Ultrasonics of High- and Other Unconventional Superconductors: Physical Acoustics

470 Pages·1992·7.112 MB·1-465\470

by  MOISES LEVY (Eds.)

Physical Acoustics
Volume XX
R.N. THURSTON AND ALLAN D. PIERCE, Series Editors
CONTRIBUTORS TO VOLUME XX
S. ADENWALLA
D. P. ALMOND
S. BHATTACHARYA
BRAGE GOLDING
J. B. KETTERSON
VLADIMIR Z. KRESIN
MOÏSES LEVY
J. D. MAYNARD
M. J. MCKENNA
A. MIGLIORI
BlMAL K. SARMA
KEUN JENN SUN
WILLIAM M. VISSCHER
MIN-FENG XU
Z. ZHAO
Ultrasonics of and Other
High-r
c
Unconventional Superconductors
Edited by MOISES LEVY
UNIVERSITY OF WISCONSIN
MILWAUKEE, WISCONSIN
PHYSICAL A C O U S T I CS
Volume XX
ACADEMIC PRESS, INC.
Harcourt Brace Jovanovich, Publishers
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London Sydney Tokyo Toronto
This book is printed on acid-free paper. («)
COPYRIGHT © 1992 BY ACADEMIC PRESS, INC.
All rights reserved.
No part of this publication may be reproduced or
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PRINTED IN THE UNITED STATES OF AMERICA
92 93 94 95 BB 9 8 7 6 5 4 3 2 1
This book is dedicated to the seventeen students who obtained their
Ph.D.'s under my supervision and without whom this work would not have
been possible, and to my wife who provided the encouragement
and incentive required to complete it.
Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
S. ADENWALLA (23, 107) VLADIMIR Z. KRESIN (435)
Northwestern University Materials and Chemical Science
Physics Department Division
2145 Sheridan Road Lawrence Berkeley Laboratory
Evanston, IL 60208 University of California
Berkeley, CA 94720
D. P. ALMOND (409)
School of Materials Science
MOÏSES LEVY (1, 107, 191, 237)
University of Bath
Department of Physics
Claverton Down
P.O. Box 413
Bath, BA2 7AY, United Kingdon
University of Wisconsin—Milwaukee
Milwaukee, WI 53201
S. BHATTACHARYA (303)
NEC Research Institute
J. D. MAYNARD (381)
4 Independence Way
Department of Physics
Princeton, NJ 08540
The Pennsylvania State University
University Park, PA 16802
BRAGE GOLDING (349)
Department of Physics and
Astronomy M. J. MCKENNA (381)
Department of Physics
Michigan State University
The Pennsylvania State University
East Lansing, Michigan 48824-1116
University Park, PA 16802
J. B. KETTERSON (23, 107)
Northwestern University A. MIGLIORI (381)
Physics Department Los Alamos National Laboratory
2145 Sheridan Road PO Box 1663, MS k-764
Evanston, IL 60208 Los Alamos, New Mexico 87545
xiv Contributors
BIMAL K. SARMA (23, 107, 237) MIN-FENG XU (237)
Department of Physics Department of Physics
University of Wisconsin—Milwaukee University of Wisconsin—Milwaukee
Milwaukee, WI 53201 Milwaukee, WI 53201
KEUN JENN SUN (191, 237) Z. ZHAO (23)
Department of Physics Northwestern University
The College of William and Mary Physics Department
Williamsburg, VA 23185 2145 Sheridan Road,
Evanston, IL 60208
WILLIAM M. VISSCHER (381)
Los Alamos National Laboratory
Los Alamos, New Mexico 87545
Preface
In 1911 Kammerlingh Onnes (1991) discovered superconductivity in mercury
at a temperature near 4 K. Seventy-five years later, an unprecedented set of
discoveries led to the birth of high-r superconductivity. Mainly because of the
c
efforts of Bednorz and Muller (1986) and Chu ΗNxxet al., 1987), superconduc-
tivity above liquid nitrogen temperatures has become a reality.
