.J. Kossler, J.R. Kempton, X.H. Yu, D. Opie, H.E. Schone, Systematic variation of magnetic-field penetration depth in high-T\(_{c}\) superconductors studied by muon spin relaxation. Phys. Rev. B38, 909–912 (1988)CrossRefADSGoogle Scholar
  74. 74.
    Y.J. Uemura, G.M. Luke, B.J. Sternlieb, J.H. Brewer, J.F. Carolan, W.N. Hardy, R. Kadono, J.R. Kempton, R.F. Kiefl, S.R. Kreitzman, P. Mulhern, T.M. Riseman, D. LI Williams, B.X. Yang, S. Uchida, H. Takagi, J. Goparakrishnan, A.W. Sleight, M.A. Subramanian, C.L. Chien, M.Z. Cieplak, G. Xiao, V.Y. Lee, B.W. Statt, C.E. Stronach, W.J. Kossler, X.H. Yu, Universal correlations between Tc and n\(_{s}\)/m\(^{*}\) (carrier density over effective mass) in high-T\(_{c}\) Cuprate superconductors. Phys. Rev. Lett. 62, 2317–2320 (1989)CrossRefADSGoogle Scholar
  75. 75.
    Y.J. Uemura, A. Keren, G.M. Luke, L.P. Le, B.J. Sternlieb, W.D. Wu, J.H. Brewer, R.L. Whetten, S.M. Huang, S. Lin, R.B. Kaner, F. Diederich, S. Donovan, G. Gruner, K. Holczer, Magnetic field penetration depth in K\({}_{3}\)C\({}_{60}\) measured by muon spin relaxation. Nature 352, 605–607 (1991)CrossRefADSGoogle Scholar
  76. 76.
    Y.J. Uemura, A. Keren, L.P. Le, G.M. Luke, W.D. Wu, J.S. Tsai, K. Tanigaki, K. Holczer, S. Donovan, R.L. Whetten, System dependence of the magnetic-field penetration depth in C\(_{60}\) superconductors. Physica C 235–240, 2501–2502 (1994)Google Scholar
  77. 77.
    Y.J. Uemura, L.P. Le, G.M. Luke, B.J. Sternlieb, W.D. Wu, J.H. Brewer, T.M. Riseman, C.L. Seaman, M.B. Maple, M. Ishikawa, D.G. Hinks, J.D. Jorgensen, G. Saito, H. Yamochi, Basic similarities among Cuprate, Bismuthate, Organic, Chevrel phase, and heavy-fermion superconductors shown by penetration depth measurements. Phys. Rev. Lett. 66, 2665–2668 (1991)CrossRefADSGoogle Scholar
  78. 78.
    J.P. Carlo, Y.J. Uemura, T. Goko, G.J. MacDougall, J.A. Rodriguez, W. Yu, G.M. Luke, P. Dai, N. Shannon, S. Miyasaka, S. Suzuki, S. Tajima, G.F. Chen, W.Z. Hu, J.L. Luo, N.L. Wang, Static magnetic order and superfluid density of RFeAs(O, F) (R=La, Nd, Ce) and LaFePO studied by muon spin relaxation: unusual similarities with the behavior of Cuprate superconductors. Phys. Rev. Lett. 102, 087001 (2009)CrossRefADSGoogle Scholar
  79. 79.
    T. Goko, A.A. Aczel, E. Baggio-Saitovitch, S.L. Bud’ko, P.C. Canfield, J.P. Carlo, G.F. Chen, P. Dai, A.C. Hamann, W.Z. Hu, H. Kageyama, G.M. Luke, J.L. Luo, B. Nachumi, N. Ni, D. Reznik, D.R. Sanchez-Candela, A.T. Savici, K.J. Sikes, N.L. Wang, C.R. Wiebe, T.J. Williams, T. Yamamoto, W. Yu, Y.J. Uemura, Superconductivity coexisting with phase-separated static magnetic order in (Ba, K)Fe\({}_{2}\)As\({}_{2}\), (Sr, Na)Fe\({}_{2}\)As\({}_{2}\) and CaFe\({}_{2}\)As\({}_{2}\). Phys. Rev. B 80, 024508 (2009)CrossRefADSGoogle Scholar
  80. 80.
