Advertisement

Molecular magnetism

  • Jürgen Schnack
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 645)

Abstract

Magnetic molecules are fascinating new substances with a wide variety of applications in physics, magneto-chemistry, biology, biomedicine and material sciences as well as in quantum computing. Each of the identical molecular units can contain as few as two and up to several dozens of paramagnetic ions whose interaction is rather well described by the Heisenberg model with isotropic nearest neighbor interaction sometimes augmented by anisotropy terms. Studying such finite spin systems focuses on qualitatively new physics caused by the finite size of the system. Among the findings discussed in this chapter are extensions of the theorems of Lieb, Schultz, and Mattis, the introduction of rotational bands as well as the discovery of giant magnetization jumps.

Keywords

Quantum Number Spin System Ground State Energy Total Spin Hamilton Operator 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Sessoli, D. Gatteschi, A. Caneschi, and M. A. Novak. Nature 365, 141 (1993).ADSCrossRefGoogle Scholar
  2. 2.
    D. Gatteschi, A. Caneschi, L. Pardi, and R. Sessoli, Science 265, 1054 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    D. Gatteschi, Adv. Mater. 6, 635 (1994).CrossRefGoogle Scholar
  4. 4.
    in Localized and Itinerant Molecular Magnetism: From Molecular Assemblies to the Devices, Vol. 321 of NATO Advanced Studies Institute, Series E: Applied Sciences, edited by E. Coronado, P. Delhaes, D. Gatteschi, and J. Miller (Kluwer Academic, Dordrecht, 1996).Google Scholar
  5. 5.
    A. Müller, F. Peters, M. Pope, and D. Gatteschi, Chem. Rev. 98, 239 (1998).CrossRefGoogle Scholar
  6. 6.
    A. Caneschi et al., J. Magn. Magn. Mater. 200, 182 (1999).ADSCrossRefGoogle Scholar
  7. 7.
    A. Müller et al., Angew. Chem. Int. Ed. 38, 3238 (1999).CrossRefGoogle Scholar
  8. 8.
    M. N. Leuenberger and D. Loss, Nature 410, 789 (2001).ADSCrossRefGoogle Scholar
  9. 9.
    X. Wang and P. Zanardi, Phys. Lett. A 301, 1 (2002).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    X. Wang, Phys. Rev. A 66, 034302 (2002).ADSCrossRefGoogle Scholar
  11. 11.
    P. Gütlich, A. Hauser, and H. Spiering, Angew. Chem. 106, 2109 (1994).CrossRefGoogle Scholar
  12. 12.
    A. Bencini and D. Gatteschi. Electron parametric resonance of exchange coupled systems (Springer, Berlin. Heidelberg. ADDRESS, 1990).CrossRefGoogle Scholar
  13. 13.
    C. Delfs et al. Inorg. Chem. 32, 3099 (1993).CrossRefGoogle Scholar
  14. 14.
    A. Caneschi et al., Inorg. Chem. 34, 4660 (1995).CrossRefGoogle Scholar
  15. 15.
    B. Pilawa et al., J. Magn. Magn. Mater. 177, 748 (1997).ADSGoogle Scholar
  16. 16.
    O. Waldmann et al., Inorg. Chem. 38, 5879 (1999).CrossRefGoogle Scholar
  17. 17.
    W. Heisenberg, Z. f. Phys. 49, 619 (1928).ADSCrossRefGoogle Scholar
  18. 18.
    K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).ADSCrossRefGoogle Scholar
  19. 19.
    R. Boča, Theoretical Foundations of Molecular Magnetism, Vol. 1 of Current Methods in Inorganic Chemistry (Elsevier, Amsterdam, 1999).Google Scholar
  20. 20.
    T. Lis, Acta Chrytallogr. B 36, 2042 (1980).CrossRefGoogle Scholar
  21. 21.
    L. Thomas et al. Nature 383, 145 (1996)ADSCrossRefGoogle Scholar
  22. 22.
    Z. H. Jang, A. Laselalfari, F. Borsa, and D. Gatteschi. Phys. Rev. Lett. 84, 2977 (2000).ADSCrossRefGoogle Scholar
  23. 23.
    Y. Furukawa et al. Phys. Rev. B 64, 104401 (2001).ADSCrossRefGoogle Scholar
  24. 24.
