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saLofoeamrrbs osearoaannrnt odtdar a yln wRRdhae eessnRreeede aahs rreecc hahd ri rcehc ts xieseses engineering sciences. the team of oxides. Author of several scientific d DiDreircetocDtroi rare tca tttoh btreho a oePtk Pshth hyeasyn siPdcihc sisy nDs tDeiecresnpp aaDatrioerttmnpmaaele rntnpmtut eobolnffi c ttt ahhoteiefo tnBBhseaa, ddBhjjeiai dhjia s e Sa SamMir oMkKohkhthaMetraon Urke hUn tinavciiresav Ur rersinrePistidvyirt eo oyoru fofset fAirts eAynss nonoenfaar Aa rbcbnahana .nfa. oH dHbr e ateh . be RbH eepeelaloos bsnente ggtalwossrenc ttngohots y tt hhtyoeee ta hrse in s m DirecRtoaRrd aiaadtti Raitohtaineod n iPaP thPhtiohyhyensys isfPicicieschsl dsy L DsLoaicefab spbmo aoLraarragattbnmotoeoretrryiasyn mt wtow rohhayefn e wrdtrhee hse ehuh rpBeeee arddhcdiieorrje ein dcdciutrtsesc c tivtsit y. ir K RMaodkihtbahtotaetbioohr o kentUoes ktanP tbeshmiaohav enoyme a okdtsrne ssfi odc a iHpioft smna yrexio otnn L eoijxoddhetarfeifac ed n Abrtsioessnan on x.sdatt ireiin.niAtdoar ir eaAoen ntutcobhnsuaattie.hraasttl yhi d olA.o a opHnruwsprr uaeet oeuhhboval fb oee.bf lpi lrsrrciesa cueeaoellab o vfttvht lihneiioesoceegrenransa asvsedtslil e so, t,i sr so rneaacchh stnlciihee ,eed ts esnn chh h ttierieiafeaf inicsscshte iafaicsrc h SaSaSahen cacrarirerdiec ador uoriteu rdte roseeustae rraecrshceh fa ofrorc rht ht hfeoe rp ptahaess tpt ttawwseet ntnwttyye nyyteeyaa yrrses a iinrns in mmme the team of oxides. Author of several scientific booktsh etHha eefni edhftHli ahdeeseil nd ohtd fefiaoie rrsfmeln d cmad atoitegraifeod ngc nmnestaeetaeildtsgv i smnepsmereu at vabilsa enltminrhcdad ea la ssttsinehuoudsepnp sessaeer,unrs ccpd ohoae nennr cddr deouuh sncc aedrttesiiauvvs rciiectttyyihav.. ri tc yh. Sair Kir Kir K He has directed several theses and research mhh carriedp oroujtep crretossj ee icnat sr tc h ihins f ot ahrri seth a ae.r epaa.st twenty years in ehe the fpieroldje octfs m ina g thniest i samre aa.nd superconductivity. irnen He has directed several theses and reKs2e996a 76r83c14h9 8 775106 Kenee h projects in this area. e n 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 e 711 Third Avenue New York, NY 10017 9 781498 775106 2 Park Square, Milton Park 9 781498 775106 Abingdon, Oxon OX14 4RN, UK 9 781498 775106 A SCIENCE PUBLISHERS BOOK 9 781498 775106 ii i Critical Currents and Superconductivity Ferromagnetism Coexistence in High-T Oxides C ii iii Critical Currents and Superconductivity Ferromagnetism Coexistence in High-T Oxides C Samir Khene Department of Physics, Faculty of Sciences Badji Mokhtar University of Annaba Annaba, Algeria CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20160419 International Standard Book Number-13: 978-1-4987-7511-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com v Preface The field of superconductivity is constantly evolving. Very important discoveries were made since the beginning of the last century; some of them have even rewarded with Nobel Prizes. In 1911, K.H. Onnes discovered that the electrical resistivity of many metals vanishes below certain very low critical temperatures (Nobel Prize). In 1933, W. Meissner and R. Ochsenfelds showed that cooled to temperatures below its critical temperature, a superconductor expels the magnetic field. In 1935, F. and H. London followed in 1950 by V.L. Ginzburg and L.D. Landau developed phenomenological theories which provided a better understanding of superconductivity (Nobel Prize). Based on these models, A. Abrikosov presented in 1957 a theory of the mixed state of type-II superconductors, which stipulates that the magnetic flux penetrates in these materials in the form of vortices (Nobel Prize). The same year, J. Bardeen, L.N. Cooper and J.R. Schrieffers elucidated the physical causes of the superconductivity phenomenon (Nobel Prize). In 1962, B.D. Josephson explained the tunneling junction behavior between the superconductors (Nobel Prize). Around the same time, the discovery of type-II superconductors which support very high magnetic fields (20 teslas) led to their intensive use for the generation of strong fields. In 1986, J.G. Bednorz and K.A. Muller discovered superconductivity in a copper and lanthanum oxide doped with barium with a critical temperature of the order of 30K (Nobel Prize). This was the beginning of the high-T superconductors’ era. C The highest critical temperature reached to date is 133K in a compound of the type HgBaCa CunO with n = 3, at ambient pressure. It reached n-1 2n+2+d 164K in the HgBa Ca CuO compound under high pressure. With