Quantum Oscillation Measurements Applied to Strongly Correlated Electron Systems

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


The de Haas-van Alphen effect and related quantum oscillation measurements are powerful tools for studying the behaviour of electron quasiparticles in conducting strongly correlated electron systems. Using them, one can: measure the size and shape of Fermi surfaces; determine quasiparticle effective masses on a Fermi-surface-specific basis; determine mean-free paths on a Fermi-surface-specific basis; and obtain information about quasiparticle g-factors. This chapter first gives an outline of the theory of quantum oscillations, and then reviews experimental methods, focusing on aspects that are of particular relevance to strongly correlated electron systems. The chapter concludes by describing, as a ‘case study’, quantum oscillation measurements on the \(p\)-wave superconductor Sr\(_2\)RuO\(_4\), a material that is of great current interest, and that illustrates many aspects of quantum oscillation measurements that are applicable across a broad range of strongly correlated electron systems.


Fermi Surface Landau Level Quantum Oscillation Correlate Electron System Mass Enhancement 
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  1. 1.
    M.M. Altarawneh, N. Harrison, S.E. Sebastian, L. Balicas, P.H. Tobash, J.D. Thompson, F. Ronning, E.D. Bauer, Sequential spin polarization of the Fermi surface pockets in URu\(_2\)Si\(_2\) and its implications for the hidden order. Phys. Rev. Lett. 106, 146403 (2011)CrossRefADSGoogle Scholar
  2. 2.
    H. Aoki, S. Uji, A.K. Albessard, K. Motoki, H. Ikezawa, T. Ebihara, R. Settai, Y. Onuki, Transition of \(f\)-electron nature from itinerant to localized - metamagnetic transition in CeRu\(_2\)Si\(_2\) studied via the de Haas-van Alphen effect. Phy. Rev. Lett. 71, 2110 (1993)CrossRefADSGoogle Scholar
  3. 3.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt, Reinhart and Winston, 1976)Google Scholar
  4. 4.
    A.F. Bangura, J.D. Fletcher, A. Carrington, J. Levallois, M. Nardone, B. Vignolle, P.J. Heard, N. Doiron-Leyraud, D. LeBoef, L. Taillefer, S. Adachi, C. Proust, N.E. Hussey, Small Fermi surface pockets in underdoped high temperature superconductors: observation of Shubnikov-de Haas oscillations in YBa\(_2\)Cu\(_4\)O\(_8\). Phys. Rev. Lett. 100, 047004 (2008)CrossRefADSGoogle Scholar
  5. 5.
    K. Behnia, M.A. Measson, Y. Kopelevich, Oscillating Nernst-Ettingshausen effect in bismuth across the quantum limit. Phys. Rev. Lett. 98, 166602 (2007)CrossRefADSGoogle Scholar
  6. 6.
    C. Bergemann, S.R. Julian, A.P. Mackenzie, S. NishiZaki, Y. Maeno, Detailed topography of the Fermi surface of Sr\(_2\)RuO\(_4\). Phys. Rev. Lett. 84, 2662–2665 (2000)CrossRefADSGoogle Scholar
  7. 7.
    C. Bergemann, A.P. Mackenzie, S.R. Julian, D. Forsythe, E. Ohmichi, Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr\(_2\)RuO\(_4\). Adv. Phys. 52, 639–725 (2003)CrossRefADSGoogle Scholar
  8. 8.
    P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2K: An Augmented PlaneWave \(+\) Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001)Google Scholar
  9. 9.
    YuA Bychkov, L.P. Gor’kov, Quantum oscillations of the thermodynamic quantities of a metal in a magnetic field according to the Fermi-liquid model. JETP 14, 1132 (1962)Google Scholar
  10. 10.
    A. Carrington, Quantum oscillation studies of the Fermi surface of iron-pnictide superconductors. Rep. Prog. Phys. 74, 124507 (2011)CrossRefADSGoogle Scholar
  11. 11.
    R.G. Chambers, Wave function of a Bloch electron in a magnetic field. Proc. Phys. Soc. 89, 695 (1966)CrossRefADSGoogle Scholar
  12. 12.