    L. Thomas and B. Barbara, J. Low Temp. Phys. 113, 1055 (1998).ADSCrossRefGoogle Scholar
  25. 25.
    N. Regnault et al., Phys. Rev. B 66, 054409 (2002).ADSCrossRefGoogle Scholar
  26. 26.
    G. Chaboussant et al., (2003), in preparationGoogle Scholar
  27. 27.
    C. A. Christmas et al., J. Am. Chem. Soc. 115, 12483 (1993).CrossRefGoogle Scholar
  28. 28.
    K. L. Taft et al., J. Am. Chem. Soc. 116, 823 (1994).CrossRefGoogle Scholar
  29. 29.
    A. Lascialfari, D. Gatteschi, F. Borsa, and A. Cornia. Phys. Rev. B 55, 14341 (1997)ADSCrossRefGoogle Scholar
  30. 30.
    A. Lascialfari, D. Gatteschi, F. Borsa, and A. Cornia, Phys. Rev. B 56, 8434 (1997).ADSCrossRefGoogle Scholar
  31. 31.
    M.-H. Julien et al., Phys. Rev. Lett. 83, 227 (1999).ADSCrossRefGoogle Scholar
  32. 32.
    G. L. Abbati et al., Inorg. Chim. Acta 297, 291 (2000).CrossRefGoogle Scholar
  33. 33.
    O. Waldmann et al., Inorg. Chem. 40, 2986 (2001).CrossRefGoogle Scholar
  34. 34.
    F. Meier and D. Loss. Phys. Rev. Lett. 86, 5373 (2001).ADSCrossRefGoogle Scholar
  35. 35.
    R. W. Saalfrank et al., Chem. Eur. J. 7, 2765 (2001).CrossRefGoogle Scholar
  36. 36.
    A. Müller et al., Chem. Phys. Chem. 2, 517 (2001).Google Scholar
  37. 37.
    M. Axenovich and M. Luban. Phys. Rev. B 63, 100407 (2001).ADSCrossRefGoogle Scholar
  38. 38.
    A. Müller et al., Angew. Chem. Int. Ed. 39, 1612 (2000).CrossRefGoogle Scholar
  39. 39.
    A. Müller et al., Solid State Sciences 2, 847 (2000).ADSCrossRefGoogle Scholar
  40. 40.
    A. Müller et al., Angew. Chem. Int. Ed. 41, 579 (2000).CrossRefGoogle Scholar
  41. 41.
    E. Ruiz, P. Alemany, S. Alvarez, and J. Cano. J. Am. Chem. Soc. 119, 1297 (1997).CrossRefGoogle Scholar
  42. 42.
    E. Ruiz, J. Cano, S. Alvarez, and P. Alemany, J. Am. Chem. Soc. 120, 11122 (1998).CrossRefGoogle Scholar
  43. 43.
    C. Calzado, J. Sanz, J. Malrieu, and F. Illas. Chem. Phys. Lett. 307, 102 (1999).ADSCrossRefGoogle Scholar
  44. 44.
    J. Kortus, C. S. Hellberg, and M. R. Pederson, Phys. Rev. Lett. 86, 3400 (2001).ADSCrossRefGoogle Scholar
  45. 45.
    M. R. Pederson, N. Bernstein, and J. Kortus, Phys. Rev. Lett. 89, 097202 (2002).ADSCrossRefGoogle Scholar
  46. 46.
    J. Kortus, T. Baruah, N. Bernstein, and M. R. Pederson, Phys. Rev. B 66, 092403 (2002).ADSCrossRefGoogle Scholar
  47. 47.
    H.-J. Schmidt, J. Schnack, and M. Luban, Phys. Rev. B 64, 224415 (2001).ADSCrossRefGoogle Scholar
  48. 48.
    J. Schuack, M. Luban, and R. Modler. Europhys. Lett. 56, 863 (2001).ADSCrossRefGoogle Scholar
  49. 49.
    W. Wernsdorfer, K. Hasselbach, D. Mailly, and B. Barbara, J. Magn. Magn. Mater. 145, 33 (1995).ADSCrossRefGoogle Scholar
  50. 50.
    W. Wernsdorfer, Adv. Chem. Phys. 118, 99 (2001).Google Scholar
  51. 51.
