SILVA, Wanêssa Façanha. Ondas de spin em redes decoradas. 2014. 62 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-22T20:40:26Z No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-22T20:40:38Z (GMT) No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) / Made available in DSpace on 2015-10-22T20:40:38Z (GMT). No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) Previous issue date: 2014 / Low-dimensional systems have attracted much attention lately due to systems such as graphene and carbon nanotubes. Such systems have great potential for technological applications. In particular the creation of electronic devices due to their specific electronic properties. In this sense , the study of other systems in low dimension becomes urgent. More specifically , the study of magnetic properties of materials at low dimensionality also brings great new features in the behavior of ferromagnetic systems . The behavior of spin waves in such systems may be important to the study of spintronic and the development of new devices and magnetic memories . Thus in this work we aim to study the behavior of ferromagnetic spin waves in two-dimensional systems . For two-dimensional systems we consider here two-dimensional networks decorated . The decorations are introduced to generate networks with more than one basic atom in the unit cell of the system to study the richness of the spectrum of spin waves due to these changes . At first deal with a superimposition of square networks where the displacement of these networks depends on the control parameters alpha and beta . We also use the superposition of a square on a hexagonal network. / Sistema de baixa dimensionalidade têm atraído uma grande atenção ultimamente devido a sistemas como grafeno e nanotubos de carbono. Tais sistemas têm grandes possibilidades de aplicações tecnológicas, em particular na criação de dispositivos eletrônicos, devido às suas propriedades eletrônicas específicas. Nesse sentido, o estudos de outros sistemas em baixa dimensão se torna urgente. Mais especificamente, o estudo de propriedades magnéticas de materiais de materiais em baixa dimensionalidade também trás grandes novidades no comportamento de sistemas ferromagnéticos. O comportamento de ondas de spin em tais sistemas pode ser para o estudo da spintrônica e o desenvolvimento de novos aparelhos e memórias magnéticas. Dessa forma temos como objetivo nesse trabalho estudar o comportamento de ondas de spin em sistemas bidimensionais ferromagnéticos. Por sistemas bidimensionais consideramos aqui redes bidimensionais decoradas. As decorações são introduzidas para gerar redes com mais de um átomo na base da célula unitária da rede para estudarmos a riqueza do espectro das ondas de spin devido a essas modificações. A princípio tratamos com uma superposição de redes quadradas onde o deslocamento dessas redes depende dos parâmetros de controle α e β. Também usamos a superposição de um rede quadrada sobre um hexagonal.

We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory. Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0) and at the magnetic ordering wavevectors ±[Q= (4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.

