Spin dynamics of magnonic crystals and ferromagnetic nanorings

SPIN DYNAMICS OF MAGNONIC CRYSTALS AND FERROMAGNETIC NANORINGS MA FUSHENG (B. Sc, SHANDONG UNIV) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE (2012) ACKNOWLEDGEMENTS The work presented in this thesis, and indeed this thesis itself, represents the cumulative help and support of my colleagues, friends, and family. While it is impossible to acknowledge all of those people here, I will always remember them, and hopefully they will know their contribution to this work by making me the person I am today. I would like to acknowledge the influence of several people in particular. To begin with I would like to express my deepest gratitude and appreciations to my supervisor Prof. Kuok Meng Hau for his unwavering dedication, encouragement, and advice throughout. Without his patient guidance, it is impossible for me to obtain the necessary research skills in such a short time and finish this thesis in four years. I would also like to thank Prof. Kuok for providing the opportunity to work on BLS experiments and lithography technique, both of which have been invaluable experiences for me. Finally, I would like to thank Prof. Kuok for his time to read and critically comment on several versions of this thesis. A big thank to my co-supervisor A/Prof. Lim Hock Siah for his great and endless help in my theory work. His patience and experience help me make a big improvement on the understanding of the required concepts and my script coding ability as well as micromagnetic simulations skills. I would also like to thank A/Prof. Lim for his reading and comments on several versions of my thesis. I also want to thank my co-supervisor Dr. S.N. Piramanayagam for providing the chance for me to use the lithography facilities in DSI. I have learnt lots of knowledge on the lithography technology during the fruitful discussion with him. -i- A special thanks to Prof. Ng Ser Choon for his patient and fruitful discussion on anything physics (and more) each time I came knocking on his office door. I would also like to thank Prof. Ng for his suggestions on my thesis writing. Thanks to Dr Wang Zhikui for his careful and experienced teaching on the using of the BLS experiments as well as the discussion of the results. Thanks to Dr Zhang Li for her technical help and advice during the experiments and analysis of experimental results. Thanks to our lab officer Mr Foong Chee Kong and other lab fellows for their help and support. Additionally, I would also like to thank A/Prof. A. O. Adeyeye from Department of Electrical and Computer Engineering of NUS for providing all samples I studied. I also want to thank NUS Physics Department and NUSNNI for providing me the scholarship. In addition to the people already mentioned, friends and colleagues outside of the Laser Brillouin Group have also made my time as a PhD student a rich and memorable one. Thanks to all my friends for their help and encouragement. My families have been a huge inspiration. I would like to thank my parents and my older sister for their their constant support over the years. I cannot thank you all enough for all of your love and support over the last twenty-seven years. Finally, I would like to appreciate Miss Summer, who has offered endless support, encouragement and love over the last two years. Thank you summer, I cannot complete this work without your support. -ii- LIST OF PUBLICATIONS Journal articles Submitted 1. F. S. Ma, H. S. Lim, V. L. Zhang, S. N. Piramanayagam, S. C. Ng, and M. H. Kuok, "Optimization of the magnonic band structures in one-dimensional bicomponent magnonic crystals", submitted. In Press 1. F. S. Ma, H. S. Lim, V. L. Zhang, Z. K. Wang, S. N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Materials optimization of the magnonic bandgap in twodimensional bi-component magnonic crystal waveguides”, Nanosci. Nanotechnol. Lett. In press. Published 6. V. L. Zhang, F. S. Ma, H. H. Pan, C. S. Lin, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, "Observation of dual magnonic and phononic bandgaps in bi-component nanostructured crystals", Appl. Phys. Lett. 100, 163118 (2012). [It has been selected for the April 30, 2012 issue of Virtual Journal of Nanoscale Science & Technology.] 5. F. S. Ma, H. S. Lim, V. L. Zhang, Z. K. Wang, S. N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Band structures of exchange spin waves in one-dimensional bi-component magnonic crystals”, J. Appl. Phys. 111, 064326 (2012). 4. F. S. Ma, H. S. Lim, Z. K. Wang, S. N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Micromagnetic study of spin wave propagation in bi-component magnonic crystal waveguides”, Appl. Phys. Lett. 98, 153107 (2011). [Research highlighted by Appl. Phys. Lett. and also published in the April 25, 2011 issue of Virtual Journal of Nanoscale Science & Technology.] -iii- 3. F. S. Ma, H. S. Lim, Z. K. Wang, S. N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Effect of magnetic coupling on band structures of bi-component magnonic crystal waveguides”, IEEE Trans. Magn. 47, 2689 (2011). 2. F. S. Ma, V. L. Zhang, Z. K. Wang, H. S. Lim, S. C. Ng, M. H. Kuok, Y. Ren, and A. O. Adeyeye, “Magnetic-field-orientation dependent magnetization reversal and spin waves in elongated permalloy nanorings”, J. Appl. Phys. 108, 053909 (2010). 