Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-10T18:29:15Z No. of bitstreams: 1 DAMARES SANTOS SILVA BORGES – DISSERTAÇÃO (PPGFísica) 2018.pdf: 14903609 bytes, checksum: 19118754fe275415f701d012e1d4515e (MD5) / Made available in DSpace on 2018-10-10T18:29:15Z (GMT). No. of bitstreams: 1 DAMARES SANTOS SILVA BORGES – DISSERTAÇÃO (PPGFísica) 2018.pdf: 14903609 bytes, checksum: 19118754fe275415f701d012e1d4515e (MD5) Previous issue date: 2018-07-26 / Capes / Os defeitos topológicos são caracterizados como soluções estáveis de equações de movimento em uma ou mais dimensões espaciais e desempenham papel importante na ciência não-linear. Neste trabalho de dissertação, damos ênfase a defeitos em (1+1) e (2+1) dimensões espaço-temporais. No primeiro caso, abordamos configurações conhecidas como twistons (soluções topológicas tipo kink) presentes em cristais de polietileno. Nessa primeira abordagem, revisitamos trabalhos anteriores e, a partir do método de extensão, construímos novas famílias de potenciais que descrevem bem sistemas desse tipo. Apresentamos soluções topológicas analíticas e que não possuem problemas de degenerescência infinita. No segundo caso, estudamos estruturas conhecidas como skyrmions com base na sua descrição em materiais magnéticos, em que são denotados como configurações da magnetização em nanoescala e topologicamente estáveis. Recorremos novamente ao método de extensão e apresentamos um potencial, função de dois campos escalares acoplados, a partir do qual conseguimos modelar essas estruturas magnéticas. Além disso, o novo modelo de dois campos tem soluções analíticas conhecidas, permitindo análises interessantes como a determinação de uma quantidade topológica conservada, estudo das diferentes configurações da magnetização e cálculo do raio médio de matéria. / Topological defects are characterized as stable equation of motion solutions in one or more spatial dimensions and play an important role in nonlinear science. In this study, space-time (1 + 1) and (2 + 1) dimension defects are emphasized. In the first case, configurations known as twistons (kink-like topological solutions) present in polyethylene crystals are assessed. In this first approach, previous works were reviewed and new families of potentials that adequately describe these types of systems were constructed from the extension method, presenting analytical topological solutions that do not display infinite degeneracy problems. In the second case, structures known as skyrmions were studied based on their description in magnetic materials, where they are denoted as topologically stable nanoscale magnetization configurations. The extension method was applied and a potential from which such magnetic structures can be modelled, function of two coupled scalar fields was presented. In addition, the new two-field model possesses known analytical solutions, allowing for interesting analyses, such as the determination of a conserved topological quantity, the study of the different magnetization configurations and calculation of mean matter radius.

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

A new tetragonal Heusler compound Mn1.4PtSn is synthesized. Crystal growth techniques that require growth directly from melt, such as Bridgman method, always result in microtwinned crystals. To get microtwin free crystals, another technique, flux method is employed, where growth can be done far below the melting point and martensitic transition temperature. The flux method results in successful large microtwin free crystals of Mn1.4PtSn. The single-crystal diffraction is done on a small piece of single crystals of Mn1.4PtSn. From structural analysis, it is found out that the crystal structure of Mn1.4PtSn is the first tetragonal superstructure in the family of Heusler compounds. The superstructure reflections are clearly observed in the powder X-ray diffraction patterns. Direction-dependent magnetic properties are measured. The compound is found to undergo two magnetic transitions. First, at 392 K, which corresponds to Curie temperature and second, at 170 K, which corresponds to the spin-reorientation transition temperature. The saturation magnetic moment at 2 K is very large of 4.7 µB/f.u. The refinement of powder neutron diffraction reveals that in the temperature range of 170 to 392 K, the magnetic structure is collinear ferromagnet whereas below 170 K, it is a non-coplanar spin structure. The magnetic moment, obtained from refinement, is close to the saturation moment obtained from magnetization. The electric transport properties are studied along the different crystallographic directions of the compound. The longitudinal resistivity measurement indicates that the compound is metallic and reveals the magnetic transitions at the same temperature as seen in the magnetization. An overall negative magnetoresistance of 3 percent is found. The Hall resistivity measurements reveal the presence of a large topological Hall resistivity (THE) of 0.9 µΩ cm and -0.1 µΩ cm for the magnetic field applied along [100] and [001], respectively. Two types of contributions in the THE for the field along [100] are seen. One that follows the quadratic form of longitudinal resistivity and second, that is independent of longitudinal resistivity. Anomalous Hall conductivity is found to be 250 and 165 Ω-1cm-1 for the field along [100] and [001], respectively. This value is close to the value obtained from theoretical calculations. The topological Hall conductivity is found to be approximately the same as its anomalous analog. A new series of polycrystalline samples with iridium substitution at the place of platinum in Mn1.4PtSn are prepared. The structural characterization show the crystal structure of these compounds is the same as Mn1.4PtSn, therefore, they also possess the tetragonal superstructure form. Magnetic properties, along with powder neutron diffraction data, reveal that the magnetic structure changes from out-of-plane ferromagnet to in-plane ferrimagnet with Ir-substitution. All the compounds are found to have metallic character. A large anomalous Hall conductivity of 405 Ω-1cm-1 is found for compound Mn1.4Pt0.7Ir0.3Sn. Three new series of compounds are prepared as an attempt to fill the vacancies present in the crystal structure of Mn1.4PtSn with transition-metal elements cobalt, nickel, and copper. The tetragonal superstructure survives up to 0.2 cobalt addition, 0.4 nickel addition and 0.6 copper addition. Further addition of elements leads to transformation to the inverse cubic Heusler structure. The magnetic properties show that the compounds with tetragonal structure have spin-reorientation transition, which is absent in the compounds with cubic structure. A new compound Mn1.7Pt0.8In is discovered. The single crystals are prepared by flux-method. Upon structural analysis from single-crystal refinement, it is found that the crystal structure is 3 × 3 × 3 superstructure of a Heusler structure and is so far the largest discovered in the Heusler family of compounds. Two magnetic transitions are revealed in the magnetization measurements. First, at 330 K, which corresponds to Curie temperature and second, at 220 K, which corresponds to spin-reorientation transition. The magnetic moment is 0.4 µB/Mn at 2 K and 0.07 µB/Mn at 300 K. Such a low moment might be due to possible compensated ferrimagnetic structure. Therefore, the compound is a potential candidate for spintronics devices.

We study the application of Bose-Einstein condensates (BECs) to simulations of phenomena across a number of disciplines in physics, using theoretical and computational methods. ¶ Collapsing condensates as created by E. Donley et al. [Nature 415, 39 (2002)] exhibit potentially useful parallels to an inflationary universe. To enable the exploitation of this analogy, we check if current quantum field theories describe collapsing condensates quantitatively, by targeting the discrepancy between experimental and theoretical values for the time to collapse. To this end, we couple the lowest order quantum field correlation functions to the condensate wavefunction, and solve the resulting Hartree-Fock-Bogoliubov equations numerically. Complementarily, we perform stochastic truncated Wigner simulations of the collapse. Both methods also allow us to study finite temperature effects. ¶ We find with neither method that quantum corrections lead to a faster collapse than is predicted by Gross-Pitaevskii theory. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be explained by Gaussian quantum fluctuations or finite temperature effects. Further studies are thus required before the full analogue cosmology potential of collapsing condensates can be utilised. ¶ As the next project, we find experimental parameter regimes in which stable three-dimensional Skyrmions can exist in a condensate. We show that their stability in a harmonic trap depends critically on scattering lengths, atom numbers, trap rotation and trap anisotropy. In particular, for the Rb87 |F=1,m_f=-1>, |F=2,m_f=1> hyperfine states, stability is sensitive to the scattering lengths at the 2% level. We find stable Skyrmions with slightly more than 2*10^6 atoms, which can be stabilised against drifting out of the trap by laser pinning. ¶ As a stepping stone towards Skyrmions, we propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a ``hollow'' laser beam containing an optical vortex, which realises an optical tunnel for the condensate. Using realistic experimental parameters, we demonstrate numerically that our method can stabilise up to 9 vortex rings. ¶ Finally, we focus on analogue gravity, further exploiting the analogy between flowing condensates and general relativistic curved space time. We compare several realistic setups, investigating their suitability for the observation of analogue Hawking radiation. We link our proposal of stable ring flows to analogue gravity, by studying supersonic flows in the optical tunnel. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons, and discuss whether these could be employed to study extreme cases in analogue gravity. ¶ Beyond these, our survey indicates that for conventional analogue Hawking radiation, simple outflow from a condensate reservoir, in effectively one dimension, has the best properties. We show with three dimensional simulations that stable sonic horizons exist under realistic conditions. However, we highlight that three-body losses impose limitations on the achievable analogue Hawking temperatures. These limitations vary between the atomic species and favour light atoms. ¶ Our results indicate that Bose-Einstein condensates will soon be useful for interdisciplinary studies by analogy, but also show that the experiments will be challenging.

