MICROMAGNETIC SIMULATION ON MAGNETIC NANOSTRUCTURES AND THEIR APPLICATIONS YONG YANG (B. E., LANZHOU UNIVERSITY, CHINA) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING 2014 Declaration I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Yong Yang 1/14/2014 I Acknowledgements First, I would like to express my sincere appreciation to my supervisor Prof. Jun Ding in Materials Science and Engineering Department (MSE) of National University of Singapore (NUS), for his guidance and encouragement throughout my PhD study. His patience, enthusiasm, creative ideas and immense knowledge shined the light for me in all my research work and writing of this thesis. I also would like make a grateful acknowledgement to Dr Haiming Fan and Dr Jiabao Yi for helping me revise my manuscripts. Moreover, I greatly appreciate the kind assistance from Ms Xiaoli Liu, Dr Yang Yang and Ms Yunbo Lv for the sample preparation. Also, I would like to acknowledge all my research group members: Dr Tun Seng Herng, Dr Jie Fang, Dr Li Tong, Dr Xuelian Huang, Dr Weimin Li, Dr Dipak Maity, Mr Wen Xiao, Mr Xiaoliang Hong, Ms Olga Chichvarina, Ms Viveka Kalidasan. A special mention is given to the lab officers in Department of Materials Science and Engineering for their technical support in sample characterization. Additionally, I would like to offer my deep gratitude to the financial support provided by the China Scholarship Council (CSC). Last but not least, I would like thank to my family: my parents for giving birth to me and supporting me throughout my life; and my wife, Ms Yanwen Wang, for her accompanying all the way. II List of Publications Yong Yang, Yang Yang, ChyePoh Neo and Jun Ding, “A Predictive Method for High Frequency Complex Permeability of Magnetic structures” (2014 submitted) Yong Yang, Xiaoli Liu, Yang Yang, Yunbo Lv, Jie Fang, Wen Xiao and Jun Ding “Synthesis and Enhanced Magnetic Hyperthermia of Fe3O4 Nanodisc” (2014 submitted) Yong Yang, Xiaoli Liu, Jiabao Yi, Yang Yang, Haimin Fan and Jun Ding, “Stable Vortex Magnetite Nanorings Colloid: Micromagnetic Simulation and Experimental Demonstration” J. Appl. Phys. 111 (2012) 044303-9 Yong Yang, Yang Yang, Wen Xiao and Jun Ding “Microwave Electromagnetic and Absorption Properties of Magnetite Hollow Nanostructures” J. Appl. Phys. 115 (2014), 17A521 Weimin Li, Yong Yang, Yunjie Chen, T.L. Huang, J.Z. Shi, Jun Ding,“Study of magnetization reversal of Co/Pd bit-patterned media by micro-magnetic simulation” J. Magn. Magn. Mater. 324 (2012), 1575-1580. Yang Yang, Xiaoli Liu, Yong Yang, Wen Xiao, Zhiwen Li, Deshen Xue, Fashen Li, Jun Ding, “ Synthesis of nonstoichiometric zinc ferrite nanoparticles with extraordinary room temperature magnetism and their diverse applications” J. Mater. Chem. C (2013), 2875-2885. Jie Fang, Prashant Chandrasekharan, Xiaoli Liu, Yong Yang, Yunbo Chang-Tong Yang and Jun Ding “Manipulating the surface coating of ultra-small Gd2O3 nanoparticles for improved T1-weighted MR imaging” Biomaterials 35, (2014),1636-1642. Xiaoli Liu, Eugene Shi Guang Choo, Anansa S. Ahmed, Ling Yun Zhao, Yong Yang, Raju V. Ramanujan, Jun Min Xue, Dai Di Fan, Hai Ming Fan and Jun Ding, “Magnetic nanoparticle-loaded polymer nanospheres as magnetic hyperthermia agents” J. Mater. Chem. B (2014), 120-128. Awards 2013: “ICMAT 2013 Best Poster Award” 2012: “Best Poster Award at the 5th MRS-S Conference on Advanced Materials” III Table of Contents Declaration . I Acknowledgements . II List of Publications III Table of Contents .IV Summary IX List of Figures XV List of Tables XXI CHAPTER 1: Introduction 1.1 Micromagnetics . 1.1.1 Theory of Operation 1.1.2 Micromagnetic packages 1.1.3 Application of micromagnetics . 1.2 Magnetic nanostructures 12 1.2.1 Magnetism of magnetic nanostructures 12 1.2.2 Fabrication of magnetic nanostructures 18 1.2.3 Applications of magnetic nanostructures 23 1.2.3.1 Ferrofluids 25 1.2.3.2 Magnetic Hyperthermia . 29 IV 1.2.3.3 Microwave Electromagnetic (EM) Applications . 33 1.3 Research objectives 39 1.4 Scope of the thesis . 