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FundamentalsofMagnetism Mathias Getzlaff Fundamentals of Magnetism With292 Figures and 18 Tables ABC Prof.Dr.MathiasGetzlaff Univ.Düsseldorf Inst.AngewandtePhysik Universitätsstr.1 40225Düsseldorf Germany [email protected] LibraryofCongressControlNumber:2007934345 ISBN978-3-540-31150-8 SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright. Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermitted onlyundertheprovisions oftheGermanCopyright LawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliableforprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com (cid:2)c Springer-VerlagBerlinHeidelberg2008 Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:bytheauthorandIntegra,IndiausingaSpringerLATEXmacropackage Coverdesign:eStudioCalamar Printedonacid-freepaper SPIN:11551591 543210 To my wife Anette Preface Magnetismisafascinatingsubjectwhichisknownsinceafewthousandyears. This means that this phenomenon was already observed before recorded his- tory began. In the Near Eastregionsome oreswere found to be “attractive”or “magnetic”.InEurope,the useofthisironorecalledLodestonefornavigationina compassisunquestionablydatedtoabout1300.But,thefirstincontrovertible mention of a magnetic device used for establishing direction is to be found in a Chinese manuscript dated about 1040. The Lodestone was located into a spoon that was placed on a plate being of bronze. Rather than navigation this pointer was used for geomancy being a technique for aligning buildings in order to be in harmony with the forces of nature. Todayourunderstandingofmagnetismiscloselyrelatedtotheconceptof spinwhicharisesfromtherelativisticdescriptionofanelectroninanexternal electromagnetic field and becomes manifest in the Dirac equation. This con- cept results in the spin magnetic moment and the orbital magnetic moment which is due to the motion of electronic charges. Asthroughouthistorymagnetismiscloselyrelatedtoapplications.Alotof common today’s devices would be unthinkable without the forefrontresearch areas in magnetism. One example is given by read heads in hard disks which alloweda tremendous enhancement ofstoragedensity.They are basedonthe discoveryoftheGiantMagnetoresistance(GMR)in1988byP.Gru¨nbergand A. Fert. And also today technology is driven by the aim to develop devices which are smaller, faster, and cheaper than every one before. Alreadythesefewannotationsprovethatthefieldofmagnetismwasexcit- ing in the past. Nevertheless, in the future we will discover many new effects which will be beyond our imagination and will have a strong influence on several things “around us”. Thus, they will shape our daily lives. Tomyopinionmostofthenewdiscoverieswillberelatedtolow-dimensional systems. VIII Preface Therefore,the first partof this book deals with the fundamentals of magnetism whereas the secondone is devotedto magnetic phenomena of systems which are reduced in at least one-dimension. InChap. 1wewillstarttheintroductionbysummarizingsomebasicterms of magnetism, give a classification of magnetic materials, and schematically showwhy magnetismcannotbe explainedusing classicalmechanics andelec- trodynamics. Chapter 2 deals with magnetic moments of free, i.e. isolated, atoms in a magnetic field. After the discussion of atomic dia- and paramagnetism we will develop some simple rules which allow to determine the magnitude of magnetic moments concerning an atom of a given chemical element. Using the model of free electrons we will see in Chap. 3 that collective magnetismcanbestabilizedabove0Kwithoutapplyinganexternalmagnetic field in a solid state due to interaction between magnetic moments. Chapter 4 is devoted to the question how magnetic moments in different atoms can interact with each other. The description of different types of magnetic order in the solid state, i.e.collectivemagnetism(ferromagnetism,antiferromagnetism,ferrimagnetism, helical order), is given in Chap. 5. The vanishing of long range ferromagnetic order above a critical temper- ature is related to a breaking of a symmetry and can be characterized by a phasetransition.Thisdistincttemperaturedependenceofspecificparameters like the magnetization is discussed in Chap. 6. InChap. 7wewilllearnabouttheinfluenceofanisotropyonthemagnetic behaviorwhichcanbeinducedby,e.g.,theshapeandthecrystallinestructure of a sample. Chapter 8 deals with magnetic domains being uniformly magnetized re- gions which exhibit a parallel orientation of all magnetic moments and the boundaries between them, the domains walls. In Chap. 9 we will discuss the “answer” of the magnetization concerning themagnitudeandthedirectionifavaryingexternalmagneticfieldisapplied. The next six chapters are devoted to magnetism in reduced dimensions. In Chap. 10 we will start our discussion with the behavior of single magnetic atoms on a surface and proceed with ensembles consisting of only a few atoms,so-calledclusters,inChap.11.Thepropertiesoflargeragglomerations, nanoparticles, will be presented in Chap. 12. The behavior of wires with di- mensionsinthenanometerregimewillbeexplainedinChap.13.Thenexttwo chapters contain the description of magnetic thin film systems. In Chap. 14 we will restrict our discussion to single thin metallic films and explain the properties