The aim of the current thesis was to investigate the preparation of MnSi film on Si substrates. The preparation process includes room temperature sputtering Mn films with different thicknesses and flash-lamp annealing with different energy density (annealing temperature). Systematic investigations on their structural, electrical, magnetic, and magneto-transport properties were performed. The key findings are summarized below: Thin films with the B20-MnSi phase on Si(100) substrates were fabricated for the first time. They exhibit magnetic skyrmion behaviour. In comparison with Si(111) substrates, Si(100) substrates are more preferred from the practical application point of view. The nucleation of B20-MnSi on Si(100) is believed to be triggered by the fast solid-state phase reaction between Mn and Si via ms-range flash-lamp annealing. Compared with the corresponding bulk material, our films show an increased Curie temperature of around 43 K. The magnetic and transport measurements reveal that skyrmions in B20-MnSi on Si(100) made by sub-seconds solid-state reaction are stable within much broader field and temperature windows than bulk MnSi. The parasitic MnSi1.7 phase can be further minimized or eliminated by optimizing the annealing conditions, the quality of the deposited Mn film, and its interface with the Si substrate. Our work demonstrates a promising route for the fabrication of B20-type transition metal silicides for integrated and/or hybrid spintronic applications on Si(100) wafers, which are more preferable for industry applications. The growth of MnSi films on Si(111) substrates has been widely realized by solid phase epitaxy or molecular beam epitaxy since the lattice mismatch and symmetry fit better. One problem is the parasitic MnSi1.7 phase. By controlling the reaction parameters using strongly non-equilibrium flash lamp annealing, we have achieved full control over the phase formation of Mn-silicides in thin films from single-phase B20-MnSi or MnSi1.7 to mixed phases. The obtained films are highly textured and reveal sharp interfaces to the Si substrate. The obtained B20-MnSi films exhibits a high Curie temperature of 41 K. The skyrmion phase can be stabilized over broad temperature and magnetic field ranges. We propose flash-lamp-annealing-induced transient reaction as a general approach for phase separation in transition-metal silicides and germanides and for growth of B20-type films with enhanced topological stability. By comparing the magnetic properties of MnSi films grown on both Si(111) and Si(100) substrates by ourselves and by others in literature, we found one common feature. It is the increased Curie temperature of around 41-43 K for all MnSi films. It is much higher than 29.5 K for bulk MnSi. We try to understand the puzzling Curie temperature widely reported in MnSi films. We have prepared MnSi films with a large variation regarding their thickness, crystallinity, strain and phase separation. Particularly, polycrystalline MnSi films on Si(100) and textured MnSi films on Si(111), both with different mixture ratio with MnSi1.7 have been grown and systematically characterized. Surprisingly, all obtained MnSi films exhibit a high Curie temperature at around 43 K. The skyrmion phase has also been detected in these films. However, we find no correlation between the increased Curie temperate and the film thickness, strain, lattice volume or the mixture with MnSi1.7. Our work has not provided a conclusive picture for this question, but is rather calling a revisit, especially to the effect by the interface, stoichiometry and point defects. Further studies are essential to understand the B20 transition-metal silicide/germanides films and therefore to utilize them for spintronic applications.:Contents Abstract iii Kurzfassung v 1. Introduction 1 1.1 B20 compounds and magnetic skyrmions 1 1.2 B20 MnSi with magnetic Skyrmions 8 1.2.1 Crystallization process 10 1.2.2 Phase diagram of Mn-Si binary compounds 13 1.2.3 Bulk B20-MnSi 14 1.2.4 B20-MnSi thin film 18 1.2.5 B20-MnSi nanowire 25 1.3 Fast annealing method 27 1.4 Objectives and the structure of the thesis 30 2. Experiment 32 2.1 Sample preparation 32 2.1.1 DC magnetron sputtering 32 2.1.2 Sub-second annealing 35 2.2 Structure characterization: X-ray diffraction 