It was the purpose of this thesis to evaluate two-dimensional (2D) magneto-thermoelectric (MTE) phenomena in thinner regime. Mostly this work was motivated by the recent discovery of MTE properties in transition metal dichalcogenides (TMD). In general, TMD thin films have attracted much attention due to their very good electrical, optical, and electrochemical properties. However the total amount of studies of the MTE in TMD is rather small compared to the other properties, such as electric, opto-electric, and catalyst. Hence, in this thesis, we aimed to evaluate the MTE properties in TMD materials. Before we started to measure TMDs, we established a measurement platform and studied MTE properties in ferromagnetic CoFeB, and Weyl semimetal Co2MnGa.:1. Introduction a. Physical background i. Seebeck Effect ii. Anomalous Hall Effect and Anomalous Nernst Effect iii. Mott relation 2. Sample Preparation and evaluation a. Physical vapor deposition b. Mechanical Exfoliation c. Patterning Process 3. Data Evaluation 4. State of the art in Transition Metal Dichalcogenids a. Introduction b. TMD in use c. Magneto-thermoelectric properties in TMD 5. Magneto-thermoelectrical properties in CoFeB thin film a. Introduction b. Results and Discussion c. Conclusion 6. Anomalous Nernst and Anomalous Hall effect in Co2MnGa thin film a. Introduction b. Results and Discussion c. Summary 7. Anomalous Hall effect in exfoliated VS2 flake a. Introduction b. Experiment c. Results and Discussion d. Summary 8. Summary Acknowledgement and References

Magnetic materials are of great research interest because of their potential applications. Most Mn-based compounds exhibit magnetic ordering, being antiferromagnetic or ferromagnetic depending on their crystal structure. Many of these compounds have complex non-collinear magnetic structures that can give rise to exotic and robust phenomena. The scope of this thesis encompasses two independent projects on exploring single-crystalline Mn-based compounds with magnetic properties: (i) the study of the thickness-dependent magnetic textures in ferromagnetic Mn1.4PtSn by means of Focused Ion Beam (FIB) for sample shaping and Magnetic Force Microscopy (MFM) for imaging, and (ii) the experimental demonstration of an anomalous Hall effect in non-collinear antiferromagnetic Mn3Pt, revealed with the aid of uniaxial pressure tuned in-situ. The first chapter motivates the study of magnetic materials and introduces the theoretical framework on which they are understood. In particular, refers to the energy contributions of magnetic origin and gives an overview of the Hall effect and how it is used to probe magnetic properties, from ferromagnetism to non-collinear antiferromagnetism and non-coplanar spin textures (such as the so-called skyrmions). The second chapter is dedicated to the ferromagnetic compound Mn1.4PtSn. It starts by introducing concepts important in the context of magnetic domains. A variety of magnetic textures are discussed, in particular antiskyrmions which differ from regular skyrmions by their internal structure. A material-specific introduction is given, starting by its discovery as the first antiskyrmion-hosting compound (when in thin-plate shape) and including recent literature showing by means of neutron scattering how magnetic domains in bulk single crystals are best described as anisotropic fractals. This study complements our first observations in real-space MFM images of the magnetic texture in this material. The detailed study of the dependence of the magnetic domains as a function of sample thickness is presented and analyzed. The third and final chapter focuses on antiferromagnetic Mn3Pt. To motivate the experiment, the theoretical study that predicts the presence of an intrinsic zero-field anomalous contribution to the Hall effect for this material is introduced. Next, the experimental investigation of single crystals of Mn3Pt is presented, where a Hall effect dominated by the ordinary contribution in the temperature range from 10 to 300 K is found. Thereafter, the response of the Hall effect to uniaxial pressure tuned in-situ is explored. When the sample is compressed, a hysteresis is observed to open up. The magnitude of this anomalous Hall conductivity (when compressing the sample by ∼0.2 GPa) is estimated to be at least ∼ 10 Ω-1cm-1 at room temperature and ∼ 40 Ω-1cm-1 at 100 K, and it is demonstrated that the measured value originates in the antiferromagnetic structure, rather than in a stress-induced ferromagnetism.:1 Introduction 1 1.1 Overview of elemental properties . . . . . . . . . . . . . . . . 1 1.1.1 Notes on Mn . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Notes on Pt . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Notes on Sn . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Magnetic Interactions . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Zeeman interaction . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Magnetostatic energy . . . . . . . . . . . . . . . . . . . 5 1.2.3 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . 6 1.2.4 Magnetoelastic coupling . . . . . . . . . . . . . . . . . 7 1.2.5 Exchange interaction . . . . . . . . . . . . . . . . . . . 8 1.2.6 Antisymmetric exchange . . . . . . . . . . . . . . . . . 10 1.3 Antiferro-, ferri- and helimagnets . . . . . . . . . . . . . . . . 11 1.4 Hall effect in magnetism . . . . . . . . . . . . . . . . . . . . . 14 1.4.1 Geometrical phase in quantum mechanics . . . . . . . 14 In the context of the anomalous Hall effect . . . . . . 16 1.4.2 Complementary anomalous Hall theories . . . . . . . . 18 Skew scattering . . . . . . . . . . . . . . . . . . . . . . 18 Inelastic scattering . . . . . . . . . . . . . . . . . . . . 18 Side jump . . . . . . . . . . . . . . . . . . . . . . . . . 18 Spin chirality mechanism . . . . . . . . . . . . . . . . 19 I The uniaxial ferromagnet Mn1.4PtSn 21 2 Mn1.4PtSn 23 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Background physics . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1 Topology in magnetism . . . . . . . . . . . . . . . . . 27 2.2.2 Domain theory . . . . . . . . . . . . . . . . . . . . . . 29 Domain refinement . . . . . . . . . . . . . . . . . . . . 31 2.2.3 Literature overview . . . . . . . . . . . . . . . . . . . . 32 SANS studies on bulk Mn1.4PtSn . . . . . . . . . . . . 34 2.3 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 37 2.3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . 37 2.3.2 Lamellae fabrication . . . . . . . . . . . . . . . . . . . 37 2.3.3 Magnetic Force Microscopy . . . . . . . . . . . . . . . 38 History . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Operating principle . . . . . . . . . . . . . . . . . . . . 39 Specifications for our experiments . . . . . . . . . . . . 40 2.4 Results and discussions . . . . . . . . . . . . . . . . . . . . . . 40 2.4.1 Bulk samples characterization . . . . . . . . . . . . . . 40 Mn1.4Pt0.9Pd0.1Sn polycrystal . . . . . . . . . . . . . . 40 Mn1.4PtSn single crystal . . . . . . . . . . . . . . . . . 43 Mn1.4PtSn single crystal in applied field . . . . . . . . 45 Mn1.4PtSn single crystal below TSR . . . . . . . . . . . 46 2.4.2 Lamellae characterization . . . . . . . . . . . . . . . . 48 Thickness dependence . . . . . . . . . . . . . . . . . . 48 Temperature dependence . . . . . . . . . . . . . . . . 54 Magnetic field dependence . . . . . . . . . . . . . . . . 56 2.5 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . 63 II The non-collinear antiferromagnet Mn3Pt under strain 65 3 Mn3Pt 67 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2 Background physics . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2.1 Thin film study of Mn3Pt . . . . . . . . . . . . . . . . 71 3.2.2 Our contribution . . . . . . . . . . . . . . . . . . . . . 73 3.3 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Results and discussions . . . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Characterization of unstrained crystals . . . . . . . . . 75 3.4.2 Elastic response of Mn3Pt single crystals . . . . . . . . 79 Electrical transport response to strain . . . . . . . . . 81 3.4.3 Onset of AHE in single crystals under uniaxial pressure 84 Sample III4 . . . . . . . . . . . . . . . . . . . . . . . . 84 Sample IV1 . . . . . . . . . . . . . . . . . . . . . . . . 89 Sample IV2 . . . . . . . . . . . . . . . . . . . . . . . . 91 3.4.4 Temperature dependence of the AHE . . . . . . . . . . 94 3.4.5 Elastic limit of Mn3Pt . . . . . . . . . . . . . . . . . . 98 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A On Mn3Pt resistivity 101 B On Mn3Pt sample mounting 103

<p dir="ltr">Since the discovery of graphene in 2004, numerous other materials with intriguing electronic, optical, and magnetic properties have been found to be layered and exfoliatable down to atomic thickness. Owing to their weak interlayer coupling, mediated only by van der Waals forces, this new class of 2-dimensional materials, also known as van der Waals (vdW) materials, allows layer-by-layer stacking, overcoming some of the limitations of growth techniques. In particular, the growing inventory of vdW materials has expanded to include magnetic materials, further broadening the possibilities of novel devices based on stacked heterostructures. These magnetic heterostructures can find applications in spintronics and memory devices and may be combined with other vdW materials with optical properties for applications in optoelectronics. In this thesis, we assembled heterostructures via mechanical transfer or growth to modify the magnetism in these vdW materials. We used various optical and electrical techniques to probe the modified magnetism or its effects on the novel heterostructure. Thus, we observed the emergence of the magnetic proximity effect on the topological insulator BiSbTeSe₂ after dry transferring a thin flake of Cr₂Ge₂Te₆ on top, taking steps towards the observation of novel topological phases, such as the quantum Hall insulator. Additionally, we demonstrated an increased Curie temperature and magnetic anisotropy, effectively enhancing the magnetism, in thin flakes of Cr₂Ge₂Te₆ and Cr₂Si₂Te₆ after sputtering NiO or MgO. Finally, noting that the effect of modified magnetism in Cr2Ge2Te6 after sputtering NiO or MgO is induced due to wrinkle formation and strain, we further reproduce similar wrinkle formation on other 2D materials such as hBN, graphite, and 2D antiferromagnets (XPS₃, (X= Mn, Fe, Ni), CrSBr, RuCl₃). We used polarized Raman spectroscopy to characterize the induced biaxial strain in hBN and showed that such wrinkle formation can lead to moderately (up to 1.4% strain) spatially inhomogeneous and anisotropic strain profiles. These efforts demonstrate the versatility of tailoring the properties of these vdW materials.</p>

