Skip to main content
SpringerLink
Log in

Magnetic Anisotropy of Heterostructures

  • Chapter
Magnetic Heterostructures

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 227))

Abstract

The chapter provides a detailed introduction to magnetic anisotropy of ferromagnetic ultrathin films and its analysis by ferromagnetic resonance on a tutorial level. While the microscopic origins of the magnetic anisotropy as well as recent developments in its theoretical description are shortly discussed, emphasis is put on a phenomenological description using the free energy of the system together with its symmetries. The formalism is used to describe ferromagnetic resonance experiments which present an extremely sensitive method to experimentally investigate magnetic anisotropy in thin film heterostructures. Expressions for the free energy and the resonance equations are derived for the most widely used crystal symmetries such as cubic, tetragonal and hexagonal. The general equations are illustrated by giving selected examples of current research on thin metallic films on different kinds of substrates (MgO, GaAs and Cu).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.M. Stocks, M. Eisenbach, B. Újfalussy, B. Lazarovits, L. Szunyogh, P. Weinberger: Progress in Materials Science 52, 371 (2007)

    Google Scholar 

  2. H.J. Richter: J. Phys. D: Appl. Phys. 40, R149 (2007)

    ADS  Google Scholar 

  3. U. Gradmann: Magnetism in ultrathin transition metal films. In: Handbook of Magnetic Materials, Vol. 7, ed. by K.H.J. Buschow (Elsevier Science Publishers B.V. 1993)

    Google Scholar 

  4. B. Heinrich, J.F. Cochran: Adv. Phys. 42, 523 (1993)

    ADS  Google Scholar 

  5. M. Farle: Rep. Prog. Phys. 61, 755 (1998)

    ADS  Google Scholar 

  6. J.A.C. Bland, B. Heinrich (Eds.): Ultrathin magnetic structures I – An Introduction to the Electronic, Magnetic and Structural Properties, 2nd edn (Springer, Berlin Heidelberg New York 2005)

    Google Scholar 

  7. B. Heinrich, J.A.C. Bland (Eds.): Ultrathin magnetic structures II – Measurement Techniques and Novel Magnetic Properties, 2nd edn (Springer, Berlin Heidelberg New York 2005)

    Google Scholar 

  8. J.A.C. Bland, B. Heinrich (Eds.): Ultrathin magnetic structures III – Fundamentals of Nanomagnetism, 2nd edn (Springer, Berlin Heidelberg New York 2005)

    Google Scholar 

  9. B. Hillebrands, K. Ounadjela (Eds.): Spin Dynamics in confined magnetic Structures I, Topics in Applied Physics 83 (Springer, Berlin Heidelberg New York 2003)

    Google Scholar 

  10. B. Hillebrands, K. Ounadjela (Eds.): Spin Dynamics in confined magnetic Structures II, Topics in Applied Physics 87 (Springer, Berlin Heidelberg New York 2003)

    Google Scholar 

  11. B. Hillebrands, K. Ounadjela (Eds.): Spin Dynamics in confined magnetic Structures III, Topics in Applied Physics 101 (Springer, Berlin Heidelberg New York 2003)

    Google Scholar 

  12. K. Baberschke, M. Donath, W. Nolting (Eds.): Band-Ferromagnetism, Lecture Notes in Physics 580 (Springer, Berlin Heidelberg New York 2001)

    Google Scholar 

  13. M. Donath, W. Nolting (Eds.): Local-Moment Ferromagnets – Unique Properties for Modern Applications, Lecture Notes in Physics 678 (Springer, Berlin Heidelberg New York 2005)

    Google Scholar 

  14. J. Lindner, K. Baberschke: J. Phys.: Condens. Matter 15, R193 (2003); J. Lindner, K. Baberschke: J. Phys.: Condens. Matter 15, S465 (2003)