Le caractère ultra-mince de couches magnétiques y exacerbe les effets d’interfaces. Dans ces systèmes, l’interaction d'échange dite "de Dzyaloshinskii-Moriya" (DMI) est autorisée par la brisure de symétrie d'inversion inhérente aux interfaces. Contrairement à l’interaction d’échange de Heisenberg, la DMI favorise une rotation de l’état d’aimantation, et ce avec une chiralité donnée. L'existence de la DMI dans les films ultra-minces était jusqu’à récemment sujette à débat, de sorte qu'il est apparu nécessaire de la quantifier et de caractériser ses manifestations observables. En partenariat avec le National Institute of Materials Science, le laboratoire Aimé Cotton et le laboratoire des Sciences des Procédés et des Matériaux, j'ai caractérisé l’interaction de Dzyaloshinskii-Moriya dans des films de CoFeB/MgO avec différentes couches tampons. Ce système matériau d’intérêt technologique reste suffisamment simple pour permettre une modélisation sans équivoque. Les méthodes utilisées recouvrent le déplacement de paroi de domaine dans un régime de reptation par microscopie magnéto-optique, la cartographie des champs de fuite de paroi par centre NV et la spectroscopie d’onde de spin par diffusion Brillouin. Quand l’interaction de Dzyaloshinskii-Moriya est relativement faible, ces différentes méthodes s'accordent quant à son amplitude et son signe. Néanmoins dans le cas général, les différentes façons de mesurer de l’interaction de Dzyaloshinskii-Moriya ne convergent pas vers des valeurs consensuelles. Pour comprendre ces différences, j’ai modélisé le comportement des parois de domaine sous champ planaire. J’ai montré qu’il existe un domaine en champ planaire où l’interaction de Dzyaloshinskii-Moriya déstabilise les parois rectilignes en formant préférentiellement des parois en Zigzag. L’élasticité des parois de domaine en est dramatiquement modifiée. Le champ dipolaire dans les parois de domaine amplifie ce phénomène. La reptation de paroi nécessite aussi la bonne compréhension du piégeage des parois de domaine. J’ai développé un modèle permettant d’estimer les champs de dépiégeage en fonction des différents paramètres matériau. Ce modèle permet aussi d’expliquer le comportement à haute fréquence des parois dans les échantillons en présence de défauts d’anisotropie variable. / In ultrathin ferromagnetic layer all interfacial effects are strongly enhanced. In these systems the so-called “Dzyaloshinskii-Moriya” exchange interaction (DMI) is allowed due to the inversion symmetry breaking at the interface. Unlike the Heisenberg exchange interaction, the DMI promotes rotation of the magnetization with a given chirality. Until recently, the DMI in ultrathin layer was a matter of debate and it has been needed to quantify and characterize its effects on the magnetization. In close relation with the National Institute of Materials Science, the laboratoire Aimé Cotton and the laboratoire des Sciences des Procédés et des Matériaux, I have characterized the Dzyaloshinskii-Moriya interaction in CoFeB/MgO films with different underlayers. This materials system presents a technological interest while keeping a low complexity for models its dynamics easily. The diverse used methods cover the field driven creep dynamic observed by Magneto-Optical Kerr Effect microscopy, the mapping of dipolar field by NV-center magnetometer and the spin wave spectroscopy measured Brillouin Light Scattering. When the DMI is relatively weak these different methods are in accordance with its sign and its order of magnitude. However the different methods do not converge to similar DMI values. I used a model to understand the behavior of domain wall under in-plane magnetic field. I have shown that there is an in-plane field range where the DMI destabilize a straight domain wall while stabilizing Zig-Zag walls. The elasticity is then dramatically modified. The dipolar energy enhances this phenomenon. The domain wall creep also needs a good understanding of the domain wall pinning. I developed a model to estimate the depinning field with respect to the different material parameters. This model also allows explaining of the high frequency behavior of pinned domain wall in samples containing variable anisotropy defects.

