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Tailoring the interfacial properties of magnetic multilayers for the observation of skyrmions at room temperature / Etude et contrôle des propriétés interfaciales de multicouches magnétiques pour l'observation de skyrmions à température ambianteMoreau-Luchaire, Constance 21 December 2016 (has links)
Dans cette thèse, nous montrons que nous avons réussi à observer des skyrmions isolés sub-100nm dans des échantillons Ir|Co|Pt. Ces observations ont été faites via deux techniques différentes : le STXM (technique synchrotron qui permet d’imager l’aimantation hors du plan de l’échantillon) et le MFM (technique de laboratoire qui permet d’imager le gradient de l’aimantation). Nous avons également montré que nous les avions observés à la fois dans les films étendus ainsi que dans des nanostructures (nanodisques de diamètre entre 200 nm et 1 μm, ainsi que les bandes dont la largeur varie de 400 nm à 1 μm). Nous avons également développé deux approches différentes pour estimer l’amplitude DMI dans les échantillons. La première est basée sur la périodicité des domaines dans les échantillons après désaimantation. La deuxième technique est basée sur l’évolution de la taille des skyrmions avec un champ magnétique appliqué hors-plan. Pour la nécessité des simulations micromagnétiques, nous avons également essayé de déterminer l’échange de nos échantillons. Avec cette valeur, le DMI trouvé dans nos échantillons est d’environ 2 mJ/m². Nous avons effectué une étude systématique sur des échantillons avec variation de différents paramètres: nombre de répétitions de la tricouche principale, épaisseur du Co, épaisseur du Pt, épaisseur de l’Ir, composition des couches d’Ir avec W ou AlOx. Nous avons montré que pour tous les systèmes, nous avons pu observer des skyrmions stabilisés à température ambiante grâce au MFM. Nous avons également observé que la densité des skyrmions diminue avec l’augmentation de l’anisotropie effective. / We have been able to successfully observe isolated sub-100nm skyrmions in Ir|Co|Pt samples. Moreover, we have been able to observe them with two different techniques: STXM - a synchrotron technique that maps the out-of-plane magnetization of a sample, and MFM - a laboratory technique that images the gradient of the magnetization. We have also shown that we have stabilized them in extended films as well as in nanostructures (nanodisks with diameter from 200 nm to 1 μm, as well as stripes with width from 400 nm to 1 μm). Secondly, we have developed two different approaches to estimate the DMI amplitude in samples. The first one is based on the mean domain periodicity in samples after demagnetization. The second technique is based on the size evolution of skyrmions with applied out-of-plane magnetic field. For the need of the micromagnetic simulations, we have also tried to determine the exchange stiffness of our samples. With this value, the DMI aplitude found in our samples is about 2 mJ/m². We have performed a systematic study on samples with variation of different parameters : number of repetitions of the main trilayers, Co thickness, Pt thickness, Ir thickness, composition of the buffer layers, and switching Ir with W or AlOx. We also observed that the density of skyrmions is decreasing with increasing effective anisotropy.
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Étude de la vésignieite-Sr par RMNVerrier, Aimé January 2017 (has links)
Dans ce mémoire, je rapporte l'étude par RMN d'un nouveau composé synthétique avec une structure magnétique kagomé hautement frustrée : la vésigniéite-Sr. Ce sont les noyaux de $^{51}\mathrm{V}$ et de $^{63,65}\mathrm{Cu}$ qui servent de sonde magnétique pour les mesures effectuées sur l'échantillon qui prend la forme d'une poudre. Les résultats montrent que l'interaction Dzyaloshinskii-Moriya pousse les moments à s'ordonner à $120^\mathrm{o}$ les uns par rapport aux autres dans une configuration $q=0$ mais avec un léger angle au-dessus du plan kagomé. Cette configuration est source de ferromagnétisme faible dans l'échantillon malgré l'interaction antiferromagnétique entre atomes de cuivre voisins.
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Magnetic Skyrmion Phase in MnSi Thin FilmsWilson, Murray 01 April 2013 (has links)
Detailed magnetometry and polarized neutron reflectometry studies were conducted
on MnSi thin films grown epitaxially on Si(111) substrates. It is demonstrated that
with an in-plane applied field H || [110], a broadly stable skyrmion phase exists at
elevated temperatures and fields.