The Hall resistivity in ferromagnetic materials has an anomalous contribution proportional to the magnetization, which is defined as the anomalous Hall effect (AHE). Being a central topic in the study of ferromagnetic materials for many decades, the AHE was revived in recent years by generating many new understandings and phenomena, e.g. spin-Hall effect, topological insulators. The phase diagram of the AHE was shown recently to exhibit three distinct regions: a skew scattering region in the high conductivity regime, a scattering-independent normal metal regime, and an insulating regime. While the origin of the metallic regime scaling has been understood for many decades through the expected dependence of each contribution, the origin of the surprising scaling in the insulating regime was completely unexplained, leaving the primary challenge to the last step to understand fully the AHE. In this dissertation work we developed a theory to study the AHE in the disordered insulating regime, whose scaling relation is observed to be omega_xy^AH is proportional to omega_xx^(1.40∼1.75) in a large range of materials. This scaling is qualitatively different from the ones observed in metals. In the metallic regime where kFl > > 1, the linear response theory predicts that omega_xx is proportional to the quasi-particle lifetime tau, while omega_xy^AH scales as alpha*tau beta*tau^0, indicating that the upper limit of the scaling exponent is 1.0. Basing our theory on the phonon-assisted hopping mechanism and percolation theory, we derived a general formula for the anomalous Hall conductivity (AHC), and showed that the AHC scales with the longitudinal conductivity as omega_xy^AH ~ omega_xx^gamma with gamma predicted to be 1.33 <= gamma <= 1.76, quantitatively in agreement with the experimental observations. This scaling remains similar regardless of whether the hopping process is long range type (varible range hopping) or short range type (activation E3 hopping), or is influenced by interactions, i.e. Efros-Shklovskii (E-S) regime. Our theory completes the understanding of the AHE phase diagram in the insulating regime.

La loi de Moore est basée sur l’observation empirique qu’environ chaque deux années, le nombre de transistors dans des circuits denses intégrées double. Cette tendance s'est bien maintenue au cours des dernières décennies (années 1970 et suivantes). Cependant, la miniaturisation continue des transistors entraîne une augmentation significative des pertes d’énergie par le courant de fuite, ce qui augmente la consommation d'énergie de veille. Cette perte d’énergie est devenue un problème majeur dans la microélectronique pendant les dernières années, ce qui rend plus difficile le développement des nouvelles technologies. L’une des solutions est de placer des éléments mémoire non-volatile dans le puce, qui retiennent la configuration du transistor pendant la mise hors tension et permettent de le restaurer à la mise sous tension. Les Magnetic Random Access Memories (MRAM) sont considérées par l'ITRS comme un candidat crédible pour le remplacement potentiel de SRAM et de DRAM au-delà du nœud technologique de 20 nm. Bien que les exigences de base pour la lecture et l'écriture d'un élément de mémoire unique sont remplies, l'approche actuelle basée sur Spin Torque Transfer (STT) souffre d'un manque inné de la flexibilité. Le courant électrique entraine le retournement de l’aimantation de la couche ferromagnétique libre par le transfert du moment angulaire d’une couche ferromagnétique adjacent. Ainsi les éléments de mémoire basées sur STT ont deux terminaux dont les voies de courant pour « écriture » et « lecture » sont définies par la forme de «pillar». L’optimisation indépendant des paramètres d’écriture et de lecture reste, donc, très difficile. Au même temps, la densité de courant trop haute, nécessaire pour écrire, conduit à la vieillissement prémature du jonction tunnel. En conséquence, l’intégration MRAM dans la technologie du semi-conducteur reste, donc, difficile.Démonstrations récentes de reversement d’aimantation entrainées par l’injection d’un courant planaire dans des heterostructures métal lourd/ferromagnet ont attiré l’attention croissante sur les couples de spin basé sur le transfert du moment angulaire par l’effet Hall de spin et les effets d’interface. Contrairement à STT-MRAM, la