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Generating, miniaturizing and controlling spin waves on the nanometer scale is of great interest for magnonics. For instance, this holds the prospect of exploring wave-based logic concepts and reduced Joule heating, by avoiding charge transport, in spin-wave circuitry. In this work, a novel approach is for the first time confirmed experimentally, which allows confining spin-wave transport to nanometre-wide channels defined by magnetic domain walls. This is investigated for different domain wall types( 90deg and180deg Néel walls) in two material systems of polycrystalline Ni81Fe19 and epitaxial Fe. The study covers the thermal, linear and non-linear regime utilizing micro- focused Brillouin light scattering microscopy complemented by micromagnetic simulations. An initially linear dispersion dominated by dipolar interactions is found for the guided spin waves. These are transversally confined to sub-wavelength wide beams with a well-defined wave vector along the domain wall channel. In the non-linear regime, higher harmonic generation of additional spin-wave beams at the sides of the domain wall channel is observed. Furthermore, the possibility to shift the position of the domain wall over several microns by small magnetic fields is demonstrated, while maintaining its spin-wave channeling functionality. Additionally, spin-wave transmittance along domain walls, which change direction at the edges of the structure as well as between interconnected walls of identical and different type is studied. Characterization of spin-wave transmission through interconnected domain walls is an important step towards the development of magnonic circuitry based on domain wall(-networks). With respect to developing flexible and scalable spin-wave sources, the second part of this thesis addresses auto-oscillations in spin Hall oscillators (based on a Pt / Ni81Fe19 bilayer) of tapered nanowire geometry. In these systems, a simultaneous formation of two separate spin-wave bullets of distinct localization and frequency has been indicated. This spin-wave bullet formation is con- firmed experimentally and investigated for different driving currents. Subsequently, control over these bullets by injecting external microwave signals of varying frequency and power is demon- strated, switching the oscillator into single-mode operation. Three synchronized auto-oscillatory states are observed, which can be selected by the frequency of the externally imprinted signal. This synchronization results in linewidth reduction and frequency-locking of the individual bullet modes. Simultaneously the bullet-amplitude is amplified and is found to scale as P2/3 with the injected microwave power P. This amplification and control over position and frequency of the spin-wave bullets is promising for the development of microwave amplifiers/detectors and spin- wave sources on the nanoscale based on spin Hall oscillators.:1 Introduction 1 2 Theoretical background 4 2.1 Energy density of thin film ferromagnets and domain(wall) formation 2.2 Magnetizationdynamicsinthinfilmferromagnets 11 2.2.1 Spin-wavedispersioninthelinearregime 13 2.2.2 Magnetizationdynamicsinthenon-linearregime 17 2.3 SpinHallOscillators 21 2.3.1 Spin Hall effect and spin transfer torque in a ferromagnet/heavy-metal bi- layersystem 21 2.3.2 Characteristics of magnetization auto-oscillations 25 2.3.3 Improvement of monochromaticity, coherence and output power by injec- tionlocking 28 3 Materials and Methods 31 3.1 ElectronBeamLithography,EBL 31 3.2 Ni81Fe19 microstructures 32 3.3 Femicrostructures 34 3.4 TaperedspinHalloscillators 35 3.5 Micro-focused Brillouin Light Scattering Spectroscopy, μBLS 36 3.5.1 μBLSspatialresolution 40 4 Experimental results 43 4.1 Spin-wave dynamics in multi-domain magnetic configurations 43 4.1.1 Spin-wave dynamics of 180◦ Néel walls in rectangular elements 44 4.1.2 Spin-wave dynamics of 90◦ Néel walls in square elements 63 4.1.3 Spin-wave dynamics of interconnected Néel walls in Fe wires 76 4.2 Auto-oscillationintaperedwiregeometries 88 4.2.1 Initial static magnetic configuration and effective field 89 4.2.2 Thermally excited dynamics and spectral properties 91 4.2.3 Direct microwave excitation of spin-wave dynamics 93 4.2.4 Auto-oscillatoryresponse 96 4.2.5 Microwaveamplificationandinjectionlocking 104 5 Summary and outlook 114 Own publications 118 Bibliography 120 Acknowledgement 141 A Appendix 143 A.1 Splitting process in magnetic domains confined by domain walls 143 A.2 reconfigurable remanent states in square structures stabilized by local ion irradiation 144 A.3 Domain wall displacements induced by a scanning laser beam 145 A.4 Magnetic Force Microscopy investigation of the domain wall type and width 147 A.5 Micromagnetic simulations: problem definition and analysis 149 A.6 Current dependence of auto-oscillations in the tapered SHO 152 A.7 Fabrication of Ni81Fe19 microstructures for spin waves in domain walls 153