    T. Moriya, Prog. Theor. Phys. 16, 23 (1956).ADSCrossRefGoogle Scholar
  52. 52.
    A. Lascialfari et al., Physica B 289, 110 (2000).ADSCrossRefGoogle Scholar
  53. 53.
    Z. Sahnan et al., Phys. Rev. B 65, 132403 (2002).ADSCrossRefGoogle Scholar
  54. 54.
    E. Balear and S. Lovesey. Theory of magnelic neutron and photon scattering (Clarendon Oxford, 1989).Google Scholar
  55. 55.
    L. Mirebean et al., Phys. Rev. Lett. 83, 628 (1999).ADSCrossRefGoogle Scholar
  56. 56.
    H. Andres et al., Chem. Eur. J. 8, 4867 (2002).CrossRefGoogle Scholar
  57. 57.
    A. Caneschi et al., J. Phys. Condes. Matter 11, 3395 (1999).ADSCrossRefGoogle Scholar
  58. 58.
    S. G. Chiuzbaian et al., Surf. Sci. 482, 1272 (2001).ADSCrossRefGoogle Scholar
  59. 59.
    J. S. Kang et al., J. Korean Phys. Soc. 40, L402 (2002).Google Scholar
  60. 60.
    A. Gomes et al., Phys. Rev. B 57, 5021 (1998).ADSCrossRefGoogle Scholar
  61. 61.
    J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo. Phys. Rev. Lett. 76, 3830 (1996).ADSCrossRefGoogle Scholar
  62. 62.
    J. Tejada, J. M. Hernandez, and E. del Barco, J. Magn. Magn. Mater. 197, 552 (1999).ADSCrossRefGoogle Scholar
  63. 63.
    J. R. Friedman et al., Nature 406, 43 (2000).ADSCrossRefGoogle Scholar
  64. 64.
    D. Gatteschi and R. Sessoli, Angew. Chem. Int. Edit. 42, 268 (2003).CrossRefGoogle Scholar
  65. 65.
    F. Lionti et al., J. Appl. Phys. 81, 4608 (1997).ADSCrossRefGoogle Scholar
  66. 66.
    I. Chiorescu et al., Phys. Rev. Lett. 85, 4807 (2000).ADSCrossRefGoogle Scholar
  67. 67.
    M. Affronte et al., Phys. Rev. B 66. art. no. (2002).Google Scholar
  68. 68.
    W. Wernsdorfer et al., Phys. Rev. Lett. 89, 197201 (2002).ADSCrossRefGoogle Scholar
  69. 69.
    O. Waldmann, Phys. Rev. B 61, 6138 (2000).ADSCrossRefGoogle Scholar
  70. 70.
    K. Bärwinkel, H.-J. Schmidt, and J. Schnack, J. Magn. Magn. Mater. 212, 240 (2000).ADSCrossRefGoogle Scholar
  71. 71.
    W. Feller. An introduction to probability theory and its applications, 3 ed. (John Wiley & Sons, New York, 1968), Vol. 1.zbMATHGoogle Scholar
  72. 72.
    D. Kouzoudis, J. Magn. Magn. Mater. 173, 259 (1997).ADSCrossRefGoogle Scholar
  73. 73.
    D. Konzoudis, J. Magn. Magn. Mater. 189, 366 (1998).ADSCrossRefGoogle Scholar
  74. 74.
    J. Bonner and M. Fisher. Phys. Rev. 135, A640 (1964).ADSCrossRefGoogle Scholar
  75. 75.
    R. Botet and R. Jullien, Phys. Rev. B 27, 631 (1983).ADSCrossRefGoogle Scholar
  76. 76.
    K. Fabricius, U. Löw, K.-H. Mütter, and P. Ueberholz, Phys. Rev. B 44, 7476 (1991).ADSCrossRefGoogle Scholar
  77. 77.
    E. Manousakis, Rev. Mod. Phys. 63, 1 (1991).ADSCrossRefGoogle Scholar
  78. 78.
    O. Golinelli, T. Jolicoeur, and R. Lacaze. Phys. Rev. B 50, 3037 (1994).ADSCrossRefGoogle Scholar
  79. 79.