Magnetometry and transport measurements with an out-of-plane applied field
H || [111] prove that no skyrmion phase exists in this geometry. However, Hall effect
measurements in this geometry show unexpected evidence of a topological Hall effect.
This can be explained with a multi-dimensionally modulated cone phase, which proves
that contrary to recent literature, a topological Hall effect is not sufficient proof of
skyrmions.
The results of this thesis represent a significant step towards a technologically
relevant material in which skyrmions are broadly stable. A material of this type
could be used in novel magnetic storage devices and signi ficantly impact our future
computing capabilities.
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Analyzing Creep Mobility of Dzyaloshinskii Domain Walls with an Effective Elastic Band ModelPellegren, James Price 01 October 2017 (has links)
No description available.
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Effects of interfacial interactions on optical switching in magnetic heterostructures / Effets des interactions d’interface sur le renversement optique dans des hétérostructures magnétiquesVallobra, Pierre 05 February 2019 (has links)
Pendant les 20 dernières années, le nanomagnétisme a suscité un intérêt grandissant au sein de la communauté scientifique du fait de ses nombreuses applications pour les mémoires magnétiques. A l’échelle nanométrique beaucoup de propriétés des matériaux magnétiques découlent de leurs interfaces avec d’autres matériaux (magnétiques ou non). Cela explique l’omniprésence des hétérostructures composées de plusieurs couches d’épaisseur nanométrique dans le domaine du nanomagnétisme. Dans les hétérostructures que nous étudions, ces propriétés interfaciales sont le décalage d’échange, l’interaction Dzyaloshinskii-Moriya, l’anisotropie magnétique perpendiculaire et l’échange entre deux couches ferromagnétiques. D’abord nous étudions la modification du champ de décalage d’échange dans une bicouche [Pt/Co]xN/IrMn lorsque l’on l’expose à des impulsions laser de lumière polarisée circulairement. Nous montrons que le champ de décalage d’échange après exposition au laser résulte de la configuration du ferromagnétique [Pt/Co]xN. Nous étudions ensuite les conditions nécessaires à un retournement tout optique dépendant de l’hélicité d’un matériau ferrimagnétique de synthèse composé de deux couches de CoFeB /Pt /CoFeB et Co couplées antiferromagnétiquement et concluons que les facteurs clés qui gouvernent le renversement de l’aimantation totale sont les températures respectives des deux couches. Nous nous sommes aussi concentrés sur la propagation de parois de domaine de Néel de même chiralité stabilisées par interaction Dzyaloshinskii-Moriya dans des multicouches de [Pt/Co/Ni]N. Nous avons finalement démontré la possibilité de générer des bulles skyrmioniques par le laser femtoseconde / During the last 20 years, nanomagnetism has attracted a growing interest in the scientific community due to its multiple applications for magnetic memories. At the nanometer scale, many of the properties of the magnetic materials arise from their interfaces with other materials (magnetic or non-magnetic). This explains the omnipresence of heterostructures composed of several layers of thicknesses in the range of the nanometer in the field of nanomagnetism. In the heterostructures we study, those interfacial properties are the exchange bias, the Dzyaloshinskii-Moriya interaction, the perpendicular magnetic anisotropy and the interlayer exchange between two ferromagnetic layers. First we study the modification of the exchange bias field in a [Pt/Co]xN/IrMn bilayer when we expose it to laser pulses of a femtosecond circularly polarized light. We demonstrate that the final exchange bias field after laser pulses results from the magnetic configuration of the [Pt/Co]xN multilayer. We then study the conditions required for a helicity-dependent all optical switching of a synthetic ferromagnetic material composed of a CoFeB /Pt /CoFeB and a Co ferromagnetic layers coupled antiferromagnetically and conclude that the key factors that drive the switching of the total magnetization are the Curie temperatures of both layers. We focused also on the field-driven propagation of Néel domain walls of the same chirality stabilized by the Dzyaloshinskii-Moriya interaction in [Pt/Co/Ni]xN multilayers. We finally demonstrated the possibility to generate skyrmionic bubbles with the femtosecond laser
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Phenomenological theory of chiral states in magnets with Dzyaloshinskii-Moriya interactionsButenko, Ganna 25 June 2013 (has links) (PDF)
This thesis presents the theoretical studies of chiral magnetic structures, which exist or are affected by antisymmetric Dzyaloshinskii-Moriya interactions. The theoretical approach is based on the phenomenological model of ferromagnetic materials lacking inversion symmetry. Equilibrium magnetic states are described as static structures in the micromagnetic low temperature limit with a fixed magnitude of the magnetization. The studies are focused on two cases: (i) magnetization structures that are affected by chiral exchange so that a particular chirality of these structures is selected, and (ii) novel solitonic states that are called chiral Skyrmions and only exist because of the chiral exchange.
