Spintronics is a newly emerging field in physics, aimed at using the spin of electrons to carry information. One of the primary ways in which this could be done is through the use of spin waves. In order to do this, it will be necessary to have a complete understanding of spin waves and how they behave in various materials and structures. In this dissertation, we aim to create a thorough model of spin waves in both one-dimensional and two-dimensional magnonic crystals in an effort to understand and control their dispersion properties and propagation patterns. Using the Landau-Lifshitz-Gilbert equation, we have derived a model for spin waves in magnonic crystals that allowed us to calculate their dispersion and propagation properties. In the first part of this work we considered two-dimensional magnonic crystals consisting of magnetic cylinders arrange in a lattice and embedded in a second magnetic material. The dispersion relations were found to be heavily dependent on the magnetic properties of the two materials, with band gaps appearing more readily when the magnetization was larger in the cylinders than in the host. It was also found that the dipolar field reduced the symmetry of the results, with reflection symmetry not appearing in the dispersion relations even when it was present in the physical lattice. For the propagation of spin waves in two-dimensional magnonic crystals, we found that their directionality was highly dependent on changes in frequency. Propagation patterns varied from roughly isotropic for spin waves in the middle of a band level, to highly directional propagation along the x and y axes for a frequency near the edge of a band. The absence of propagation was also found for frequencies in a band gap. For spin waves in one-dimensional magnonic crystals, we investigated the effects of applying an electric field to the system. When a uniform electric field was applied to a magnonic crystal consisting of a periodic variation in magnetic materials, the band levels were found to shift downward in frequency, with the magnitude of the shift being dependent on the strength of the electric field. While this method could move existing band gaps, it was not capable of creating a band gap in the dispersion relations. Creation of band gaps was found to occur when a periodically varying electric field was applied to a uniform magnetic material. This effect could be used to create a magnonic device where the dispersion properties can be dynamically controlled with an electric field.

Magnetic materials are one of the most interesting and promising class of materials for technological applications [1]. Among them, patterned ferromagnetic systems have an important role especially in the prospect of high density data storage [2], domain wall logic devices [3] and magnetic memory [4, 5]. Coupled systems of ferromagnetic and antiferromagnetic materials have been implemented to design sensors such as giant magnetoresistance (GMR) [6-8] and tunnel magnetoresistance (TMR) [9, 10]. Ferromagnetic nanoparticles have been used for the drug targeting, cancer therapy, MRI and many more applications [11, 12]. In addition, more recently, significant attention has been paid to explore the dynamic properties of magnetic materials in the GHz range and use them for technological applications such as microwave filters, signal processing, phase shifter, nonreciprocal microwave devices, spin wave guide, high frequency memory, logic elements [13-19] Boundary conditions, interactions between individual entities, and lateral confinement of magnetic charges generate diverse magnetic properties especially at nanoscale length [20, 21]. The variation of magnetic properties are even quite different when the size of the magnetic structure is smaller or comparable with the magnetic characteristic length such as mean free path of electron, width of domain wall and even the spin diffusion length [22-24]. In this study, we have considered different magnetic systems. Firstly, the multilayer of coupled ferromagnetic and antiferromagnetic system has been considered to evaluate the exchange bias anisotropy. [FeNi/IrMn]n multilayer systems with different thicknesses of ferromagnetic layer were studied. Static and dynamic properties were revealed through magnetometry measurements (VSM) and VNA-FMR techniques respectively. Angular variation of first order reversal curve (AFORC) and ferromagnetic resonance (AFMR) were performed to learn the intrinsic exchange bias distribution. Secondly, patterned magnetic structures were synthesized to understand the magnetization dynamics in confined geometry. Surface modulated thin films with different periodicity, dumbbell-shaped structures with variable size and three dimensional magnonic crystals have been studied using both static and dynamic measurement techniques. Micromagnetic simulations were performed to understand and explain the experimental results.

