Magnetic Flux Structures in Superconductors: Extended Reprint of a Classic Text

323 Pages·2001·10.634 MB·English

by  Prof. Dr. Rudolf Peter Huebener (auth.)

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R. P. Hu ebener
Magnetic Flux Structures
in Superconductors
Extended Reprint of a Classic Text
Second Edition
With 111 Figures
, Springer
Prof. Dr. Rudolf Peter Huebener
Physikalisches Institut
Lehrstuhl fur Experimentalphysik II
Auf der Morgenstelle 14
72076 Tubingen
Germany
Series Editors:
Professor Dr., Dres. h. c. Manuel Cardona
Professor Dr., Dres. h. c. Peter Fulde*
Professor Dr., Dres. h. c. Klaus von Klitzing
Professor Dr., Dres. h. c. Hans-Joachim Queisser
Max-Planck-Institut fur Festkorperforschung, Heisenbergstrasse 1, D-70s69 Stuttgart, Germany
• Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38
D-01187 Dresden, Germany
Professor Dr. Roberto Merlin
Department of Physics, SOOO East University, University of Michigan
Ann Arbor, MI 48109-1120, USA
Professor Dr. Horst Stormer
Dept. Phys. and Dept. Appl. Physics, Columbia University, New York, NY 10023 and
Bell Labs., Lucent Technologies, Murray Hill, NJ 07974, USA
ISSN 0171-1873
Library of Congress Cataloging-in-Publication Data. Huebener, Rudolf Peter, 1931- . Magnetic flux structures
in superconductors: extended reprint of a classic text 1R .P. Huebener.--[2nd ed.J. p. cm. --(Springer series in
solid-state sciences, ISSN 0171-1873; 6) Includes bibliographical references and index. ISBN 3540679537 (alk.
paper) 1. Superconductors. 2. Magnetic flux. I. Title. II. Series. QC611.95.H84 2000 537.6'23--dC21 00-061911
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ISBN 978-3-642-08753-0 ISBN 978-3-662-08446-5 (eBook)
DOI 10.1007/978-3-662-08446-5
© Springer-Verlag Berlin Heidelberg 1979, 2001
Originally published by Springer-Verlag Berlin Heidelberg New York in 2001.
Softcover reprint of tlIe hardcover 2nd edition 2001
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To Gerda,
Ingrid, Christoph, and Monika
Preface to the Second Edition
The first edition of this book provided an introduction to the many static and
dynamic features of magnetic flux structures in what are now called classical
or low-temperature superconductors. It went out of print not long after the
discovery of high-temperature superconductors in 1986 by J.G. Bednorz and
K.A. Miiller, a discovery which resulted worldwide in an explosive growth of
research and development in the field of superconductivity. Because of this
upsurge of activities, a strong demand for this book clearly continued.
Since the contents of the fourteen chapters of the first edition are still valid
and continue to represent a useful introduction into the various subjects, it
was felt that a reprinting of these chapters in this second edition would be
highly attractive. In this way, the reader is also able to trace the earlier scienti
fic developments, themselves constituting important ideas sometimes forgot
ten by the new community dealing with high-temperature superconductivity.
However, because of the exciting and important recent progress in the field
of high-temperature superconductivity, an extensive chapter has been added
in this second edition. It provides a summary of the new developments and
a discussion of the highlights. Here keywords such as vortex matter, vortex
imaging, and half-integer magnetic flux quanta describe surprising new issues.
Like the first edition, this text is intended for researchers and graduate
students, and it may serve as supplementary material for a graduate course
on low-temperature solid-state physics. The static and dynamic properties
of magnetic flux structures in low-temperature and high-temperature super
conductors continue to playa crucial role in many technological applications
of these materials. Hence, in addition to researchers and graduate students,
this new edition may also be useful to electronic engineers.
In preparing this new edition, I benefitted from helpful comments by
many people, of which I would like to mention in particular A.A. Abrikosov,
E.H. Brandt, U.R. Fischer, R. Kiimmel, Yu.N. Ovchinnikov, N. Schopohl,
O.M. Stoll, A. Tonomura, and C. C. Tsuei.
Tiibingen,
November 2000 R.P. Huebener
Preface to the First Edition
The idea for this book originated from an International Conference on Ma
gnetic Structures in Superconductors organized by John R Clem and the
author at Argonne National Laboratory (ANL) in September of 1973. Large
parts of the book evolved from lectures given to graduate students at the
University of Tiibingen during the past three years.
It is the purpose of this book to provide an introduction to the many
features of magnetic flux structures in superconductors and to discuss the
recent developments in this field. Here, in addition to the static properties of
magnetic flux structures, the time-dependent phenomena represent an impor
tant subject including flux flow and the transport effects in superconductors.
Throughout the book the emphasis is placed on the physical phenomena and
the experimental results. We do not attempt a general introduction to super
conductivity. Except for a brief discussion of the Ginzburg-Landau theory,
with respect to the theoretical developments we only give an outline and refer
to the original papers or other reviews for the detail of the calculations.
The book is intended for researchers and graduate students interested in
the subject of magnetic flux structures in superconductors. It may serve as
supplementary material for a graduate course on low-temperature solid-state
physics. During recent years technological applications of superconducting
materials are becoming increasingly important. Here the static and dynamic
behavior of magnetic flux structures playa distinguished role. The book may
be helpful for people involved in these engineering aspects of superconduct
ivity.