    T. Coffey, Z. Bayindir, J.F. DeCrolis, G. Esper, C.C. Agosta, Measuring radio frequency properties of materials in pulsed magnetic fields with a tunnel diode oscillator. Rev. Sci. Inst. 71, 4600 (2000)CrossRefADSGoogle Scholar
  13. 13.
    A. Damascelli, D.H. Lu, K.M. Shen, N.P. Armitage, F. Ronning, D.L. Feng, C. Kim, Z.X. Shen, T. Kimura, Y. Tokura, Z.Q. Mao, Y. Maeno, Fermi surface, surface states, and surface reconstruction in Sr\(_2\)RuO\(_4\). Phys. Rev. Lett. 84, 5194–5197 (2000)CrossRefADSGoogle Scholar
  14. 14.
    W.J. de Haas, P.M. van Alphen, The dependence of the susceptibility of diamagnetic metals upon the field. Proc. Netherlands Roy. Acad. Sci. 33, 1106 (1930)zbMATHGoogle Scholar
  15. 15.
    N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J. Levallois, J.B. Bonnemaison, R.X. Liang, D.A. Bonn, W.N. Hardy, L. Taillefer, Quantum oscillations and the Fermi surface in an underdoped high-T-c superconductor. Nature 447, 565–568 (2007)CrossRefADSGoogle Scholar
  16. 16.
    T. Ebihara, N. Harrison, M. Jaime, S. Uji, J.C. Lashley, Emergent fluctuation hot spots on the Fermi surface of CeIn\(_3\) in strong magnetic fields. Phys. Rev. Lett. 93, 246401 (2004)CrossRefADSGoogle Scholar
  17. 17.
    M. Endo, N. Kimura, H. Aoki, T. Terashima, S. Uji, T. Matsumoto, T. Ebihara, Evolution of spin and field dependences of the effective mass with pressure in CeIn\(_3\). Phys. Rev. Lett. 93, 247003 (2004)CrossRefADSGoogle Scholar
  18. 18.
    S. Engelsberg, G. Simpson, Influence of electron-phonon interactions on de Haas-van Alphen effects. Phys. Rev. B 2, 1657 (1970)CrossRefADSGoogle Scholar
  19. 19.
    D. Forsythe, S.R. Julian, C. Bergemann, E. Pugh, M.J. Steiner, P.L. Alireza, G.J. McMullan, F. Nakamura, R.K.W. Haselwimmer, I.R. Walker, S.S. Saxena, G.G. Lonzarich, A.P. Mackenzie, Z.Q. Mao, Y. Maeno, Evolution of Fermi-liquid interactions in Sr\(_2\)RuO\(_4\) under pressure. Phys. Rev. Lett. 89, 166402 (2002)CrossRefADSGoogle Scholar
  20. 20.
    R.G. Goodrich, N. Harrison, Z. Fisk, Fermi surface changes across the Néel phase boundary of NdB\(_6\). Phys. Rev. Lett. 97, 146404 (2006)CrossRefADSGoogle Scholar
  21. 21.
    J.E. Graebner, E.S. Greiner, W.D. Ryden, Magnetothermal oscillations in RuO\(_2\), OsO\(_2\) and IrO\(_2\). Phys. Rev. B 13, 2426–2432 (1976)CrossRefADSGoogle Scholar
  22. 22.
    D.E. Graf, R.L. Stillwell, K.M. Purcell, S.W. Tozer, Nonmetallic gasket and miniature plastic turnbuckle diamond anvil cell for pulsed magnetic field studies at cryogenic temperatures. High Pressure Res. 31, 533 (2011)CrossRefADSGoogle Scholar
  23. 23.
    T. Helm, M.V. Kartsovnik, M. Bartkowiak, M. Bittner, M. Lambacher, A. Erb, J. Wosnitza, R. Gross, Evolution of the Fermi surface of the electron-doped high-temperature superconductor Nd\(_{2-x}\)Ce\(_x\)CuO\(_4\) revealed by Shubnikov-de Haas oscillations. Phys. Rev. Lett. 103, 157002 (2009)CrossRefADSGoogle Scholar
  24. 24.
