UUnniivveerrssiittyy ooff NNeeww OOrrlleeaannss SScchhoollaarrWWoorrkkss@@UUNNOO University of New Orleans Theses and Dissertations and Theses Dissertations 5-16-2008 IInntteerraaccttiioonn EEffffeeccttss iinn NNiicckkeell NNaannoowwiirreess AArrrraayyss Ovidiu Cezar Trusca University of New Orleans Follow this and additional works at: https://scholarworks.uno.edu/td RReeccoommmmeennddeedd CCiittaattiioonn Trusca, Ovidiu Cezar, "Interaction Effects in Nickel Nanowires Arrays" (2008). University of New Orleans Theses and Dissertations. 696. https://scholarworks.uno.edu/td/696 This Thesis is protected by copyright and/or related rights. It has been brought to you by ScholarWorks@UNO with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights- holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. This Thesis has been accepted for inclusion in University of New Orleans Theses and Dissertations by an authorized administrator of ScholarWorks@UNO. For more information, please contact [email protected]. Interaction Effects in Nickel Nanowires Arrays A Thesis Submitted to the Graduate Faculty of the University of New Orleans In Partial fulfillment of the Requirements for the degree of Master of Science in Physics By Ovidiu Cezar Trusca BS in Metallurgical Engineering, Technical University Cluj-Napoca, Romania, 1989 MBA “Babes-Bolyai” University, Cluj-Napoca, Romania, 1999 May, 2008 Acknowledgments I would like to thank first to Dr. Leonard Spinu, my advisor, who guided me throughout my whole experience as a graduate student. He gave me a lot of suggestions and his advice was always very valuable for me. I would like to thank my Thesis Committee Members for their insightful suggestions, their help and guidance for this work: Dr. Leonard Spinu, my Committee Chair, Dr. John B. Wiley from the Department of Chemistry and Advanced Materials Research Institute (AMRI) (University of New Orleans) for providing the materials used in this work and for his continuous support and useful discussions, Dr. Leszek Malkinski from Department of Physics and AMRI (UNO) and Dr. Ashok Puri from the Department of Physics, who were always available when I needed their help. I am deeply grateful to my colleagues Dr. Dorin Cimpoesu, Ms. Jin Hee Lim, Dr. Xiequn Zhang, Cosmin Radu, Dr Ioan Dumitru and Huy Pham for their support and valuable opinions. My work wouldn’t have been possible without their continuous help and commitment. I would like to thank all of my friends and colleagues from Department of Physics and AMRI (UNO) for their assistance. Also, I would like to thank Department of Physics and AMRI for making possible my teaching and research assistantships during these years. I would like to thank Mrs. Sandra Merz, Mrs. Jennifer Tickle and Mr. Poncho De Leon for taking care of my paperwork during my study at UNO. Also, I would like to thank to all the great professors I have met here, at UNO, who made all the difference in my life: Dr. G. Seab, Dr. J. Murphy, Dr. J. Ioup, Dr. G. Ioup, Dr. K. Stokes, Dr. M. Slaughter and Dr. J. Tang. ii Finally, I would like to thank and dedicate this thesis to my family: my wife Maria, my mother Lina, my father Vasile, my brother Horatiu, and my sister-in-law Mariana, for their financial support and emotional contributions. iii Table of Contents List of Figures....................................................................................................................vi List of Tables...................................................................................................................viii Abstract..............................................................................................................................ix Introduction..........................................................................................................................1 Chapter 1. Overview of Magnetism.....................................................................................5 1.1. Magnetic hysteresis loop of nanowires...........................................................5 1.2 Magnetic free energy.......................................................................................7 1.2.1 Magnetocrystalline anisotropy ...............................................................7 1.2.2 Magnetostriction and Stress Anisotropy.................................................9 1.2.3. Shape Anisotropy...................................................................................9 1.2.4 Zeeman energy......................................................................................13 1.2.5 Exchange energy...................................................................................13 1.2.6. Magnetostatic interactions among nanowires......................................14 1.3. Magnetization process...................................................................................14 1.3.1. Stoner-Wolfarth model ....................................................................14 1.3.2. Landau-Lifshitz-Gilbert equation........................................................16 1.4 Ferromagnetic Resonance..............................................................................18 1.4.1. General formula for resonance frequency............................................19 1.4.2. The influence of the shape in the resonance frequency.......................20 1.4.3. The influence of the crystal magnetic anisotropy on the resonance frequency...............................................................................................21 1.4.4. The influence of the domain structure on the resonance frequency....22 1.4.5. The line width of resonance absorption...............................................22 iv Chapter 2. Experiment.......................................................................................................24 2.1. Anodized Alumina Oxide (AAO) templates preparation..............................24 2.2. Nanowires Electrodeposition........................................................................26 2.3. Vibrating Sample Magnetometer (VSM) measurements..............................27 2.4. Ferromagnetic Resonance (FMR) measurements.........................................28 Chapter 3. Results and Discussions...................................................................................30 3.1. Magnetic measurements................................................................................30 