1. Z. J. Liu, Q. P. Wang, X. Y. Zhang, Z. J. Liu, H. Wang, J. Chang, S. Z. Fan, F. S. Ma, G. F. Jin, “Intracavity optical parametric oscillator pumped by an actively Q-switched Nd: YAG laser”, Appl. Phys. B 90, 439 (2008). Conference presentations 5. F. S. Ma, H. S. Lim, Z. K. Wang, S.N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Materials optimization of the magnonic bandgap in two-dimensional magnonic crystals”, ICMAT2011 (International Conference on Materials for Advanced Technologies), Symposium L, 2011, Singapore. 4. F. S. Ma, H. S. Lim, Z. K. Wang, S.N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Numerical calculation of dispersion relations in one- and twodimensional magnonic crystals”, IEEE Magnetics Society Summer School, 2011, New Orleans, USA. 3. F. S. Ma, H. S. Lim, Z. K. Wang, S.N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Micromagnetic study of the magnonic bandgap in two-dimensional magnonic crystals”, Intermag2011 (IEEE International Magnetics Conference), Symposium 7, 2011, Taipei, Taiwan. 2. F. S. Ma, H. S. Lim, Z. K. Wang, S. C. Ng, M. H. Kuok, S. Jain and A. O. Adeyeye, “Brillouin scattering study of spin waves in ferromagnetic nanostructures”, The 5th Mathematics and Physical Sciences Graduate Congress, 2009, Bangkok. 1. F. S. Ma, H. S. Lim, Z. K. Wang, S. C. Ng, M. H. Kuok, S. Jain and A. O. Adeyeye, “Spin waves in ferromagnetic rectangular arrays”, ICMAT2009 (International Conference on Materials Symposium E, 2009, Singapore. -iv- for Advanced Technologies), Table of Contents Chapter Introduction . 1  § 1.1 Overview of Magnonics . 3  § 1.2 Review of Magnonic Crystals 4  § 1.2.1 Experimental Studies of Magnonic Crystals 6  § 1.2.2 Micromagnetic Studies of Magnonic Crystals . 9  § 1.3 Objectives . 10  § 1.4 Outline of This Thesis 11 Chapter Brillouin Light Scattering from Spin Waves 13  § 2.1 Introduction 13  § 2.2 Spin Waves . 14  § 2.2.1 Magnetostatic Spin Waves . 16  § 2.2.2 Exchange Spin Waves 21  § 2.2.3 Confined Spin Wave Modes in Magnetic Structures . 21  § 2.2.4 Experimental Techniques for Spin Waves . 23  § 2.3 Kinematics of Brillouin Light Scattering . 25  § 2.4 Spin Wave Scattering Mechanism . 27  § 2.5 Spin Wave Scattering Profile . 29  § 2.6 Polarization of Photons Scattered from Magnons 30  § 2.7 Experimental Setup 32  § 2.8 Instrumentation . 34  § 2.8.1 Laser . 34  § 2.8.2 Light Modulator . 34  § 2.8.3 Multi-pass Tandem FP Interferometer . 35  § 2.8.4 Photon Detector 38  § 2.8.5 Electromagnet . 38  § 2.9 Analysis of Brillouin Spectrum 40 Chapter Micromagnetics . 41  § 3.1 Introduction 41  § 3.2 Magnetic Energies and Fields 42  § 3.2.1 Zeeman Energy . 43  § 3.2.2 Demagnetizing Energy . 44  § 3.2.3 Exchange Energy 44  § 3.2.4 Anisotropy Energy . 45  § 3.3 Magnetization Dynamics 46  § 3.3.1 Gyromagnetic precession 46  § 3.3.2 The Landau-Lifshitz equation . 48  § 3.3.3 The Landau-Lifshitz-Gilbert equation . 49  § 3.4 Micromagnetic Simulations . 52  § 3.4.1 Introduction to OOMMF 52  § 3.4.2 Simulation procedures 54 -v- Chapter Brillouin Light Scattering Study of One-dimensional Bi-component Magnonic Crystals . 57  § 4.1 Introduction 57  § 4.2 Sample Description 59  § 4.3 BLS Experiments and Theoretical Model 61  § 4.4 Results and Discussions . 64  § 4.5 Conclusions 71 Chapter Spin Waves in Elongated Nanorings . 73  § 5.1 Introduction 73  § 5.2 Experiment and Simulations 74  § 5.3 Results and Discussion . 77  § 5.4 Conclusion 87 Chapter Micromagnetic Study of One-dimensional Bi-component Magnonic Crystal Waveguides . 89  § 6.1 Introduction 89  § 6.2 Simulation Method . 90  § 6.3 Transversely Magnetized 1D MCWs . 93  § 6.3.1 Co/Ni 1D MCWs 93  § 6.3.2 Comparison between 1D MCWs of Different Material Combinations 100  § 6.4 Longitudinally Magnetized MCWs 106  § 6.4.1 Co/Ni 1D MCWs 106  § 6.4.2 Comparison between 1D MCWs of Different Material Combinations 110  § 6.5 Comparison between Transversely and Longitudinally Magnetized 1D MCWs . 117  § 6.6 Conclusions 119 Chapter Micromagnetic Study of Two-dimensional Bi-component Magnonic Crystal Waveguides . 121  § 7.1 Introduction 121  § 7.2 Simulation Method . 122  § 7.3 Transversely Magnetized 2D MCWs . 124  § 7.4 Longitudinally Magnetized 2D MCWs 132  § 7.5 Comparison between Transversely and Longitudinally Magnetized 2D MCWs . 139  § 7.6 Conclusions 142 Chapter Conclusions and Perspectives 145 References . 149  -vi- Summary The main objectives of this doctoral research are to elucidate the spin dynamics of elongated nanorings and the magnonic band structures of spin waves (SWs) in onedimensional (1D) and 2D bi-component magnonic crystals (MCs), using experimental Brillouin light scattering (BLS) and micromagnetic simulations. In Chapter 1, a brief introduction of spin dynamics, an overview of magnonics and MCs, the objectives and the outline of this thesis are presented. Chapter introduces the basic theory of spin waves and the theory of Brillouin light scattering from SWs as well as the experimental instruments used in this thesis. The theory of micromagnetics and the micromagnetic simulation methods employed are discussed in Chapter 3. Chapter presents the BLS mapped magnonic band structure of dipolardominated SWs in 1D bi-component MCs in the form of periodic array of alternating contacting magnetic stripes of different ferromagnetic materials. The observed bandgaps are demonstrated to be tunable by varying the geometrical and material parameters, as well as the applied magnetic field. The entire magnonic band structures observed are blue shifted in