    ADS  Google Scholar 

  15. D. Sander: J. Phys.: Condens. Matter 16, R603 (2004)

    ADS  Google Scholar 

  16. J.C. Slonczewski: J. Magn. Magn. Mater. 159, L1 (1996)

    ADS  Google Scholar 

  17. Y. Tserkovnyak. A. Brataas, G.E.W. Bauer: Phys. Rev. Lett. 88, 117601 (2002)

    ADS  Google Scholar 

  18. M.D. Stiles, A. Zangwill: Phys. Rev. B 66, 014407 (2002)

    ADS  Google Scholar 

  19. J.A. Katine, F.J. Albert, R.A. Buhrman: Phys. Rev. Lett. 84, 3149 (2000)

    ADS  Google Scholar 

  20. B. Heinrich, Y. Tserkovnyak, G. Woltersdorf, A. Brataas, R. Urban, G. Bauer: Phys. Rev. Lett. 90, 187601 (2003)

    ADS  Google Scholar 

  21. K. Lenz, T. Toliński, E. Kosubek, J. Lindner, K. Baberschke: phys. stat. sol. (c) 1, 3260 (2004)

    Google Scholar 

  22. M. Zwierzycki, Y. Tserkovnyak, P.J. Kelly, A. Brataas, G.E.W. Bauer: Phys. Rev. B 71, 64420 (2005)

    ADS  Google Scholar 

  23. Ch. Kittel: Introduction to solid state physics, 8. edn (Wiley and Sons 2005)

    Google Scholar 

  24. M. Farle, A. Berghaus, and K. Baberschke: Phys. Rev. B 39, 4838 (1989)

    ADS  Google Scholar 

  25. W. Szmaja: Advances in Imaging and Electron Physics 141, 175 (2006)

    Google Scholar 

  26. R.P. Cowburn, A.O. Adeyeye, M.E. Welland: Phys. Rev. Lett. 81, 5414 (1998)

    ADS  Google Scholar 

  27. J. Nogués, I.K. Schuller: J. Magn. Magn. Mater 192, 203 (1999)

    ADS  Google Scholar 

  28. A.E. Berkowitz, Kentaro Takano: J. Magn. Magn. Mater 200, 552 (1999)

    ADS  Google Scholar 

  29. M. Kiwi: J. Magn. Magn. Mater 192, 584 (2001)

    ADS  Google Scholar 

  30. J. Nogués, J. Sort, V. Langlais, V. Skumryev, S. Suriñach, J. S. Muñoz, M.D. Baró: Physics Reports 422, 65 (2005)

    ADS  Google Scholar 

  31. P.J. Jensen, K.H. Bennemann: Surface Science Reports 61, 129 (2006)

    ADS  Google Scholar 

  32. Landolt-Börnstein, Vol. III/19a, ed. by H.P.J. Wijn (Springer Berlin 1986)

    Google Scholar 

  33. P. Bruno: Phys. Rev. B 39, 865 (1989)

    Google Scholar 

  34. P. Poulopoulos, K. Baberschke: J. Phys.: Condens. Matter 11, 9495 (1999)

    ADS  Google Scholar 

  35. G. van der Laan: Phys. Rev. Lett. 82, 640 (1999)

    ADS  Google Scholar 

  36. P. Strange, J.B. Staunton, B.L. Gyorffy, H. Ebert: Physica B 1720, 51 (1991)

    ADS  Google Scholar 

  37. J.B. Staunton, P. Strange, B.L. Gyorffy, M. Matsumoto, J. Poulter, H. Ebert, N.P. Archibald: Theory of Magnetocrystalline Anisotropy. In: The effects of relativity in atoms and molecules and the solid-state, ed. by S. Wilson, I. P. Grant and B. L. Gyorffy (Plenum Press 1991) pp 295

    Google Scholar 

  38. B. Nonas, I. Cabria, R. Zeller, P.H. Dederichs, T. Huhne, H. Ebert: Phys. Rev. Lett. 86, 2146 (2001)

    ADS  Google Scholar 

  39. J.G. Gay, Roy Richter: Phys. Rev. Lett. 56, 2728 (1986)

    ADS  Google Scholar 

  40. Ding-Sheng Wang, Ruqian Wu, A.J. Freeman: Phys. Rev. Lett. 70, 869 (1993); Phys. Rev. Lett. 71, 2166 (1993)

    ADS  Google Scholar 

  41. O. Hjortstam, J. Trygg, J.M. Wills, B. Johansson, O. Ericksson: Phys. Rev. B 53, 9204 (1996)

    ADS  Google Scholar 

  42. B. Újfalussy, L. Szunyogh, P. Bruno, P. Weinberger: Phys. Rev. Lett. 77, 1805 (1996)

    ADS  Google Scholar 

  43. J. Dorantes-Dávila, G.M. Pastor: Phys. Rev. Lett. 77, 4450 (1996)

    ADS  Google Scholar 

  44. C. Uiberacker, J. Zabloudil. P. Weinberger, L. Szunyogh, C. Sommers: Phys. Rev. Lett. 82, 1289 (1999)

    ADS  Google Scholar 

  45. E. Sjöstedt, L. Nordström, F. Gustavsson, O. Eriksson: Phys. Rev. Lett. 89, 267203 (2002)

    ADS  Google Scholar 

  46. J. Dorantes-Dávila, H. Dreyssé, G.M. Pastor: Phys. Rev. Lett. 91, 197206 (2003)

    ADS  Google Scholar 

  47. J.B. Staunton, S. Ostanin, S.S.A. Razee, B.L. Gyorffy, L. Szunyogh, B. Ginatempo, E. Bruno: Phys. Rev. Lett. 93, 257204 (2004)