SOT-MRAM a trois terminaux, dont les voies de courant pour « écriture » et « lecture » sont indépendantes. Cela permet d’améliorer les paramètres « écriture » et « lecture » de manière indépendante. Pour contrôler et optimiser les SOT il est nécessaire de comprendre très bien leur origine. Cela reste l’une des plus importantes questions dont on n’a pas une réponse définitive. Dans ce contexte, plusieurs études ont conclu sur un modèle basé seulement sur l’effet Hall de spin, en même temps que d’autres ont suggéré un modèle basé sur une contribution combiné de l’effet Hall de spin et l’effet d’interface.L’objectif de cette thèse est de réaliser une étude systématique sur les effets d’interface sur les SOT dans des heterostructures métal lourde/ferromagnet a base de Pt, avec aimantation planaire.Dans ce but, cette thèse explore trois voies différentes. Premièrement nous avons modifié le rapport entre les effets d’interface et les effets bulk en changeant l’épaisseur de la couche de Pt et en suivant l’évolution des SOT. En deuxième nous avons exploré des différents empilements métal lourde/ferromagnet afin d’étudier différentes interfaces. Finalement, nous avons changé les propriétés des interfaces soit par changer la structure cristalline soit par oxydation. La technique de mesure, la méthode d’analyse de données associé et les aspects théoriques nécessaires pour l’interprétation des données sont aussi détaillés dans ce manuscrit. / Moore’s law is based on empirical observation and states that every two years approximately, the number of transistors in dense integrated circuits doubles. This trend has held up well in the past several decades (1970s and onwards). However, the continuous miniaturisation of transistors brings about a significant increase in leakage current, which increases the stand-by power consumption. This energy loss has become a major problem in microelectronics during the last several years, making the development of new technologies more difficult. One of the solutions that can address this issue is to place non-volatile memory elements inside the chip, that retain the configuration of the transistor during power-off and allow to restore it at power-on. Magnetic Random Access Memories (MRAM) are considered by the ITRS as a credible candidate for the potential replacement for SRAM and DRAM beyond the 20 nm technological node. Though the basic requirements for reading and writing a single memory element are fulfilled, the present approach based on Spin Transfer Torque (STT) suffers from an innate lack of flexibility. The electric current drives the magnetization switching of a free ferromagnetic layer by transferring angular momentum from an adjacent ferromagnet. Therefore, STT-based memory elements are two terminal devices in which the “pillar” shape defines both the “read” and the “write” current paths. Independent optimisation of the reading and writing parameters is therefore difficult, while the large writing current density injected through the tunnel barrier causes its accelerated ageing, particularly for fast switching. Consequently, the integration of MRAM into semiconductor technology poses significant difficulties.Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal (HM)/ferromagnet (FM) heterostructures have drawn increasing attention to spin-torques based on orbital-to-spin momentum transfer induced by Spin Hall and interfacial effects (SOTs). Unlike STT-MRAM, the in-plane current injection geometry of SOT-MRAM allows for a three-terminal device which decouples the “read” and “write” mechanisms, allowing the independent tuning of reading and writing parameters. However, an essential first step in order to control and optimise the SOTs for any kind of application, is to better understand their origin. The origin of the SOTs remains one of the most important unanswered questions to date. While some experimental studies suggest a SHE (Spin Hall Effect)-only model for the SOTs, others point towards a combined contribution of the bulk (SHE) and interface (Rashba Effect and Interfacial SHE). At the same time, many studies start with a SHE only hypothesis and do not consider interfacial effects. Furthermore, there are not so many systematic studies on the effects of interfaces. This thesis tries to fill in this gap, by providing a systematic study on the effects of interfaces on the SOTs, in Pt-based NM/FM/HM multilayers with in-plane magnetic anisotropy. For this purpose, this thesis explores three different, but related avenues. First, we changed the interface/bulk effect ratio by modifying the Pt thickness and following the evolution of the SOTs. Second, we explored different HM/FM/NM combinations, in order to study different interfaces. And third, we changed the properties of the interfaces by changing the crystallographic structure of the interface and by oxidation. The measurement technique and associated data analysis method, as well as the theoretical considerations needed for the interpretation of the results are also detailed in this manuscript.