    M. Bendele, S. Weyeneth, R. Puzniak, A. Maisuradze, E. Pomjakushina, K. Conder, V. Pomjakushin, H. Luetkens, S. Katrych, A. Wisniewski, R. Khasanov, H. Keller, Anisotropic superconducting properties of single-crystalline FeSe\({}_{0.5}\)Te\({}_{0.5}\). Phys. Rev. B 81, 224520 (2010)CrossRefADSGoogle Scholar
  81. 81.
    Y.J. Uemura, A. Keren, L.P. Le, G.M. Luke, W.D. Wu, Y. Kubo, Y. Shimakawa, M. Subramanian, J.L. Cobb, J.T. Markert, Magnetic-field penetration depth in Tl\({}_{2}\)Ba\({}_{2}\)CuO\({}_{6+\delta }\) in the overdoped regime. Nature 364, 605–607 (1993)CrossRefADSGoogle Scholar
  82. 82.
    Ch. Niedermayer, C. Bernhard, U. Binninger, H. Glckler, J.L. Tallon, E.J. Ansaldo, J.I. Budnick, Muon spin rotation study of the correlation between Tc and n\(_{s}\)/m\(^{*}\) in overdoped Tl\({}_{2}\)Ba\({}_{2}\)CuO\({}_{6+\delta }\). Phys. Rev. Lett. 71, 1764–1767 (1993)CrossRefADSGoogle Scholar
  83. 83.
    T.J. Williams, A.A. Aczel, E. Baggio-Saitovitch, S.L. Budko, P.C. Canfield, J.P. Carlo, T. Goko, H. Kageyama, A. Kitada, J. Munevar, N. Ni, S.R. Saha, K. Kirschenbaum, J. Paglione, D.R. Sanchez-Candela, Y.J. Uemura, G.M. Luke, Superfluid density and field-induced magnetism in Ba(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{2}\)As\({}_{2}\) and Sr(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{2}\)As\({}_{2}\) measured with muon spin relaxation. Phys. Rev. B82, 094512 (2010)CrossRefADSGoogle Scholar
  84. 84.
    C.J. Arguello, Y.J. Uemura, P.C.Dai, unpublished workGoogle Scholar
  85. 85.
    Y.J. Uemura, Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs. CuO, heavy fermion and other exotic superconductors. Physica B 404, 3195–3201 (2009)Google Scholar
  86. 86.
    C.A. Regal, M. Greiner, D.S. Jin, Observation of resonance condensation of fermionic atom pairs. Phys. Rev. Lett. 92, 040403 (2004)CrossRefADSGoogle Scholar
  87. 87.
    T. Moriya, K. Ueda, Antiferromagnetic spin fluctuation and superconductivity. Rep. Prog. Phys. 66, 1299–1341 (2003)CrossRefADSGoogle Scholar
  88. 88.
    T. Moriya, K. Ueda, Spin fluctuations and high temperature superconductivity. Adv. Phys. 49, 555–606 (2000)CrossRefADSGoogle Scholar
  89. 89.
    C. Stassis, B. Batlogg, J.P. Remeika, J.D. Axe, G. Shirane, Y.J. Uemura, Polarized neutron study of the paramagnetic scattering from CeCu\({}_{2}\)Si\({}_{2}\). Phys. Rev. B33, 1680–1683 (1986)CrossRefADSGoogle Scholar
  90. 90.
    Y.J. Uemura, C.F. Majkrzak, G. Shirane, C. Stassis, G. Aeppli, B. Batlogg, J.P. Remeika, Polarized neutron scattering from CeCu\({}_{2}\)Si\({}_{2}\) in applied magnetic fields. Phys. Rev. B33, 6508–6511 (1986)CrossRefADSGoogle Scholar
  91. 91.