40 2.3 Property characterization 41 2.3.1 Magnetic properties 41 2.3.2 Magneto-transport properties 44 3. B20-MnSi films grown on Si(100) substrates with magnetic skyrmion signature 46 3.1 Introduction 46 3.2 Experiment 47 3.3 Results and Discussions 48 3.4 Conclusions 56 4. Phase selection in Mn-Si alloys by fast solid-state reaction with enhanced skyrmion stability 57 4.1 Introduction 57 4.2 Experiment 59 4.3 Results 61 4.3.1 MnSi and MnSi1.7 phase reaction 61 4.3.2 Magnetic Skyrmion 68 4.3.3 Discussion 76 4.4 Conclusion 78 5. On the Curie temperature of MnSi films 80 5.1 Introduction 80 5.2 Experiment 82 5.3 Results 83 5.4 Conclusion 89 6. Summary and outlook 90 6.1 Summary 90 6.2 Outlook 91 6.2.1 Film thickness effect on formation of (111)-textured B20-MnSi 91 6.2.2 MnSi1.7% influence on Skyrmion stability 96 6.2.3 Preparation of other transition-metal monosilicides and germanides 98 Acknowledgement 99 References 101 Publication list 117 Curriculum Vitae 119 Erklärung 120

<div> <div> <div> <p>Process variations and increasing leakage current are major challenges toward memory realization in deeply-scaled CMOS devices. Spintronic devices recently emerged as one of the leading candidates for future information storage due to its potential for non-volatility, high speed, low power and good endurance. In this thesis, we start with the basic concepts and applications of three spintronic devices, namely spin or- bit torque (SOT) based spin-valves, SOT-based magnetic tunnel junctions and the magnetic skyrmion (MS) for both logic and machine learning hardware. </p> <p>We propose a new Spin-Orbit Torque based Domino-style Spin Logic (SOT-DSL) that operates in a sequence of Preset and Evaluation modes of operations. During the preset mode, the output magnet is clocked to its hard-axis using spin Hall effect. In the evaluation mode, the clocked output magnet is switched by a spin current from the preceding stage. The nano-magnets in SOT-DSL are always driven by orthogonal spins rather than collinear spins, which in turn eliminates the incubation delay and allows fast magnetization switching. Based on our simulation results, SOT-DSL shows up to 50% improvement in energy consumption compared to All-Spin Logic. Moreover, SOT-DSL relaxes the requirement for buffer insertion between long spin channels, and significantly lowers the design complexity. This dissertation also covers two applications using MS as information carriers. MS has been shown to possess several advantages in terms of unprecedented stability, ultra-low depinning current density, and compact size. </p><p><br></p><p>We propose a multi-bit MS cell with appropriate peripheral circuits. A systematic device-circuit-architecture co-design is performed to evaluate the feasibility of using MS-based memory as last-level caches for general purpose processors. To further establish the viability of skyrmions for other applications, a deep spiking neural network (SNN) architecture where computation units are realized by MS-based devices is also proposed. We develop device architectures and models suitable for neurons and synapses, provide device-to-system level analysis for the design of an All-Spin Spiking Neural Network based on skyrmionic devices, and demonstrate its efficiency over a corresponding CMOS implementation.</p> <div> <div> <div> <p><br></p><p>Apart from the aforementioned applications such as memory storage elements or logic operation, this research also focuses on the implementation of spin-based device to solve combinatorial optimization problems. Finding an efficient computing method to solve these problems has been researched extensively. The computational cost for such optimization problems exponentially increases with the number of variables using traditional von-Neumann architecture. Ising model, on the other hand, has been proposed as a more suitable computation paradigm for its simple architecture and inherent ability to efficiently solve combinatorial optimization problems. In this work, SHE-MTJs are used as a stochastic switching bit to solve these problems based on the Ising model. We also design an unique approach to map bi-prime factorization problem to our proposed device-circuit configuration. By solving coupled Landau- Lifshitz-Gilbert equations, we demonstrate that our coupling network can factorize up to 16-bit binary numbers. </p> </div> </div> </div> </div> </div> </div>