Orientadores: Iakov Veniaminovitch Kopelevitch, George Gershon Kleiman / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-11T13:15:15Z (GMT). No. of bitstreams: 1 MedinaPantoja_JuanCarlos_D.pdf: 3933664 bytes, checksum: 33f9dc730779c11f8c3d83b7ee0e56b4 (MD5) Previous issue date: 2007 / Resumo: Esta tese é o resultado da investigação das propriedades elétricas e magnéticas de dois semimetais: bismuto (Bi) policristalino romboédrico e grafite pirolítica altamente orientada (HOPG). Inicialmente nós discutimos o efeito Hall no limite quântico, que acontece em amostras de grafite HOPG com certo grau de desordem e onde a desordem é reduzida. Em particular, a resistência Hall R xy (B) exibe platôs em amostras HOPG menos desordenadas que possuem uma característica quase-bidimensional e uma forte anisotropia. Em amostras com maior desordem é observada a ocorrência de picos em lugar de platôs, evidenciando, experimentalmente, a predição de T. Ando. A condutância Hall reduzida Rxy (v) G0xy . fornece uma evidencia experimental para a coexistência de ambos os tipos de férmions de Dirac, normais e sem massa. Este resultado revela que o efeito Hall quântico inteiro e semi-inteiro tomam lugar simultaneamente na amostra HOPG. Nós encontramos as transições metal¿isolante (MIT) e isolante¿metal (IMT) induzidas por campo magnético em amostras de bismuto (Bi), quando o campo é aplicado paralelo ao eixo-c cristalográfico e observamos que estas transições têm enormes semelhanças com o MIT e IMT achados em HOPG e amostras monocristalinas Kish. As análises destes resultados experimentais sugerem que estas transições devem estar associadas à transição entre o estado metal de Bose (líquido não superfluido de pares de Cooper) e isolante excitônico. O aumento do momento diamagnético em bismuto e sua supressão próxima do campo crítico do MIT evidenciam a existência de correlações supercondutoras (metal de Bose) e excitônicas. Nós reportamos a observação experimental do efeito Hall anômalo Hall (AHE) em amostras de bismuto e de grafite HOPG. Os resultados indicam que este AHE pode ser compreendido, autoconsistentemente, através de modelos de pareamento excitônico induzido pelo campo magnético, possivelmente, devido ao surgimento de ferromagnetismo / Abstract: This thesis is the result of the investigation of the electric and magnetic properties of two semimetals: highly oriented pyrolitic graphite (HOPG) and polycrystalline bismuth (Bi), rhomboedral. Initially we discuss the Hall effect in the quantum limit that occurs in HOPG samples with a certain degree of disorder and with reduced disorder. In particular, the Hall resistance R xy (B) exhibits plateaus in less disordered HOPG samples, which present characteristic quasi-bidimensional and strongly anisotropic. In more disordered samples there occur peaks instead of plateaus, experimentally evidencing the T. Ando's prediction. The reduced Hall conductance G xy (v)/ G 0xy gives evidence experimental for the coexistence of both massless and massive Dirac fermions. This result reveals that the integer- and semi-integer QHE take place simultaneously in HOPG samples. We observed magnetic field induced metal-insulator (MIT) and insulator-metal (IMT) transitions, when this field is in the crystallographic c-axis direction, and observed that these transitions are very similar to the MIT and IMT observed in HOPG and monocrystalline samples (Kish). The analysis of the experimental results suggests that these transitions must be associated with the transition from the Bose metal state (a non superfluid liquid of Cooper pairs) to the excitonic insulator. The increase of the diamagnetic momentum in bismuth and its suppression in the vicinity of the critical field of the MIT evidences the existence of superconducting (Bose metal) and excitonic correlations. We report the experimental observation of the anomalous Hall effect (AHE) in HOPG samples. This AHE may be autoconsistently understood by means of magnetic field induced excitonic pairing models, possibly, due to the onset of ferromagnetism / Doutorado / Física da Matéria Condensada / Doutor em Ciências