    M. Wang, C. Zhang, X. Lu, G. Tan, H. Luo, Y. Song, M. Wang, X. Zhang, E.A. Goremychkin, T.G. Perring, T.A. Maier, Z. Yin, K. Haule, G. Kotliar, P. Dai, A magnetic origin for high temperature superconductivity in iron pnictides. Nat. Commun. 4, 2874 (2013). and references thereinADSGoogle Scholar
  92. 92.
    Y.J. Uemura, Energy scales of exotic superconductors, in Polarons and Bipolarons in High-Tc Superconductors and Related Materials, Proc. Int. Workshop on Polarons and Bipolarons in High-T\(_{c}\) Superconductors and Related Materials (Cambridge, UK,1994) ed E. Salje, A.S. Alexandrov and Y Liang (Cambridge: Cambridge University Press) pp. 453–460 (1995)Google Scholar
  93. 93.
    Y.J. Uemura, Energy scales of high- \(T_{c}\) cuprates, doped fullerenes, and other exotic superconductors, in Proc. Int. Symp. Workshop on High-T\(_{c}\) Superconductivity and the C\(_{60}\) Family (Beijing, 1994) ed H C Ren New York: Gordon and Breach pp. 113–142 (1995)Google Scholar
  94. 94.
    Y.J. Uemura, Condensation, excitation, pairing, and superfluid density in high-T\(_{c}\) superconductors: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing. J. Phys.: Condens. Matter 16, S4515–S4540 (2004)MathSciNetADSGoogle Scholar
  95. 95.
    Y.J. Uemura, Twin spin/charge roton mode and superfluid density: primary determining factors of T\(_{c}\) in high-T\(_{c}\) superconductors observed by neutron, ARPES, and \(\mu \)SR. Physica B 374–375, 1–8 (2006)Google Scholar
  96. 96.
    B. Nachumi, A. Keren, K. Kojima, M. Larkin, G.M. Luke, J. Merrin, O. Tchernyshyov, W.D. Wu, Y.J. Uemura, N. Ichikawa, M. Goto, S. Uchida, Muon spin relaxation studies of Zn-substitution effects in high-T\(_{c}\) Cuprates. Phys. Rev. Lett. 77, 5421–5424 (1996)CrossRefADSGoogle Scholar
  97. 97.
    S.H. Pan, E.W. Hudson, K.M. Lang, H. Eisaki, S. Uchida, J.C. Davis, Imaging the effects of individual zinc impurity atoms on superconductivity in Bi\({}_{2}\)Sr\({}_{2}\)CaCu\({}_{2}\)O\({}_{8+}\) \({}_{\delta }\). Nature 415, 746–750 (2000)ADSGoogle Scholar
  98. 98.
    K.M. Kojima, S. Uchida, Y. Fudamoto, I.M. Gat, M.I. Larkin, Y.J. Uemura, G.M. Luke, Superfluid density and volume fraction of static magnetism in stripe-stabilized La\({}_{1.85-y}\)Eu\({}_{y}\)Sr\({}_{0.15}\)CuO\({}_{4}\). Physica B 36, 316–320 (2003)Google Scholar
  99. 99.
    A.T. Savici, Y. Fudamoto, I.M. Gat, T. Ito, M.I. Larkin, Y.J. Uemura, G.M. Luke, K.M. Kojima, Y.S. Lee, M.A. Kastner, R.J. Birgeneau, K. Yamada, Muon spin relaxation studies of incommensurate magnetism and superconductivity in stage-4 La\({}_{2}\)CuO\({}_{4.11}\) and La\({}_{1.88}\)Sr\({}_{0.12}\)CuO\({}_{4}\). Phys. Rev. B66, 014524 (2002)CrossRefADSGoogle Scholar
  100. 100.
    H.E. Mohottala, B.O. Wells, J.I. Budnick, W.A. Hines, C. Niedermayer, L. Udby, C. Bernhard, A.R. Moodenbaugh, F.C. Chou, Phase separation in superoxygenated La\({}_{2-x}\)Sr\({}_{x}\)CuO\({}_{4+y}\). Nat. Mater. 5, 377–382 (2006)CrossRefADSGoogle Scholar
  101. 101.