Skyrmions are spin textures with particle character that order themselves into so-called “skyrmion lattices” (SkLs). A skyrmion is topologically nontrivial, which adds stability against external perturbations and attracts tremendous interest from the theoretical side. Since skyrmions can be moved with small electrical currents, they are being discussed for novel spintronic applications, such as racetrack memory. Further interest has been spurred by the discovery of multiferroic compounds that also host SkLs, resulting in additional properties that are highly interesting both for applications and for fundamental research. The scope of this thesis encompasses the investigation of two completely different exemplary SkL-hosting multiferroic systems using a broad set of scanning probe microscopy techniques. These can probe multiple properties on a local scale in real space with a single measurement, examining details not resolved by non-local techniques. In the first part, there is a brief introduction to magnetic skyrmions and scanning probe microscopy with a short review of the theoretical background. The materials of interest and their known properties are then introduced. These are Cu2OSeO3, an insulator exhibiting the emergence of Bloch-type skyrmions as well as type-II multiferroicity, and the lacunar spinel chalcogenides, which were recently found to exhibit multiferroic Néel-type skyrmions pinned to magnetic easy-axes/planes together with type-I multiferroicity originating from a structural Jahn–Teller transition. The second part first presents various scanning probe studies and their results for Cu2OSeO3, where, aside from the magnetic textures of the various magnetic phases, the magnetoelectric effect and the magnetic phase transitions are investigated and described with basic theoretical models. Results show a good correlation between observations and theory, as well as with other experimental methods. Various lacunar spinels are then investigated, mostly GaV4S8 and GaMo4S8. Observation of the structural phase transition leads to the observation of {100}-type domain boundaries compatible with the compatibility critera based on crystal geometry. Furthermore, measurements of the magnetic textures of the different magnetic phases for GaV4S8 are presented and analysed. Results highlight a pinning of the pitch vector to the magnetic hard plane, and that the structural domain boundaries are by necessity magnetic domain boundaries. Analysing the influence of surface anisotropy and structural domain boundaries reveals a strong effect of both on the formation of magnetic patterns in their vicinity. Finally, the magnetoelectric effect of different lacunar spinels is investigated by measuring the surface potential with changing magnetic fields leading to a hysteretic behaviour in all materials.:Abstract/Kurzdarstellung 1 Introduction – Skyrmions meet Multiferroicity 2 Magnetic Skyrmion Lattices 2.1 What is a Skyrmion? 2.2 Formation of Skyrmion Lattices 2.2.1 Basic Considerations 2.2.2 Emergence of Skyrmion Lattices 2.3 General Properties of Skyrmions 2.4 Ways to Observe Skyrmions 3 Scanning Probe Microscopy 3.1 General Aspects 3.2 SPM in Contact Mode 3.2.1 Atomic Force Microscopy 3.2.2 Conductive Atomic Force Microscopy 3.2.3 Piezoresponse Force Microscopy 3.3 SPM in Non-Contact Mode 3.3.1 Atomic Force Microscopy 3.3.2 Kelvin Probe Force Microscopy 3.3.3 Magnetic Force Microscopy 3.4 About Scanning Dissipation Microscopy 3.4.1 Possible Origins of Dissipation 3.4.2 Measuring Dissipation 3.4.3 Mathematical Background 3.5 Experimental Setup 4 Investigated Materials 4.1 Cubic copper(II)-oxo-selenite Cu2O(SeO3) 4.2 Lacunar Spinel Chalcogenides 4.2.1 General Aspects and Materials Chosen 4.2.2 Structural Phase Transition and Expected Piezoresponse 4.2.3 Magnetic Phase Transition 4.2.4 Investigated Crystals 5 Investigations on Cu2OSeO3 5.1 Observing the Different Magnetic Phases 5.1.1 Analysis of Magnetic Textures with Magnetic Force Microscopy 5.1.2 Analysis of Magnetic Textures with Scanning Dissipation Microscopy 5.2 Analysis of the Magnetoelectric Effect 5.2.1 Observing the Magnetoelectric Effect with KPFM 