Characterization of Hysteresis in Magnetic Systems: A Preisach Approach Patricia Darlene Mitchler A Thesis Submitted to the Faculty of Graduate Studies in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy University of Manitoba Winnipeg, Manitoba National Library Bibliothèque nationale !*m of Canada du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395, rue Wellington Ottawa ON K1A ON4 ûttawa ON KIA ON4 Canada Canada The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, disûibute or seil reproduire, prêter, distribuer ou copies of this thesis in microfonn, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique. 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FACULT'Y OF GRADUATE STUDIES *a*** COf YRIGaT PERMISSION PAGE Characterizatioa of Hysterais in Magnetic Systems: A Preisach Approach Patricia Darlene Mitchler A ThesidPracticum submitted to the Facnlty of Gradnate Studies of The University of Manitoba in partial fuINlment of the reqnirements of the degret of Doctor of Phiiosophy PATRICIA DAEUENE haTCHLER O 2000 Permission has been granted to the Library of The University of Manitoba to lend or oeil copies of this thesidpracticum, to the Nationai Library of Canada to microfilm this thesis/practicum and to lend or sen copies of the f?ii.m, and to Dissertations Abstracts International to publish an abstract of this thesidpracticum. The author reserves other publication rights, and neither this thesidpracticum nor extensive extracts from it may be printed or otherwise reprodnced without the author's Wfitten permission. Abstract The phenornenon of hysteresis is perhaps the most widely recognized microscopie manifestation of magnetic ordering, and is the principal feature which is responsible for technologicallysriented applications of magnetic materials such as permanent magnets and recording media Interest in a phenomenological model of hysteresis originally proposed by Preisach in 1935 has been renewed recently, particularly in engineering applications, such as the characterization of magnetic recording media and magnetostrictive materials. Thus, a ngorous assessrnent of the capabilities and limitations of the Preisach model for charactenzing magnetic materials is of considerable importance from both fundamental and technological perspectives. The fundamental characteristics of hysteresis are discussed and a theoretical background for the processes involved in magnetic systems is established. A generalized version of the scalar Preisach model, which includes original contributions, is developed to extend the model's abilities to describe the effects of the structure of the initially demagnetized state, the presence and nature of interactions, the system's coercive field distribution, and especially, the effects of temperature and expenmental wait time, on the observed hysteretic properties of a variety of magnetic systems including spin glasses, ferromagnets, ferrimagnets, and superparamagnets. The moment and remanence of magnetic systems are rneasured as a fùnction of applied fieid and temperature, using both a vibrating sample magnetometer (VSM) and a SQUID-based magnetometer. A Preisach analysis of the data is used to characterize the irreversible response of six magnetic systems: Crû, audio tape; magnetofemtin; a Nqe,,B permanent magnet; a floppy disk medium; and longitudinal and perpendicular cobdtshromium-based hard disk materials. The ambiguous nature of tools presently used to analyze the nature of magnetic systems, such as the application of Heakel plots to the aoalysis of interaction effects, is demonstrated and alternative Preisach-based analysis schemes are presented. The physical significance of parameters, which emerged from the Preisach calculations, is discussed in detail and modifications are proposed to model this array of real magnetic systerns. These changes to the scalar Preisach model extend its capabilities, while maintainhg the inherent simplicity of a scaiar model. Limitations of the model are also discussed critically, and suggestions for future generaiizations are made. Acknowledgements Special thanks to my thesis advisor Dr. R. M. Roshko, who htinspind me to study physics. His guidance, support, patience, and encouragement during the course of my research and throughout my undergraduate studies are deeply appreciated. 1 also thank the advisory committee, Dr. A. H. Momsh, Dr. J. H. Page, and Dr. D. Thomson,. for their time and suggestions throughout my graduate program, and Dr. C. Campbell, for acting as extemal examiner. Thank you to Dr. P. W. Zetner for our many discussions and for his dvice and encouragement dunng the completion of this thesis. 