In den letzten Jahren führte die Verbindung zwischen Topologie und kondensierter Materie zur Entdeckung vieler interessanter und exotischer elektronischer Effekte. Während sich die Forschung anfangs auf elektronische Systeme mit einer Bandlücke wie den topologischen Isolator konzentrierte, erhalten in letzter Zeit topologische Halbmetalle viel Aufmerksamkeit. Das bekannteste Beispiel sind Weyl-Halbmetalle, die an beliebigen Punkten in der Brillouin-Zone lineare Kreuzungen von nicht entarteten Bändern aufweist. An diese Punkte ist eine spezielle Quantenzahl namens Chiralität gebunden, die die Existenz von Weyl-Punktpaaren erzwingt. Diese Paare sind topologisch geschützt und wirken als Quellen und Senken der Berry-Krümmung, einem topologischen Feld im reziproken Raum. Diese Berry-Krümmung steht in direktem Zusammenhang mit dem anomalen Hall-Effekt, der die Entstehung einer Querspannung aus einem Längsstrom in einem magnetischen Material beschreibt. Analog existiert auch der anomale Nernst-Effekt, bei dem der longitudinale Strom durch einen thermischen Gradienten ersetzt wird. Dieser Effekt ermöglicht die Umwandlung von Wärme in elektrische Energie und ist zudem stark an die Berry-Krümmung gebunden. In dieser Arbeit werden die anomalen Transporteffekte zunächst in fundamentalen Modellsystemen untersucht. Hier wird eine Kombination aus analytischen und numerischen Methoden verwendet, um Quantisierungen sowohl des Hall- und Nernst- als auch des thermischen Hall-Effekts in zweidimensionalen Systemen mit und ohne externen Magnetfeldern zu zeigen. Eine Erweiterung in drei Dimensionen zeigt eine Quasi-Quantisierung, bei der die Leitfähigkeiten Werte der jeweiligen zweidimensionalen Quanten skaliert durch charakteristische Wellenvektoren annehmen. Im nächsten Schritt werden verschiedene Mechanismen zur Erzeugung starker Berry-Krümmung und damit großer anomaler Hall- und Nernst-Effekte sowohl in Modellsystemen als auch in realen Materialien untersucht. Dies ermöglicht die Identifizierung und Isolierung vielversprechender Effekte in den einfachen Modellen, in denen wichtige Merkmale untersucht werden können. Die Ergebnisse können dann auf die realen Materialien übertragen werden, wo die jeweiligen Effekte erkennbar sind. Hier werden sowohl Weyl-Punkte als auch Knotenlinien in Kombination mit Magnetismus als vielversprechende Eigenschaften identifiziert und Materialrealisierungen in der Klasse der Heusler-Verbindungen vorgeschlagen. Diese Verbindungen sind eine sehr vielseitige Materialklasse, in der unter anderem auch magnetische topologische Metalle zu finden sind. Um ein tieferes Verständnis der anomalen Transporteffekte zu erhalten sowie Faustregeln für Hochleistungsverbindungen abzuleiten, wurde eine High-Throughput-Rechnung von magnetisch-kubischen Voll-Heusler-Verbindungen durchgeführt. Diese Berechnung zeigt die Bedeutung von Spiegelebenen in magnetischen Materialien für große anomale Hall- und Nernst-Effekte und zeigt, dass einige der Heusler-Verbindungen die höchsten bisher berichteten Literaturwerte bei diesen Effekten übertreffen. Auch andere interessante Effekte im Zusammenhang mit Weyl-Punkten werden untersucht. Beim bekannten Weyl-Halbmetall NbP weisen die Weyl-Punkte aufgrund der hohen Symmetrie des Kristalls eine hohe Entartung auf. Die Anwendung von einachsigem Zug reduziert jedoch die Symmetrien und hebt damit die Entartungen auf. Eine theoretische Untersuchung zeigt, dass die Weyl-Punkte bei einachsigem Zug energetisch verschoben werden und, was noch wichtiger ist, dass sie bei realistischen Werten das Fermi-Niveau durchschreiten. Dies macht NbP zu einer vielversprechenden Plattform, um die Weyl-Physik weiter zu untersuchen. Die theoretischen Ergebnisse werden mit experimentellen Messungen von Shubnikov-de-Haas-Oszillationen unter einachsigem Zug kombiniert und es wird eine gute Übereinstimmung mit den theoretischen Ergebnissen gefunden. Als erster Schritt in Richtung neuer Berechnungsmethoden wird die Idee eines Weyl-Halbmetall-basierten Chiralitätsfilters für Elektronen untersucht. An der Grenzfläche zweier Weyl-Halbmetalle kann in Abhängigkeit von den genauen Weyl-Punktparametern nur eine Chiralität übertragen werden. Hier wird ein effektives geometrisches Modell erstellt und zur Untersuchung realer Materialgrenzflächen eingesetzt. Während im Allgemeinen eine Filterwirkung möglich erscheint, zeigten die untersuchten Materialien keine geeignete Kombination. Hier können weitere Studien mit Fokus auf magnetische Weyl-Halbmetalle oder Multifold-Fermion-Materialien durchgeführt werden.:List of publications Preface 1. Theoretical background 1.1. Berry curvature and Weyl semimetals 1.1.1. From the adiabatic evolution to the Berry phase 1.1.2. From the Berry phase to the Berry curvature 1.1.3. Topological phases of condensed matter 1.1.4. Weyl semimetals 1.1.5. Dirac semimetals 1.1.6. Nodal line semimetals 1.2. Density-functional theory 1.2.1. Born-Oppenheimer approximation 1.2.2. Hohenberg-Kohn theorems 1.2.3. Kohn-Sham formalism 1.2.4. Exchange-correlation functional 1.2.5. Pseudopotentials 1.2.6. Basis functions 1.2.7. VASP 1.3. Tight-binding Hamiltonian from Wannier functions 1.3.1. Wannier functions 1.3.2. Constructing Wannier functions from DFT 1.3.3. Generating a Wannier tight-binding Hamiltonian 1.3.4. Necessity of the tight-binding Hamiltonian 1.4. Linear response theory 1.4.1. General introduction to linear response 1.4.2. Anomalous Hall effect 1.4.3. Anomalous Nernst effect 1.4.4. Anomalous thermal Hall effect 1.4.5. Common features of anomalous transport effects 1.4.6. Symmetry considerations for Berry curvature related transport effects 1.4.7. Magneto-optic Kerr effect 1.4.8. About the efficiency of the calculations 2. (Quasi-)Quantization in the Hall, thermal Hall, and Nernst effects 2.1. Quantization with an external magnetic field 2.1.1. Two-dimensional case 2.1.2. Three-dimensional case 2.2. Quantization without an external field 2.2.1. Two-dimensional case 2.2.2. Three-dimensional case . 