5.2.2 Heuristic Description of the Magnetoelectric Effect 5.3 Analysing the Magnetic Phase Transitions with SPM 5.3.1 Motivation from Theory 5.3.2 Distinguishing the Helical, Conical and Field-Polarised Phases 5.3.3 The Helical–Conical Phase Transition 5.3.4 Passing through the Conical Phase 6 Investigations on GaV4S8 6.1 Observing the Structural Phase Transition 6.1.1 Results from nc-AFM 6.1.2 Results from ct-AFM and PFM 6.2 Observing the Magnetic Phases 6.3 Analysing the Magnetic SDM Images 6.3.1 Theoretical Considerations 6.3.2 Rescaling from the Measured to the Magnetic Hard Plane 6.3.3 Influence of the Surface on the Patterns Observed 6.4 Influence of Structural Domain Walls on Magnetic Patterns 7 Further Investigation on Lacunar Spinels 7.1 Investigations on GaMo4S8 7.1.1 Experimental Results 7.1.2 Theoretical Considerations 7.1.3 Evaluation of the Experimental Data 7.2 Magnetoelectric Effect of Lacunar Spinels 8 Remarks About Magnetic Non-Contact Dissipation 9 Summary and Outlook 9.1 Synopsis 9.2 Outlook – Probing the Future A Permissions For Usage of Content B Some Additional Information on Non-Contact Dissipation C Bonus Images Bibliography Publications Acknowledgements Erklärung / Skyrmionen sind teilchenartige Spintexturen, welche sich in sogenannten Skyrmionengittern anordnen. Jedes Skyrmion besitzt eine topologische Ladung. Dieses Konzept ist von bedeutendem Interesse für die Theorie und führt zu zusätzlicher Stabilität gegen externe Störungen. Da Skyrmionen mit geringen elektrischen Strömen bewegt werden können, sind sie auch Kanditaten für neuartige, spintronische Anwendungen wie den Racetrack-Speicher. Zusätzlich wurden vor einiger Zeit multiferroische Materialien entdeckt, welche ebenso Skyrmionengitter bilden und aufgrund dessen weitere, interessante Eigenschaften besitzen, welche sowohl für Anwendungen als auch für die Grundlagenforschung interessant sind. Inhalt dieser Dissertation ist die Untersuchung zweier verschiedener, exemplarischer multiferroischer Materialien mit Skyrmiongitterphasen mittels verschiedener Rastersondentechniken. Dies erlaubt das gleichzeitige Erfassen mehrerer Parameter auf einer lokalen Skala im Realraum mit einer einzigen Messung und somit die Untersuchung von Details, welche durch nicht-lokale Techniken nicht erfasst werden können. Im ersten Teil wird eine kurze Einleitung über magnetische Skyrmionen und die Rastersondenmikroskopie sowie Abrisse über deren theoretischen Hintergrund gegeben. Im Anschluß werden die untersuchten Materialien und deren Eigenschaften vorgestellt. Das erste System ist Cu2OSeO3, ein Isolator, welcher Bloch-artige Skyrmionengitter formiert und ein Typ-II Multiferroikum ist. Weitere Systeme gehören zur Klasse der lakunären Spinell-Chalkogenide, welche nach neuesten Erkenntnissen multiferroische Néel-artige Skyrmionen formieren, deren Modulationsvektor zur magnetisch harten Achse/Ebene fixiert ist. Ebenso sind diese aufgrund eines strukturellen Jahn-Teller Überganges Typ-I Multiferroika. Im zweiten Teil werden verschiedene Rastersondenuntersuchungen und ihre Ergebnisse präsentiert. Beginnend mit Cu2OSeO3, werden, neben den den magnetische Texturen der verschiedenen magnetischen Phasen, der magnetoelektrische Effekt und der helisch-konische Phasenübergang untersucht sowie mit grundlegenden theoretischen Modellen verglichen. Die Ergebnisse zeigen eine gute Übereinstimmung zwischen den Beobachtungen und der Theorie sowie mit anderen Meßmethoden. Im Anschluß werden verschiedene lakunäre Spinell-Chalkogenide, vor allem GaV4S8 und GaMo4S8, untersucht. Beobachtungen des strukturellen Phasenüberganges ergeben die Formierung von {100}-artigen Domänenwänden, welche mit den Vorhersagen der Kompatibilitätskriterien resultierend aus der Kristallgeometrie übereinstimmen. Des Weiteren werden Messungen der magnetischen Texturen der verschiedenen magnetischen Phasen von GaV4S8 präsentiert sowie analysiert. Die Ergebnisse heben hervor, daß der Modulationsvektor an der magnetisch harten Ebene fixiert ist und daß die strukturellen Domänengrenzen notwendigerweise auch die magnetischen Domänengrenzen sein müssen. Eine Analyse des Einflusses der Oberflächenanisotropie sowie der strukturellen Domänengrenzen zeigt eine starke Wirkung beider auf die Formierung magnetischer Texturen in ihrer Nähe. Schließlich wird der magnetoelektrische Effekt der lakunären Spinell-Chalkogenide durch Messung des Oberflächenpotentiales als Funktion des angelegten Magnetfeldes untersucht. Beobachtungen ergeben ein hysteretisches Verhalten in allen Materialen.:Abstract/Kurzdarstellung 1 Introduction – Skyrmions meet Multiferroicity 2 Magnetic Skyrmion Lattices 2.1 What is a Skyrmion? 