Localized Ferromagnetic Resonance Using Magnetic Resonance Force Microscopy
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LOCALIZED FERROMAGNETIC RESONANCE USING MAGNETIC RESONANCE FORCE MICROSCOPY DISSERTATION Presented in Partial Ful¯llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Jongjoo Kim, B.S.,M.S. ***** The Ohio State University 2008 Dissertation Committee: Approved by P.C. Hammel, Adviser D. Stroud Adviser F. Yang Graduate Program in K. Honscheid Physics ABSTRACT Magnetic Resonance Force Microscopy (MRFM) is a novel approach to scanned probe imaging, combining the advantages of Magnetic Resonance Imaging (MRI) with Scanning Probe Microscopy (SPM) [1]. It has extremely high sensitivity that has demonstrated detection of individual electron spins [2] and small numbers of nuclear spins [3]. Here we describe our MRFM experiments on Ferromagnetic thin ¯lm structures. Unlike ESR and NMR, Ferromagnetic Resonance (FMR) is de¯ned not only by local probe ¯eld and the sample structures, but also by strong spin-spin dipole and exchange interactions in the sample. Thus, imaging and spatially localized study using FMR requires an entirely new approach. In MRFM, a probe magnet is used to detect the force response from the sample magnetization and it provides local magnetic ¯eld gradient that enables mapping of spatial location into resonance ¯eld. The probe ¯eld influences on the FMR modes in a sample, thus enabling local measurements of properties of ferromagnets. When su±ciently intense, the inhomogeneous probe ¯eld de¯nes the region in which FMR modes are stable, thus producing localized modes. This feature enables FMRFM to be important tool for the local study of continuous ferromagnetic samples and structures. ii In our experiments, we explore the properties of the FMR signal as the strength of the local probe ¯eld evolves from the weak to strong perturbation limit. This un- derlies the important new capability of Ferromagnetic resonance imaging, a powerful new approach to imaging ferromagnet. The new developed FMR imaging technique enables FMR imaging and localized FMR spectroscopy to combine spectroscopy and lateral information of ferromagnetic resonance images [4][5]. Our theoretical approach agrees well with spatially localized spectroscopy and imaging results. This approach also allows analysis and reconstruction of FMR modes in a sample. Finally we consider the e®ect of strong probe ¯elds on FMR modes. In this regime the probe ¯eld signi¯cantly modi¯es the FMR modes. In particular we observe the complete local suppression of the FMR mode under the probe. This provides as a new tool for local study of continuous ferromagnetic thin ¯lms and microstructures. iii To Sohyun and Reeya iv Acknowledgement First of all, I would like to express my sincere gratitude to Professor P. Chris Hammel for his endless interests, encouragements, supports, and guides to Physics. The ¯rst day when I knocked his door and decided to join the best Physics group is not unforgettable in my life. I found the future, the attitude, the energy, and the promise as one of physicists in the ¯rst day. In the group, he kindly opened any topics during so-called co®ee hours. Everyday I have learned and exchanged valuable ideas and social news. This activity also made me move toward the goal of my life. In addition, there was another luck with the group because I met solid scientists and mentors, and friends. I am grateful to Dr. Tim Mewes who taught and promoted my interests to the FMRFM system and treats me as a friend, Dr. Denis Pelekhov who supported our results of FMRFM and helped all other things even though they were not related to physics, Prof. Philip E. Wigen who regularly visited me and gave endless interests and discussions, Dr. Palash Banerjee who prepared for many cantilevers and advices for me, and ¯nally Dr. Yuri Obukhov who could not be forgotten through my research and life in many aspects. Dr. Yuri Obukhov was not only the physicist who has endless promotions but also the right mentor who keeps suggesting the guideline in my future research. My physics was being developed and becomes matures with him. His attitude was always appreciated because he tried to make me understand hidden physics and problems. Sometimes we spent many hours or days to solve some problems. With all scientists and friends whom I mentioned above, I thank Ross, Inhee, Jay, Vidya, Mike, Claudia, Tom, Bob, and Physics department at the Ohio State Univerisity. v Finally I appreciate Sohyun, Reeya, mothers, and Woojae who are always standing with me. vi TABLE OF CONTENTS Page Abstract ....................................... ii Dedication ...................................... iv List of Figures ................................... xi Chapters: 1. Introduction .................................. 