An investigation has been made of the propagation characteristics of magnetostatic waves with frequencies in the range 890-990 MHz in a crystal of Yttrium Iron Garnet. The sample was mounted in a two port strip line assembly and magnetised axially along the (100) direction. The experiments were performed at room temperature. Magnetostatic waves were observed in external magnetic fields in the neighbourhood of 500 Cersteds. and to explain the experimental results a non-uniform distribution of magnetisation along the axial direction is proposed for the unsaturated sample. Theoretical results for the demagnetising field and the time delay have been computed using this model to explain the excitation and transmission of the observed magnetostatic waves. / Thesis / Master of Engineering (ME)

This thesis compiles results of research in two mutuallydependent parts: 1) development of ferromagnetic resonance(FMR) spectrometer to study microwave properties offerromagnetic materials, and 2) characterization of new irongarnets: pulsed laser deposited Y3Fe5O12and Bi3Fe5O12films and Ce:Y3Fe5O12single crystal. First part describes a novelBroadbandFMRSpectrometerdesigned to characterize thin ferromagneticfilms. The spectrometer uses two probeheads: one is the X-bandmicrowave reflection cavity for room temperature measurementsand the in-cryostat microstrip line probe to perform FMRexperiments in the frequency range from 50 MHz to 40 GHz. Veryuniform and stable magnetic field up to 2.4 T, temperatures 4 Kto 420 K, and continuous frequency scan performed byHP8722Dvector network analyzer provide various modes ofoperation. Both probeheads are equipped with two-circlegoniometers to ensure accurate study of magneticanisotropy. The spectrometer was used to make express-analysis ofquality thus to optimize processing parameters of epitaxialiron garnet films grown by pulsed laser deposition (PLD).Comprehensive study of uniaxial and cubic magnetocrystallineanisotropy has been performed for Ce:Y3Fe5O12bulk crystal as well as for Y3Fe5O12and Bi3Fe5O12films grown on different substrates by PLD andreactive ion beam sputtering techniques. BroadbandFMR-spectroscopy revealed difference in spectra of domain wallresonances: instead of“soft”spin modes in filmsgrown by liquid phase epitaxy, PLD-made films show“diffuse”transformation of domains near thesaturation field. This effect indicates non-uniformity ofsaturation magnetization and field of uniaxial anisotropy inPLD-iron garnets. Spin wave resonances in comparison withuniform FMR have been studied to evaluate“localquality”of ferromagnetic films. The resonance field andFMR linewidth behavior were studied at various crystallographicdirections determined by X-ray diffraction. FMR was used to choose PLD-made YIG films with low losses atmicrowave frequencies and to build magnetostatic surface wavesmicrowave bandpass filter. The filter was designed as a planarfilm structure with a microstrip line for transducers. It is afirst demonstration of feasibility to introduce PLD processingtechnique to magnetostatic wave technology. Magneto-optical study of Ce:Y3Fe5O12single crystal complements results ofFMR-spectroscopy of new garnets. <b>Keywords:</b>ferrites, thin films, ferromagnetic resonance,microwaves, FMR spectrometer, magnetic anisotropy,magnetostatic waves.

<p>This thesis compiles results of research in two mutuallydependent parts: 1) development of ferromagnetic resonance(FMR) spectrometer to study microwave properties offerromagnetic materials, and 2) characterization of new irongarnets: pulsed laser deposited Y₃Fe₅O₁₂and Bi₃Fe₅O₁₂films and Ce:Y₃Fe₅O₁₂single crystal.</p><p>First part describes a novel<i>Broadband</i>FMR<i>Spectrometer</i>designed to characterize thin ferromagneticfilms. The spectrometer uses two probeheads: one is the X-bandmicrowave reflection cavity for room temperature measurementsand the in-cryostat microstrip line probe to perform FMRexperiments in the frequency range from 50 MHz to 40 GHz. Veryuniform and stable magnetic field up to 2.4 T, temperatures 4 Kto 420 K, and continuous frequency scan performed by<i>HP8722D</i>vector network analyzer provide various modes ofoperation. Both probeheads are equipped with two-circlegoniometers to ensure accurate study of magneticanisotropy.</p><p>The spectrometer was used to make express-analysis ofquality thus to optimize processing parameters of epitaxialiron garnet films grown by pulsed laser deposition (PLD).Comprehensive study of uniaxial and cubic magnetocrystallineanisotropy has been performed for Ce:Y₃Fe₅O₁₂bulk crystal as well as for Y₃Fe₅O₁₂and Bi₃Fe₅O₁₂films grown on different substrates by PLD andreactive ion beam sputtering techniques. BroadbandFMR-spectroscopy revealed difference in spectra of domain wallresonances: instead of“soft”spin modes in filmsgrown by liquid phase epitaxy, PLD-made films show“diffuse”transformation of domains near thesaturation field. This effect indicates non-uniformity ofsaturation magnetization and field of uniaxial anisotropy inPLD-iron garnets. Spin wave resonances in comparison withuniform FMR have been studied to evaluate“localquality”of ferromagnetic films. The resonance field andFMR linewidth behavior were studied at various crystallographicdirections determined by X-ray diffraction.</p><p>FMR was used to choose PLD-made YIG films with low losses atmicrowave frequencies and to build magnetostatic surface wavesmicrowave bandpass filter. The filter was designed as a planarfilm structure with a microstrip line for transducers. It is afirst demonstration of feasibility to introduce PLD processingtechnique to magnetostatic wave technology.</p><p>Magneto-optical study of Ce:Y₃Fe₅O₁₂single crystal complements results ofFMR-spectroscopy of new garnets.</p><p><b>Keywords:</b>ferrites, thin films, ferromagnetic resonance,microwaves, FMR spectrometer, magnetic anisotropy,magnetostatic waves.</p>

Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.

Microwave near-field probes (MNPs) confine evanescent fields to regions that are substantially smaller than the wavelength at the operation frequency. Such probes are able to resolve subwavelength features, thus providing resolution much higher than the classical Abb?? limit. These abilities of MNPs are primarily due to the evanescent nature of the field generated at the tip of the probes. In the past, MNPs with ultra-high resolution were designed by tapering a resonant opening to provide high field concentration and high sensitivity. The limitations of these MNPs were subject to low surface roughness and practical realization challenges due to their geometrical features and vibration control constraints. Metamaterials with their ability to enhance evanescent fields, lead to the speculation that they could potentially increase the sensitivity of near-field probe. Periodically arranged metamaterial unit elements such as split-ring-resonators (SRRs) can create negative permeability media. Placing such material layer in the proximity of a probe leads to enhancement of the evanescent waves. Guided by this remarkable feature of metamaterials, I proposed an MNP consisting of a wire loop concentric with a single SRR. The evanescent field behavior of the probe is analyzed using Fourier analysis revealing substantial enhancement of the evanescent field consistent with metamaterial theory predictions. The resolution of the probe is studied to especially determine its ability for sub-surface detection of media buried in biological tissues. The underlying physics governing the probe is analyzed. Variations of the probe are developed by placement of lumped impedance loads. To further increase the field confinement to smaller region, a miniaturized probe design is proposed. This new probe consists of two printed loops whose resonance is tunable by a capacitor loaded in the inner loop. The sensing region is decreased from ??/20 to ??/55, where ?? is the wavelength of the probe???s unloaded frequency. The magnetic-sensitive nature of the new probe makes it suitable for sensing localized magnetostatic surface resonance (LMSR) occurring in electrically very small particles. Therefore, I proposed a sensing methodology for detecting localized magnetostatic surface (LMS) resonant particles. In this methodology, an LMS resonant sphere is placed concentrically with the loops. A circuit model is developed to predict the performance of the probe in the presence of a magnetic sphere having Lorentz dispersion. Full-wave simulations are carried out to verify the circuit model predictions, and preliminary experimental results are demonstrated. The Lorentzian fit in this work implies that the physical nature of LMSR may originate from spin movement of charged particle whose contribution to effective permeability may be analogous to that of bound electron movement to effective permittivity in electrostatic resonance. Detection of LMSR can have strong impact on marker-based sensing applications in biomedicine and bioengineering.

Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.