The first microscopic theory for superconductivity was given by Bardeen,
Cooper, and Schrieffer (BCS) (Bardeen et al., 1957), and it invoked electron-
phonon interaction as being responsible for the pairing mechanism. The mea-
surement of ultrasonic attenuation in the superconducting state was one of the
experimental techniques that provided definitive confirmation for the validity of
the BCS theory. Both attenuation and velocity measurements have proven to be
essential in the discovery of new effects and new phases in both conventional
and unconventional superconductors. Therefore, it appears appropriate at this
time to publish a volume on the acoustic study of the high-7 superconductors.
c
Since these new superconductors are very much different from the conventional
superconductors that can be reasonably well explained by the BCS theory, we
have included three chapters on some unconventional superconducting systems:
superfluid 3He, heavy Fermion superconductors, and magnetic reentrant super-
conductors. We hope that their inclusion will set the groundwork for our study
of the high-7 superconductors, which is covered in the succeeding five chapters.
c
The last chapter will attempt to provide a theoretical understanding of the different
mechanisms that may be responsible for superconductivity in these novel su-
perconducting systems, and for the contributions that sound measurements have
made and could make to our understanding of these systems.
The authors of most of the chapters in this book assume that the readers
possess some familiarity with sound attenuation in conventional BCS supercon-
ductors. Therefore, Chapter I summarizes the principal results that have been
observed in these systems as functions both of temperature and of magnetic
field.
Chapter II is on the ultrasonic study of superfluid 3H3. Ever since the
xv
xvi Preface
publication of the BCS theory in 1957, explaining the physics of s-wave su-
perconductors, we have been looking for a p-wave superconductor. In 1972,
this was discovered in 3He (Osheroff et al., 1972), where, because of the
large hard core repulsion, the pairing is in the €=1 (p-wave), s=l (triplet)
state. This system is by far the best studied, both theoretically and experi-
mentally, of the unconventional superconductors. Surprisingly, the theory can
be explained on the basis of the BCS theory modified for triplet p-wave
pairing, which includes strong coupling effects at higher pressures. The in-
teraction is spin-spin. The order parameter is a complex tensor, and many
superfluid phases exist in the P-T-H planes (pressure, temperature, magnetic
field). Because of the low superfluid transition temperature (2.5 mK), the pair
breaking energy is only 180 MHz in frequency units. Because of the com-
plex nature of the order parameter, many collective mode states exist in the
energy gap, and as these couple to density, they can be observed by ultra-
sonic methods. There is a very large absorption and dispersion of the sound
waves as one goes through these modes. Ultrasonic techniques have been
developed to study these modes, and absorption in excess of 1,000 dB/cm
and group velocities less than 25 m/s have been measured. The chapter in-
cludes experimental techniques and data, as well as the necessary theory.
Chapter III is on the ultrasonic study of the heavy-Fermion superconductors.
These materials are characterized by a very large electronic heat capacity (100-
1,000 times that of copper), and surprisingly, some of these have a supercon-
ducting ground state. A reasonable theory for these systems is lacking, though
it seems likely that there may be many things in common between these and
superfluid 3He, viz., a higher angular momentum pairing. Most of the ultrasonic
measurements are on UPt. The attenuation is very much different from that of
3
a conventional BCS superconductor such as niobium or vanadium, showing
evidence of an anisotropic energy gap. UPt also shows evidence of multiple
3
phases in the H-T plane, the first evidence of which came from ultrasonic
measurements. Spin fluctuations seem to play a dominant role in the pairing
mechanism, and the study of these systems may reveal their pairing mechanisms
that may prove useful in building a theoretical understanding of the high-r
c
superconductors.
Chapter IV is on the magnetic reentrant superconductors. These form an
interesting system. The ground state seems to be a magnetic state, over which
lies a superconducting state. Again, ultrasonic attenuation has proved to be a
useful tool to study the subtle interplay among magnetism, electromagnetic
screening, and superconductivity. Measurements have been performed on the
Er!_Ho^RhB4 system, where, as the concentration of Ho is changed from zero
x 4
to one, the system goes from a reentrant superconductor with a superconducting
Preface xvii
transition at 8.9 Κ and a ferromagnetic transition at around 1 K, to a purely
magnetic system with a ferromagnetic transition at 6.9 K. In fact, in the con-
centration range 0 ^ ÷ ^ 0.3, there is a coexistence temperature range between
superconductivity and a sinusoidal modulated antiferromagnetic state. Atten-
uation measurements have been performed on several members of this system.