3.1.1 Samples with length of wires of 500 nm.................................................30 3.1.2 Samples with length of wires of 1000 nm...............................................34 3.1.3. Conclusions of magnetostatic measurements.........................................38 3.2. Ferromagnetic Resonance measurements.....................................................40 3.2.1. Samples with length of wires of 500 nm................................................40 3.2.2. Samples with length of wires of 1000 nm..............................................44 3.2.3. FMR measurements conclusions............................................................47 Chapter 4. Modeling of interactions in ferromagnetic nanowire arrays ...........................48 4.1 Modeling of interaction effects...................................................................48 Chapter 5. Conclusions and future work............................................................................52 References..........................................................................................................................55 Vita.....................................................................................................................................57 v List of Figures Figure 1.1 Magnetic hysteresis loop for nanowires array...................................................5 Figure 1.2 The prolate, slender and oblate spheroid.........................................................11 Figure 1.3 The demagnetizing factor (N) as function of aspect ratio (m).........................12 Figure 2.1 AAO templates preparation in two steps anodization.....................................24 Figure 2.2 Hexagonally ordered nanopore arrays of the AAO template..........................25 Figure 2.3 SEM images of the top surfaces of AAO templates........................................26 Figure 2.4 SEM image of Ni nanowire arrays of 60 nm diameter....................................27 Figure 2.5 Vibrating Sample Magnetometer, Lakeshore 7300 Series..............................28 Figure 2.6 (a) the FMR spectra for a sample of Ni nanowires at 00 orientation...............29 Figure 2.6 (b) the FMR-EPR spectrometer system...........................................................29 Figure 3.1Hysteresis curve for the sample d40l500 .........................................................31 Figure 3.2Hysteresis curve for the sample d60l500 .........................................................32 Figure 3.3 Hysteresis curve for the sample d80l500.........................................................33 Figure 3.4 The squareness ratio S for the nanowires with the length of 500 nm..............33 Figure 3.5 The hysteresis curve for the sample d40l1000................................................35 Figure 3.6 The hysteresis curve for the sample d60l1000................................................36 Figure 3.7 The hysteresis curve for the sample d80l1000................................................37 Figure 3.8 The squareness ratio vs aspect ratio for the samples with length of 1000 nm...........................................................................................................38 Figure 3.9 The coercive field vs. aspect ratio for the samples of 500 nm length.............39 Figure 3.10 The coercive field vs. aspect ratio for the samples of 1000 nm length.........40 Figure 3.11 The FMR spectra of sample d40l500............................................................41 Figure 3.12 The FMR spectra of sample d60l500............................................................41 vi Figure 3.13 The FMR spectra of sample d80l500............................................................42 Figure 3.14 The angular dependence of the resonance field for the 500 nm length set...43 Figure 3.15 The resonance field vs. apect ratio for the set of samples with the length of wires of 500 nm at different orientations...................................................43 Figure 3.16 The FMR spectra of sample d40l1000..........................................................44 Figure 3.17 The FMR spectra of sample d60l1000..........................................................45 Figure 3.18 The FMR spectra of sample d80l1000..........................................................45 Figure 3.19 Angular dependence of the resonance field for the 1000 nm length set........46 Figure 3.20 The resonance field vs. aspect ratio for the set of samples with the length of wires of 500 nm at different orientations...................................................46 Figure 4.1 Experimental and simulated angular dependence of the resonance field for the samples with l=500 nm (a.) and l=1000 nm (b.).................................51 Figure 5.1 Drawings of magnetic nanotubes and magnetic nanotubes with magnetic core...................................................................................................53 Figure 5.2 Magnetic moment vs. temperature for the sample Co nanotube with Ni core...................................................................................................................54 vii List of Tables Table2.1 Magnetic field intervals (Oe) chosen for VSM measurements..........................28 viii Abstract Systems of magnetic nanowires are considered strong candidates in many technological applications as microwave filters, sensors or devices for data storage. Because of their strong potential as candidates in such applications they became lately the object of many studies. However, due to the very complicated nature of the interwire interactions, their magnetic behavior is very difficult to be interpreted. The main parameter controlling the response of magnetic nanowires assemblies is the aspect ratio of the nanowires that is defined as the ratio of the length to the wire's diameter. In our study we choose to modify the aspect ratio by keeping a constant length of nanowires and modifying the wire’s diameter while keeping the same interwire distance. The samples were studied at room temperature, using vibrating sample magnetometer and X-band ferromagnetic resonance experiments. The results are explained taking into account the effects of the magnetostatic interactions and shape anisotropy. Key words: magnetic nanowires, magnetic interactions, hysteresis loop, ferromagnetic resonance, magnetic moment ix