    ADS  Google Scholar 

  48. M. Kosuth, V. Popescu, H. Ebert, et al., Europhys. Lett. 72, 816 (2005)

    ADS  Google Scholar 

  49. L.F. Yin, D.H. Wei, N. Lei, L.H. Zhou, C.S. Tian, G.S. Dong, X.F. Jin, L.P. Guo, Q.J. Jia, R.Q. Wu: Phys. Rev. Lett. 97, 067203 (2006)

    ADS  Google Scholar 

  50. D. Weller, J. Stöhr, R. Nakajima, A. Carl, M.G. Samant, C. Chappert, R. Mégy, P. Beauvillain, P. Veillet, G.A. Held: Phys. Rev. Lett. 75, 3752 (1995); Comment on Phys. Rev. Lett. 75, 3752 (1995) by H. A. Dürr, G. van der Laan, B. T. Thole: Phys. Rev. Lett. 76, 3464 (1996)

    ADS  Google Scholar 

  51. P. Gambardella, S. Rusponi, T. Cren, N. Weiss, H. Brune: Comptes Rendus Physique 6, 75 (2005)

    ADS  Google Scholar 

  52. L. Néel: J. Physique Radium 15, 225 (1954)

    Google Scholar 

  53. H.J. Elmers, T. Furubayashi, M. Albrecht and U. Gradmann: J. Appl. Phys. 70, 5764 (1991)

    ADS  Google Scholar 

  54. O.N. Mryasov, U. Nowak, K.Y. Guslienko, R.W. Chantrell: Europhys. Lett. 69, 805 (2005)

    ADS  Google Scholar 

  55. R.R. Birss: Symmetry and Magnetism. In: Series of Monographs on selected Topics in Solid State Physics, ed by E. P. Wohlfarth (North-Holland Publishing Co., Amsterdam, John Wiley and Sons, New York 1966)

    Google Scholar 

  56. A. Berghaus, M. Farle, Yi Li, K. Baberschke: In: Springer Proceedings in Physics, Vol. 50 (Springer Berlin 1990) pp 61

    Google Scholar 

  57. P.J. Jensen, K.H. Bennemann, Phys. Rev. B 52, 16012 (1995)

    ADS  Google Scholar 

  58. M. Farle, B. Mirwald-Schulz, A.N. Anisimov, P. Poulopoulos, K. Baberschke: Phys. Rev. B 55, 3708 (1997)

    ADS  Google Scholar 

  59. Y.T. Millev, H.P. Oepen, J. Kirschner: Phys. Rev. B 57, 5837 (1998)

    ADS  Google Scholar 

  60. P. Bruno P: J. Appl. Phys. 64, 3153 (1988)

    ADS  Google Scholar 

  61. P. Poulopoulos, J. Lindner, M. Farle, K. Baberschke: Surf. Sci. 437, 277 (1999)

    ADS  Google Scholar 

  62. M. Benson, D.L. Mills: Phys. Rev. 178, 839 (1969)

    Google Scholar 

  63. H. Fritzsche, J. Kohlhepp, U. Gradmann: Phys. Rev. B 51, 15933 (1995)

    ADS  Google Scholar 

  64. P. Bruno: Physical origins and theoretical models of magnetic anisotropy. In: Vorlesungsmanuskripte des 24.IFF-Ferienkurses im Forschungszentrum Jülich (Forschungszentrum Jülich 1993)

    Google Scholar 

  65. C. Chappert, P. Bruno: J. Appl. Phys. 64, 5736 (1988)

    ADS  Google Scholar 

  66. R.F.S. Hearmon: In: Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology Group III, vol 2, (Berlin, Springer 1969); R.F.S. Hearmon: The Elastic Constants of Crystals and Other Anisotropic Materials. In: Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology Group III, vol 18, (Springer, Berlin 1984)