1 extend my sincere appreciation to Wanda Kiassen for her invaluable assistance in the preparation of this manuscript. 1 acknowledge the financial support of NSERC, which provided fellowships and grants for this research, and 1 am grateful to the School of Physics and Astronomy, University of Minnesota, which made available the equipment used to gather the data presented in this thesis. A special th& you to my sister, Mary-Am, for her ffiendship and for providing me with transportation. Fmally, 1express heartfelt gratitude to my parents, Dan and Stephanie Mitchier for their unwave~gsupport, patience, and unconditional encouragement for ail my academic eadeavours, throughout my iife. Thank you, Mom, for instilling in me a love of science. I am forever in your debt. Table of Contents Page Abstract iv Acknowledgements Chapter 1: An Overview of Hysteresis 1.1 The Hysteresis Luop 1.2 Physical Origins of Hysteresis 1.3 The Anhysteretic Curve 1.4 Technical Applications of Hysteresis 1.5 Modelling Hysteresis 1.6 Investigating Hysteresis Using the Preisach Approach Chapter 2: The Theoretical Basis of Hysteresis 2.1 Magnetization 2.2 Magnetostatic Energy 2.3 Exchange Interaction 2.4 Magnetic Anisotropy 2.5 Domain Structure 2.6 Single Domain Particles 2.7 Mechanisms of Magnetization Reversal 2.7.1 Coherent Revend: The Stoner-Wohifarth Mode1 2.7.2 Incoherent Reversal Modes vii 2.7.3 Dipole-Dipole Interactions 2.7.4 Dornain Wall Motion 2.7.5 Brown's Paradox 2.7.6 Becker's Model 2.8 Types of Magnetic Materials 2.8.1 Paramagnetism 2.8.2 Ferromagnetism 2.8.3 Ferrimagnetism 2.8.4 Superparamagnetism 2.8.5 Spin Glasses Chapter 3: The Preisach Model: Generalizing the Formalism 3.1 Scdar Preisach Model 3.2 Moving Preisach Model 3.3 Preisach Plane 3.3.1 Using the Preisach Plane 3 -3.2 The Demagnetized Plane 3.4 Henkel PIots 3.4.1 Wohlfarth Relation Derivation 3.4.2 The Lower Limit 3.4.3 Interpretation of Henkel Plots 3.4.4 Henkel Plots and the Random ThemaiIy Demagnetized Plane 3.4.5 Compensated Henkel Plots 3.5 Thermal and Time Relaxation Effects 3 S. 1 Generalized Preisach Model 3.5.2 Effects of Relaxation on Hysteresis Loops and on Henkel Plot Curvature 3.6 Reversibility in the Preisach Model 3.7 The Moving Coercive Field Distribution: The Preisach Model and Spin Glasses Chapter 4: Equipment, Experimental Protocols, and Magnetic Systems 4.1 Magnetic Measurement Equipment 4.1.1 S QUiD Magnetometer 4.1.2 Vibrating Sample Magnetometer (VSM) 4.2 Experimental Protocols 4.2.1 Generating Magnetization Curves as a Function of Temperature 4.2.2 Demagnetization 4.2.3 Magnetization and Remanence Measurements: Generating a Henkel Plot 4.2.4 Magnetization as a Function of The 4.3 Magnetic Systems 4.3.1 Chromium Dioxide Audio Tape 4.3.2 Magnetofemtin 4.3.3 Neodymium Iron Boron: A Permanent Magnet 4.3.4 Commercial Floppy Disk 4.3.5 Commercial Hard Disk: Cobalt Chromiurn-Based 4.3.6 Perpendicular Hard Disk: Cobalt Chromium Chapter 5: A Preisach-based Analysis and Discussion of the Hysteretic Properties of Magnetic Systems 5.1 Parameter Selection and Fitting 5.1.1 ][nitid Pararneter Values 5.1.2 The Preisach Distribution 5.1.3 The Reversible Component 5.1.4 The "Fitting" Procedure 5.2 Commercial Fioppy Disk 5.3 Commercial Cobalt-Chromium-Based Hard Disk 5.4 Perpendicular Co,Cr,, Hard Disk 5.5 Chromium Dioxide Audio Tape 5.5.1 Generd Features of the Magnetic Response 5.5.2 Analysis of AC Demagnetized Sample Data (25 OC s T s 120 OC) 5.5.3 Cornparison of AC and Thennaily Demagnetized Sample Data (25 OCs T r 120 OC) 5.5.4 Alternative Parameter Selection (25 OC s T s 120 OC) 5.5.5 Analysis of AC and Thermally Denagnetized Low Temperature Data (10 K s T s 300 K) 5.6 Magnetofemtin 5.6.1 Generai Features of the Magnetic Response 5.6.2 Analysis of ThermaUy Demagnetized Hysteresis Data 5.7 Neodymium Iron Boron 5.7.1 General Features of the Magnetic Response 5.7.2 Analysis of the Hysteresis Data: Modifymg the Elernentary Hysteresis Loop Chapter 6: A Critical Appraisal of the Preisach Approach Appendix 1: Additional Data and Fits Appendix 2: Fortran Programs for Preisach Caiculations M.1 Fortran Program for Preisach Calculations (General) A2.2 Fortran Program for Preisach Calculations (N&Fe,,B) References Chapter 1 An Overview of Hysteresis The phenomenon of magnetic hysteresis refers to the observation that strongly exchange-coupled magnetic materials (ferromagnets (Section 2.8.2), antiferromagnets (Section 2.8.3), spin glasses (Section 2.8.5), etc.) exhibit a nonunique, path dependent response to a variable external field stimulus. Essentially, hysteresis originates from the presence of many local metastable minima in the free energy landscape of the system in configuration space.