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Theory of Mesoscopic Quantum Tunneling in Magnetism: A WKB Approach

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Quantum Tunneling of Magnetization — QTM ’94

Part of the book series: NATO ASI Series ((NSSE,volume 301))

Abstract

This is a comprehensive and self-contained review of WKB theory for mesoscopic quantum tunneling in magnetism. It describes the behavior of a large quantum spin, e.g., a magnetic moment, in an anisotropic surroundings and its penetration into a classically forbidden region. The tunneling rate of a quantum spin is obtained in the semiclassicaJ limit when ħ → 0 and the spin quantum number S → ∞ in such a way that ħS remains constant. The key idea is to single out one of the anisotropy axes, say the z-axis, to work in a representation with S z diagonal, and to describe quantum tunneling as a hopping process on the spectrum of S z . We sketch the original motivation of our theory, present the WKB basics, compute the tunneling rate, prove its universal power-law dependence upon the anisotropy constants which is independent of the specific form of the anisotropy, and discuss the underlying physics. We treat several examples, including antiferromagnetic tunneling. In addition, we provide a general theory of quantum coherence, including Kramers degeneracy.

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Author information

Author notes

  1. A. Sütö

    Present address: Research Institute for Solid State Physics, P.O. Box 49, H-1525, Budapest 114, Hungary

Authors and Affiliations

  1. Physik-Department der TU München, D-85747, Garching bei München, Germany

    J. L. Van Hemmen

  2. Institut de Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    A. Sütö

Authors
  1. J. L. Van Hemmen
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  2. A. Sütö
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Editor information

Editors and Affiliations

  1. Department of Physics and Astronomy, Tufts University, Medford, MA, USA

    Leon Gunther

  2. Laboratoire de Magnétisme Louis Néel, CNRS, Grenoble, France

    Bernard Barbara

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Van Hemmen, J.L., Sütö, A. (1995). Theory of Mesoscopic Quantum Tunneling in Magnetism: A WKB Approach. In: Gunther, L., Barbara, B. (eds) Quantum Tunneling of Magnetization — QTM ’94. NATO ASI Series, vol 301. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0403-6_2

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  • DOI: https://doi.org/10.1007/978-94-011-0403-6_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4180-5

  • Online ISBN: 978-94-011-0403-6

  • eBook Packages: Springer Book Archive

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