    Google Scholar 

  67. J.M. Luttinger: Helv. Phys. Acta 21, 480 (1948)

    Google Scholar 

  68. J.H. van Vleck: Phys. Rev. 78, 266 (1950)

    MATH  ADS  Google Scholar 

  69. J. Smit, H.G. Beljers: Phillips Res. Rep. 10, 113 (1955)

    Google Scholar 

  70. H. Suhl: Phys. Rev. 97, 555 (1955)

    ADS  Google Scholar 

  71. T.L. Gilbert: Phys. Rev. 100, 1243 (1955)

    Google Scholar 

  72. H. Goldstein: Klassische Mechanik, 11. edn (AULA-Verlag, Wiesbaden 1991)

    Google Scholar 

  73. L. Baselgia, M. Warden, F. Waldner, S.L. Hutton, J.E. Drumheller, Y.Q. He, P.E. Wigen, M. Marysko: Phys. Rev. B 38, 2237 (1988)

    ADS  Google Scholar 

  74. A.N. Anisimov, M. Farle, P. Poulopoulos, W. Platow, K. Baberschke, P. Isberg, R. Wäppling, A.M.N. Niklasson, O. Eriksson: Phys. Rev. Lett. 82, 2390 (1999)

    ADS  Google Scholar 

  75. S.V. Vonsovskii: Magnetism, (Wiley, New York 1974) pp 946ff

    Google Scholar 

  76. H.B. Callen, E. Callen: J. Phys. Chem. Solids 27, 1271 (1966)

    ADS  Google Scholar 

  77. W.J. Car, Jr: Phys. Rev. 109, 1971 (1958)

    ADS  Google Scholar 

  78. D.P. Pappas: J. Vac. Sci. Technol. 14, 3203 (1996)

    Google Scholar 

  79. O. Fruchart, J.-P. Nozieres, D. Givord: J. Magn. Magn. Mater. 165, 508 (1997)

    ADS  Google Scholar 

  80. S. Okamoto, N. Kikuchi, O. Kitakami, T. Miyazaki, Y. Shimada, K. Fukamichi: Phys. Rev.B 66, 024413 (2002)

    ADS  Google Scholar 

  81. J.-U. Thiele, K.R. Coffey, M.F. Toney, J.A. Hedstrom, and A.J. Kellock: J. Appl. Phys. 91, 6595 (2002)

    ADS  Google Scholar 

  82. J. Lindner: Ferromagnetische Resonanz an ultradünnen magnetischen Einfach- und Mehrfachlagen der 3d-übergangsmetalle – Statik und Dynamik. PhD thesis, Freie Universität Berlin, Berlin (dissertation.de 2003)

    Google Scholar 

  83. Kh. Zakeri, Th. Kebe, J. Lindner, M. Farle: Phys. Rev. B 73, 052405 (2006)

    ADS  Google Scholar 

  84. C. Li, A.J. Freeman: Phys. Rev. B 43, 780 (2002)

    ADS  Google Scholar 

  85. Yu.V. Goryunov, N.N. Garif’yanov, G.G. Khaliullin, I.A. Garifullin, L.R. Tagirov, F. Schreiber, Th. Mühge, H. Zabel: Phys. Rev. B 52, 13450 (1995)

    ADS  Google Scholar 

  86. Th. Mühge, A. Stierle, N. Metoki, U. Pietsch, H. Zabel: Appl. Phys. A 59, 659 (1994)

    ADS  Google Scholar 

  87. G.A. Prinz, G.T. Rado, J.J. Krebs: J. Appl. Phys. 53, 2087 (1982)

    ADS  Google Scholar 

  88. R. Meckenstock, K. Harms, O. von Geisau, J. Pelzl: J. Magn. Magn. Mater. 148, 139 (1995)

    ADS  Google Scholar 

  89. M. Klaua, D. Ullmann, J. Barthel, W. Wulfhekel, J. Kirschner, R. Urban, T.L. Monchesky, A. Enders, J.F. Cochran, B. Heinrich: Phys. Rev. B 64, 134411 (2001)

    ADS  Google Scholar 

  90. G. Wastlbauer, J.A.C. Bland: Adv. Phys. 54, 137 (2005)

    ADS  Google Scholar 

  91. Kh. Zakeri, Th. Kebe, J. Lindner, M. Farle: J. Magn. Magn. Mater. 299, L1 (2006)

    ADS  Google Scholar 

  92. T. Toliñski, K. Lenz, J. Lindner, E. Kosubek, K. Baberschke, D. Spoddig, R. Meckenstock: Sol. Stat. Comm. 128, 385 (2003)