    R.J. Higgins, D.H. Lowndes, Electrons at the Fermi surface, in Waveshape Analysis in the dHvA Effect, ed. by M. Springford (Cambridge University Press, Cambridge, 1980)Google Scholar
  25. 25.
    N.E. Hussey, A.P. Mackenzie, J.R. Cooper, S. Nishizaki, Y. Maeno, T. Fujita, Normal state magnetoresistance of Sr\(_2\)RuO\(_4\). Phys. Rev. B 57, 5505 (1998)CrossRefADSGoogle Scholar
  26. 26.
    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 (1997)CrossRefADSGoogle Scholar
  27. 27.
    C. Kallin, Chiral p-wave order in Sr\(_2\)RuO\(_4\). Rep. Prog. Phys. 75, 042501 (2012)CrossRefADSGoogle Scholar
  28. 28.
    G. Knebel, R. Boursier, E. Hassinger, G. Lapertot, P.G. Nicklowitz, A. Pourret, B. Salce, J.P. Sanchez, I. Sheikin, P. Ponville, H. Harima, J. Flouquet, Localization of 4f State in YbRh\(_2\)Si\(_2\) under magnetic field and high pressure: comparison with CeRh\(_2\)Si\(_2\). J. Phys. Soc. Jpn. 75, 114709 (2006)CrossRefADSGoogle Scholar
  29. 29.
    L. Landau, Diamagnetism of metals. Z. Phys. 64, 629 (1930)CrossRefzbMATHADSGoogle Scholar
  30. 30.
    L.D. Landau, E.M. Lifshitz, Motion in a magnetic field, Quantum Mechanics, Course of Theoretical Physics (Pergamon Press, UK, 1977), pp. 456–461Google Scholar
  31. 31.
    I.M. Lifshitz, L.M. Kosevich, On the theory of the Shubnikov-de Haas effect. Soviet Physics JETP 2, 636–645 (1956)Google Scholar
  32. 32.
    G.G. Lonzarich, Magnetic oscillations and the quasiparticle bands of heavy electron systems. J. Magn. Magn. Mater. 76&77, 1–10 (1988)CrossRefGoogle Scholar
  33. 33.
    A.P. Mackenzie, N.E. Hussey, A.J. Diver, S.R. Julian, Y. Maeno, S. Nishizaki, T. Fujita, Hall effect in the two-dimensional metal Sr\(_2\)RuO\(_4\). Phys. Rev. B 54, 7425–7429 (1996)CrossRefADSGoogle Scholar
  34. 34.
    A.P. Mackenzie, S. Ikeda, Y. Maeno, T. Fujita, S.R. Julian, G.G. Lonzarich, The Fermi surface topography of Sr\(_2\)RuO\(_4\). J. Phys. Soc. Jpn. 67, 385 (1998)CrossRefADSGoogle Scholar
  35. 35.
    A.P. Mackenzie, S.R. Julian, A.J. Diver, G.J. McMullan, M.P. Ray, G.G. Lonzarich, Y. Maeno, S. Nishizaki, T. Fujita, Quantum oscillations in the layered perovskite superconductor Sr\(_2\)RuO\(_4\). Phys. Rev. Lett. 76, 3786 (1996)CrossRefADSGoogle Scholar
  36. 36.
    A.P. Mackenzie, Y. Maeno, Superconductivity of Sr\(_2\)RuO\(_4\) and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003)CrossRefADSGoogle Scholar
  37. 37.
    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 (1995)CrossRefADSGoogle Scholar
  38. 38.
    Y. Maeno, K. Yoshida, H. Hashimoto, S. Nishizaki, S. Ikda, M. Nohara, T. Fujita, A.P. Mackenzie, N.E. Hussey, J.G. Bednorz, F. Lichtenberg, Two-dimensional Fermi liquid behaviour of the superconductor Sr\(_2\)RuO\(_4\). J. Phys. Soc. Jpn. 66, 1405 (1997)CrossRefADSGoogle Scholar
  39. 39.