frequency while the bandgap widths become narrower, with increasing applied field strength. Results of a BLS and micromagnetic simulation study of the effects of the orientation of an in-plane magnetic field on the spin dynamics of elongated nanorings are presented in Chapter 5. Permalloy rings of three different sizes were studied. Our Brillouin data on the two larger rings reveal a splitting of each SW mode into two modes, corresponding to the transition from the onion to the vortex state, when the -vii- field was applied along their magnetization easy axis. However, this mode splitting was not observed when the field was applied 5° from the magnetization easy axis. In contrast, for the smallest ring, SW mode splitting was observed in both field orientations. The simulated temporal evolution of the magnetization distribution during transitions of magnetic states reveals that the magnetic field orientation determines the nucleation site of the domain walls, and hence the magnetic state. The micromagnetic simulation results of the magnonic band structures of exchange-dominated SWs in transversely and longitudinally magnetized 1D and 2D bi-component magnonic crystal waveguides (MCWs) are presented in Chapters and respectively. The 1D MCWs studied are in the form of periodic arrays of alternating contacting magnetic nanostripes of different ferromagnetic materials, while the 2D ones are in the form of regular square arrays of square dots embedded in a ferromagnetic matrix. The calculated bandgap widths are of the order of 10 GHz. These bandgaps were found to be tunable by separately varying the filling fraction, lattice constant, applied magnetic field strength as well as the material combinations. It is interesting to note that the bandgap widths are independent of the applied field strength, in contrast to the width narrowing reported in Chapter 4. The bandgaps were also found to be dependent on the in-plane orientations of the applied field. Another interesting feature is that there are n+1 zero-width points associated with the nth bandgap. Chapter summarizes the findings of this thesis and presents overall conclusions as well as recommended further studies that can be undertaken. -viii- Chapter Micromagnetic Study of 2D MCWs Fig. 7.12 Maximum width of the magnonic bandgap for all the considered material combinations under applied field H = 200 mT applied (a) transversely and (b) longitudinally to the waveguide. The MCWs are arranged in decreasing order by exchange constant ratio. § 7.6 Conclusions The magnonic band structures of exchange SWs in two-dimensional bicomponent magnonic crystal waveguides were investigated using the micromagnetic methods. Two kinds of SW modes, which depend on the orientation of the applied field, in transversely and longitudinally magnetized waveguides were investigated. From the calculated dispersion curves of SWs, wide forbidden bandgaps of the order of 10 GHz were observed. While the bandgap center frequencies increase with increasing applied magnetic field, the bandgap widths are independent of the field. Additionally, we found that the widths and center frequencies of the bandgaps are controllable by the width of the embedded square dots of the magnonic crystals. An interesting feature is that there are n+1 zero-width points for the nth bandgap for both the transverse and longitudinal cases. -142- Chapter Micromagnetic Study of 2D MCWs It is also found that the higher the order of the transmission bands and bandgaps, the narrower the widths of the transmission bands and bandgaps for the dCo/Fe MCWs. In contrast, the higher are the order of the transmission bands and bandgaps, the wider are the widths of the transmission bands and bandgaps for the other five types of MCWs. The largest bandgap widths were observed in the dCo/Ni MCWs, which have the largest exchange constant ratio. Hence, the magnonic band structures of exchange SWs are more related to the exchange constant contrast ratios. By comparing the band structures of exchange SWs in both the transverse and the longitudinal cases, we found that for the same MCW, the widths of the bandgaps in the longitudinal case are wider than those in the transverse case. And the center frequencies of the bandgaps in the longitudinal case are lower than those in the transverse case. -143- Chapter Micromagnetic Study of 2D MCWs -144- Chapter Conclusions and Perspectives Chapter Conclusions and Perspectives Objective of this PhD research study is to investigate the magnonic band structures of spin waves in 1D and 2D bi-component magnonic crystals using both experimental BLS measurements and the micromagnetic simulation technique. The influences of the in-plane orientation of an applied magnetic field on the spin dynamics of elongated rings were also investigated. In Chapter 4, the experimentally observed magnonic band structures of SWs in 1D bi-component MCs, carried out by the BLS technique, were presented. The BLS measurements were in good accord with finite-element-based theoretical calculations. The linearized Landau-Lifshitz equations, together with Maxwell’s equations, were solved with the Bloch theorem applied along the periodicity direction. Lateral arrays of contacting magnetic nanostripes of different materials were used to study a number of basic properties of SWs in these novel artificial materials. Our results show that the discrete set of allowed frequencies of