Vortex states in magnetic nanodisks provide the simplest example of a handed magnetization structure, where effects of the chiral couplings may become noticeable. A chiral exchange here favours one chirality of such a vortex state over the other. This effect can stem from surface-induced or other defect-related chiral Dzyaloshinskii-Moriya exchange. The different chiral versions of the vortex states are shown to display strong dependencies on the materials properties of such nanodisks. Within a micromagnetic model for these effects, numerical calculations of the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters provide a general analysis of the influence of the broken mirror symmetry caused by the surface/interfaces or structural defect on their properties. The Dzyaloshinskii-Moriya interactions impose differences in the energies and sizes of vortices with different chirality: these couplings can considerably increase sizes of vortices with one sense of rotation and suppress vortices with opposite sense of rotation. Torsions related to lattice defects can cause similar to the surface-induced chiral couplings. A general phenomenological magneto-elastic formulation for this torsional chirality selection is given. It is applied to calculate similar effects on vortex states in magnetic disks with a screw dislocation at their center.
In systems with strong chiral exchange the magnetic equilibrium states themselves become chiral twisted structures. The most interesting structures in this context are the two-dimensional solitonic states that are now known as chiral Skyrmions. The properties and stability of multiply twisted states composed of these particle-like units are the subject of the second part of this thesis. These states compete with the well known onedimensionally modulated helical states in non-centrosymmetric magnetic systems. Studies of modulated states in cubic helimagnets have shown, that in absence of additional effects, the only thermodynamically stable state is a cone helix. Uniaxial distortions, that can be caused by uniaxial stresses in the bulk samples or arise due to surface effects in thin films, suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using the phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states have been derived as functions of applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field, Skyrmion lattices can be formed as thermodynamically stable states.
The theoretical results provide a comprehensive description of the evolution of modulated states in an applied magnetic field depending on type of anisotropy. The cases of a uniaxial anisotropy of easy axis and easy plane type with fields applied along its axis are investigated in detail. Existence of Skyrmion-lattice states in the easy axis case as thermodynamic field-induced phase is demonstrated. The results explain recent observation of Skyrmion lattices by magnetic Lorentz microscopy in thin foils of cubic chiral magnets. In systems with easy plane type of anisotropy, Skyrmion states do not form thermodynamic phases in applied fields along the axis. However, distorted Skyrmion phases can exist in fields applied perpendicularly to the axis. In this configuration of anisotropy axis and fields, both the helical states and the Skyrmions display elliptical distortions. The investigated micromagnetic model maps out the basic helical and Skyrmionic states expected to exist in cubic and nearly cubic chiral magnets.
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Phenomenological theory of chiral states in magnets with Dzyaloshinskii-Moriya interactionsButenko, Ganna 20 March 2013 (has links)
This thesis presents the theoretical studies of chiral magnetic structures, which exist or are affected by antisymmetric Dzyaloshinskii-Moriya interactions. The theoretical approach is based on the phenomenological model of ferromagnetic materials lacking inversion symmetry. Equilibrium magnetic states are described as static structures in the micromagnetic low temperature limit with a fixed magnitude of the magnetization. The studies are focused on two cases: (i) magnetization structures that are affected by chiral exchange so that a particular chirality of these structures is selected, and (ii) novel solitonic states that are called chiral Skyrmions and only exist because of the chiral exchange.