    C. Bernhard, C.N. Wang, L. Nuccio, L. Schulz, O. Zaharko, J. Larsen, C. Aristizabal, M. Willis, A.J. Drew, G.D. Varma, T. Wolf, Ch. Niedermayer, Muon spin rotation study of magnetism and superconductivity in Ba(Fe\(_{1-x}\)Co\(_{x}\))\(_{2}\)As\(_{2}\) single crystals. Phys. Rev. B 86, 184509 (2012)CrossRefADSGoogle Scholar
  102. 102.
    C. J. Arguello, J. Munevar, T. Goko, E. Andrade, B.A. Frandsen, L. Liu, F.L. Ning, A.N. Pasupathy, E. Rosenthal, H. Micklitz, J. Aguero, E. Baggio-Saitovitch, R. dOrtenzio, T. Medina, T.J.S. Munsie, T.J. Williams, G.M. Luke, Pengcheng Dai, H.Q. Luo, X.Y. Lu, S. Carr, F. Ronning, E.D. Bauer, R.M. Fernandes, E. Uykur, S. Miyasaka, S. Tajima, M. Nakajima, S. Uchida, Y.J. Uemura, Multi-probe characterization of coexisting antiferromagnetic and superconducting orders in \(Ba(Fe, Ni)_{2} As_{2}\) near the phase boundary, submitted for publication (2013)Google Scholar
  103. 103.
    O.W. Dietrich, E.H. Graf, C.H. Huang, L. Passell, Neutron scattering by rotons in liquid Helium. Phys. Rev. A5, 1377–1391 (1972)CrossRefADSGoogle Scholar
  104. 104.
    C. Stock, C. Broholm, J. Hudis, H.J. Kang, C. Petrovic, Spin resonance in the d -wave superconductor CeCoIn\({}_{5}\). Phys. Rev. Lett. 100, 087001 (2008)CrossRefADSGoogle Scholar
  105. 105.
    O. Stockert, J. Arndt, E. Faulhaber, C. Geibel, H.S. Jeevan, S. Kirchner, M. Loewenhaupt, K. Schmalzl, W. Schmidt, Q. Si, F. Steglich, Magnetically driven superconductivity in CeCu\({}_{2}\)Si\({}_{2}\). Nat. Phys. 7, 119–124 (2011)CrossRefGoogle Scholar
  106. 106.
    M.M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G.O. Andreev, B.-J. Kim, S.J. Yun, A.V. Balatsky, M.B. Maple, F. Keilmann, H.-T. Kim, D.N. Basov, Mott transition in VO\({}_{2}\) revealed by Infrared spectroscopy and nano-imaging. Science 318, 1750 (2007)CrossRefADSGoogle Scholar
  107. 107.
    Y.J. Uemura, T. Goko, I.M. Gat-Malureanu, J.P. Carlo, P.L. Russo, A.T. Savici, A. Aczel, G.J. MacDougall, J.A. Rodriguez, G.M. Luke, S.R. Dunsiger, A. McCollam, J. Arai, Ch. Pfleiderer, P. Boni, K. Yoshimura, E. Baggio-Saitovitch, M.B. Fontes, J.J. Larrea, Y.V. Sushko, J. Sereni, Phase separation and suppression of critical dynamics at quantum phase transitions of MnSi and (Sr\({}_{1-x}\)Ca\({}_{x}\))RuO\({}_{3}\). Nat. Phys. 3, 29–35 (2007)CrossRefGoogle Scholar
  108. 108.