an isolated nanoelement becomes a finite-width frequency band for an array of identical interacting elements. Bandgap tunability, arising from variations in the geometrical and material parameters, as well as the applied magnetic field has also demonstrated. The entire band structures observed were blue frequency shifted to higher frequencies while the bandgap widths became narrower with increasing applied field strength. Our findings on magnonic structures are expected to stimulate further development of the theory and applications of magnonics. For instance, the observed bandgap tunability could find applications in -145- Chapter Conclusions and Perspectives the control of the generation and propagation of information-carrying SWs in MCbased devices. Possible examples of such devices are filters and waveguides, in which SWs are generated by microwave techniques for use in microwave communication systems. Considering that research in this area is still at its infancy, the following aspects are recommended for future research. On the one hand, it has been shown that the damping of the SWs in the MCs could limit the propagation to take place only among a finite number of periods. Thus, efforts should be devoted to find new materials characterized by a high-saturation magnetization and a low damping. This combination will maximize both group velocity and free propagation path of SWs. On the other hand, it should be noted that the structures studied in Chapter comprised repetition cells comprising only two elements having simple shape (stripes in this chapter). However, new features are expected to appear when the unit cell contains more elements of different shapes and materials. Therefore, further research is needed to extend the simple model to more complex magnonic structures. In chapter 5, we have investigated, using MOKE, Brillouin spectroscopy and micromagnetic simulations, the magnetic-field-orientation dependence of magnetization reversal and SW modes in nanorings of three different sizes. Two switching mechanisms, viz. the single-step and two-step switching, resulting from different magnetic field orientations, were found to exist for the two larger rings. However, the smallest ring was found to exhibit only the two-step switching. The simulated temporal evolution of the magnetization distribution during transitions of magnetic states reveals that the magnetic field orientation determines the nucleation site of the domain walls, and hence the magnetic state. Our Brillouin data on the two -146- Chapter Conclusions and Perspectives larger rings reveal a splitting of each SW mode into two modes, corresponding to the transition from the onion to the vortex state, when the field was applied along their magnetization easy axis. However, this mode splitting was not observed when the field was applied 5° from the magnetization easy axis. In contrast, for the smallest ring, SW mode splitting was observed in both field orientations. The edge-to-edge spacing of the rings in the arrays investigated in Chapter was chosen to be 450 nm. Such a big spacing reduced the magnetostatic interactions between rings in each array. Therefore, for future work, the spacing between neighboring rings could be reduced in order to enhance the interaction between neighboring rings. Such a dense array of rings will be useful sample in the study of 2D MCs as the collective SW modes could be detected and hence the existence of magnonic bandgaps. Furthermore, the 1D chains of interacting nanoring could be used as magnonic waveguides in MC-based devices. In Chapters and 7, micromagnetic simulation results of the magnonic band structures of exchange-dominated SWs in 1D and 2D bi-component MCs of nanoscale lattice constants were presented. It was found that SWs could be excited and emitted from a local area, and hence propagate along the MC-based waveguides. Large bandgap widths of the order of 10 GHz were observed. These calculated bandgaps were found to be tunable by separately varying the filling fraction, lattice constant, applied magnetic field strength as well as the material combinations. The bandgaps were also found to be dependent on the in-plane orientations of the applied field. Another interesting feature was that there were n+1 zero-width points for the nth bandgap. The significance of the presented simulation results is that they contribute to better understanding of the nature and characteristics of SWs in 1D and 2D MCs -147- Chapter Conclusions and Perspectives having nanoscale periods. From the application point of view, the simulated data could motivate the design and realization of novel information-processing magnonic devices. Although, due to the time-consuming nature of such simulations, the dimensions of the waveguides studied were restricted to hundreds of nanometers, and the mesh size was not sufficiently small, the precision of the results obtained is acceptable in most cases. With further enhanced computation power as well as the development of a graphics processing unit, that is, with faster computation times than ever before, smaller mesh cell simulations in systems of large-scale volume would be feasible and promising. For future work based on the results of Chapters and 7, one possible avenue is the development of first-principle calculations at the atomic level. This is necessary in order to study the responses of magnetic moments to light, heat