Ultrasonics of High- and Other Unconventional Superconductors: Physical Acoustics PDF
Preview Ultrasonics of High- and Other Unconventional Superconductors: Physical Acoustics
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 Boston San Diego New York 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 transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. ACADEMIC PRESS, INC. 1250 Sixth Avenue, San Diego, CA 92101-4311 United Kingdom Edition published by ACADEMIC PRESS LIMITED 24-28 Oval Road, London NW1 7DX ISSN 0893-388X ISBN 0-12-477920-4 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
The list of books you might like