40 CHAPTER 2: Fabrication, Characterization and Micromagnetic Simulation Techniques . 42 2.1 Fabrication . 43 2.1.1 Synthesis Fe3O4 nanodiscs 43 2.1.2 Synthesis Fe3O4 nanorings and nanorods . 45 2.1.3 Synthesis of Fe3O4 nanoparticles 45 3.2.3 Synthesis of phosphorylated-MPEG modified Fe3O4 nanoring 46 2.2 Characterization . 47 2.2.1 X-ray Diffraction (XRD) 48 2.2.2 Scanning Electron Microscopy (SEM) . 49 2.2.3 Transmission Electron Microscopy (TEM) 51 2.2.4 Dynamic Light Scattering (DLS) 53 2.2.5 Vibrating Sample Magnetometer (VSM) 54 2.2.6 Superconducting Quantum Interface Device (SQUID) 56 2.2.7 Magnetic Hyperthermia 57 2.2.8 PNA Network Analyzer 59 2.3 Micromagnetic Simulation . 62 V CHAPTER 3: Stable Vortex Fe3O4 Nanorings Colloid: Micromagnetic Simulation and Experimental Demonstration 65 3.1 Introduction 66 3.2 Methods 69 3.3 Results and Discussion 71 3.3.1 Micromagnetic modeling of Fe3O4 nanorings 71 3.3.2 Stability of phosphorylated-MPEG Fe3O4 nanoring colloid . 85 3.4 Conclusion . 89 CHAPTER 4: Magnetic Hyperthermia of Fe3O4 Nanoring . 90 4.1 Introduction 91 4.2 Methods 92 4.2.2 Micromagnetic simulation setup . 92 4.2.3 Magnetic Hyperthermia Measurement . 93 4.3 Results and discussion . 93 4.4 Conclusion . 100 CHAPTER 5: Magnetic Hyperthermia of Fe3O4 Nanodiscs . 102 5.1 Introduction 103 5.2 Methods 104 5.2.2 Micromagnetic simulation setup . 104 5.2.3 Magnetic Hyperthermia Measurement . 105 VI 5.3 Results and discussion . 105 5.4 Conclusion . 121 CHAPTER 6: A Predictive Method for Microwave Permeability of Magnetic Nanostructures . 122 6.1 Introduction 123 6.2 Theoretical Model and Experiment . 125 6.2.1 Micromagnetic simulation for magnetic domain evaluation. . 125 6.2.2 The calculation of complex permeability for single magnetization 126 6.2.3 The calculation of local effective magnetic field (Heff) 127 6.2.4 Average complex permeability of magnetic nanostructure 129 6.3 Results and Discussion 130 6.3.1 “Single spin” test . 130 6.3.2 Heff in single domain nanosphere and nanorod . 131 6.3.3 Microwave permeability of single domain nanosphere and nanorod136 6.3.4 Comparison with micromagnetic simulation 142 6.3.5 The bond between resonance frequency and initial permeability in TFC 144 6.3.6 Comparison between experiment and the present model . 146 6.3.7 Influence of orientation on the permeability of nanodisc . 160 6.4 Conclusion . 163 CHAPTER 7: Conclusions and Future Work 165 VII 7.1 Conclusions 166 7.2 Future works 170 References 174 VIII Summary In this project, we investigated the static and dynamic magnetic applications (i.e. ferrofluid, hyperthermia, microwave permeability) of different Fe3O4 magnetic nanostructures (i.e. nanoparticle, nanoring, nanodisc and nanorod) fabricated by chemical methods. During investigation, 3D Landau-Liftshitz-Gilbert (LLG) micromagnetic simulation was used as theoretical guidelines. Upon performing the micromagnetic simulation, we could look into the microcropic magnetic domain structures, which are crucial for both static (i.e. hysteresis loops) and dynamic magnetic properties (i.e. microwave permeability). Comparisons between the simulated and experimental results were also provided closely for verification. In the first part, a new kind of stable Fe3O4 nanoring colloid based on the vortex domain structure was developed by micromagnetic simulation and subsequently experimental demonstration. Compared with the conventional ferrofluid containing superparamagnetic nanoparties, the Fe3O4 nanoring colloid could achieve much better magnetic response due to the ferromagnetic nature of the large Fe3O4 nanoring. Meanwhile, the high colloidal stability can be also retained because of weak magnetic IX Chapter 7: Conclusions and Future Work micromagnetic simulation revealed different magnetic domain structures for the fabricated nanodiscs. In order to investigate their hyperthermia performance, the nanodiscs as well as other two references samples, namely superparamagnetic nanoparticles (SNP) and ferrimagnetic nanoparticles (FNP), were coated with CTAB then dispersed into water and gel. The hyperthermia measurement of aqueous suspension suggests that the nanodiscs exhibit excellent heat dissipation ability, which is almost and times higher than the traditional SNP and FNP, respectively. By contrast, in gel suspension the nanodisc exhibit slightly higher SAR values than FNP, which is demonstrated micromagnetically by simulating the hysteresis loss. Through the comparison of the SAR values between the water and gel suspension, a prominent Brownian relaxation loss (about kW/g) was surprisingly observed on the nanodisc at AC magnetic field larger than 0.3 kOe, which is about times higher than that of the isotropic FNP. Based on this phenomenon, a novel “flipping” Brownian relaxation model was proposed for the disc shaped nanostructures. When subjected in the AC field, the nanodisc in aqueous suspension could flip and stir the water, converting the field energy into the kinetic energy of surrounding carrier. Compared with the traditional spherical nanoparticles, whose Brownian relaxation in liquid carrier relies on the friction between nanoparticles and carrier, the nanodisc could 168 Chapter 7: Conclusions and Future Work transfer energy more effectively by “stirring” effect. This study may open a new window for high efficiency magnetic hyperthermia. 4) Lastly, a predictive model is developed for the calculation of microwave magnetic permeability, which could take both the magnetic domain and wave orientation into account. In this model, starting from the ground state magnetic domain structure, a local effective field (Heff) is evaluated within each mesh cell by micromagnetic simulation. At a relative orientation of magnetic domain structure with respect to the microwave, a permeability spectrum can be calculated by using the local Heff and subsequent average over all the cells. The validity of this model in two extreme conditions, namely Longitudinal Field Case (LFC) and Transverse Field Case (TFC) is proved on single domain nanospheres and nanorods by the comparison with analytical formulas. Equipped with this model, it is found that the initial permeability remains the same while the resonance frequency could be well tuned by changing the relative angle between wave vector and magnetization. Furthermore, a bond between initial permeability and resonance frequency is proposed for TFC, as the complement of Snoek’s limit (which is only valid in LFC). Meanwhile, the good agreement between the experimental results and our calculation on different Fe3O4 nanostructures (i.e. octahedral, nanoring, nanodisc and nanorod) proved the validity of the present model. All these results 169 Chapter 7: Conclusions and Future Work indicate that the present model is able to predict the microwave magnetic properties of different nanostructures. It is believed that this model could offer valuable guidance for the design of microwave devices. 7.2 Future works Based on the substantial experimental results and theoretical simulation obtained from this work, several potential directions for future research are highlighted below: 1) In chapter and 4, it has been proved that the vortex Fe3O4 nanorings could achieve high colloidal stability and outstanding hyperthermia performance, which could be potentially used in cancer treatment. However, in-vivo hyperthermia of the nanoring has not been investigated yet. Therefore, the in-vivo hyperthermia test is needed to be done in the future. Upon cell uptake, the Fe3O4 nanorings should be absorbed into the living tumor cells, which are then subjected into an AC field for hyperthermia treatment. After a period of exposure, the efficiency of the treatment can be estimated by counting the induced tumor cell death. 