This dissertation consists of two parts, connected by the overarching theme of the dynamics of structured waves with internal degrees of freedom. Part I concerns light, whose internal degree of freedom is polarisation. We investigate the helicity, or handedness of light, which is a good quantum number for massless fields in general and light in particular. In free space it is always possible to describe the light field in a basis left- and right handed helicity modes which are solutions of Maxwell's equations, regardless what spatial structure is chosen. This is useful for bases of highly inhomogeneous waves, such as Bessel waves, for which the spin cannot be unambiguously defined. In chapter 1 we study the conservation of helicity and the preservation of its underlying symmetry, electric-magnetic duality symmetry when light travels through inhomogeneous and/or anisotropic media. We will discuss some of the unique properties of duality symmetric media and reformulate Maxwell's equations in such a way that the decoupling of different helicities for duality symmetric media becomes apparent. The feasibility of constructing duality symmetric media is discussed at the end of the chapter. In chapter 2 we consider superpositions of plane electromagnetic waves in free space. Such superpositions typically interfere. We present superpositions of up to six plane waves which defy this expectation by having a perfectly homogeneous mean square of the electric field. Because most matter interacts much stronger with the electric than with the magnetic field, these superpositions can be considered noninterfering. Our superpositions show complex patterns in their helicity densities, of which we will show many examples. We study the effects on our helicity patterns of imperfections that may occur in a realistic experiment: deviations from the optimal amplitudes, phases and polarisations of the superposed waves, small misalignments and partially coherent light. Our superpositions can be used to write chiral patterns in light sensitive liquid crystals. Conversely, these liquid crystals can be used for an `optical helicity camera' which records spatial variations in helicity. In the final paragraph of chapter 2 we discuss some mathematical questions concerning noninterfering superpositions. Part II concerns electrons, whose internal degree of freedom is spin. In chapter 3 we will present analytical solutions of the Dirac equation for an electron vortex beam in a homogeneous magnetic field. Including spin from the beginning reveals that spin polarised electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exist vortex beam solutions with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. Chapter 4 treats the interaction between electron vortex states in a homogeneous magnetic field and light, where we expand and quantise the radiation field in a basis of Bessel modes with definite helicity. Our results apply for magnetic field strength beyond the critical field strength at which the spin contributes as much to the electron's energy as its rest mass. We are able to compute spin flip rates for low lying states, finding a much higher degree of equilibrium spin polarisation than approximations for high lying electron states suggested.

Paramagnetické niklem stabilizované tenké vrstvy plošně centrovaného kubického Fe, epitaxně narostené na monokrystalickém substrátu Cu(100) jsou známy svou schopností strukturní a magnetické fázové přeměny při ozáření iontovým svazkem, a to do prostorově centrované kubické struktury charakteristické feromagnetickými vlastnostmi. Monokrystalický Cu(100) substrát je možné také nahradit Si(100) s mezivrstvou Cu(100). Pomocí fokusovaného iontového svazku lze dále snadno lokálně modifikovat magnetické vlastnosti ozařované vrstvy. Tato metoda přímého zápisu magnetických struktur je alternativou k běžným litografickým technikám, nabízející nové jimi nedosažitelné možnosti. Připravené magnetické struktury následně využíváme k propagaci spinových vln. V práci je představen celý proces od růstu vrstev, přes přípravu mikrostruktur, až po studium jejich struktury a statických i dynamických magnetických vlastností. S využitím vektorového síťového analyzátoru studujeme ve vrstvách a v mikrostrukturách připravených fokusovaným iontovým svazkem feromagnetickou rezonanci a propagující se spinové vlny. Zdrojem spinových vln o definovaných vlnových vektorech jsou litograficky připravené koplanární vlnovody, sloužící také k induktivní detekci vln. Pomocí feromagnetické rezonance kvantitativně určujeme materiálové charakteristiky jako jsou saturační magnetizace a parametr útlumu a ze spekter propagujících módů následně určujeme charakteristiky spinových vln, které porovnáváme s dalšími feromagnetickými materiály.

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.

In this thesis, the interplay between electron transport and magnetization dynamics is explored in order to access to fundamental properties of ferromag- netic metal thin films. With the aim of extracting the influence of the electron surface scattering on the spin-dependent resistivities, thickness series of permal-loy (Ni80Fe20) films were grown and studied. In addition to standard electrical and magnetic measurements, a detailed study of the propagation of spin waves along these films was performed. Resorting to the current-induced spin-wave Doppler shift technique, the degree of spin-polarization of the electrical current was extracted. This degree of spin-polarization was found to decrease when the film thickness decreases, which suggests that the film surfaces contribute to the spin dependent resistivities and tend to depolarize the electrical current.