A short remark on notation: different symbols are used for different phy
sical quantities as much as possible. For distinction, different types of the
same letter, subscripts, underlines, etc. are employed. In some cases where
the possibility for confusion hardly exists the same symbol refers to different
quantities. A list of all important symbols used throughout the book is added
at the end.
During recent years I benefitted greatly from discussions with many
people, in particular with my former colleagues at ANL and my present
associates an the University of Tiibingen. Here I wish to mention W. Buck,
D.E. Chimenti, John R Clem, KE. Gray, RT. Kampwirth, K Noto,
M.C.L. Orlowski, and K-P. Selig. I am grateful to D.E. Chimenti, U. Ess-
X Preface to the First Edition
mann, A. Kiendl, B. Obst, L. Rinderer, P. Thorel, and H. Ullmaier for
providing photographs or drawings for some of the figures. Thanks are due
to John R. Clem for critically reading various sections of the manuscript
and to H.-G. Wener for helping with the preparation of the photographs and
drawings. Finally I am pleased to thank my secretary, Miss M.-L. Weisschuh,
for her expert and always cheerful assistance in preparing the material for
this book.
Tiibingen,
December 1978 R.P. Huebener
Contents
1. Introduction.............................................. 1
2. Magnetic Properties of Type-I Superconductors . . . . . . . . . . 4
2.1 Meissner Effect, Penetration Depth, and Coherence Length. . 4
2.2 Intermediate State and Wall Energy. . . . . . . . . . . . . . . . . . . . .. 13
2.3 Landau Domain Theory ................................ 16
2.4 Domain Patterns ...................................... 21
3. Ginzburg-Landau Theory ................................. 33
3.1 Free Energy and the Ginzburg-Landau Equations. . . . . . . . .. 34
3.2 The Two Characteristic Lengths ~(T), >..(T)
and the Wall-Energy Parameter ......................... 37
3.3 Critical Current in a Thin Film or Wire ........ . . . . . . . . .. 41
3.4 Quantization of the Fluxoid . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 44
3.5 Nucleation of Superconductivity in Bulk Samples .......... 46
3.6 Nucleation of Superconductivity at Surfaces. . . . . . . . . . . . . .. 48
3.7 Abrikosov Vortex State Near Hc2 ........................ 50
4. Magnetic Properties of Type-II Superconductors. ... . . . .. 58
4.1 Mixed State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58
4.2 London Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.2.1 Isolated Vortex Line ............................ 61
4.2.2 Lower Critical Field Hcl ......................... 64
4.2.3 Interaction Between Vortex Lines ................. 65
4.2.4 Magnetization Near Hc1 ......................... 67
4.3 Clem Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
4.4 Theory of the Static Vortex Structure .. . . . . . . . . . . . . . . . . .. 72
4.5 Flux-Line Lattices ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75
4.5.1 Correlation Between the Vortex Lattice
and the Crystal Lattice . . . . . . . . . . . . . . . . . . . . . . . . .. 75
4.5.2 Defects in the Vortex Lattice. . . . . . . . . . . . . . . . . . . .. 78
4.6 Surface Effects ........................................ 82
4.6.1 Energy Barrier Near a Surface. . . . . . . . . . . . . . . . . . .. 83
4.6.2 Vortex Nucleation at the Surface. . . . . . . . . . . . . . . . .. 86
XII Contents
4.7 Attractive Vortex Interaction. . . . . . . . . . . . . . . . . . . . . . . . . . .. 87
4.7.1 Experiments... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88
4.7.2 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92
5. Thin Films ............................................... 94
6. Experimental Techniques ................................. 100
6.1 Bitter Method ......................................... 100
6.2 Magneto Optics ....................................... 102
6.3 Micro Field Probes ..................................... 110
6.4 Neutron Diffraction .................................... 110
6.5 Magnetization ......................................... 114
6.6 Miscellaneous ......................................... 118
7. Lorentz Force and Flux Motion ........................... 121
7.1 Motion of Magnetic Flux Structures ...................... 121
7.2 Lorentz Force ......................................... 122
7.3 Flux Flow Resistance ................................... 124
7.4 Flux Penetration into a Superconductor .................. 130
7.5 Hall Effect ............................................ 134
7.6 Ettinghausen and Peltier Effect .......................... 136
7.7 Josephson Relation ..................................... 138
7.8 Instabilities ........................................... 141
7.9 Force-Free Configurations ............................... 143
8. Special Experiments ...................................... 144
8.1 Magneto Optics ....................................... 144
8.2 Nuclear Magnetic Resonance ............................ 145
8.3 Neutron Diffraction .................................... 145
8.4 Sharvin Point Contact .................................. 147
8.5 Magnetic Coupling ..................................... 148
8.6 Micro Field Probes ..................................... 152
8.7 Simulation Experiments ................................ 154
9. Thermal Force and Flux Motion .......................... 155
9.1 Thermal Force ......................................... 155
9.2 Nernst and Seebeck Effect .............................. 156
9.3 Transport Entropy ..................................... 160
10. Time-Dependent Theories ................................ 165
10.1 Phenomenological Theories .............................. 165
10.2 Time-Dependent Ginzburg-Landau Theory ................ 170
Flux-Flow Resistivity ................................... 174
Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 177
Transport Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177