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Spin Dynamics and Quantum Tunneling in Fe8 Nanomagnet and in AFM Rings by NMR Seung-Ho Baek Iowa State University

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Spin Dynamics and Quantum Tunneling in Fe8 Nanomagnet and in AFM Rings by NMR Seung-Ho Baek Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2004 Spin dynamics and quantum tunneling in Fe8 nanomagnet and in AFM rings by NMR Seung-Ho Baek Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Condensed Matter Physics Commons, Electromagnetics and Photonics Commons, and the Other Physics Commons Recommended Citation Baek, Seung-Ho, "Spin dynamics and quantum tunneling in Fe8 nanomagnet and in AFM rings by NMR " (2004). Retrospective Theses and Dissertations. 1143. https://lib.dr.iastate.edu/rtd/1143 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Spin dynamics and quantum tunneling in Fe8 nanomagnet and in AFM rings by NMR by Seung-Ho Baek A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Condensed Matter Physics Program of Study Committee: Ferdinando Borsa, Co-major Professor Marshall Luban, Co-major Professor Joerg Schmalian Joseph Shinar Jianwei Qiu Gordon J Miller Jr. Iowa State University Ames, Iowa 2004 Copyright © Seung-Ho Baek, 2004. All rights reserved. UMI Number: 3158315 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3158315 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 11 Graduate College Iowa State University This is to certify that the doctoral dissertation of Seung-Ho Baek has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. iii TO EUN-Jl AND FLORA iv TABLE OF CONTENTS CHAPTER 1 Introduction 1 1.1 Single molecule magnets (SMMs) 1 1.2 Nuclear magnetic resonance as a tool to investigate SMMs 7 1.3 Organization of the dissertation 7 CHAPTER 2 Nuclear magnetic resonance and relaxation 9 2.1 Magnetic resonance theory 9 2.1.1 Isolated nuclear spins 9 2.1.2 Relaxation 10 2.1.3 Generalized nuclear susceptibilities 14 2.1.4 Nuclear dipolar broadening and methods of moments 16 2.1.5 Hyperlinc interaction 17 2.2 NMR in molecular magnets 18 2.2.1 High temperature region (kgT J) 18 2.2.2 Low temperature region 4C J) 20 2.2.3 Intermediate temperature region (AgT ^ J) 21 2.3 Detection methods 23 2.3.1 Free induction decay (FID) and spin echoes 23 2.3.2 Measurement of spin-spin relaxation time, 23 2.3.3 Measurement of spin-lattice relaxation time, 7% 25 CHAPTER 3 Magnetic properties and spin dynamics in Fe8 molecular cluster 26 3.1 Introduction 26 V 31.1 Structure of Fe8 26 3.1.2 Magnetization and magnetic susceptibility 28 3.2 Magnetic properties of Fe8 30 3.3 Quantum tunneling of the magnetization 40 3.3.1 Tunneling in zero held 41 3.3.2 Tunneling in a longitudinal field 51 3.3.3 Tunneling in a transverse field 52 CHAPTER 4 57Fe NMR and relaxation in isotopically enriched Fe8 .... 67 4.1 Introduction 68 4.2 Sample properties and experimental details 69 4.3 Experimental results 72 4.3.1 57Fe NMR spectrum 72 4.3.2 Nuclear relaxation rates 74 4.4 Hyperfine interactions and static magnetic properties 75 4.4.1 Hyperfine interactions 75 4.4.2 Reduction of the hyperfine field due to thermal fluctuations 77 4.4.3 Determination of the local spin arrangement in the ground state .... 79 4.5 Spin dynamics 82 4.5.1 Nuclear relaxation due to thermal fluctuations 82 4.5.2 Nuclear relaxation due to quantum tunneling 85 4.6 Analysis of the experimental results for nuclear relaxation rates 86 4.6.1 Spin-lattice relaxation rate (1/7%) 86 4.6.2 Spin-spin relaxation rate (l/Tz) 92 4.6.3 Comparison of ^Fe relaxation rate in Fe8 with ^H relaxation in Fe8 and ^Mn relaxation in Mnl2 96 4.7 Summary and conclusions 99 CHAPTER 5 Scaling behavior of the proton spin-lattice relaxation rate in antiferromagnetic molecular rings 101 vi 5.1 Introduction 101 5.2 Experimental results and discussion 102 5.3 Summary and conclusion Ill CHAPTER 6 General summary 112 APPENDIX A 1/Ti in terms of the wave vector (g) components of the electronic spins 113 APPENDIX B Derivation of the correlation function for two-state random Held fluctuation 115 APPENDIX C Nuclear relaxation in strong collision limit 117 ACKNOWLEDGEMENTS 119 BIBLIOGRAPHY 121 VITA 131 1 CHAPTER 1 Introduction 1.1 Single molecule magnets (SMMs) For a few decades, chemists have developed new classes of magnets baaed on molecules rather than on metals or oxides. The idea