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T TA/F.T Dissertation Vjlvjll Information Service INFORMATION TO USERS This reproduction was made from a copy of a manuscript sent to us for publication and microfilming. While the most advanced technology has been used to pho­ tograph and reproduce this manuscript, the quality of the reproduction is heavily dependent upon the quality of the material submitted. Pages in any manuscript may have indistinct print. In all cases the best available copy has been filmed. The following explanation of techniques is provided to help clarify notations which may appear on this reproduction. 1. Manuscripts may not always be complete. When it is not possible to obtain missing pages, a note appears to indicate this. 2. When copyrighted materials are removed from the manuscript, a note ap­ pears to indicate this. 3. 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Zeeb Road, Ann Arbor, Michigan 48106 8625262 Mitchell, Terry Blake MAGNETIC AND MAGNETO-OPTIC BEHAVIOR OF BISMUTH AND THULIUM SUBSTITUTED YTTRIUM IRON GARNETS The Ohio State University Ph.D. 1986 University Microfilms international300 N. Zeeb Road, Ann Arbor, Ml 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or pages______ 2. Colored illustrations, paper or print_______ 3. Photographs with dark background_____ 4. Illustrations are poor copy_______ 5. Pages with black marks, not original copy_______ 6. Print shows through as there is text on both sides of page________ 7. Indistinct, broken or small print on several pages 8. Print exceeds margin requirements______ 9. Tightly bound copy with print lost in spine________ 10. Computer printout pages with indistinct print_______ 11. Page(s) ___________ lacking when material received, and not available from school or author. 12. Page(s)_____________ seem to be missing in numbering only as text follows. 13. Two pages numbered________. Text follows. 14. Curling and wrinkled pages_ 15. Dissertation contains pages with print at a slant, filmed as receivedl/ 16. Other_____________________________________________________________________ ________ University Microfilms International MAGNETIC AND MAGNETO-OPTIC BEHAVIOR OF BISMUTH AND THULIUM SUBSTITUTED YTTRIUM IRON GARNETS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Terry Blake Mitchell, B.S., M.S. The Ohio State University 1986 Approved by Reading Committee: Dr. Philip E. Wigen Dr. David G. Stroud Philipp. Wigen, Advrser Dr. James T. Tough Department of Physics To My Parents ii ACKNOWLEDGEMENTS I would like to thank my advisor, Professor Philip Wigen, for the friendship and support he has given me during my work at Ohio State. I am deeply grateful for his guidance and the encouragement he has given me to fulfill my educational goals. I would like to thank Dr. Ladislav Pust, Dr. Martha Pardhavi- Horvath, and Dr. Sharat Batra for the stimulating discussions and help in pursuit of solutions to problems that arose during the course of the investigations. I would like to thank Dr. Andrea Lehmann-Szweykowska for the discussion and help she gave during her visits at Ohio State. I would like to thank the NSF grant //DMR-8304250 and the Department of Physics of The Ohio State University for financial support of myself and the research projects. I am also indebted to the technical assistance and professional quality of the staff I have worked with especially Tony Bernardo, Vijay Sehgal, Roy Tucker, and Claire McDonald. I would especially like to thank Pat Kimball for the superb job of typing this manuscript. There is no way of expressing the gratitude I feel for the friend­ ships I have made while at Ohio State. There is no way I can include all my friends that had a pronounced affect on this work. Don, Sharat, Ramesh, Arvind, Gregg, Ewa, Martha, Ladia, and Andrea are especially acknowledged for the support only very close friends can give. iii VITA January 27, 1958 .........Born, Ft. Worth, Texas 1981 ..................... B.Sc., The Ohio State University Columbus, Ohio 1983 ..................... M.Sc., The Ohio State University Columbus, Ohio 1981-1984 ................. Teaching Assistant, Department of Physics, The Ohio State University Columbus, Ohio 1984-1986 ................. Research Assistant, Department of Physics, The Ohio State University, Columbus, Ohio PRESENTATIONS "The Faraday Rotation In TmBl Substituted YIG Thin Films" T. B. Mitchell and P. E. Wigen. Presented at the International Colloquium on Thin Films and Surfaces in Asilomar, CA in September 1985. "Anisotropic Magnetic and Magnetooptic Behavior of Thin Garnet Films with High Q-values" T. B. Mitchell, L. Pust, and P. E. Wigen. Presented at the March 1986 meeting of the American Physical Society at Las Vegas, Nevada and to be published in JAP. iv TABLE OF CONTENTS DEDICATION .......................................................... ii ACKNOWLEDGEMENTS ................................................. iii VITA ................................................................. iv LIST OF T A B L E S ..................................................... vii LIST OF FIGURES ............................................... viiii CHAPTER PAGE 1. INTRODUCTION .............................................. 1 2. T H E O R Y .................................................... 6 Crystal Structure ................................ 6 Magnetization .................................... 8 Ferromagnetic Resonance .......................... 13 Effective g-value ................................ 18 Twin Peak Effect ..................................... 23 Faraday Effect .................................... 35 3. EXPERIMENTAL PROCEDURES ................................. 43 Saturation Magnetization .......................... 43 Ferromagnetic Resonance .......................... 45 Sample Characterization .......................... 50 Magneto-optic Measurements ........................ 51 4. EXPERIMENTAL RESULTS AND CONCLUSIONS .................... 57 Sample Characterization .......................... 57 Saturation Magnetization .......................... 57 Ferromagnetic Resonance .......................... 63 Twin Peak Results ................................... 68 Faraday Rotation .................................. 81 5. CONCLUSION.................................................. 90 v APPENDICES A. Computer Program to Calculate the Magnetization Using MET ................................ 93 B. Computer Program to Calculate the Effective g-value, and Heff from F M R ................. 97 BIBLIOGRAPHY ...................................................... 102 vi LIST OF TABLES TABLE PAGE I. Effects on B for Different Cases of a Assuming H a > 0 ................................................30 II. Sample Characteristics ................................... 58 III. Faraday Rotation of Quartz Windows and Blank Substrate ..............................................82 IV. Faraday Rotation Coefficients of the Sublattice Magnetizations ........................................... 88 vii LIST OF FIGURES FIGURE PAGE 1. View of the domain structure using the magneto-optic Faraday Effect. From top left clockwise; ring pattern, stripe pattern, labrynth pattern, and bubble pattern. (Ref. 8) ........... A 2. The underlying symmetries of the cubic garnet system. An oxygen ion is located at the corners of each polyhedra. (Ref. 9) ...................... 7 3. The temperature dependence of the total magnetization for pure YIG calculated by MFT using the molecular field coefficients of Equation 8 and the program in Appendix A ..................... 11 A. The temperature dependence of the total magnetization for pure TmlG calculated by MFT using the molecular field coefficients of Equation 9 and the program In Appendix A ................... 12 5. The coordinate system used in the theoretical discussion........................................ 14 6. The temperature dependence of the effective g-value of pure YIG. The experimental data (H ) is from Ref. 18 and the solid line represents the spin wave theory predicted by Equation 27 ............... 20 7. The theoretical temperature dependence of the effective g-value of pure TmlG. Notice the g-value increases with decreasing temperature and the divergence at 70 K is an angular momentum compensation point................................... 22 8. Thin film geometry for light propagation along the z direction. The sign of the Faraday rotation is determined by the direction of the magnetization in each domain................................................. 25 viii 9.
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