of multilayers in Chap. 15. Theinfluenceofthespinarrangementinamagneticlayerontheelectrical resistance will be discussed in Chap. 16. This effect called magnetoresistance can be rather huge and thus acts as the basis to realize technologically important applications like read heads in hard disks and various sensors which will be presented in Chap. 17. Preface IX Severalchaptersexhibitproblemsinordertoimprovetherespectiveknowl- edge. The solutions are given at the end of the book. In the appendices abbreviations, symbols, and important constants are listed. In this textbook we make use of the units and definitions of the système international SI. In some figures the properties are given in the cgs-system (centimeter,gram,second).Thisobservationandproblemshouldadditionally sensitize the readerthat different “languages”are often spokenin the field of magnetism. A comparison of important quantities in both systems is also given in order to round off this textbook. Last but not least it is a pleasure for me to thank all the people which significantlyimpartedmyknowledgeonthiswidefieldofmagnetism:Joachim Bansmann,MatthiasBode,UlrichHeinzmann,GerdScho¨nhense,andRoland Wiesendanger. Du¨sseldorf, June 2007 Mathias Getzlaff Contents 1 Introduction............................................... 1 1.1 Fundamental Terms...................................... 1 1.2 Classification of Magnetic Material ........................ 3 1.3 Bohr–van Leeuwen Theorem .............................. 6 2 Magnetism of Atoms ...................................... 7 2.1 Atoms in a Magnetic Field................................ 7 2.2 Atomic Diamagnetism ................................... 9 2.3 Atomic Paramagnetism .................................. 10 2.4 Hund’s Rules for the Ground State of Atoms................ 21 Problems ................................................... 24 3 Solid State Magnetism..................................... 25 3.1 Model of Free Electrons .................................. 25 3.2 Pauli Paramagnetism .................................... 29 3.3 Spontaneously Spin Split States ........................... 30 3.4 Magnetism of 3d Transition Metals and Alloys .............. 36 Problems ................................................... 39 4 Magnetic Interactions ..................................... 41 4.1 Magnetic Dipole Interaction .............................. 41 4.2 Direct Exchange......................................... 42 4.3 Indirect Exchange ....................................... 43 5 Collective Magnetism...................................... 47 5.1 Ferromagnetism......................................... 48 5.2 Antiferromagnetism...................................... 55 5.3 Ferrimagnetism ......................................... 62 5.4 Helical Order ........................................... 65 5.5 Spin Glasses ............................................ 67 Problems ................................................... 68 XII Contents 6 Broken Symmetry ......................................... 71 6.1 Breaking of the Symmetry................................ 71 6.2 Different Models of Magnetic Behavior ..................... 73 6.3 Consequences ........................................... 77 6.4 Phase Transitions ....................................... 78 6.5 Magnetic Excitations .................................... 83 7 Magnetic Anisotropy Effects............................... 89 7.1 Overview of Magnetic Anisotropies ........................ 89 7.2 Magneto Crystalline Anisotropy ........................... 90 7.3 Shape Anisotropy .......................................102 7.4 Induced Magnetic Anisotropy .............................105 7.5 Stress Anisotropy (Magnetostriction) ......................108 7.6 Magnetic Surface and Interface Anisotropies ................112 Problems ...................................................114 8 Magnetic Domain Structures ..............................117 8.1 Magnetic Domains.......................................117 8.2 Domain Walls...........................................120 8.3 Domain Wall Width .....................................121 8.4 Closure Domains ........................................124 9 Magnetization Dynamics ..................................133 9.1 Magnetic After-Effect ....................................133 9.2 Influence of High-Frequent Magnetic Fields .................139 9.3 Damping Processes ......................................141 9.4 Ferromagnetic Resonance.................................145 Problems ...................................................149 10 Magnetism in Reduced Dimensions – Atoms...............151 10.1 Single Atoms on a Surface ................................152 10.2 Quantum Mirage ........................................156 10.3 Reversal of the Spin in a Single Atom......................159 10.4 Influence of the Substrate ................................161 11 Magnetism in Reduced Dimensions – Clusters .............165 11.1 “Every Atom Counts”....................................165 11.2 Influence of the Geometrical Arrangement and Surface Symmetry ...................................168 11.3 Clusters at Step Edges ...................................172 11.4 ComparisonBetween Free and Supported Clusters...........174