and elastic stress, not to mention their reverse effects such as generation of electromagnetic waves and the inverse magnetostriction effect from perturbed oscillating magnetic dipoles. Another interesting area for further work would be the development of an atomistic model, which considers such factors as atomic lattice configurations, interface effects, along with high time-resolutions shorter-than-1ps for SW propagations in arbitrary-shaped waveguides of nanoscale width. -148- References References [1] F. Bloch, Z. Phys. 61, 206-219 (1930). [2] A. I. Akhiezer, V. G. Bar’yakhtar, and S. V. Peletminskii, Spin Waves (Amsterdam: North-Holland, 1968). [3] A. G. Gurevich and G. A. Melkov, Magnetization Oscillations and Waves (New York: Chemical Rubber Corp., 1996). [4] T. Holstein and H. Primakoff, Phys. Rev. 58, 1098 (1940). [5] F. J. Dyson, Phys. Rev. 102, 1217 (1956). [6] T. Neumann, A. A. Serga, B. Hillebrands, and M. P. Kostylev, Appl. Phys. Lett. 94, 042503 (2009). [7] U.-H. Hansen, M. Gatzen, V. E. Demidov, and S. O. Demokritov, Phys. Rev. Lett. 99, 127204 (2007). [8] C. Mathieu, J. Jorzick, A. Frank, S. O. Demokritov, A. N. Slavin, B. Hillebrands, B. Bartenlian, C. Chappert, D. Decanini, F. Rousseaux, and E. Cambril, Phys. Rev. Lett. 81, 3968 (1998). [9] J. Jorzick, S. O. Demokritov, C. Mathieu, B. Hillebrands, B. Bartenlian, C. Chappert, F. Rousseaux, and A. N. Slavin, Phys. Rev. B 60, 15194 (1999). [10] J. Jorzick, S. O. Demokritov, B. Hillebrands, B. Bartenlian, C. Chappert, D. Decanini, F. Rousseaux, and E. Cambril, Appl. Phys. Lett. 75, 3859 (1999). [11] C. Bayer, J. Jorzick, B. Hillebrands, S. O. Demokritov, R. Kouba, R. Bozinoski, A. N. Slavin, K. Y. Guslienko, D. V. Berkov, N. L. Gorn, and M. P. Kostylev, Phys. Rev. B 72, 064427 (2005). [12] J. Jorzick, S. O. Demokritov, B. Hillebrands, M. Bailleul, C. Fermon, K. Y. Guslienko, A. N. Slavin, D. V. Berkov, and N. L. Gorn, Phys. Rev. Lett. 88, 047204 (2002). [13] J. Podbielski, F. Giesen, and D. Grundler, Phys. Rev. Lett. 96, 167207 (2006). [14] S. Choi, K.-S. Lee, K. Y. Guslienko, and S.-K. Kim, Phys. Rev. Lett. 98, 087205 (2007). [15] V. V. Kruglyak, S. O. Demokritov, and D. Grundler, J. Phys. D: Appl. Phys. 43, 264001 (2010). -149- References [16] A. A. Serga, A. V. Chumak, and B. Hillebrands, J. Phys. D: Appl. Phys. 43, 264002 (2010). [17] G. Gubbiotti, S. Tacchi, M. Madami, G. Carlotti, A. O. Adeyeye, and M. Kostylev, J. Phys. D: Appl. Phys. 43, 264003 (2010). [18] S.-K. Kim, J. Phys. D: Appl. Phys. 43, 264004 (2010). [19] A. Khitun, M. Bao, and K. L. Wang, J. Phys. D: Appl. Phys. 43, 264005 (2010). [20] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. v Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001). [21] D. Grundler, Phys. World 15, 39 (2002). [22] Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, Nature 414, 289 (2001). [23] J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997). [24] Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, Appl. Phys. Lett. 94, 083112 (2009). [25] K.-S. Lee, D.-S. Han, and S.-K. Kim, Phys. Rev. Lett. 102, 127202 (2009). [26] M. Krawczyk and H. Puszkarski, Phys. Rev. B 77, 054437 (2008). [27] H. Puszkarski and M. Krawczyk, Solid State Phenom. 94, 125 (2003). [28] V. V. Kruglyak and R. J. Hicken, J. Magn. Magn. Mater. 306, 191 (2006). [29] S. A. Nikitov, C. S. Tsai, Y. V. Gulyaev, Y. A. Filimonov, A. I. Volkov, S. L. Vysotskii, and P. Tailhades, Mater. Res. Soc. Symp. Proc. 834, 87 (2005). [30] S. A. Nikitov, P. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001). [31] V. V. Kruglyak and A. N. Kuchko, Phys. B. 339, 130 (2003). [32] H. Xi, X. Wang, Y. Zheng, and P. J. Ryan, J. Appl. Phys. 105, 07A502 (2009). [33] S. Neusser and D. Grundler, Adv. Mater. 21, 2927 (2009). [34] M. Krawczyk and H. Puszkarski, J. Appl. Phys. 100, 073905 (2006). [35] K.-S. Lee and S.-K. Kim, J. Appl. Phys. 104, 053909 (2008). [36] A. Kozhanov, D. Ouellette, Z. Griffith, M. Rodwell, A. P. Jacob, D. W. Lee, S. X. Wang, and S. J. Allen, Appl. Phys. Lett. 94, 012505 (2009). [37] A. V. Chumak, A. A. Serga, S. Wolff, B. Hillebrands, and M. P. Kostylev, J. Appl. Phys. 105, 083906 (2009). [38] A. V. Chumak, A. A. Serga, S. Wolff, B. Hillebrands, and M. P. Kostylev, Appl. Phys. Lett. 94, 172511 (2009). -150- References [39] A. V. Chumak, A. A. Serga, B. Hillebrands, and M. P. Kostylev, Appl. Phys. Lett. 93, 022508 (2008). [40] M. N. Baibich, J. M. Broto, A. Fert, F. N. V. Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988). [41] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39, 4828 (1989). [42] G. Gubbiotti, S. Tacchi, G. Carlotti, N. Singh, S. Goolaup, a O. Adeyeye, and M. Kostylev, Appl. Phys. Lett. 90, 092503 (2007). [43] M. Kostylev, P. Schrader, R. L. Stamps, G. Gubbiotti, G. Carlotti, A. O. Adeyeye, S. Goolaup, and N. Singh, Appl. Phys. Lett. 92, 132504 (2008). [44] L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. B 75, 024416 (2007). [45] V. V. Kruglyak, P. S. Keatley, R. J. Hicken, J. R. Childress, and J. A. Katine, J. Appl. Phys. 99, 08F306 (2006). [46] P. S. Keatley, V. V. Kruglyak, A. Neudert, E. A. Galaktionov, R. J. Hicken, J. R. Childress, and J. A. Katine, Phys. Rev. B 78, 214412 (2008). [47] V. V. Kruglyak, P. S. Keatley, A. Neudert, R. J. Hicken, J. R. Childress, and J. A. Katine, Phys. Rev. Lett. 104, 027201 (2010). [48] G. N. Kakazei, Y. G. Pogorelov, M. D. Costa, T. Mewes, P. E. Wigen, P. C. Hammel, V. O. Golub, T. Okuno, and