This thesis contains results of numerical investigations of magnetisation dynamics in nanostructed ferromagnetic materials. Magnetic systems have been simulated using the open source micromagnetic solver: Object Oriented Micromagnetic Framework (OOMMF), and thoroughly analysed using my own software: semargl. A systematic study of collective magnonic modes confined in 2D and 3D systems of rectangular ferromagnetic nano-elements is presented. The collective character of the excitations results from the dynamic magnetic dipole field. The magnetization dynamics of isolated rectangular elements is found to be spatially non-uniform which means that the dynamic dipolar coupling is highly anisotropic. A semi-analytical theory of collective magnonic modes has been developed to evaluate the properties of the dynamic magnetic dipole field. It was found that the theory is only valid for certain eigenmodes of the isolated element. In particular the modes where the magnetic dipole coupling between the elements is much lower than the internal energy of the corresponding eigenmodes of the isolated element. It is then demonstrated that the confinement of spin waves is strongly affected by the ground state of the system. In particular it has been found that symmetry properties of the topology of 2D arrays affect the dynamics of the strongly localised modes. The effect is found to be significant for arrays of any number of elements. At the same time the relative contribution of the localized modes to the uniform response decreases with the number of elements in the array. The dispersion relation of spin waves in 2D arrays of rectangular nano-elements has been calculated for the first time using micromagnetic simulations. The form of the dispersion is used to estimate the spatial anisotropy of the dynamic dipolar coupling. Simulations of the 3D confinement of spin waves in stacks of magnetic nano-elements have been performed. The calculation of both the dispersion and spatial profiles of the corresponding magnonic modes facilitates the investigation of the localisation of collective spin waves. Furthermore the dispersion of collective magnonic modes has been calculated for stacks of rectangular nano-elements for a range of in-plane aspect ratios. Finally, a numerical method has been developed to extract the scattering parameters of magnonic logic devices. This method has been demonstrated by applying it to the simplest possible magnonic device so that the results could be compared to an analytical expression of the scattering parameters.

This thesis reports on results in the fields of experimental spin- and general wave dynamics.

Made available in DSpace on 2014-12-17T15:15:00Z (GMT). No. of bitstreams: 1 CarlosHOC_TESE.pdf: 15589268 bytes, checksum: 5a0a25bd59fcc76f4d53ba73163991d0 (MD5) Previous issue date: 2013-12-12 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In this paper we investigate the spectra of band structures and transmittance in magnonic quasicrystals that exhibit the so-called deterministic disorders, specifically, magnetic multilayer systems, which are built obeying to the generalized Fibonacci (only golden mean (GM), silver mean (SM), bronze mean (BM), copper mean (CM) and nickel mean (NM) cases) and k-component Fibonacci substitutional sequences. The theoretical model is based on the Heisenberg Hamiltonian in the exchange regime, together with the powerful transfer matrix method, and taking into account the RPA approximation. The magnetic materials considered are simple cubic ferromagnets. Our main interest in this study is to investigate the effects of quasiperiodicity on the physical properties of the systems mentioned by analyzing the behavior of spin wave propagation through the dispersion and transmission spectra of these structures. Among of these results we detach: (i) the fragmentation of the bulk bands, which in the limit of high generations, become a Cantor set, and the presence of the mig-gap frequency in the spin waves transmission, for generalized Fibonacci sequence, and (ii) the strong dependence of the magnonic band gap with respect to the parameters k, which determines the amount of different magnetic materials are present in quasicrystal, and n, which is the generation number of the sequence k-component Fibonacci. In this last case, we have verified that the system presents a magnonic band gap, whose width and frequency region can be controlled by varying k and n. In the exchange regime, the spin waves propagate with frequency of the order of a few tens of terahertz (THz). Therefore, from a experimental and technological point of view, the magnonic quasicrystals can be used as carriers or processors of informations, and the magnon (the quantum spin wave) is responsible for this transport and processing / Neste trabalho investigamos espectros de estruturas de banda e de transmit?ncia em quasicristais magn?nicos que apresentam as chamadas desordens determin?sticas, especificamente, sistemas de multicamadas magn?ticas que s?o constru?dos obedecendo as sequ?ncias substitutionais de Fibonacci generalizada (apenas os casos golden mean (GM), silver mean (SM), bronze mean (BM), copper mean (CM) e nickel mean (NM)) e k-componente de Fibonacci. O modelo te?rico ? baseado no hamiltoniano de Heisenberg para o regime de troca, juntamente com o poderoso m?todo da matriz transfer?ncia, e levando em conta a aproxima??o RPA. Os materiais magn?ticos considerados s?o ferromagnetos c?bicos simples. O principal interesse deste estudo ? investigar o efeito da quasi-periodicidade nas propriedades f?sicas dos sistemas citados analisando o comportamento da propaga??o de ondas de spin por meio dos espectros de dispers?o e de transmiss?o dos magnons nestas estruturas. Entre os resultados destacamos: (i) a fragmenta??o das bandas de volume que, no limite de altas gera??es, se tornam conjuntos de Cantor, e a presen?a da frequ?ncia de mid-gap na transmit?ncia das ondas de spin, na sequ?ncia de Fibonacci generalizada; e (ii) a forte depend?ncia do band gap magn?nico com rela??o aos par?metros k, que determina a quantidade de materiais magn?ticos diferentes presentes no quasi-cristal, e n, que ? o n?mero da gera??o da sequ?ncia k-componente de Fibonacci. Neste ?ltimo caso, verificamos que o sistema apresenta uma banda magn?nica proibida, cuja largura e regi?o de frequ?ncia podem ser controladas variando k e n. No regime de troca, as ondas de spin propagam-se com frequ?ncia da ordem de algumas dezenas de terahertz (THz). Portanto, do ponto de vista experimental e tecnol?gico, os quasi-cristais magn?nicos podem ser utilizados como transportadores ou processadores de informa??es, sendo o magnon (o quantum da onda de spin) o respons?vel por esse transporte e processamento