2.3. A remark on the spin Hall effect 2.4. A remark on the quasi-quantization of the three-dimensional conductivities 2.5. Conclusions 3. Understanding anomalous transport 3.1. Anomalous transport without a net magnetic moment 3.1.1. Toy model 3.1.2. Ti2MnAl and related compounds 3.2. Large Berry curvature enhancement from nodal line gapping 3.2.1. Toy model 3.2.2. Fe2MnP and related compounds 3.2.3. Co2MnGa 3.3. Topological features away from the Fermi level and the anomalous Nernst effect 3.3.1. Toy model . 3.3.2. Co2FeGe and Co2FeSn 3.4. Conclusions 4. Heusler database calculation 4.1. Workflow 4.2. Importance of mirror planes 4.3. The right valence electron count 4.4. Correlation between anomalous Hall and Nernst effects 4.5. Selected special compounds 4.6. Conclusions 5. NbP under uniaxial strain 5.1. NbP and its symmetries 5.2. The influence of strain on the electronic structure 5.2.1. Shifting of the Weyl points 5.2.2. Splitting of the Fermi surfaces 5.3. Comparison with experimental results 5.4. Conclusions 6. A tunable chirality filter 6.1. Concept 6.2. Geometrical simplification and expansion for more Weyl points 6.3. Material selection 6.3.1. Workflow 6.3.2. Results for NbP and TaAs 6.3.3. Results for Ag2Se and Ag2S 6.4. Conclusions and perspective . Summary and outlook A. Numerical tricks A.1. Hamiltonian setup at several k points at once A.2. Precalculating prefactors B. Derivation of the conductivity (quasi-)quanta B.1. Two dimensions B.1.1. General formula and necessary approximations B.1.2. Useful integrals B.1.4. Quantized thermal Hall effect B.1.5. Quantized Nernst effect B.1.6. Flat bands and the Nernst effect B.2. Three dimensions B.2.1. General formula B.2.2. Three-dimensional electron gas B.2.3. Three-dimensional Weyl semimetal C. Heusler database tables D. Details on the NbP strain calculations E. Details on the geometrical matching procedure References List of abbreviations List of Figures List of Tables Acknowledgements Eigenständigkeitserklärung / In recent years, the connection between topology and condensed matter resulted in the discovery of many interesting and exotic electronic effects. While in the beginning, the research was focused on gapped electronic systems like the topological insulator, more recently, topological semimetals are getting a lot of attention. The most well-known example is the Weyl semimetal, which hosts linear crossings of non-degenerate bands at arbitrary points in the Brillouin zone. Tied to these points there is a special quantum number called chirality, which enforces the existence of Weyl point pairs. These pairs are topologically protected and act as sources and sinks of the Berry curvature, a topological field in reciprocal space. This Berry curvature is directly connected to the anomalous Hall effect, which describes the emergence of a transverse voltage from a longitudinal current in a magnetic material. Analogously, there also exists the anomalous Nernst effect, where the longitudinal current is replaced by a thermal gradient. This effect allows for the conversion of heat into electrical energy and is also strongly tied to the Berry curvature. In this work, the anomalous transport effects are at first studied in fundamental model systems. Here, a combination of analytical and numerical methods is used to reveal quantizations in both the Hall, the Nernst, and the thermal Hall effects in two-dimensional systems with and without external magnetic fields. An expansion into three dimensions shows a quasi-quantization, where the conductivities take values of the respective two-dimensional quanta scaled by characteristic wavevectors. In the next step, several mechanisms for the generation of strong Berry curvature and thus large anomalous Hall and Nernst effects are studied in both model systems and real materials. This allows for the identification and isolation of promising effects in the simple models, where important features can be studied. The results can then be applied to the real materials, where the respective effects can be recognized. Here, both Weyl points and nodal lines in combination with magnetism are identified as promising features and material realizations are proposed in the class of Heusler compounds. These compounds are a very versatile class of materials, where among others also magnetic topological metals can be found. To get a deeper understanding of the anomalous transport