V. Novosad, Phys. Rev. B 74, 060406(R) (2006). [49] G. Gubbiotti, S. Tacchi, G. Carlotti, P. Vavassori, N. Singh, S. Goolaup, A. Adeyeye, A. Stashkevich, and M. Kostylev, Phys. Rev. B 72, 224413 (2005). [50] Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, ACS Nano 4, 643-648 (2010). [51] S. Jain, M. Kostylev, and A. O. Adeyeye, Phys. Rev. B 82, 214422 (2010). [52] A. O. Adeyeye and S. Jain, J. Appl. Phys. 109, 07B903 (2011). [53] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, A. O. Adeyeye, S. Neusser, B. Botters, and D. Grundler, IEEE Trans. Magn. 46, 172 (2010). [54] M. Kostylev, G. Gubbiotti, G. Carlotti, G. Socino, S. Tacchi, C. Wang, N. Singh, A. O. Adeyeye, and R. L. Stamps, J. Appl. Phys. 103, 07C507 (2008). [55] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, A. O. Adeyeye, S. Neusser, B. Botters, and D. Grundler, IEEE Trans. Magn. 46, 1440 (2010). [56] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, H. Tanigawa, T. Ono, and M. P. Kostylev, Phys. Rev. B 82, 024401 (2010). -151- References [57] S. Neusser, B. Botters, and D. Grundler, Phys. Rev. B 78, 054406 (2008). [58] S. Neusser, B. Botters, M. Becherer, D. Schmitt-Landsiedel, and D. Grundler, Appl. Phys. Lett. 93, 122501 (2008). [59] N. M. Kreines, Phys. Rep. 81, 351-408 (1982). [60] M. G. Cottam and D. J. Lockwood, Light Scattering in Magnetic Solids (John Willey & Sons, 1986). [61] S. O. Demokritov, B. Hillebrands, and A. N. Slavin, Phys. Rep. 348, 441-489 (2001). [62] J. Stöhr and H. C. Siegmann, Magnetism: From Fundamentals to Nanoscale Dynamics (Springer, n.d.). [63] M. Getzlaff, Fundamentals of Magnetism (Springer, Berlin, Heidelberg, New York, 2008). [64] B. Lax and K. J. Button, Microwave Ferrites and Ferromagnetics (Mc-GrawHill, New York, 1962). [65] R. W. Damon and J. R. Eshbach, J. Phys. Chem. Solids 19, 308-320 (1961). [66] B. Hillebrands, Phys. Rev. B 41, 530-540 (1990). [67] B. Hillebrands, Brillouin Light Scattering from Layered Magnetic Structures, in Light Scattering in Solids VII, (Springer Verlag, Berlin Heidelberg, 2008). [68] R. W. Damon and J. R. Eshbach, J. Appl. Phys. 31, 104-105 (1960). [69] B. A. Kalinikos and A. N. Slavin, J. Phys. C 19, 7013-7033 (1986). [70] T. Schneider, Bestimmung Und Beeinflussung Der Phaseneigenschaften Von Spinwellen in Yttrium-Eisen-Granat-Wellenleiterstrukturen (Diplomathesis, TU Kaiserslautern, 2005). [71] R. Arias and D. L. Mills, Phys. Rev. B 60, 7395-7409 (1999). [72] C. Bayer, J. P. Park, H. Wang, M. Yan, C. E. Campbell, and P. A. Crowell, Phys. Rev. B 69, 134401 (2004). [73] S. O. Demokritov and B. Hillebrands, Spin Dynamics in Confined Magnetic Structures I (Springer Verlag, Berlin, 2002). [74] M. Sparks, Ferromagnetic Relaxation Theory (Mc-Graw-Hill, New York, 1966). [75] C. Kittel, Phys. Rev. 73, 155-161 (1948). [76] M. Sparks, Solid State Comm. 8, 731-733 (1970). [77] G. T. Rado and J. R. Weertman, J. Phys. Chem. Solids 11, 315-333 (1959). -152- References [78] K. Y. Guslienko, S. O. Demokritov, B. Hillebrands, and A. N. Slavin, Phys. Rev. B 66, 132402 (2002). [79] N. W. Ashcroft and D. Mermin, Solid State Physics (Brooks Cole, 1976). [80] A. Schreyer, T. Schmitte, R. Siebrecht, P. Bödeker, H. Zabel, S. H. Lee, R. W. Erwin, C. F. Majkrzak, J. Kwo, and M. Hong, J. Appl. Phys. 87, 5443-5448 (2000). [81] E. Burkel, Rep. Prog. Phys. 63, 171-232 (2000). [82] H. I. and D. L. Mills, Electron Energy Loss and Surface Vibrations (Academic Press, San Francisco, 1982). [83] P. A. Fleury, S. P. S. Porto, L. E. Cheesman, and H. J. Guggenheim, Phys. Rev. Lett. 17, 84-87 (1966). [84] B. Heinrich, Ultrathin Magnetic Structures II (Springer, Berlin, 1994). [85] Z. Zhang, P. C. Hammel, M. Midzor, M. L. Roukes, and J. R. Childress, Appl. Phys. Lett. 73, 2036-2038 (1998). [86] A. B. Kos, T. J. Silva, and P. Kabos, Rev. Sci. Instrum. 73, 3563-3569 (2002). [87] J. R. Sandercock, Light Scattering in Solid III (Springer, Berlin, 1982). [88] J. F. Cochran, Ultrathin Magnetic Structures II (Springer, Berlin, 1994). [89] D. J. Griffiths, Introduction to Electrodynamics 3rd Edition (Prentice Hall, New Jersey, 1999). [90] Spectra-Physics, “User’s Manual for BeamLok 2060 and 2080 Ion Lasers” (1994). [91] J. R. Sandercock, “Operator Manual for the Tandem Fabry-Perot Interferometer” (1999). [92] J. R. Sandercock, Second Int. Conf. On Light Scattering in Solids (Flammarion, Paris, 1971). [93] B. and S. O. D. Hillebrands, Encyclopedia of Nanoscience and Nanotechnology.Vol. (American Scientific Publishers, Los Angeles, 2004). [94] GMW, User’s Manual for GMW 3470 Electromagnet (1997). [95] W. F. Brown Jr., Micromagnetics (Intersience Publishers, J. Wiley and Sons, New York, 1963). [96] P. Weiss, J. Phys. 6, 401 (1907). [97] L. D. Landau and E. M. Lifshitz, Phys. Z. Sowjet. 