    S.M. Markus, S.R. Butler, Measurement of de Haas-van Alphen effect in rutile structure RuO\(_2\). Phys. Lett. A 26A, 518–519 (1968)CrossRefADSGoogle Scholar
  40. 40.
    A. McCollam, R. Daou, S.R. Julian, C. Bergemann, J. Flouquet, D. Aoki, Spin-dependent masses and field-induced quantum critical points. Physica B 359, 1–8 (2005)CrossRefADSGoogle Scholar
  41. 41.
    A. McCollam, S.R. Julian, P.M.C. Rourke, D. Aoki, J. Flouquet, Anomalous de Haas-van Alphen oscillations in CeCoIn\(_5\). Phys. Rev. Lett. 94, 186401 (2005)CrossRefADSGoogle Scholar
  42. 42.
    A. McCollam, J.S. Xia, J. Flouquet, D. Aoki, S.R. Julian, De Haas-van Alphen effect in heavy fermion compounds - effective mass and non-Fermi-liquid behaviour. Physica B 403, 717–720 (2008)CrossRefADSGoogle Scholar
  43. 43.
    G.J. McMullan, M.P. Ray, R.J. Needs, Comparison of the calculated and observed Fermi surfaces of Sr\(_2\)RuO\(_4\). Physica B 223–24, 529–531 (1996)CrossRefGoogle Scholar
  44. 44.
    G.J. McMullan, P.M.C. Rourke, M.R. Norman, A.D. Huxley, N. Doiron-Leyraud, J. Flouquet, G.G. Lonzarich, A. McCollam, S.R. Julian, The Fermi surface and f-valence electron count of UPt\(_3\). New J. Phys. 10, 053029 (2008)CrossRefADSGoogle Scholar
  45. 45.
    H. Ohkuni, Y. Inada, Y. Tokiwa, K. Sakurai, R. Settai, T. Honma, Y. Haga, E. Yamamoto, Y. Onuki, H. Yamagami, S. Takahashi, T. Yanagisawa, Fermi surface properties and de Haas-van Alphen oscillation in both the normal and superconducting mixed states of URu\(_2\)Si\(_2\). Phil. Mag. B 79, 1045–1077 (1999)ADSGoogle Scholar
  46. 46.
    E. Ohmichi, Y. Maeno, S. Nagai, Z.Q. Mao, M.A. Tanatar, T. Ishiguro, Magnetoresistance of Sr\(_2\)RuO\(_4\) under high magnetic fields parallel to the conducting plane. Phys. Rev. B 61, 7101 (2000)CrossRefADSGoogle Scholar
  47. 47.
    E. Ohmichi, T. Osada, Torque magnetometry in pulsed magnetic fields with use of a commercial microcantilever. Rev. Sci. Inst. 73, 3022 (1999)CrossRefADSGoogle Scholar
  48. 48.
    B.J. Ramshaw, B. Vignolle, J. Day, R.X. Liang, W.N. Hardy, C. Proust, D.A. Bonn, Angle dependence of quantum oscillations in YBa\(_2\)Cu\(_3\)O\(_{6.59}\) shows free-spin behaviour of quasiparticles. Nat. Phys. 7, 234–238 (2011)CrossRefGoogle Scholar
  49. 49.
    J.J. Randall, R. Ward, The preparation of some ternary oxides of the platinum metals. J. Am. Chem. Soc. 81, 2629–2631 (1959)CrossRefGoogle Scholar
  50. 50.
    P.H.P. Reinders, M. Springford, de Haas-van Alphen effect in the Kondo lattice CeAl\(_2\). J. Magn. Magn. Mater. 79, 295–302 (1989)CrossRefADSGoogle Scholar
  51. 51.
    T.M. Rice, M. Sigrist, Sr\(_2\)RuO\(_4\): and electronic analogue of \(^3\)He? J. Phys.: Condens. Matter 7, L643–L648 (1995)ADSGoogle Scholar
  52. 52.
    S.C. Riggs, O. Vafek, J.B. Kemper, J.B. Betts, A. Migliori, F.F. Balakirev, W.N. Hardy, R.X. Liang, D.A. Bonn, G.S. Boebinger, Heat capacity through the magnetic-field-induced resistive transition in an underdoped high-temperature superconductor. Nature Phys. 7, 332–335 (2011)CrossRefADSGoogle Scholar
  53. 53.