out 2 2 3 x one well understands the physical mechanisms, responsible for the properties of these materials. However, the common feature of these new vi Preface superconductors is the lamellar structure made up of elements with poor conductivity which are juxtaposed to copper-oxygen superconducting layers. This quasi-two-dimensional character induces in these compounds the anisotropy of all their superconducting properties. Indeed, the electrical conductivity is very high along the ab planes, whereas it is much lower in the perpendicular direction to them. The critical current is very large when the current circulates in these planes, and it is much lower in the perpendicular direction. The critical fields are higher in the direction of planes than in the perpendicular direction. This book consists of six chapters. It begins by gathering key data for superconducting state and the fundamental properties of the conventional superconductors, followed by a recap of the basic theories of the superconductivity. It then discusses the differences introduced by the structural anisotropy on the Ginzburg-Landau approach and the Lawrence-Doniach model before addressing the dynamic of vortices and the ferromagnetism-superconductivity coexistence in high-Tc oxides, and provides an outline of the pinning phenomena of vortices in these materials, in particular the pinning of vortices by the spins. This book elicits the methods to improve the properties of super- conducting materials for industrial applications. This optimization aims at obtaining critical temperatures and densities of critical current as high as possible. Whereas the primary objective concerns the basic mechanisms pushing the superconductivity towards high temperatures, the secondary objective is to achieve a better understanding of the vortices pinning. It is suitable for students of various streams of higher education and for the students in the doctoral program of all branches of the fundamental sciences and the engineering sciences. It will be beneficial to the experienced teachers and researchers. I thank S. Senoussi, D. Feinberg, B. Barbara and G. Fillion for all their help. Prof. Dr. Samir Khene Badji Mokhtar University of Annaba (Algeria) vii Contents Preface v Chapter 1: Superconducting State 1 1. History of the Superconductivity 1 2. Definition of a Superconducting Material 4 3. Meissner Effect 5 3.1. Type-I Superconductors 6 3.2. Type-II Superconductors 7 4. Description of the Superconducting State 10 4.1. Origin of Superconductivity 10 4.2. Wave Function of the Superconducting State 10 4.3. Persistent Current 11 5. Electronic Specific Heat 11 6. Electromagnetic Absorption 13 7. Isotopic Effect 14 8. Flux Quantification 14 9. Josephson Effects 15 9.1. DC Josephson Effect 16 9.2. AC Josephson Effect 17 References 17 Chapter 2: Basic Models 21 1. London Model 21 2. Phenomenological Theory of Ginzburg-Landau 27 3. BCS theory 32 3.1. Main Results of the Theory 32 3.2. Superconducting Gap 32 3.3. Comparison between Ginzburg-Landau Theory and BCS Theory 35 References 35 viii Contents Chapter 3: Characteristics of High-T Superconductors 37 C 1. Introduction 37 2. Crystallographic Structures 38 2.1. La M CuO (M = Ba, Sr, Ca) System 38 2-x x 4-y 2.2. RBa CuOx System 39 2 3 2.3. Thallium and Bismuth Compounds 40 2.4. Artificial Multilayers 42 3. Properties 43 4. Elaboration 43 4.1. Introduction 43 4.2. Thin Films 44 4.3. Single Crystals 46 4.4. Textured Polycrystals 47 References 48 Chapter 4: Phenomenoligical Theories of the Anisotropic Superconductors 51 1. Anisotropic Ginzburg-Landau Model 51 1.1. Free Energy 51 1.2. Coherence Lengths 52 1.3. Penetration Depths 53 1.4. Ginzburg-Landau Parameters 54 1.5. Critical Fields 54 1.5.1. Example of the Experimental Determination of H 56 C1 1.6. Anisotropy of the Magnetization 57 1.6.1. Magnetization Near H 57 C2 1.6.2. Magnetization Within the Limit of London 58 1.6.3. Magnetization in the Interval H << H < H 58 C1 C2 1.7. Structure of the Vortices Lattice 59 1.8. Transverse Component of the Magnetization 60 2. Lawrence-Doniach Model 65 2.1. Josephson Effects 65 2.1.1. Continuous Josephson Effect 65 2.1.2. Alternative Josephson Effect 66 2.2. Free Energy 66 2.3. Characteristic Lengths 69 2.4. Change of the Dimensional Regime 70 2.4.1. Magnetic Field Parallel to the Layers 70 2.4.2. Magnetic Field Perpendicular to the Layers 73 2.4.3. Magnetic Field Inclined in Relation to the Layers 74 References 74 Chapter 5: Dynamic of Vortices 77 1. Hysteresis Origin in the Magnetization Curves 77 2. Breaking Current of Cooper Pairs 77