8, 153 (1935). -153- References [98] J. Fidler, R. W. Chantrell, T. Schrefl, and M. A. Wongsam, Encyclopedia of Materials: Science and Tecnology; Micromagnetics: Basic Principles (Elsevier Science Ltd., 2001). [99] S. Blundell, Magnetism in Condensed Matter (Oxford University Press, 2001). [100] M. Mansuripur, The Physical Principles of Magneto-optic Recording (Cambridge University Press, 1995). [101] T. L. Gilbert, Phys. Rev. 100, 1243 (1955). [102] G. Bertotti, Tutorial Session Notes: Micromagnetics and Nonlinear MagNetization Dynamics (10th Biennal Conference on Electromagnetic Fields Computation, Perugia, 2002). [103] A. Arrott, Plenary Lecture: Progress in Micromagnetics, Moscow International Symposium on Magnetism (Moscow International Symposium on Magnetism, Moscow, 2002). [104] P. Podio-Guidugli, Euro. Phys. J. B 19, 417 (2001). [105] R. Kikuchi, J. Appl. Phys. 27, 1352 (1956). [106] J. C. Mallinson, On Damped Gyromagnetic Precession (IEEE Transactions on Magnetics, 1987), p. 2003. [107] M.J. Donahue and D. G. Porter, OOMMF User’s Guide, Version 1.0, Interagency Report NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD (Sept 1999). (n.d.). [108] H. Kronmüller and M. Fähnle, Micromagnetism and the Microstructure of Ferromagnetic Solids, 1st ed. (Cambridge University Press, 2003). [109] C. Seberino and H. N. Bertram, IEEE Trans. Magn. 37, 1078-1086 (2001). [110] R. P. Boardman, Computer Simulation Studies of Magnetic Nanostructures (2005), p. PhD thesis. [111] A. V. Chumak, A. A. Serga, B. Hillebrands, and M. P. Kostylev, Appl. Phys. Lett. 93, 022508 (2008). [112] Y. V. Gulyaev, S. A. Nikitov, L. V. Zhivotovskii, A. A. Klimov, P. Tail-Hades, L. Presmanes, C. Bonningue, C. S. Tsai, S. L. Vysotskii, and Y. A. Filimonov, J. Exp. Theor. Phys. 77, 567 (2003). [113] S. L. Vysotskii, S. A. Nikitov, and Y. A. Filimonov, J. Exp. Theor. Phys. 101, 547 (2005). [114] M. E. Dokukin, K. Togo, and M. Inoue, J. Magn. Soc. Jpn. 32, 103 (2008). -154- References [115] V. L. Zhang, Z. K. Wang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, J. Nanosci. Nanotechnol. 11, 2657-2660 (2011). [116] Z. K. Wang, M. K. Kuok, S. C. Ng, D. J. Lockwood, M. G. Cottam, K. Nielsch, R. B. Wehrspohn, and U. Gösele, Phys. Rev. Lett. 89, 027201 (2002). [117] Z. K. Wang, H. S. Lim, H. Y. Liu, S. C. Ng, M. H. Kuok, L. L. Tay, D. J. Lockwood, M. G. Cottam, K. L. Hobbs, P. P. Larson, J. C. Keay, G. D. Lian, and M. B. Johnson, Phys. Rev. Lett. 94, 137208 (2005). [118] J. O. Vasseur, L. Dobrzynski, B. Djafari-Rouhani, and H. Puszkarski, Phys. Rev. B 54, 1043-1049 (1996). [119] V. V. Kruglyak, R. J. Hicken, A. N. Kuchko, and V. Y. Gorobets, J. Appl. Phys. 98, 014304 (2005). [120] M. P. Kostylev and A. A. Stashkevich, Phys. Rev. B 81, 054418 (2010). [121] M. P. Kostylev and N. A. Sergeeva, “Collective and Individual Modes on One Dimensional Bilayered Magnetic Structures”, in Magnetic Properties of Laterally Confined Nanometric Structures (Transworld Research Network, Kerala: India, 2006). [122] C. S. Lin, H. S. Lim, Z. K. Wang, S. C. Ng, and M. H. Kuok, Appl. Phys. Lett. 98, 022504 (2011). [123] J. G. Zhu, Y. F. Zheng, and G. A. Prinz, J. Appl. Phys. 87, 6668 (2000). [124] R. L. White, R. M. H. New, and R. F. W. Pease, IEEE Trans. Magn. 33, 990 (1997). [125] B. D. Terris, T. Thomson, and G. Hu, Microsyst. Technol. 13, 189 (2007). [126] C. B. Muratov and V. V. Osipov, IEEE Trans. Magn. 45, 3207-3209 (2009). [127] P. Vavassori, V. Metlushko, and B. Ilic, Appl. Phys. Lett. 91, 093114 (2007). [128] J. Wang, A. O. Adeyeye, and N. Singh, Appl. Phys. Lett. 87, 262508 (2005). [129] S. Jain and A. O. Adeyeye, Appl. Phys. Lett. 94, 062510 (2009). [130] L. J. Chang, C. Yu, T. W. Chiang, K. W. Cheng, W. T. Chiu, S. F. Lee, Y. Liou, and Y. D. Yao, J. Appl. Phys. 103, 07C514 (2008). [131] E. Saitoh, J. Appl. Phys. 95, 1986 (2004). [132] M. Klaui, U. Rdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, C. David, E. H. C. P. Sinnecker, and A. P. Guimares, J. Appl. Phys. 95, 6639 (2004). [133] Y. G. Yoo, M. Klaui, C. a F. Vaz, L. J. Heyderman, and J. a C. Bland, Appl. Phys. Lett. 82, 2470 (2003). -155- References [134] F. Zhu, G. Chern, O. Tchernyshyov, X. Zhu, J. Zhu, and C. Chien, Phys. Rev. Lett. 96, 1-4 (2006). [135] K. J. Kirk, J. N. Chapman, S. McVitie, P. R. Aitchison, and C. D. W. Wilkinson, Appl. Phys. Lett. 75, 3683 (1999). [136] C. K. Lim, G. Yi, J. N. Chapman, W. A. P. Nicholson, S. McVitie, and C. D. W. Wilkinson, J. Phys. D: Appl. Phys. 36, 3099 (2003). [137] J. Topp, J. Podbielski, D. Heitmann, and D. Grundler, Phys. Rev. B 78, 024431 (2008). [138] Y. Ren and A. O. Adeyeye, J. Appl. Phys. 105, 063901 (2009). [139] G. Gubbiotti, S. Tacchi, G. Carlotti, N. Singh, S. Goolaup, A. O. Adeyeye, and M. Kostylev, Appl. Phys. Lett. 90, 092503 (2007). [140] M. Kostylev, P. Schrader, R. L. Stamps, G. Gubbiotti, G. Carlotti, A. O. Adeyeye, S. Goolaup, and N. Singh, Appl. Phys. Lett. 92, 132504 (2008). [141] Z. K. Wang, M. H. Kuok, S. C. Ng, D. J. Lockwood, M. G. Cottam, K. Nielsch, R. B. Wehrspohn, and U. Gosele, Phys. Rev. Lett. 89, 027201 (2002). [142] D. B. Carlton, N. C. Emley, E. Tuchfeld, and J. Bokor, Nano Letters 8, 4173-8 (2008). [143] N. Singh, S. Goolaup, and A. O. Adeyeye, Nanotechnology 15, 1539 (2004). [144] C. G. Tan, H. S. Lim, Z. K. Wang, S. C. Ng, M. H. Kuok, S. Goolaup, A. O. Adeyeye, and N. Singh, J. Magn. Magn. Mater. 320, 475-478 (2008). [145] G. Gubbiotti, G. Carlotti, T. Okuno, M. Grimsditch, L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. B 72, 184419 (2005). [146] F. Giesen, J. Podbielski, T. Korn, M. Steiner, a van Staa, and D. Grundler, Applied Physics Letters 86, 112510 (2005). [147] G. Gubbiotti, M. Madami, S. Tacchi, G. Carlotti, H. Tanigawa, T. Ono, L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. Lett. 97, 2-5 (2006). [148] I. Neudecker, M. Kläui, K. Perzlmaier, D. Backes, L. Heyderman, C. Vaz, J. Bland, U. Rüdiger, and C. Back, Phys. Rev. Lett. 96, 1-4 (2006). [149] M. Krawczyk, J. Klos, M. L. Sokolovskyy, and S. Mamica, J. Appl. Phys. 108, 093909 (2010). [150] J. Topp, D. Heitmann, M. P. Kostylev, and D. Grundler, Phys. Rev. Lett. 104, 207205 (2010). [151] N. I. Polushkin, Phys. Rev. B 82, 172405 (2010). -156- References [152] C. Sandweg, Y. Kajiwara, A. Chumak, A. Serga, V. Vasyuchka, M. Jungfleisch, E. Saitoh, and B. Hillebrands, Phys. Rev. Lett. 106, 216601 (2011). [153] M.J. Donahue and D. G. Porter, OOMMF User’s Guide, Version 1.0, Interagency Report NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD (Sept 1999). (n.d.). [154] V. E. Demidov, S. O. Demokritov, K. Rott, P. Krzysteczko, and G. Reiss, Appl. Phys. Lett. 92, 232503 (2008). [155] M. Kostylev, G. Gubbiotti, J.