behind this is the challenge of creating new classes of materials from which new exciting properties may be expected (see, for example, Kahn [1]). It was only a decade ago when physicists realized that a particular class of molecular magnets (MM) i.e., single molecule magnets (SMMs) are excellent zero-dimensional model system for the study of the nonoacopzc or mesoacopic magnetism. The prefix nano- or meso- indicates that SMMs are positioned at the frontier between single spin behavior and bulk magnetism. In this interesting regime, one can expect new physical phenomena arising from the coexistence of classical and quantum behaviors [2]. SMMs are exchange coupled clusters, at present, of two to thirty paramagnetic ions (e.g., iron dimer [3] to a giant cluster Fe3Q [4]), usually from the first period of the transition metals.1 The magnetic centers in the molecule are fairly well shielded (i.e., very weak intermolecuiar interaction) by large organic ligand shells, and thus the individual molecules are magnetically almost independent. The weak intermolecuiar interactions (or zero-dimensionality) in SMMs allow us to investigate the molecular magnetism, simply by the usual macroscopic measurement techniques. In fact, the macroscopic quantum phenomena observed in SMMs arises from the finite size system. Interestingly, some of SMMs can be viewed as reoZ nanosize quantum dots. In this case, unfilled moZecuZar orbitals, which are delocalized over the entire magnetic metal cores coupled by metal-metal bonding, provide another interesting class of molecular magnets lNote that the term "single molecule magnets" is used here not only to the ferro- or ferri-magnetic clusters but also to non-magnetic rings or clusters. 2 in analogy with the traditional magnetism of unfilled ofomic shells [5]. Thanks to the finite size of SMMs, one may sometimes perform first principles calculations from the Hamiltonian, and compare it with the experimental results. Although the exact diagonalization is limited to, for example, systems of eight spins 3/2 (in this case, the total degeneracy of the spin states is (25" + 1)^ = 65,536), this feature is very attractive from a theoretical point of view. One of the big advantages of SMMs is that one can synthesize a molecular cluster at will, in principle if not in practice, for a specific purpose of investigation. Indeed, numerous different types of SMMs have been synthesized with different features: (1) the total spin of molecule in the ground state varies from zero up to 51/2; (2) the symmetry of structure ranges from simple one dimensional (e.g., rings) to complex three dimensional clusters (e.g., Fe8, Mnl2ac); (3) the paramagnetic ions in a molecule are coupled via ferromagnetic (FM) or antiferromagnetic (AFM) interaction with various magnitude of the exchange constant J. Therefore, together with the ability to proceed with careful measurements and theoretical methods, SMMs present a wonderful laboratory to explore fundamental problems in magnetism such as spin correlation and exchange interactions at nanosize scale, which can be a key to understand the collective spin behavior in conventional magnetic materials. Among the variety of molecular magnetic systems, here we will briefly review the general properties of the two classes of SMMs. (1) Ferrimagnetic clusters with a high spin ground state and a large uniaxial anisotropy such as Fe8 and Mnl2ac; (2) Antiferromagnetic rings, which consist of an even number of metallic ions forming nearly perfect ring structures with isotropic nearest-neighbor exchange constant, such as the "ferric wheel" FelO [6]. For a comprehensive review of molecular magnetic clusters, we refer to Miller [7], Gatteschi [2, 8, 9], and Caneschi [10]. Antiferromagnetic rings Antiferromagnetic (AFM) rings may be regarded as one-dimensional (ID) chains with pe­ riodic boundary conditions due to the perfect coplanar arrangement of the paramagnetic ions. The magnetic interaction between neighboring ions within individual molecules is of the antifer- 3 romagnetic Heisenberg type yielding a ground = 0 state and dominates any other magnetic effect like single-ion and/or dipolar anisotropics. As a result, AFM rings are an attractive model system for the study of the quantum spin dynamics of one-dimensional antiferromag­ netic Heisenberg magnetic chains [11].
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