    ADS  Google Scholar 

  93. S. McPhail, C.M. Cürtler, F. Montaigne. Y.B. Yu, M. Tselepi, J.A.C. Bland: Phys. Rev. B 67 24409, (2003)

    ADS  Google Scholar 

  94. W. Platow, A.N. Anisimov, M. Farle, K. Baberschke: phys. stat. sol. (a) 173, 145 (1999)

    ADS  Google Scholar 

  95. M. Brockmann, M. Zölfl, S. Miethaner, and G. Bayreuther: J. Magn. Magn. Mater. 198, 384 (1999)

    ADS  Google Scholar 

  96. M. Gester, C. Daboo, R.J. Hicken, S.J. Gray, A. Ercole, and J.A.C. Bland: J. Appl. Phys. 80, 347 (1996)

    ADS  Google Scholar 

  97. R. Moosbuhler, F. Bensch, M. Dumm, G. Bayreuther: J. Appl. Phys. 91, 8757 (2002)

    ADS  Google Scholar 

  98. G. Wedler, B. Wassermann, R. Nötzel, R. Koch: Appl. Phys. Lett. 78, 1270 (2001)

    ADS  Google Scholar 

  99. G. Wedler, B. Wassermann, R. Koch: Phys. Rev. B 66, 064415 (2002)

    ADS  Google Scholar 

  100. R.A. Gordon, E.D. Crozier, D.-T. Jiang, T.L. Monchesky, B. Heinrich: Phys. Rev. B 62, 2151 (2000)

    ADS  Google Scholar 

  101. U. Gradmann: Annalen der Physik 17, 91 (1966)

    ADS  Google Scholar 

  102. D.P. Pappas, K.-P. Kämper, H. Hopster: Phys. Rev. Lett. 64, 3179 (1990)

    ADS  Google Scholar 

  103. R. Allenspach, A. Bischof: Phys. Rev. Lett. 69, 3385 (1992)

    ADS  Google Scholar 

  104. Dongqi Li, M. Freitag, J. Pearson, Z.Q. Qiu, and S.D. Bader: Phys. Rev. Lett. 72, 3112 (1994)

    ADS  Google Scholar 

  105. A. Berger, H. Hopster: Phys. Rev. Lett. 76, 519 (1996); A. Berger, H. Hopster: J. Appl. Phys. 79, 5619 (1996)

    ADS  Google Scholar 

  106. G. Garreau, E. Beaurepaire, K. Ounadjela, M. Farle: Phys. Rev. B 53, 1083 (1996)

    ADS  Google Scholar 

  107. D. Pescia, V. L. Pokrovsky: Phys. Rev. Lett. 65, 2599 (1990)

    ADS  Google Scholar 

  108. A. Moschel, K.D. Usadel: Phys. Rev. B 49, 12868 (1994)

    ADS  Google Scholar 

  109. D.K. Morr, P.J. Jensen, K.H. Bennemann: Surf. Sci. 307–309, 1109 (1994)

    Google Scholar 

  110. S.T. Chui: Phys. Rev. B 50, 12559 (1994)

    ADS  Google Scholar 

  111. X. Hu, R. Tao, Y. Kawazoe: Phys. Rev. B 54, 65 (1996)

    ADS  Google Scholar 

  112. Y. Millev, J. Kirschner: Phys. Rev. B 54, 4137 (1996)

    ADS  Google Scholar 

  113. S. van Dijken, R. Vollmer, B. Poelsema, J. Kirschner: J. Magn. Magn. Mater 210, 316 (2000)

    ADS  Google Scholar 

  114. J. Lindner, P. Poulopoulos, R. Nünthel, E. Kosubek, H. Wende, K. Baberschke: Surf. Sci. Lett. 523, L65 (2003)

    Google Scholar 

  115. W. Platow, U. Bovensiepen, P. Poulopoulos, M. Farle, K. Baberschke, L. Hammer, S. Walter, S. Müller, K. Heinz: Phys. Rev. B 59, 12641 (1999)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Physik and Center for Nanointegration, Universität Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany

    Jürgen Lindner & Michael Farle

Authors
  1. Jürgen Lindner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Farle
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Experimentalphysik, Ruhr-Universität Bochum Fakultät für Physik und Astronomie, D 44780 Bochum, Germany

    Hartmut Zabel

  2. Material Science Division, Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439, USA

    Samuel D. Bader

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lindner, J., Farle, M. (2008). Magnetic Anisotropy of Heterostructures. In: Zabel, H., Bader, S.D. (eds) Magnetic Heterostructures. Springer Tracts in Modern Physics, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73462-8_2

Download citation

Publish with us

Policies and ethics

Search

Navigation