2.2 Formation of Skyrmion Lattices 2.2.1 Basic Considerations 2.2.2 Emergence of Skyrmion Lattices 2.3 General Properties of Skyrmions 2.4 Ways to Observe Skyrmions 3 Scanning Probe Microscopy 3.1 General Aspects 3.2 SPM in Contact Mode 3.2.1 Atomic Force Microscopy 3.2.2 Conductive Atomic Force Microscopy 3.2.3 Piezoresponse Force Microscopy 3.3 SPM in Non-Contact Mode 3.3.1 Atomic Force Microscopy 3.3.2 Kelvin Probe Force Microscopy 3.3.3 Magnetic Force Microscopy 3.4 About Scanning Dissipation Microscopy 3.4.1 Possible Origins of Dissipation 3.4.2 Measuring Dissipation 3.4.3 Mathematical Background 3.5 Experimental Setup 4 Investigated Materials 4.1 Cubic copper(II)-oxo-selenite Cu2O(SeO3) 4.2 Lacunar Spinel Chalcogenides 4.2.1 General Aspects and Materials Chosen 4.2.2 Structural Phase Transition and Expected Piezoresponse 4.2.3 Magnetic Phase Transition 4.2.4 Investigated Crystals 5 Investigations on Cu2OSeO3 5.1 Observing the Different Magnetic Phases 5.1.1 Analysis of Magnetic Textures with Magnetic Force Microscopy 5.1.2 Analysis of Magnetic Textures with Scanning Dissipation Microscopy 5.2 Analysis of the Magnetoelectric Effect 5.2.1 Observing the Magnetoelectric Effect with KPFM 5.2.2 Heuristic Description of the Magnetoelectric Effect 5.3 Analysing the Magnetic Phase Transitions with SPM 5.3.1 Motivation from Theory 5.3.2 Distinguishing the Helical, Conical and Field-Polarised Phases 5.3.3 The Helical–Conical Phase Transition 5.3.4 Passing through the Conical Phase 6 Investigations on GaV4S8 6.1 Observing the Structural Phase Transition 6.1.1 Results from nc-AFM 6.1.2 Results from ct-AFM and PFM 6.2 Observing the Magnetic Phases 6.3 Analysing the Magnetic SDM Images 6.3.1 Theoretical Considerations 6.3.2 Rescaling from the Measured to the Magnetic Hard Plane 6.3.3 Influence of the Surface on the Patterns Observed 6.4 Influence of Structural Domain Walls on Magnetic Patterns 7 Further Investigation on Lacunar Spinels 7.1 Investigations on GaMo4S8 7.1.1 Experimental Results 7.1.2 Theoretical Considerations 7.1.3 Evaluation of the Experimental Data 7.2 Magnetoelectric Effect of Lacunar Spinels 8 Remarks About Magnetic Non-Contact Dissipation 9 Summary and Outlook 9.1 Synopsis 9.2 Outlook – Probing the Future A Permissions For Usage of Content B Some Additional Information on Non-Contact Dissipation C Bonus Images Bibliography Publications Acknowledgements Erklärung

Chiral magnets such as MnSi, FeGe or Cu2OSeO3 exhibit a non-centrosymmetric lattice structure which lacks inversion symmetry. The resulting Dzyaloshinskii-Moriya interaction originating from weak spin-orbit coupling stabilizes smooth modulated magnetic textures, namely helices and skyrmions. In this thesis, we study the properties of helimagnets which are systems with a magnetic helix as ground state. First, we examine the consequences of the helical texture for spin wave excitations, so-called helimagnons. We investigate magnon-focusing effects, i.e. magnon flow in very specific directions, which result from flat bands occurring in the helimagnon band structure when the momentum component perpendicular to the helix axis is large. We show that the softness of the Goldstone mode leads to a large dissipation even at very small frequencies cut off only by magnetocrystalline anisotropies or by a magnetic field. Finally, we discuss that dipolar interactions induce non-reciprocal behavior of the spectrum at finite fields and momenta, i.e. the spectrum is not symmetric under reversing the momentum anymore. We calculate the Brillouin light scattering cross section and compare it to experimental results obtained by N. Ogawa [1]. Then, we consider reorientation processes of the helix axis due to an applied magnetic field. We compare the results to magnetic force microscopy measurements in Cu2OSeO3 performed by P. Milde et al. [2]. Afterwards, we point out that the skyrmion lattice