    K. Fabricius, U. Löw, and J. Stolze, Phys. Rev. B 55, 5833 (1997).ADSCrossRefGoogle Scholar
  80. 80.
    C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255 (1950).MathSciNetCrossRefGoogle Scholar
  81. 81.
    J. K. Cullum and R. A. Willoughby, Lánczos Algorithms for Large Symmetric Eigenvalue Computations (Birkhäuser. Boston, 1985), Vol. I.zbMATHGoogle Scholar
  82. 82.
    Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, edited by Z. Bai et al. (Society for Industrial & Applied Mathematics, Philadelphia, 2000).zbMATHGoogle Scholar
  83. 83.
    S. R. White, Phys. Rev. B 48, 10345 (1993).ADSCrossRefGoogle Scholar
  84. 84.
    Density-Matrix Renormalization, edited by I. Peschel, X. Wang, M. Kaulke, and K. Hallberg (Springer, Berlin, 1999).Google Scholar
  85. 85.
    U. Schollwöck, Rev. Mod. Phys. (2004).Google Scholar
  86. 86.
    S. R. White and D. Huse, Phys. Rev. B 48, 3844 (1993).ADSCrossRefGoogle Scholar
  87. 87.
    T. Xiang, Phys. Rev. B 58, 9142 (1998).ADSCrossRefGoogle Scholar
  88. 88.
    M. Exler and J. Schnack, Phys. Rev. B 67, 094440 (2003).ADSCrossRefGoogle Scholar
  89. 89.
    J. Schnack, H.-J. Schmidt, J. Richter, and J. Schulenburg, Eur. Phys. J. B 24, 475 (2001).ADSCrossRefGoogle Scholar
  90. 90.
    J. M. Radcliff, J. Phys. A: Gen. Phys. 4, 313 (1971).ADSCrossRefGoogle Scholar
  91. 91.
    A. Honecker, F. Meier, D. Loss, and B. Normand. Eur. Phys. J. B 27, 487 (2002).ADSCrossRefGoogle Scholar
  92. 92.
    W. Marshall, Proc. Royal. Soc. A (London) 232, 48 (1955).ADSCrossRefGoogle Scholar
  93. 93.
    E. H. Lieb, T. Schultz, and D. C. Mattis, Ann. Phys. (N. Y.) 16, 407 (1961).ADSMathSciNetCrossRefGoogle Scholar
  94. 94.
    E. H. Lieb and D. C. Mattis, J. Math. Phys. 3, 749 (1962).ADSCrossRefGoogle Scholar
  95. 95.
    M. Karbach. Ph.D. thesis. Bergische Universität—Gesamthochschule Wuppertal. 1994.Google Scholar
  96. 96.
    K. Bärwinkel, H.-J. Schmidt, and J. Schnack, J. Magn. Magn. Mater 220, 227 (2000).ADSCrossRefGoogle Scholar
  97. 97.
    J. Schnack, Phys. Rev. B 62, 14855 (2000).ADSCrossRefGoogle Scholar
  98. 98.
    K. Bärwinkel, P. Hage, H.-J. Schmidt, and J. Schnack, Phys. Rev. B 68, 054422 (2003).ADSCrossRefGoogle Scholar
  99. 99.
    F. Haldane, Phys. Lett. A 93, 464 (1983).ADSMathSciNetCrossRefGoogle Scholar
  100. 100.
    F. Haldane, Phys. Rev. Lett 50, 1153 (1983).ADSMathSciNetCrossRefGoogle Scholar
  101. 101.
    J. Schnack and M. Luban, Phys. Rev. B 63, 014418 (2001).ADSCrossRefGoogle Scholar
  102. 102.
    B. Beldmann, Phys. Rev. B 65, 024424 (2002).ADSGoogle Scholar
  103. 103.
    B. Bernu, P. Lecheminam, C. Lhuillier, and L. Pierre, Phys. Rev. B 50, 10048 (1994).ADSCrossRefGoogle Scholar
  104. 104.
    M. Gross, E. Sánchez-Velasco, and E. D. Siggia, Phys. Rev. B 40, 11328 (1989).ADSCrossRefGoogle Scholar
  105. 105.
    J. Richter, Phys. Rev. B 47, 5794 (1993).ADSCrossRefGoogle Scholar
  106. 106.