In dieser Arbeit wurde magnetische und elastische Dynamik in nanostrukturierten künstlichen Materialien mit Hilfe eines optischen, zeitaufgelösten Pumpprobe Messaufbaus untersucht. Die Absorption der ultraschnellen Laserpulse erzeugt einen Wärmegradienten auf einer Zeitskala von Pikosekunden. Dieser induziert kohärente dynamische Prozesse, welche mit einem zweiten, zeitverzögerten Puls beobachtet werden. In einem zweidimensionalen magnonischen Kristall, bestehend aus einem submikrometer großen Antidotgitter auf einer ferromagnetischen CoFeB Schicht, können Spinwellenmoden beobachtet werden, die eine schwache Frequenzabhängigkeit vom externen magnetischen Feld aufweisen. Dies lässt vermuten, dass Spinwellen in der Nähe von Inhomogenitäten des internen Feldes lokalisieren. Elastische Dynamik auf denselben Strukturen zeigt Frequenzen proportional zu charakteristischen Strukturgrößen (Antidotabstand und Antidotgröße), was auf die Anregung von Spannungswellen auf der Oberfläche hindeutet. Auf CoFeB/MgO Schichtstapeln mit ähnlicher akustischer Impedanz, können sowohl Oberflächenwellen als auch Wellen im Volumen in guter Übereinstimmungmit der Theorie beobachtet werden. Anregung der elastischen Dynamik in Reflektions- und Transmissionsgeometrie zeigen, dass durch das Brechen der Periodizität des Schichtstapels die Amplitude der hochfrequenten Oberflächenwelle effektiv unterdrückt wird. Außerdem sind im W/PC Schichtstapeln mit hohem akustischem Versatz innere Wellen unterdrückt.