orientation has singular points, i.e. points where the orientation is not determined, as a function of the magnetic field direction which is a consequence of the Poincaré-Hopf theorem. Afterwards, we turn to excitations in the form of the basic defects in helimagnets: disclinations and dislocations. Due to the lamellar nature of the helimagnetic texture, analogies to liquid crystals can often be used. We present an analytic parameterization of dislocations transferred from smectic liquid crystals and illustrate that dislocations carry a topological skyrmion charge. We examine dislocation motion in the presence of weak pinning due to random impurities. We derive a Thiele-Langevin equation for the dislocation position which effectively describes one dimensional motion. When reducing the system to two dimensions, this reveals ultra slow anomalous Sinai diffusion which may explain the very long time scales observed in several experiments [3,4]. Eventually, we present our work on domain walls in helimagnets. In magnetic force microscopy experiments performed by P. Schoenherr [5], we have identified three domain wall types. At small angles between the two domains, curvature walls appear. At intermediate angles, one can observe zig-zag disclination walls and at large angles, dislocation walls occur. We present analytical descriptions for curvature and dislocation walls, which we compare to micromagnetic simulation results obtained by J. Masell [5], and comment on the non-trivial topology of helimagnetic domain walls. [1] N. Ogawa, L. Köhler, M. Garst, S. Toyoda, S. Seki, and Y. Tokura, In preparation (2019). [2] P. Milde, E. Neuber, P. Ritzinger, L. Köhler, M. Garst, A. Bauer, C. Pfleiderer, H. Berger, and L. M. Eng, In preparation (2019). [3] A. Dussaux, P. Schoenherr, K. Koumpouras, J. Chico, K. Chang, L. Lorenzelli, N. Kanazawa, Y. Tokura, M. Garst, A. Bergman, C. L. Degen, and D. Meier, Nature Communications 7, 12430 (2016). [4] A. Bauer, A. Chacon, M. Wagner, M. Halder, R. Georgii, A. Rosch, C. Pfleiderer, and M. Garst, Physical Review B 95, 024429 (2017). [5] P. Schoenherr, J. Müller, L. Köhler, A. Rosch, N. Kanazawa, Y. Tokura, M. Garst, and D. Meier, Nature Physics 14, 465 (2018).:Introduction 1. Introduction to chiral magnets 1.1. Helimagnets 1.1.1. Magnetic phase diagram of chiral magnets 1.2. Skyrmions 1.2.1. Topology 1.2.2. Magnetic skyrmions 1.2.3. Skyrmion motion 1.2.4. Emergent electrodynamics 1.3. Model for chiral magnets 2. Spin waves in helimagnets 2.1. Linear spin wave theory for helimagnons 2.1.1. Fluctuations in the harmonic approximation 2.1.2. Spectrum at small momenta and fields 2.1.3. Frequency broadening from Gilbert damping 2.2. Magnon-focusing effects 2.3. Enhanced local dissipation 2.3.1. Global static susceptibility in the limit k, k' → 0 2.3.2. Local damping 2.4. Non-reciprocity 2.4.1. Non-reciprocity of the spectrum 2.4.2. Brillouin light scattering cross section 3. Orientation of magnetic order 3.1. Helix reorientation transition in MnSi 3.1.1. Effective Landau potential for the helix pitch 3.1.2. Experimental results 3.2. Helix reorientation in Cu2OSeO3 3.3. Skyrmion lattice orientation 4. Disclinations and dislocations 4.1. Liquid crystals 4.1.1. Types of liquid crystals 4.1.2. Energetics of liquid crystals 4.2. Disclinations 4.2.1. Elasticity theory for disclinations 4.3. Dislocations 4.3.1. Volterra process and Burgers vector 4.3.2. Elasticity theory for dislocations 4.3.3. Mermin-Ho relation in helimagnets 4.3.4. Topological skyrmion charge 5. Dislocation motion 5.1. Thiele approach for one helimagnetic dislocation 5.1.1. Motion in the presence of pinning 5.1.2. Corrections from elastic deformations 5.2. Dislocation diffusion 5.2.1. Sinai diffusion and toy model simulations 5.2.2. Susceptibility with Sinai diffusion 5.2.3. Dislocation string 6. Domain walls 6.1. Experimental and numerical methods 6.2. Domain wall types in helimagnets 6.3. Energetics of helimagnetic domain walls 6.3.1. Curvature wall 6.3.2. Dislocation wall 6.4. Topological domain wall structures 7. Discussion and outlook Appendix A. Details on helimagnons B. Formalism of linear-spin wave theory in helimagnets C. Deviations from the helix Bibliography List of Figures Index Danksagung

No description available.

No description available.