Cette thèse vise à développer une méthode alternative à la méthode des éléments finis pour pré-dimensionner des machines électriques tournantes. Le pré-dimensionnement consiste en un calcul rapide du champ magnétique à l’intérieur d’une machine électrique pour en extraire des caractéristiques physiques. Les caractéristiques physiques recherchées sont le couple appliqué sur le rotor ainsi que les flux à travers les bobines du moteur électrique. Après une revue des différentes méthodes existantes dans le domaine de la modélisation des moteurs électriques, on retiendra pour ces travaux les méthodes intégrales qui sont développées au laboratoire de génie électrique de Grenoble pour résoudre la problématique du calcul du champ magnétique à l’intérieur du moteur. Ces méthodes permettent un calcul précis du champ magnétique à l’intérieur de tout dispositif électromagnétique dans un temps de calcul relativement réduit par rapport à la méthode des éléments finis grâce à une meilleure évaluation des interactions entre les éléments du maillage. La formulation intégrale utilisée dans ces travaux est une formulation intégrale de volume dont l’inconnue est le potentiel vecteur interpolé sur les arêtes des éléments du maillage utilisé pour discrétiser la machine tournante. Cette formulation a été adaptée aux spécificités des moteurs électriques et optimisée dans le cadre de résolutions paramétriques. Enfin, des méthodes originales sont présentées pour calculer les caractéristiques physiques du moteur : deux méthodes de calcul de couple ont été mises au point, une première se basant sur le tenseur de Maxwell adapté aux méthodes intégrales de volume et une seconde basée sur la dérivée de la co-énergie magnétique dont une nouvelle formule ne nécessitant que la connaissance de l’induction dans les matériaux actifs est présentée. Une méthode semi-analytique de calcul de flux dans les bobines maillées du moteur est présentée.Il ressort de cette étude que le couplage entre la méthode intégrale de volume en potentiel vecteur et les trois méthodes évoquées ci-dessus fournit dans des temps inférieurs à la méthode des éléments finis certaines des caractéristiques recherchées. / This PhD thesis aims to develop an alternative method to the finite elements method for an efficient electrical rotating machines pre-design.Electrical engine pre-design involve of a quick calculation of the magnetic field within the rotating machine and be able to extract of this field the main physical characteristics of the machine. The physical characteristics searched for are the magnetic torque applied on the rotor and the magnetic flux through the coils of the engine.After a quick review of the existing methods for electrical engine pre-design, integral methods developed in Grenoble electrical laboratory will be took on to carry out the calculation of the magnetic field in the engine. Those methods allow a fast and precise calculation of the magnetic field thanks to an excellent evaluation of the interaction between the elements of the mesh.The integral formulation used in this thesis is a vector potential volume integral formulation where the vector potential is interpolated over the edges of the mesh. This formulation has been adapted to the specificities of the electrical engine simulation and optimized for the case of multi-static computations. Finally, original post functions have been developed to compute the physical characteristics of the electrical engine from the magnetic field solution provided by the volume integral formulation. Two methods of torque computation are presented along with one semi-analytical method for the computation of the flux through the coils of the engine.This study brings out that the coupling between the vector potential volume integral method and the post functions described above provides good results faster than the finite elements method for several physical characteristics of the electrical machine.

No description available.