The present work addresses in-depth magnetic films with magnonic surface patterning of variable size. Two different kinds of such structures referred to as surface-modulated magnonic crystals were investigated: Ion-irradiated magnonic crystals and structurally etched magnonic crystals. To achieve that, two different experimental approaches were pursued. On the one hand, the magnetic moment at the surface of lithographically patterned permalloy (Ni80Fe20) films was periodically reduced by means of ion irradiation. On the other hand, structural trenches were introduced at the surface of a pre-patterned thin film by sequential ion milling. The goal is the acquisition of a fundamental understanding of the behavior of spin-wave modes in the transition from a continuous magnetic thin film to a full magnonic crystal, i.e. separated periodic magnetic structures. In the framework of this thesis, the spin-wave eigen-modes of such magnonic crystals were mainly investigated spectroscopically by means of ferromagnetic resonance. Thereby, the “Two-magnon scattering perturbation theory” and the “plane-wave method” were employed as the theoretical methodologies to understand the complex dynamics of such systems. The first is a reliable method to calculate the dynamic response of surface-modulated magnonic crystals where the modulation is of a perturbation character, i.e. small compared to the film thickness. The latter is a quasi-analytical approach to calculate the dynamic eigen-modes of magnonic crystals consisting of different components with significantly varying properties. Moreover, numerical methods were employed to get further insight into the spin dynamics of these structures. In such systems, the spin-wave behavior follows the well-known dispersion relation of flat magnetic thin films as long as the surface-modulation is small compared to the film thickness. In this work, it was shown that this circumstance can be exploited for a parameter-free determination of the exchange constant A, which is not experimentally accessible for magnetic thin films in a straightforward manner. However, once the modulation height is of significant magnitude, the dynamics of surface-modulated magnonic crystals become substantially more complex. A straightforward understanding of such kind of system is hampered by the complex interplay of different effects. On the one hand, the internal demagnetizing field reveals an alternating character and depends itself on the modulation height and the field angle. On the other hand, the dynamic eigen-modes are hybridized, i.e., they reveal different characteristics in different regions of the magnonic crystal and, in addition, they couple to each other. Here, the approach is particularly favorable to investigate the spin dynamics of surface-modulated magnonic crystals by systematically altering the modulation height of the same sample. This is mainly due to two reasons. First, the two edge cases, namely the thin film and the full magnonic crystal, are already well understood and, second, other magnetic and structural parameters remain constant. With the help of the measurement results and the simulations, the quasi-analytical theory was validated. Subsequently, the mode profiles were calculated by theory and simulation in order to analyze the mode character in the transition from a thin film to a full magnonic crystal. Two kinds of dynamic eigen-modes were identified, namely hybridized modes and localized modes. For both types, simple formulae were derived describing their characteristic dynamic behavior. Besides, transition rules were found connecting the mode number n of film modes with the mode number m of modes in the full magnonic crystal. In order to correlate the symmetry and magnitude of the demagnetizing field with the spin-wave eigen-modes, the internal fields of a strongly surface-modulated magnonic crystal were reconstructed by electron holography measurements. By reemploying the measurement results for micromagnetic simulations, the dynamics of the whole system could be reproduced. This strategy allowed for a better understanding of the link between the demagnetizing field and the spin-wave mode characteristics. Based on these results, a simplified model for the analytical description of the inplane angular dependence was found. The acquired understanding of such systems led to the elaboration of specific applications, such as the spin-wave channelization. It should be noted that the coupling of uniform to non-uniform spin-wave phenomena, which is an intrinsic property of these structures, holds out the prospect of several applications in the future.

As CMOS technology scaling is fast approaching its fundamental limits, several new nano-electronic devices have been proposed as possible alternatives to MOSFETs. Research on emerging devices mainly focusses on improving the intrinsic characteristics of these single devices keeping the overall integration approach fairly conventional. However, due to high logic complexity and wiring requirements, the overall system-level power, performance and area do not scale proportional to that of individual devices. Thereby, we propose a fundamental shift in mindset, to make the devices themselves more functional than simple switches. Our goal in this thesis is to develop a new nanoscale fabric paradigm that enables realization of arbitrary logic functions (with high fan-in/fan-out) more efficiently. We leverage on non-equilibrium spin wave physical phenomenon and wave interference to realize these elementary functions called Spin Wave Functions (SPWFs). In the proposed fabric, computation is based on the principle of wave superposition. Information is encoded both in the phase and amplitude of spin waves; thereby providing an opportunity for compressed data representation. Moreover, spin wave propagation does not involve any physical movement of charge particles. This provides a fundamental advantage over conventional charge based electronics and opens new horizons for novel nano-scale architectures. We show several variants of the SPWFs based on topology, signal weights, control inputs and wave frequencies. SPWF based designs of arithmetic circuits like adders and parallel counters are presented. Our efforts towards developing new architectures using SPWFs places strong emphasis on integrated fabric-circuit exploration methodology. With different topologies and circuit styles we have explored how capabilities at individual fabric components level can affect design and vice versa. Our estimates on benefits vs. 45nm CMOS implementation show that, for a 1-bit adder, up to 40x reduction in area and 228x reduction in power is possible. For the 2-bit adder, results show that up to 33x area reduction and 222x reduction in power may be possible. Building large scale SPWF-based systems, requires mechanisms for synchronization and data streaming. In this thesis, we present data streaming approaches based on Asynchronous SPWFs (A-SPWFs). As an example, a 32-bit Carry Completion Sensing Adder (CCSA) is shown based on the A-SPWF approach with preliminary power, performance and area evaluations.