    Y.J. Uemura, A.A. Aczel, Y. Ajiro, J.P. Carlo, T. Goko, D.A. Goldfeld, A. Kitada, G.M. Luke, G.J. MacDougall, I.G. Mihailescu, J.A. Rodriguez, P.L. Russo, Y. Tsujimoto, C.R. Wiebe, T.J. Williams, T. Yamamoto, K. Yoshimura, H. Kageyama, \(\mu \)SR studies of the frustrated quasi-2d square-lattice spin system Cu(Cl, Br)La(Nb, Ta)\({}_{2}\)O\({}_{7}\): evolution from spin-gap to antiferromagnetic state. Phys. Rev. B 80, 174408 (2009)CrossRefADSGoogle Scholar
  109. 109.
  110. 110.
  111. 111.
  112. 112.
  113. 113.
    H. Chen, Y. Ren, Y. Qiu, W. Bao, R.H. Liu, G. Wu, T. Wu, Y.L. Xie, X.F. Wang, Q. Huang, X.H. Chen, Coexistence of the spin-density-wave and superconductivity in the (Ba, K)Fe\({}_{2}\)As\({}_{2}\). Europhys. Lett. 85, 17006 (2009)CrossRefADSGoogle Scholar
  114. 114.
    G. Knebel, D. Aoki, D. Braithwaite, B. Salce, J. Flouquet, Coexistence of antiferromagnetism and superconductivity in CeRhIn\({}_{5}\) under high pressure and magnetic field. Phys. Rev. B 74, 020501 (2006)CrossRefADSGoogle Scholar
  115. 115.
    M. Minakata, Y. Maeno, Magnetic ordering in Sr\(_{2}\)RuO\(_{4}\) induced by nonmagnetic impurities. Phys. Rev. B 63, 180504(R) (2001)CrossRefADSGoogle Scholar
  116. 116.
    S. Kunkemoller, A.A. Nugroho, Y. Sidis, M. Braden, Spin-density-wave ordering in Ca\({}_{0.5}\)Sr\({}_{1.5}\)RuO\({}_{4}\) studied by neutron scattering. Phys. Rev. B 89, 045119 (2014)CrossRefADSGoogle Scholar
  117. 117.
    S. Nakatsuji, Y. Maeno, Quasi-two-dimensional Mott transition system Ca\({}_{2-x}\)Sr\({}_{x}\)RuO\({}_{4}\). Phys. Rev. Lett. 84, 2666–2669 (2000)CrossRefADSGoogle Scholar
  118. 118.
    S. Nakatsuji, Y. Maeno, Switching of magnetic coupling by a structural symmetry change near the Mott transition in Ca\({}_{2-x}\)Sr\({}_{x}\)RuO\({}_{4}\). Phys. Rev. B62, 6458–6466 (2000)CrossRefADSGoogle Scholar
  119. 119.
    A.D. Christianson, E.A. Goremychkin, R. Osborn, S. Rosenkranz, M.D. Lumsden1, C.D. Malliakas, I.S. Todorov, H. Claus, D.Y. Chung, M.G. Kanatzidis, R.I. Bewley, T. Guidi, Unconventional superconductivity in Ba\({}_{0.6}\)K\({}_{0.}\) \({}_{4}\)Fe\({}_{2}\)As\({}_{2}\) from inelastic neutron scattering. Nature 456, 930–932 (2008)Google Scholar
  120. 120.
    D.G. Henshaw, A.D.B. Woods, Modes of atomic motions in liquid helium by inelastic scattering of neutrons. Phys. Rev. 121, 1266–1274 (1961)CrossRefADSGoogle Scholar
  121. 121.
    P. Bourges, B. Keimer, S. Pailhes, L.P. Regnault, Y. Sidis, C. Ulrich, The resonant magnetic mode: A common feature of high-T\(_{c}\) superconductors. Physica C424, 45–49 (2005)ADSGoogle Scholar
  122. 122.
    N.B. Christensen, D.F. McMorrow, H.M. Ronnow, B. Lake, S. Hayden, G. Aeppli, T.G. Perring, M. Mangkorntong, M. Nohara, H. Takagi, Universal dispersive excitations in the high-temperature superconductors. Phys. Rev. Lett. 93, 147002 (2004)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of PhysicsColumbia UniversityNew YorkUSA

Personalised recommendations