The most striking feature is observed for 0.6 ^ ÷ ^ 0.9 (JC = 0.9 is the upper
value for the observation of superconductivity in this system). In this range the
attenuation increased in the superconducting state, as opposed to the expected
decrease for a BCS superconductor. In ErRluB^ attenuation measurements in
a magnetic field exemplify the importance of electromagnetic screening for this
reentrant superconducting system. In addition, for 0 ^ JC ^ 0.3, the boundaries
of the coexistence region can be easily identified by features in the attenuation
measurements. Some of the high-r superconductors exhibit reentrant behavior,
c
and comparisons between future measurements on these high-r superconductors
c
and the present results may provide insight into the mechanisms that are producing
superconductivity and are responsible for the interaction with sound waves.
The next five chapters are on measurements with sound waves on the high-
ly superconductors. The first of these, Chapter V, reviews the experimental data
on the sintered oxide superconductors. Most of these measurements are done by
pulsed ultrasonics, and the samples are made by a shake-and-bake method. Some
of these samples are relatively well oriented, being either grown by a sinter-
forged technique, or grown in the presence of a strong external magnetic field
in the case of ions with strong paramagnetic moments; a large anisotropy with
propagation direction is seen in the elastic constants, as inferred from velocity
measurements. Typical results are a stiffening of the lattice at the superconducting
transition, and the observation of several attenuation peaks. Most of these at-
tenuation peaks may be due to some kind of relaxation mechanism that could
be associated with the excitations that are supposed to be responsible for the
high transition temperature of these superconductors. However, in the thallium
superconducting compounds, peaks appear in the vicinity of T that do not shift
c
with frequency and therefore may be truly associated with the superconducting
phase transition. A possible mechanism for this effect could be phonon interaction
with superconducting fluctuations associated with the phase transition.
Chapter VI covers the temperature and magnetic field dependence of the
velocity and elastic constants in sintered high-!T superconductors. It concentrates
c
mainly on velocity measurements on the 40 Κ La-Sr system. From a detailed
thermodynamic analysis of both the longitudinal and transverse velocity, the
author finds that the main elastic modulus involved at the transition is the shear
modulus. Anomalies in the velocity in applied magnetic fields have been inter-
preted as evidence of a multiple phase diagram in the H-T plane, showing their
xviii Preface
strong unconventional nature akin to that in superfluid 3He, and in the heavy
fermion superconductor UPt.
3
Chapters VII and VIII cover both sound absorption and sound dispersion
measurements on single crystals of high~r superconductors. Since the single
c
crystals are small, particularly for sound measurements, novel experimental
approaches have been developed for determining the attenuation and the elastic
constants in these small crystals. Chapter VII discusses vibrating reed techniques
at audio frequencies, bulk resonance techniques at rf frequencies, and plane wave
propagation techniques at microwave frequencies. This chapter covers some of
the most beautiful velocity data that have been obtained at microwave frequencies
at the phase transition of the high-7 superconductors. Since the measurements
c
are performed on single crystals, it becomes possible to try to separate the
different mechanisms and effects that contribute to the real and imaginary parts
of the elastic constants, such as electrons, defects, tunneling, gaplessness, and
flux lattice interactions.
The authors of Chapter VIII have perfected an intriguing new small-sample
resonant ultrasound technique that uses thin piezoelectric films or weakly coupled
lithium niobate transducers. By continuously varying the frequency at a particular
temperature, the resonant frequencies of a large number of modes may be ob-
tained, from which all of the independent elastic constants of submillimeter-
sized single crystals may be determined from a single experimental setup. Using
this technique the authors have observed minima of the shear moduli near the
structural phase transition of La^Sr^Cu 0 with ÷ = 0.14 and 0.1.
4
Chapter IX discusses both the effect of oxygen on superconducting properties
and the response of sound to these additions. An important technique in the
study of conventional superconductors was the ability to destroy superconduc-
tivity by applying an external magnetic field in excess of H. This allowed one
c2
to estimate the contribution due to superconductivity. For the high-r materials,
c
fields in excess of H or approaching this are difficult to achieve at present, but
c2
it is possible to destroy superconductivity by varying the oxygen content in the
high-r cuprates, although this is accompanied by conduction electron density
c
changes, and perhaps even structural changes. The author has measured the
velocity and attenuation in such an oxygen-modified system. Although it is
difficult to separate those effects that are due to varying oxygen content from
those that are intrinsic to the high-r superconductors, the author has attempted
c
to distinguish effects that are due to the superconductivity itself from those that
are due to the complex lattice structure of these highly interesting crystallographic
systems.
Chapter X provides a theoretical foundation for sound measurements in the
superconducting state. The author emphasizes the effects of multigap structures
and gap anisotropy on sound attenuation in the superconducting state of the