1 1.1 Motivation of the study of ferromagnetic nanostructures ...... 1 1.2 Strengths and weaknesses of conventional FMR ........... 1 1.3 New approach to magnetic resonance using Force detection ..... 2 1.4 History of MRFM ........................... 3 1.5 History of FMRFM ........................... 3 1.6 Chapter summary ........................... 5 2. Basic concept of Magnetic Resonance Force Microscopy .......... 8 2.1 Introduction .............................. 8 2.2 Brief description of Magnetic Resonance ............... 8 2.3 Geometry of MRFM experiment ................... 10 2.4 Force detection ............................. 11 2.5 Measurement approach in MRFM ................... 12 2.6 Comparison of force sensitivity in MRFM and MFM ........ 13 2.7 Force noise ............................... 14 2.8 Strengths and weaknesses of mechanical detection .......... 15 vii 3. Theory of Ferromagnetic Resonance .................... 17 3.1 Summary ................................ 17 3.2 De¯nition of e®ective magnetic ¯eld He® ............... 18 3.2.1 Zeeman Energy ......................... 18 3.2.2 Demagnetizing energy ..................... 18 3.2.3 Anisotropy energy ....................... 19 3.2.4 Exchange energy ........................ 19 3.3 Spin dynamics in ferromagnetic materials .............. 20 3.4 Herring-Kittel equation ........................ 22 3.5 Spin dynamics in thin ferromagnetic ¯lm ............... 24 3.6 Damon-Eshbach approach ....................... 25 3.7 Comparison between Kalinikos-Slavin and Damon-van de Vaart dis- persion relations ............................ 26 3.8 Dispersion relation for our experimental conditions ......... 27 3.9 Dispersion relation in presence of inhomogeneous demagnetizing ¯eld 27 4. FMRFM Experimental set-up ........................ 29 4.1 Introduction .............................. 29 4.2 Design of the experimental set-up ................... 30 4.3 Cantilever characterization ...................... 34 4.3.1 The measurement of cantilever spring constant ....... 34 4.3.2 The measurement of quality factor of cantilever ....... 35 4.3.3 Characterization of probe magnet ............... 36 4.3.4 Measurement of the probe ¯eld gradient ........... 39 4.4 Detection of the cantilever position .................. 40 4.4.1 Fiber optic interferometer ................... 40 4.4.2 Measurement of the probe-sample distance .......... 43 4.5 Microwave Resonator .......................... 45 4.6 Conclusions ............................... 46 5. FMRFM spectroscopy in circular disk array ................ 47 5.1 Introduction .............................. 47 5.2 Experimental conditions ........................ 47 5.2.1 Sample properties ....................... 47 5.3 Cantilever properties .......................... 48 5.3.1 Properties of the probe magnet ................ 49 5.3.2 FMRFM measurement protocol ................ 51 5.4 FMRFM spectra ............................ 53 viii 5.5 FMRFM in antiparallel con¯guration ................. 54 5.6 Quantization of FMR modes in a disk sample ............ 56 5.7 FMR images using local spectroscopic information ......... 58 5.8 Conclusion ............................... 60 6. Ferromagnetic resonance with weak ¯eld perturbation ........... 62 6.1 Motivation ............................... 62 6.2 Experimental conditions ........................ 63 6.2.1 MW resonator ......................... 64 6.2.2 Properties of new probe magnets ............... 65 6.2.3 Force noise of the cantilever .................. 65 6.2.4 New protocol to detect the force signal ............ 65 6.3 Results ................................. 68 6.3.1 FMR Spectra for center of permalloy disk .......... 68 6.3.2 New scanning method: spatially resolved FMR spectroscopy 71 6.3.3 Spatially resolved FMR spectroscopy for the second order FMR mode ........................... 72 6.3.4 FMR with weakly perturbing probe ¯eld ........... 72 6.3.5 Reconstruction of the probe magnetic ¯eld .......... 77 6.3.6 The influence of the probe magnetic ¯eld into FMR mode . 77 6.3.7 Observation of FMR mode splitting ............. 78 6.3.8 FMR with strongly perturbing probe ¯eld .......... 80 6.4 Conclusion ............................... 82 7. FMR Mode Suppression at strong ¯eld perturbation ............ 83 7.1 Motivation ............................... 83 7.2 Experimental conditions ........................ 84 7.2.1 An isolated disk sample .................... 84 7.3 Probe magnet .............................. 85 7.3.1 Signal measurement method .................. 86 7.4 Results ................................. 88 7.4.1 Strong probe ¯eld behavior of FMRFM spectra ....... 88 7.4.2 Theory of FMR in a strongly perturbing ¯eld ........ 89 7.4.3 Numerical simulation results ................. 94 7.4.4 Spatially resolved scanning