Vortex states in magnetic nanodisks provide the simplest example of a handed magnetization structure, where effects of the chiral couplings may become noticeable. A chiral exchange here favours one chirality of such a vortex state over the other. This effect can stem from surface-induced or other defect-related chiral Dzyaloshinskii-Moriya exchange. The different chiral versions of the vortex states are shown to display strong dependencies on the materials properties of such nanodisks. Within a micromagnetic model for these effects, numerical calculations of the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters provide a general analysis of the influence of the broken mirror symmetry caused by the surface/interfaces or structural defect on their properties. The Dzyaloshinskii-Moriya interactions impose differences in the energies and sizes of vortices with different chirality: these couplings can considerably increase sizes of vortices with one sense of rotation and suppress vortices with opposite sense of rotation. Torsions related to lattice defects can cause similar to the surface-induced chiral couplings. A general phenomenological magneto-elastic formulation for this torsional chirality selection is given. It is applied to calculate similar effects on vortex states in magnetic disks with a screw dislocation at their center.
In systems with strong chiral exchange the magnetic equilibrium states themselves become chiral twisted structures. The most interesting structures in this context are the two-dimensional solitonic states that are now known as chiral Skyrmions. The properties and stability of multiply twisted states composed of these particle-like units are the subject of the second part of this thesis. These states compete with the well known onedimensionally modulated helical states in non-centrosymmetric magnetic systems. Studies of modulated states in cubic helimagnets have shown, that in absence of additional effects, the only thermodynamically stable state is a cone helix. Uniaxial distortions, that can be caused by uniaxial stresses in the bulk samples or arise due to surface effects in thin films, suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using the phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states have been derived as functions of applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field, Skyrmion lattices can be formed as thermodynamically stable states.
The theoretical results provide a comprehensive description of the evolution of modulated states in an applied magnetic field depending on type of anisotropy. The cases of a uniaxial anisotropy of easy axis and easy plane type with fields applied along its axis are investigated in detail. Existence of Skyrmion-lattice states in the easy axis case as thermodynamic field-induced phase is demonstrated. The results explain recent observation of Skyrmion lattices by magnetic Lorentz microscopy in thin foils of cubic chiral magnets. In systems with easy plane type of anisotropy, Skyrmion states do not form thermodynamic phases in applied fields along the axis. However, distorted Skyrmion phases can exist in fields applied perpendicularly to the axis. In this configuration of anisotropy axis and fields, both the helical states and the Skyrmions display elliptical distortions. The investigated micromagnetic model maps out the basic helical and Skyrmionic states expected to exist in cubic and nearly cubic chiral magnets.
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Un microscope de champ magnétique basé sur le défaut azote-lacune du diamant : réalisation et application à l'étude de couches ferromagnétiques ultraminces / A magnetic field microscope based on the nitrogen-vacancy defect in diamond : realisation and application to the study of ultrathin ferromagnetsTetienne, Jean-Philippe 13 November 2014 (has links)
La capacité à cartographier le champ magnétique à l'échelle nanométrique serait un atout crucial pour étudier les propriétés magnétiques des solides ainsi que certains phénomènes de transport, mais aussi pour des études fondamentales en biologie. Cette thèse porte sur la réalisation d'un microscope de champ magnétique d'un genre nouveau, qui promet une résolution spatiale de quelques nanomètres, une sensibilité de l'ordre du nanotesla, et fonctionne aux conditions ambiantes. Ce microscope est basé sur le défaut azote-lacune du diamant, dont les propriétés quantiques peuvent être exploitées pour en faire un magnétomètre ultrasensible de taille atomique. Dans un premier temps, nous présenterons le fonctionnement et la réalisation du microscope à défaut azote-lacune, qui consiste essentiellement en un microscope à force atomique sur la pointe duquel un nanocristal de diamant est attaché. Nous testerons le microscope en imageant le champ de fuite généré par un cœur de vortex dans un microdisque ferromagnétique. Dans un second temps, nous appliquerons le microscope à l'étude de couches ferromagnétiques ultraminces. Ces systèmes présentent un intérêt à la fois