2) Besides nanoring, magnetic nanodisc was also demonstrated as excellent heating agent for magnetic hyperthermia. By comparing the SAR value measured in water suspension with that measured in gel suspension, we proposed a “stirring” effect of the nanodisc. However, direct experimental evidence is necessary, which would be provided in the future. Moreover, 170 Chapter 7: Conclusions and Future Work future work on in-vivo hyperthermia is also necessary for practical application. Furthermore, to our best knowledge, the magnetic resonance imaging (MRI) properties of the Fe3O4 nanodiscs have been rarely studied. Hence it is of prime interest to investigate the MRI performance of these Fe3O4 nanodiscs. 3) The new model for the calculation of microwave permeability was demonstrated to work well to predict the microwave permeability of magnetic nanostructures. Therefore, further calculation could be performed with this method to optimize the size, shape and component of magnetic nanostructures to achieve higher permeability at high frequency. In the light of the theoretical optimization, magnetic nanostructure with desired microwave magnetic properties could be fabricated accordingly. 4) As revealed by the results in Chapter 6, the microwave permeability strongly depends on the magnetic domain structure of magnetic elements. Therefore, reconfigurable switching between different magnetic domain structures could realize tunable microwave magnetic properties, which can be potentially utilized in microwave filter, microwave absorber and spintronic devices. Inspired by this fact, we are going to develop magnetic elements with reconfigurable multi-states, which could be controlled by external magnetic field. For instance, Fig. 7.1 illustrates a 2D array of reconfigurable multi-states binary magnetic element. As depicted in the 171 Chapter 7: Conclusions and Future Work figure, the individual magnetic nanostructure is composed by a soft layer on top and a hard magnetic layer on the bottom. The domain structure in the soft layer is tunable between an out-of-plane ferromagnetic state and the vortex state. Without any external magnetic field, the domain structure in the soft layer is an out-of-plane ferromagnetic state as magnetized by the field generated by the hard layer. When a magnetic field is applied in the opposite direction, the two fields cancel each other and the domain in soft layer turns to be a vortices. When the external field is removed, the vortices changes back to the ferromagnetic state. The switching between the ferromagnetic state and vortex finally results in distinct microwave dynamic properties. 172 Chapter 7: Conclusions and Future Work Figure 7.1 (a) illustration of 2D array of binary magnetic element. 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Substituting (A.3) and (A.4) into (A.1) and (A.2) (A.5) (A.6) Since (A.7) Combine (A.5) and (A.7), it gives (A.8) Therefore 181 (A.9) (A.10) (A.11) Where is the angle between wave vector, is the angle between x axis and projection of wave vector in x-y plane. Since , where is the permeability tensor According to (A.9)-(A.10) (A.12) Set , namely (A.13) The eigenvalues of permeability should be obtained through setting the determinant of (31) to zero, the result is (A.14) From LLG equation, we could btain (A.15) with (A.16) 182 (A.17) So (A.18) (A.19) (A.20) Compare (A.9-11) with (A.18-20) (A.21) (A.22) (A.23) Eqns (A.21-23) are three linear equations about hx, hy and hz. To get a non-zero solution, the determinant of these equations are requires to be zero. So, the in (A.12) can be obtained as (A.24) Substituting (A.24) into (A.14) (A.25) 183 [...]... 1.1.2 Micromagnetic packages To date, many micromagnetic packages have been established, such as OOMMF (The Object Oriented MicroMagnetic Framework) developed by Mike Donahue and Don Porter at the National Institute of Standards and Technology,9 LLG Micromagnetics Simulator,10 Magpar,11 JAMM (Java Micromagnetics),12 MicroMagus,13 MagOasis14 and muMag.15 1.1.3 Application of micromagnetics Micromagnetics... microwave frequency (gigahertz) Other applications are beyond the scope of the current thesis In this chapter, we will present an introduction on the micromagnetism Then an overall review on the magnetic nanostructures