    H.-J. Schmidt and M. Luban, J. Phys. A: Math. Gen. 36, 6351 (2003).MathSciNetCrossRefGoogle Scholar
  107. 107.
    J. Schulenburg et al. Phys. Rev. Lett. 88, 167207 (2002).ADSCrossRefGoogle Scholar
  108. 108.
    H.-J. Schmidt, J. Phys. A: Math. Gen. 35, 6545 (2002).ADSCrossRefGoogle Scholar
  109. 109.
    E. H. Lieb, Commun. Math. Phys. 31, 327 (1973).ADSMathSciNetCrossRefGoogle Scholar
  110. 110.
    F. Berezin, Commun. Math. Phys. 40, 153 (1975).ADSMathSciNetCrossRefGoogle Scholar
  111. 111.
    H.-J. Schmidt, J. Schnack, and M. Luban, Europhys. Lett. 55, 105 (2001).ADSCrossRefGoogle Scholar
  112. 112.
    K. Bärwinkel, H.-J. Schmidt, and J. Schnack, Eur. Phys. J. B. 33, 285 (2003).ADSCrossRefGoogle Scholar
  113. 113.
    I. Affleck and E. H. Lieb, Lett. Math. Phys. 12, 57 (1986).ADSMathSciNetCrossRefGoogle Scholar
  114. 114.
    P. Lancaster, Theory of Matrices (Academic Press, New York and London, 1969).zbMATHGoogle Scholar
  115. 115.
    B. Barbara et al., J. Phys. Soc. Jpn. 69, 383 (2000).Google Scholar
  116. 116.
    P. Politi, A. Rettori, F. Hartmann-Bontron, and J. Villain, Phys. Rev. Lett. 75, 537 (1995).ADSCrossRefGoogle Scholar
  117. 117.
    A. L. Burin, N. V. Prokofev, and P. C. E. Stamp, Phys. Rev. Lett. 76, 3040 (1996).ADSCrossRefGoogle Scholar
  118. 118.
    P. Politi, A. Rettori, F. Hartmann-Boutron, and J. Villain, Phys. Rev. Lett. 76, 3041 (1996).ADSCrossRefGoogle Scholar
  119. 119.
    A. Garg, Phys. Rev. B 64, 094413 (2001).ADSCrossRefGoogle Scholar
  120. 120.
    A. Garg, Phys. Rev. B 64, 094414 (2001).ADSCrossRefGoogle Scholar
  121. 121.
    C. S. Park and A. Garg, Phys. Rev. B 65, 064411 (2002).ADSCrossRefGoogle Scholar
  122. 122.
    H. A. De Raedt et al., J. Magn. Magn. Mater. 246, 392 (2002).ADSCrossRefGoogle Scholar
  123. 123.
    O. Waldmann, Europhys. Lett. 60, 302 (2002).ADSMathSciNetCrossRefGoogle Scholar
  124. 124.
    L. D. Landau, Phys. Z. Sowjetunion 2, 46 (1932).Google Scholar
  125. 125.
    C. Zener, Proc. R. Soc. London. Ser. A 137, 696 (1932).ADSCrossRefGoogle Scholar
  126. 126.
    E. C. G. Stückelberg, Helv. Phys. Acta 5, 369 (1932).Google Scholar
  127. 127.
    H. D. Raedt et al., Phys. Rev. B. 56, 11761 (1997).ADSCrossRefGoogle Scholar
  128. 128.
    W. Wernsdorfer et al., J. Appl. Phys. 87, 5481 (2000).ADSCrossRefGoogle Scholar
  129. 129.
    W. Wernsdorfer, N. Aliaga-Alcalde, D. N. Hendrickson, and G. Christon, Nature 416, 406 (2002).ADSCrossRefGoogle Scholar
  130. 130.
    R. Schenker et al., Chem. Phys. Lett. 358, 413 (2002).ADSCrossRefGoogle Scholar
  131. 131.
    O. Waldmann et al., Phys. Rev. Lett. 89, 246401 (2002).ADSCrossRefGoogle Scholar
  132. 132.
    A. J. Leggett et al., Rev. Mod. Phys. 59, 1 (1987).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Jürgen Schnack
    • 1
  1. 1.Dept. of PhysicsUniversity of OsnabrückOsnabrückGermany

Personalised recommendations