fondamental, les effets d'interfaces restant encore largement inexplorés à ce jour, et technologique, puisqu'ils sont à la base de propositions pour la réalisation de nouvelles mémoires magnétiques à basse consommation d'énergie. Nous étudierons d'abord la nature des parois de domaines dans ces couches ultraminces, ce qui nous permettra de révéler l'existence d'une interaction Dzyaloshinskii-Moriya d'origine interfaciale dans certains échantillons. Nous étudierons ensuite les sauts nanométriques d'une paroi de domaine induits par l'agitation thermique. Nous démontrerons en particulier le contrôle de ces sauts par un laser, ce qui nous permettra de visualiser et explorer le paysage énergétique de la paroi. / The ability to map the magnetic field at the nanometer scale would be a crucial advance to study the magnetic properties of solids as well as some transport phenomena, but also for fundamental studies in biology. This thesis deals with the realisation of a magnetic field microscope of a new kind, which promises a spatial resolution down to a few nanometres, a sensitivity of the order of a few nanoteslas, and operates under ambient conditions. This microscope is based on the nitrogen-vacancy defect in diamond, whose quantum properties can be harnessed to make an ultrasensitive, atomic-size magnetometre. In the first part, we will present the basic principles and the realisation of the nitrogen-vacancy defect microscope, which consists essentially in an atomic force microscope on the tip of which a diamond nanocrystal is grafted. We will test the microscope by imaging the stray field generated by a vortex core in a ferromagnetic microdisk. In the second part, we will apply the microscope to the study of ultrathin ferromagnets. These systems are interesting both from the physical point of view, as interface effects have been little explored so far, and for technology, as they are the cornerstone of several proposals for realising novel magnetic memory devices with low energy consumption. We will first study the nature of domain walls in these ultrathin ferromagnets, which will enable us to reveal the existence of an interface-related Dzyaloshinskii-Moriya interaction in some samples. Next, we will study the nanometric jumps of a domain wall induced by thermal fluctuations. In particular, we will demonstrate control over these jumps using a laser, which will allow us to visualise and explore the wall's energy landscape.
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Crafting magnetic skyrmions at room temperature : size, stability and dynamics in multilayers / Élaboration de skyrmions magnétiques à température ambiante : taille, stabilité et dynamique dans les multicouchesLegrand, William 29 March 2019 (has links)
Les skyrmions magnétiques sont des enroulements bidimensionnels et nanométriques de la configuration de spin, pouvant être stabilisés dans certains matériaux magnétiques soumis à l’interaction d’échange antisymétrique Dzyaloshinskii-Moriya. Ils présentent une topologie non-triviale et s’annoncent peut-être comme étant les plus petites configurations magnétiques pouvant être réalisées. Très récemment, des skyrmions magnétiques ont pu être stabilisés à température ambiante grâce à la conception de multicouches magnétiques brisant la symétrie d’inversion selon la direction verticale. Suite à cette avancée, l’objectif central de cette thèse est la compréhension et la maîtrise des multiples propriétés physiques des skyrmions hébergés dans ces systèmes multicouches. Pour aborder cet objectif, un modèle original est décrit puis employé, permettant la prédiction des profils adoptés par les skyrmions multicouches. Ce modèle numérique est très générique, n’utilisant que la symétrie cylindrique des skyrmions afin de simplifier la détermination des interactions magnétostatiques. Ce modèle est ensuite étendu afin de pouvoir approximer la stabilité thermique des skyrmions, ce qui constitue un élément clé dans leur obtention expérimentale. Une seconde dimension de ce travail consiste en l’étude expérimentale de la manipulation électrique des skyrmions multicouches, démontrant la possibilité de trois fonctionnalités centrales que sont leur nucléation par courants locaux, leur déplacement sous courant de spin et leur détection électrique individuelle par tension transverse. Le troisième aspect de ma thèse est l’étude des propriétés physiques influençant le déplacement des skyrmions dans les multicouches magnétiques. Un comportement d’ancrage sur des défauts est mis en évidence expérimentalement et est analysé à l’aide d’une modélisation micromagnétique. Un des résultats importants de ce travail est aussi la prédiction d’une chiralité hybride dans les configurations magnétiques de certaines multicouches, qui est ensuite démontrée expérimentalement par des mesures au synchrotron. Les conséquences attendues de cette chiralité hybride sur le déplacement des skyrmions sont étudiées pour permettre l’optimisation des multicouches, aboutissant à l’observation expérimentale de la propagation