and their applications will be provided in the following sections 1.1 Micromagnetics 1.1.1 Theory of Operation 3 Chapter 1: Introduction Micromagnetic simulation is a finite-element (FE) approach... introduction on the magnetism, fabrication and some applications of magnetic nanostructures 1.2.1 Magnetism of magnetic nanostructures 12 Chapter 1: Introduction Figure 1.6 A plot of magnetic coercivity (Hc) vs particles size.49-50 As mentioned previously, the shape and size are crucial for both the static and dynamic behaviors of magnetic nanostructures Fig 1.6 illustrates the magnetic domain evolution and. .. experimentally and theoretically to yield an accurate description of the time evolution of spin configuration With the help of micromagnetic simulation, we can obtain direct visualization of magnetization configurations, static and dynamic magnetic properties of magnetic structures More importantly, as a powerfully theoretical tool, it enables 2 Chapter 1: Introduction us to predict the magnetic properties,... (β) F, V, and O indicate ferromagnetic out-of-plane, vortex, and onion configurations Figure 1.9 Magnetic switching processes of different magnetic nanostructures Figure 1.10 Schematic illustration of the hydrothermal thermal formation process for α-Fe2O3 nanostructures mediated by phosphate and sulfate Ions Figure 1.11 Schematic drawing of ferrofluid The fluid is appears to consist of small magnetic. .. of magnetic devices with desired function Based on this fact as well as the ever growing high speed computing, the micromagnetism has become an indispensable branch in material science In this thesis, we devoted to apply the micormagnetic simulation on different magnetic nanostructures (i.e nanoring, nanodisc, nanorod, etc.) and their possible applications Generally, the application of magnetic nanostructures. .. static magnetization configurations of magnetic structures, such as discs,16-17 rings,18-19 cylinders, cubic,20 triangles,21 spheres,22 and other polygons.23-24 Fig 1.3 shows the simulated hysteresis loop with 8 Chapter 1: Introduction inset magnetization cross-section snapshots of a submicron permalloy cone.25 Moreover, the micromagnetic simulation could provide the trajectory of magnetization during the... equation In the thesis, the simulations 11 Chapter 1: Introduction were performed well below the curie temperature of material Therefore, the LLG micromagnetic simulation could still give accurate results Due to so many applications as mentioned above, the micromagnetism has become an indispensible branch in physics and material science In this thesis, we mainly used the micromagnetic simulation to... dependent magnetization process of magnetic materials at an intermediate length scale between magnetic domain and crystal lattice length.6 In micromagnetic theory, the continuous magnetic system is approximated by a discrete magnetization distribution consisting of equal volume cubes (3D) or rods (2D), so called cells Figure 1.1 FE discretization of a sphere in micromagnetic simulation Fig 1.1 illustrates... electrically driven magnetization reversal.31 9 Chapter 1: Introduction Furthermore, the spin excitation under an alternating magnetic field could be simulated by micromagnetics as well, which is widely used in the simulating ferromagnetic resonance (FMR) and susceptibility of magnetic nanostructures The basic procedure is as follows: Firstly, the magnetic spin configuration of the given magnetic nanostructure . Introduction 1 1.1 Micromagnetics 3 1.1.1 Theory of Operation 3 1.1.2 Micromagnetic packages 8 1.1.3 Application of micromagnetics 8 1.2 Magnetic nanostructures 12 1.2.1 Magnetism of magnetic nanostructures. MICROMAGNETIC SIMULATION ON MAGNETIC NANOSTRUCTURES AND THEIR APPLICATIONS YONG YANG (B. E., LANZHOU UNIVERSITY, CHINA) A THESIS. investigation, 3D Landau-Liftshitz-Gilbert (LLG) micromagnetic simulation was used as theoretical guidelines. Upon performing the micromagnetic simulation, we could look into the microcropic magnetic