La modélisation numérique est devenue incontournable dans le monde de la conception industrielle et de la recherche scientifique. Les problèmes à résoudre étant de plus en plus complexes, il est nécessaire d'adopter une approche adaptée au problème traité. Dans les domaines d'application de l'électromagnétisme basses fréquences, la méthode des éléments finis (MEF) est la méthode de référence. Actuellement, de plus en plus de dispositifs ouverts comportant de grands entrefers sont développés. Dans ce genre de problèmes, la MEF n'est pas optimale car elle nécessite de mailler un grand volume d'air pour obtenir une bonne précision. Dans cette thèse nous étudions, au travers de deux applications (représentant respectivement un système ouvert et un système à grands entrefers) une méthode alternative qui ne souffre pas des limitations évoquées : la méthode des moments (MoM) de type intégrale volumique. En effet, cette méthode nécessite de mailler uniquement les milieux magnétiques. Le principe de cette méthode est d'abord de calculer l'aimantation induite dans le milieu linéaire ou non linéaire placé sous l'effet d'un champ extérieur. Pour cela, le milieu magnétique est discrétisé en éléments hexaédriques. Dans chaque élément est localisée une aimantation considérée comme uniforme. Ensuite, la connaissance de cette aimantation induite permet de déterminer le champ magnétique en tout point de l'espace: interne, proche ou lointain. Dans un premier temps, un code basé sur la MoM a été développé pour la première application. Il permet de calculer le champ magnétostatique proche ou lointain d'une antenne basse fréquence. Une méthode permettant de calculer l'énergie magnétostatique contenue dans tout l'espace a été également mise au point. Dans deuxième temps, afin de pouvoir traiter une géométrie complexe, des modifications ont été intégrées au code afin de modéliser la deuxième application : le dispositif de test des propulseurs à effet Hall (PPS-Flex). Il s'agit de prendre en compte des symétries géométriques et physiques caractéristiques de ce dispositif. Les résultats montrent que la MoM permet de calculer le champ magnétique à l'intérieur de son canal et éventuellement au-delà. Dans les deux exemples étudiés, la méthode des moments a donné des résultats satisfaisants lors de la comparaison avec la méthode des éléments finis 3D et avec les résultats de mesures. Ces résultats montrent des gains potentiellement significatifs sur le plan des temps de calculs. A l'issu de cette thèse, nous disposons d'un outil de laboratoire permettant de modéliser le comportement du champ magnétostatique dans des systèmes ouverts et/ou à grands entrefers. / The numerical modeling has become essential in the world of industrial design and scientific research. The problems to be solved are increasingly complex making it necessary to adopt an appropriate approach for the problem addressed. In the domains of application of low frequency electromagnetic, the finite element method (FEM) is the reference method. Currently, more and more devices having large open gaps are developed. In this kind of problems, the MEF is not optimal as it requires to mesh a large volume of air to get a good accuracy. In this thesis we study, through two applications (an open system and a large gap system), an alternative method that does not suffer from the limitations discussed: the method of moments (MoM) of volume integral type. Indeed, this method requires to mesh only the magnetic media. The principle of this method is first to calculate the induced magnetization in the linear or nonlinear medium under the effect of an external field. To accomplish this, the magnetic medium is discretized into hexahedral elements. In each element, a uniform magnetization is localized. Then, the determination of this induced magnetization allows to compute the magnetic field at any point in the space: internal, near or far. In the first step, a code based on the MoM has been developed for the first application. It allows to calculate the magnetostatic field near or far from a low-frequency antenna. A method to calculate the magnetostatic energy in the whole space was also developed. Meanwhile, in the second step, in order to treat complex geometry, some modifications have been integrated into the code to model the second application: the test device of Hall effect thrusters (PPS-Flex). It consists in taking into account the physical characteristics and geometric symmetry of the device. The results show that MoM allows to calculate the magnetic field inside the channel and possibly beyond. In both examples studied, the MoM has given satisfactory results when compared with the 3D finite element method and with the results of measurements. These results show potentially significant gains in the computation time. At the end of this thesis, we have developed a laboratory tool allowing to model the behavior of the static magnetic field in open and/or wide-gap systems.

On présente ici un ensemble de méthodes numériques performantes pour lasimulation micromagnétique 3D reposant sur l’équation de Landau-Lifchitz-Gilbert, constituantun code nommé feeLLGood. On a choisi l’approche éléments finis pour sa flexibilitégéométrique. La formulation adoptée respecte la contrainte d’orthogonalité entre l’aimantationet sa dérivée temporelle, contrairement à la formulation classique sur-dissipative.On met au point un schéma de point milieu pour l’équation Landau-Lifchitz-Gilbert quiest stable et d’ordre deux en temps. Cela permet de prendre, à précision égale, des pas detemps beaucoup plus grands (typiquement un ordre de grandeur) que les schémas classiques.Un véritable enjeu numérique est le calcul du champ démagnétisant, non local. Oncompare plusieurs techniques de calcul rapide pour retenir celles, inédites dans le domaine,des multipôles rapides (FMM) et des transformées de Fourier hors-réseau (NFFT). Aprèsavoir validé le code sur des cas-tests et établi son efficacité, on présente les applications àla simulation des nanostructures : sélection de chiralité et résonance ferromagnétique d’unplot monovortex de cobalt, hystérésis des chapeaux de Néel dans un plot allongé de fer.Enfin, l’étude d’un oscillateur spintronique prouve l’évolutivité du code. / Here is presented a set of efficient numerical methods for 3D micromagneticsimulation based on the Landau-Lifchitz-Gilbert equation, making up a code named feeLLGood.The finite element approach was chosen for its geometrical flexibility. The adoptedformulation meets the orthogonality constraint between the magnetization and its time derivative,unlike the over-dissipative classical formulation. A midoint rule was developed forthe Landau-Lifchitz-Gilbert equation which is stable and second order in time. This allowsfor much bigger time steps (typically an order of magnitude) than classical schemes at thesame precision. Computing the nonlocal demagnetizing interaction is a real numerical challenge.Several fast computation techniques are compared. Those selected are novel to thefield : the Fast Multipole Method (FMM) and Non-uniform Fast Fourier Transforms (NFFT).After the code is validated on test cases and its efficiency established, applications to the simulationof nanostructures are presented : chirality selection and ferromagnetic resonanceof a cobalt monovortex dot, Neel caps hysteresis in an iron dot. Finally, the study of a spintronicoscillator proves the code’s upgradability.