-G. Hu, G. Carlotti, T. Ono, and R. Stamps, Phys. Rev. B 76, 054422 (2007). [156] M. Inoue, A. Baryshev, H. Takagi, P. B. Lim, K. Hatafuku, J. Noda, and K. Togo, Appl. Phys. Lett. 98, 132511 (2011). -157- [...]... miniaturization of microwave devices Magnonic crystals (MCs), the basis of magnonics, are SW analogs of photonic and phononic crystals, and represent materials with periodically modulated magnetic parameters The band structure of SWs in MCs, which is similar to those of elastic waves and light in phononic and photonic crystals, is strongly modified with respect -2- Chapter 1 Introduction to uniform media The band... in MCs, and studies have been performed to understand the propagation of SWs in these systems The subsequent sections provide an overview of magnonics, and a detailed discussion of previous and on-going research on MCs § 1.1 Overview of Magnonics The studies of magnonics have attracted greatly interest as recently featured in a series of review papers [15-19] Magnonics is a field of research and technology... A, and exchange length lex) of ferromagnetic metals: Co, Fe, Py and Ni (Ref 6) 92  Table 6.2 Widths and centre frequencies of magnonic bandgaps in the 16Co/4Ni, 16Co/4Py, 16Co/4Fe, 16Fe/4Ni, 16Fe/4Py and 16Py/4Ni MCWs Values are specified in GHz 100  Table 6.3 The maximal widths (GHz) and corresponding centre frequencies (GHz) of magnonic bandgaps and stripe widths M (nm) of. .. the presence of dispersion curves and Brillouin zones (BZs), the existence of allowed and forbidden frequency bands (existence of bandgaps), the appearance of acoustic and optical SWs due to the presence of a complex base (unit cell) for the MC, the existence of soft spin modes which promotes the inversion of the magnetization All these features have been foreseen from the theoretical point of view, but... processing methodologies The experimental and theoretical establishment of the existence of magnonic bandgaps in such structures could stimulate further development of the theory and applications of magnonics The tunability of bandgap could find applications in the control of generation and propagation of information-carrying SWs in MC-based devices For SW control and manipulation, we are at the early... MCs in the form of periodic arrays of alternating contacting magnetic stripes of different ferromagnetic materials Chapter 5 explores the influences of the orientation of an in-plane applied magnetic field on the spin dynamics of elongated Py nanorings using BLS and -11- Chapter 1 Introduction micromagnetic simulations The micromagnetic simulation results of the magnonic band structures of exchange-dominated... approaches are effective means of understanding the fundamentals of spin dynamics and gaining new insights into them, the limitation of these same tools and approaches have left gaps of knowledge in the pertinent physics As an alternative, however, micromagnetic simulations have recently emerged as a powerful tool for the study of a variety of phenomena related to spin dynamics of magnetic elements on the... simulations of the excitation, propagation and the novel wave characteristics of SWs, highlighting how the micromagnetic simulation approach contributed to a better understanding of spin dynamics of nanomagnets, and considering some of the merits of numerical simulation studies Lee et al [25] have performed micromagnetic simulations of SWs in magnonic crystal waveguides (MCWs) The MCWs are composed simply of. .. Widths and centre frequencies of magnonic bandgaps in the 28Co/Ni, 28Co/Py, 28Co/Fe, 28Fe/Ni, 28Fe/Py, and 28Py/Ni MCWs Values are specified in GHz 127  Table 7.2 The maximal widths (GHz) and corresponding centre frequencies (GHz) of magnonic bandgaps and square dot widths d (nm) of the dCo/Ni, dCo/Py, dCo/Fe, dFe/Ni, dFe/Py, and dPy/Ni MCWs 130  Table 7.3 Widths and centre frequencies of. .. existence of magnonic bandgaps, and it is expected to stimulate further development of the theory -8- Chapter 1 Introduction and applications of magnonics The observed bandgap tunability could find applications in the control of the generation and propagation of information-carrying SWs in MC-based devices § 1.2.2 Micromagnetic Studies of Magnonic Crystals Although experimental tools and theoretical approaches . research are to elucidate the spin dynamics of elongated nanorings and the magnonic band structures of spin waves (SWs) in one- dimensional (1D) and 2D bi-component magnonic crystals (MCs), using experimental. SPIN DYNAMICS OF MAGNONIC CRYSTALS AND FERROMAGNETIC NANORINGS MA FUSHENG (B. Sc, SHANDONG UNIV) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. frequencies (GHz) of magnonic bandgaps and square dot widths d (nm) of the dCo/Ni, dCo/Py, dCo/Fe, dFe/Ni, dFe/Py, and dPy/Ni MCWs. 130 Table 7.3 Widths and centre frequencies of magnonic bandgaps in