The present work addresses in-depth magnetic films with magnonic surface patterning of variable size. Two different kinds of such structures referred to as surface-modulated magnonic crystals were investigated: Ion-irradiated magnonic crystals and structurally etched magnonic crystals. To achieve that, two different experimental approaches were pursued. On the one hand, the magnetic moment at the surface of lithographically patterned permalloy (Ni80Fe20) films was periodically reduced by means of ion irradiation. On the other hand, structural trenches were introduced at the surface of a pre-patterned thin film by sequential ion milling. The goal is the acquisition of a fundamental understanding of the behavior of spin-wave modes in the transition from a continuous magnetic thin film to a full magnonic crystal, i.e. separated periodic magnetic structures. In the framework of this thesis, the spin-wave eigen-modes of such magnonic crystals were mainly investigated spectroscopically by means of ferromagnetic resonance. Thereby, the “Two-magnon scattering perturbation theory” and the “plane-wave method” were employed as the theoretical methodologies to understand the complex dynamics of such systems. The first is a reliable method to calculate the dynamic response of surface-modulated magnonic crystals where the modulation is of a perturbation character, i.e. small compared to the film thickness. The latter is a quasi-analytical approach to calculate the dynamic eigen-modes of magnonic crystals consisting of different components with significantly varying properties. Moreover, numerical methods were employed to get further insight into the spin dynamics of these structures. In such systems, the spin-wave behavior follows the well-known dispersion relation of flat magnetic thin films as long as the surface-modulation is small compared to the film thickness. In this work, it was shown that this circumstance can be exploited for a parameter-free determination of the exchange constant A, which is not experimentally accessible for magnetic thin films in a straightforward manner. However, once the modulation height is of significant magnitude, the dynamics of surface-modulated magnonic crystals become substantially more complex. A straightforward understanding of such kind of system is hampered by the complex interplay of different effects. On the one hand, the internal demagnetizing field reveals an alternating character and depends itself on the modulation height and the field angle. On the other hand, the dynamic eigen-modes are hybridized, i.e., they reveal different characteristics in different regions of the magnonic crystal and, in addition, they couple to each other. Here, the approach is particularly favorable to investigate the spin dynamics of surface-modulated magnonic crystals by systematically altering the modulation height of the same sample. This is mainly due to two reasons. First, the two edge cases, namely the thin film and the full magnonic crystal, are already well understood and, second, other magnetic and structural parameters remain constant. With the help of the measurement results and the simulations, the quasi-analytical theory was validated. Subsequently, the mode profiles were calculated by theory and simulation in order to analyze the mode character in the transition from a thin film to a full magnonic crystal. Two kinds of dynamic eigen-modes were identified, namely hybridized modes and localized modes. For both types, simple formulae were derived describing their characteristic dynamic behavior. Besides, transition rules were found connecting the mode number n of film modes with the mode number m of modes in the full magnonic crystal. In order to correlate the symmetry and magnitude of the demagnetizing field with the spin-wave eigen-modes, the internal fields of a strongly surface-modulated magnonic crystal were reconstructed by electron holography measurements. By reemploying the measurement results for micromagnetic simulations, the dynamics of the whole system could be reproduced. This strategy allowed for a better understanding of the link between the demagnetizing field and the spin-wave mode characteristics. Based on these results, a simplified model for the analytical description of the inplane angular dependence was found. The acquired understanding of such systems led to the elaboration of specific applications, such as the spin-wave channelization. It should be noted that the coupling of uniform to non-uniform spin-wave phenomena, which is an intrinsic property of these structures, holds out the prospect of several applications in the future.

No description available.