Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2015 NMR Study of Magnetism and Superparamagnetism Shaojie Yuan Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES NMR STUDY OF MAGNETISM AND SUPERPARAMAGNETISM By SHAOJIE YUAN A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2015 Shaojie Yuan defended this dissertation on July 20,2015. The members of the supervisory committee were: Arneil P Reyes Professor Co-Directing Dissertation Pedro Schlottmann Professor Co-Directing Dissertation Naresh Dalal University Representative Michael J.R Hoch Committee Member Irinel Chiorescu Committee Member Horst Wahl Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements. ii In memory of my adviser: Dr. James Brooks iii ACKNOWLEDGMENTS First and foremost, I would like to express my sincere gratitude to my late adviser Prof. James Brooks for his support and guidance, and for being a great mentor. His immense knowledge concerning different aspects of condensed matter physics and material science constitute a rich resource. His enthusiasm for science will keep on influencing many of us. I would also like to thank my co-advisers, Dr. Michael Hoch, Dr. Philip Kuhns, and Dr. Arneil Reyes sincerely, for their patience in teaching me in the following areas: condensed matter NMR, cryogenics, scientific writing and presenting, home-built instrumentations, and interaction and communication skills. Further, I would like to thank Dr. Pedro Schlottmann for directing this defense and his many suggestions for improving my thesis. Sincere thanks goes to the cryogenics team, Bob Carrier, Matthew N. Barrios, Dan Freeman for their help with liquid helium, especially those extra calls during weekends and holidays. During our experiments in the hybrid, I learned from them not only about hybrid magnets but also many interesting things about high field technology. I would also like my fellow labmates and group members: Shermane M Benjamin, Amouzandeh Ghoncheh, Dr. Andhika Kiswandhi, Dr. Laurel Winter, Dr. Eden Steven and Doug Wilson. It has been a great four years and it was fun hanging out together and discussing physics. I am grateful to our collaborators: Dr. Stuart Brown, Dr. Nicholas Curro, Dr. Chris Leighton, Dr. John Mitchell, Dr. Hironori Sakai and Dr. Haidong Zhou, for their help and enlightening me in my research. Finally, I would like to thank my Dad and Mom for supporting me financially and spiritually. iv TABLE OF CONTENTS List of Figures .............................................................................................................................. viii Abstract .......................................................................................................................................... xi 1. INTRODUCTION 1 1.1 Fine and hyperfine structure of atoms .............................................................................1 1.1.1 Dirac equation ........................................................................................................1 1.1.2 Hyperfine structure and dipole-dipole coupling .....................................................3 1.2 Magnetic moment of an ion .............................................................................................5 1.3 Paramagnetism ................................................................................................. 6 1.4 Magnetic ordering ............................................................................................ 7 1.4.1 Ferromagnetism ...................................................................................................8 1.4.2 Antiferromagnetism ...........................................................................................11 1.4.3 Spin glass ...........................................................................................................13 1.5 Geometrical Frustration ...............................................................................................14 1.6 Magnetic domain ..........................................................................................................16 1.7 Superparamagnetism .....................................................................................................17 2. NUCLEAR MAGNETIC RESONANCE AND EXPERIMENTAL SETUP 20 2.1 NMR basics ..................................................................................................................20 2.1.1 Free induction decay .........................................................................................20 2.1.2 The rotating frame ............................................................................................22 2.1.3 Spin echo ..........................................................................................................24 2.1.4 NMR Relaxation ...............................................................................................25 2.2 Zero field NMR ............................................................................................................28 2.1.1 Internal hyperfine field .....................................................................................28 2.1.2 Frequency sweep spectra .................................................................................29 2.1.3 Effect of a small perturbed field .......................................................................29 2.3 Radio frequency enhancement ....................................................................................31 2.4 Korringa relationship and knight shift ..........................................................................33 2.5 Redfield theory ............................................................................................................34 2.6 Experimental setup ......................................................................................................36 2.6.1 Probe and the Tank circuit ................................................................................36 2.6.2 Inductive matching .........................................................................................37 2.6.3 Pulse NMR electronics .....................................................................................38 3. SPIN CONFIGURATION IN THE EXTENDED KAGOME SYSTEM YBACO4O7 40 3.1 Introduction .................................................................................................................40 3.2 Experiment ..................................................................................................................42 3.3 Analysis ........................................................................................................................44 3.3.1 Rotational Experiment Analysis .......................................................................44 3.3.2 ANTIOPE simulation .......................................................................................45 3.3.3 Rotational experiments in a perturbed field .....................................................45 v 3.4 Result and discussion ..................................................................................................46 3.4.1 Spectra ..............................................................................................................46 3.4.2 Result of the rotational experiment ..................................................................48 3.4.3 Results in a perturbing field .............................................................................50 3.4.4 Relaxation .........................................................................................................52 3.5 Summary .......................................................................................................................54 4. SPIN ORDERING AND DYNAMICS IN THE FRUSTRATED SYSTEM YBACO4O7.1 56 4.1 Introduction .................................................................................................................56 4.2 Experiment ..................................................................................................................58 4.3 Result ...........................................................................................................................58 4.3.1 Magnetization and AC susceptibility ...............................................................58 4.3.2 Zero field NMR ................................................................................................61 4.4 Analysis and discussion ................................................................................................66 4.4.1 The proposed model .........................................................................................66 4.4.2 Low temperature NMR spectra ........................................................................67 4.4.3 Cooling rate dependency of the YBaCo4O7.1 spectra .......................................69 4.4.4 Comparison between YBaCo4O7 and YBaCo4O7.1 ..........................................70 4.5 Summary ......................................................................................................................70 5. MAGNETICALLY NANOSTRUCTURED STATE IN A Ni-Mn-Sn SHAPE MEMORY HEUSLER ALLOY