de skyrmions de 50 nm de rayon à des vitesses atteignant environ 40 m/s. La dernière partie de cette thèse vise à mettre à profit ces avancées théoriques et expérimentales afin de parvenir à réduire la taille des skyrmions à température ambiante. Après avoir analysé l’impact des interactions dipolaires sur la stabilité des skyrmions, il est entrepris d’optimiser les matériaux et la périodicité des couches. Je m’intéresse aussi à la conception expérimentale de textures magnétiques dont l’aimantation est compensée au sein de structures multicouches appelées antiferromagnétiques synthétiques, dont je montre qu’elles peuvent héberger des skyrmions antiferromagnétiques à température ambiante. Ce résultat final ouvre de nouvelles perspectives vers l’obtention de skyrmions à la fois mesurant moins de 10 nm et très mobiles, qui pourraient être utilisés dans la conception de composants de calcul et de stockage d’information plus compacts et plus efficaces. / Magnetic skyrmions are nanoscale two-dimensional windings in the spin configuration of some magnetic materials subject to the Dzyaloshinskii-Moriya antisymmetric exchange interaction. They feature a non-trivial topology and show promise to be the smallest achievable magnetic textures. Very recently, magnetic skyrmions have been successfully stabilised up to room temperature by leveraging on the design of magnetic multilayer systems breaking the vertical inversion symmetry. Following up on this achievement, the main objective of this thesis is the understanding and the control of the various physical properties of skyrmions hosted by such multilayer systems. As a first approach to this objective, an original model allowing to predict the profiles adopted by multilayer skyrmions is described and then employed. This numerical model is very generic, as it exploits only the cylindrical symmetry of multilayer skyrmions, in order to determine the magnetostatic interactions with less effort. This model is further extended in order to approximate the thermal stability of multilayer skyrmions, which is key to their experimental realisation. The next aspect of this thesis consists in the experimental study of the electrical manipulation of multilayer skyrmions, demonstrating three main functionalities that are nucleation by local currents, displacement under spin currents and individual detection by transverse voltage. The third aspect of my thesis is the study of the physical properties influencing the current-induced motion of skyrmions in magnetic multilayers. A pinning behaviour is evidenced experimentally and analysed relying on micromagnetic modelling. One of the important results of this work is also the prediction of hybrid chirality for some multilayer magnetic configurations, which is then demonstrated experimentally using a synchrotron technique. The impact of hybrid chirality on current-induced skyrmion motion is discussed and leads to the optimisation of the multilayer design, resulting in the experimental observation of motion for skyrmions below 50 nm in radius at velocities reaching around 40 m/s. The last part of this thesis aims at leveraging on these theoretical and experimental advances in order to reduce the size of skyrmions at room temperature. After the analysis of the impact of dipolar interactions on skyrmion stability, the engineering of the materials and of the layers periodicity is attempted. I also investigate experimentally the conception of magnetic textures with compensated magnetization in multilayer structures known as synthetic antiferromagnets, and show that they can host antiferromagnetic skyrmions at room temperature. This last result opens up new prospects for achieving room-temperature skyrmions combining size in the single-digit nm range and high mobility, potentially allowing applications towards energy-efficient computation and storage devices with a very dense integration.
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Comparison of different approaches of wave vector resolved Brillouin light scattering spectroscopy for investigating interfacial Dzyaloshinskii–Moriya InteractionWeinhold, Tillmann 03 June 2020 (has links)
In this thesis the effect of interfacial Dzyaloshinskii-Moriya-interaction (iDMI) is studied. This effect, which induces a frequency shift of spin waves with fixed wave vector, is investigated for different multilayers. Only spin waves with its wave vector perpendicular to the magnetization are detected. These spin waves are called surface waves. Brillouin light scattering (BLS) technique is used for the wave vector dependent detection of spin wave frequencies. Different setups were build and compared including a new setup, which does not use a focusing lens in front of the sample. This setup exhibits an increased wave vector resolution and simplifies changing between different samples. However, the signal intensity obtained by this setup is too low to measure spin waves under the given circumstances in reasonable time.
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