    P.M.C. Rourke, A.F. Bangura, T.M. Benseman, M. Matusiak, J.R. Cooper, A. Carrington, N.E. Hussey, A detailed de Haas-van Alphen effect study of the overdoped cuprate Tl\(_2\)Ba\(_2\)CuO\(_{6+\delta }\). New J. Phys. 12, 105009 (2010)CrossRefADSGoogle Scholar
  54. 54.
    P.M.C. Rourke, S.R. Julian, Numerical extraction of de Haas-van Alphen frequencies from calculated band energies. Comput. Phys. Commun. 183, 324–332 (2012)CrossRefADSGoogle Scholar
  55. 55.
    I. Sheikin, A. Groger, S. Raymond, D. Jaccard, D. Aoki, H. Harima, J. Flouquet, High magnetic field study of CePd\(_2\)Si\(_2\). Phys. Rev. B 67, 094420 (2003)CrossRefADSGoogle Scholar
  56. 56.
    H. Shishido, R. Settai, H. Harima, Y. Onuki, A drastic change of the Fermi surface at a critical pressure in CeRhIn\(_5\): dHvA study under pressure. J. Phys. Soc. Jpn. 74, 1103–1106 (2005)CrossRefADSGoogle Scholar
  57. 57.
    D.S. Shoenberg, Quantum Oscillations in Metals (Cambridge University Press, Cambridge, 1984)CrossRefGoogle Scholar
  58. 58.
    F. Steglich, J. Aaarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Schafer, Superconductivity in the presence of strong Pauli paramagnetism - CeCu\(_2\)Si\(_2\). Phys. Rev. Lett. 43, 1892–1896 (1979)CrossRefADSGoogle Scholar
  59. 59.
    L. Taillefer, G.G. Lonzarich, Heavy-fermion quasiparticles in UPt\(_3\). Phys. Rev. Lett. 60, 1570–1573 (1987)CrossRefADSGoogle Scholar
  60. 60.
    M. Takashita, H. Aoki, S. Terashima, S. Uji, K. Maezawa, R. Settai, Y. Onuki, dHvA Effect study of metamagnetic transition in CeRu\(_2\)Si\(_2\) II - The state above the metamagnetic transition. J. Phys. Soc. Jpn. 65, 515 (1996)CrossRefADSGoogle Scholar
  61. 61.
    B. Vignolle, A. Carrington, R.A. Cooper, M.M.J. French, A.P. Mackenzie, C. Jaudet, D. Vignolles, C. Proust, N.E. Hussey, Quantum oscillations in an overdoped high-T\(_c\) superconductor. Nature 455, 952–955 (2008)CrossRefADSGoogle Scholar
  62. 62.
    A. Wasserman, M. Springford, The influence of many-body interactions on the de Haas-van Alphen effect. Adv. Phys. 45, 471 (1996)CrossRefADSGoogle Scholar
  63. 63.
    S.A.J. Wiegers, A.S. van Steenbergen, M.E. Jeuken, M. Bravin, P.E. Wolf, G. Remenyi, J.A.A.J. Perenboom, J.C. Maan, A sensitive and versatile torque magnetometer for use in high magnetic fields. Rev. Sci. Inst. 69, 2369 (1998)CrossRefADSGoogle Scholar
  64. 64.
    K. Yamaji, On the angle dependence of the magnetoresistance in quasi-2-dimensional organic superconductors. J. Phys. Soc. Jpn. 58, 1520–1523 (1989)CrossRefADSGoogle Scholar
  65. 65.
    E.A. Yelland, J. Singleton, C.H. Milke, N. Harrison, F.F. Balakirev, B. Dabrowski, J.R. Cooper, Quantum oscillations in the underdoped cuprate YBa\(_2\)Cu\(_4\)O\(_8\). Phys. Rev. Lett. 100, 047003 (2008)CrossRefADSGoogle Scholar
  66. 66.
    Y.B. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005)CrossRefADSGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of TorontoTorontoCanada

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