effects as well as to derive guidelines for high-performance compounds, a high-throughput calculation of magnetic cubic full Heusler compounds was carried out. This calculation reveals the importance of mirror planes in magnetic materials for large anomalous Hall and Nernst effects and shows that some of the Heusler compounds outperform the highest so-far reported literature values in these effects. Also other interesting effects related to Weyl points are investigated. In the well-known Weyl semimetal NbP, the Weyl points have a high degeneracy due to the high symmetry of the crystal. However, the application of uniaxial strain reduces the symmetries and therefore lifts the degeneracies. A theoretical investigation shows, that the Weyl points are moved in energy under uniaxial strain and, more importantly, that at reasonable strain values they cross the Fermi level. This renders NbP a promising platform to further study Weyl physics. The theoretical results are combined with experimental measurements of Shubnikov-de Haas oscillations under uniaxial strain and a good agreement with the theoretical results is found. As a first step in the direction of new ways of computation, an idea of a Weyl semimetal based chirality filter for electrons is investigated. At the interface of two Weyl semimetals, depending on the exact Weyl point parameters, it is possible to transmit only one chirality. Here, an effective geometrical model is established and employed for the investigation of real material interfaces. While in general, a filtering effect seems possible, the investigated materials did not show any suitable combination. Here, further studies can be made with the focus on either magnetic Weyl semimetals of multifold-fermion materials.:List of publications Preface 1. Theoretical background 1.1. Berry curvature and Weyl semimetals 1.1.1. From the adiabatic evolution to the Berry phase 1.1.2. From the Berry phase to the Berry curvature 1.1.3. Topological phases of condensed matter 1.1.4. Weyl semimetals 1.1.5. Dirac semimetals 1.1.6. Nodal line semimetals 1.2. Density-functional theory 1.2.1. Born-Oppenheimer approximation 1.2.2. Hohenberg-Kohn theorems 1.2.3. Kohn-Sham formalism 1.2.4. Exchange-correlation functional 1.2.5. Pseudopotentials 1.2.6. Basis functions 1.2.7. VASP 1.3. Tight-binding Hamiltonian from Wannier functions 1.3.1. Wannier functions 1.3.2. Constructing Wannier functions from DFT 1.3.3. Generating a Wannier tight-binding Hamiltonian 1.3.4. Necessity of the tight-binding Hamiltonian 1.4. Linear response theory 1.4.1. General introduction to linear response 1.4.2. Anomalous Hall effect 1.4.3. Anomalous Nernst effect 1.4.4. Anomalous thermal Hall effect 1.4.5. Common features of anomalous transport effects 1.4.6. Symmetry considerations for Berry curvature related transport effects 1.4.7. Magneto-optic Kerr effect 1.4.8. About the efficiency of the calculations 2. (Quasi-)Quantization in the Hall, thermal Hall, and Nernst effects 2.1. Quantization with an external magnetic field 2.1.1. Two-dimensional case 2.1.2. Three-dimensional case 2.2. Quantization without an external field 2.2.1. Two-dimensional case 2.2.2. Three-dimensional case . 2.3. A remark on the spin Hall effect 2.4. A remark on the quasi-quantization of the three-dimensional conductivities 2.5. Conclusions 3. Understanding anomalous transport 3.1. Anomalous transport without a net magnetic moment 3.1.1. Toy model 3.1.2. Ti2MnAl and related compounds 3.2. Large Berry curvature enhancement from nodal line gapping 3.2.1. Toy model 3.2.2. Fe2MnP and related compounds 3.2.3. Co2MnGa 3.3. Topological features away from the Fermi level and the anomalous Nernst effect 3.3.1. Toy model . 3.3.2. Co2FeGe and Co2FeSn 3.4. Conclusions 4. Heusler database calculation 4.1. Workflow 4.2. Importance of mirror planes 4.3. The right valence electron count 4.4. Correlation between anomalous Hall and Nernst effects 4.5. Selected special compounds 4.6. Conclusions 5. NbP under uniaxial strain 5.1. NbP and its symmetries 5.2. The influence of strain on the electronic structure 5.2.1. Shifting of the Weyl points 5.2.2. Splitting of the Fermi surfaces 5.3. Comparison with experimental results 5.4. Conclusions 6. A tunable chirality filter 6.1. Concept 6.2. Geometrical simplification and expansion for more Weyl points 6.3. Material selection 6.3.1. Workflow 6.3.2. Results for NbP and TaAs 6.3.3. Results for Ag2Se and Ag2S 6.4. Conclusions and perspective . Summary and outlook A. Numerical tricks A.1. Hamiltonian setup at several k points at once A.2. Precalculating prefactors B. Derivation of the conductivity (quasi-)quanta B.1. Two dimensions B.1.1. General formula and necessary approximations B.1.2. Useful integrals B.1.4. Quantized thermal Hall effect B.1.5. Quantized Nernst effect B.1.6. Flat bands and the Nernst effect B.2. Three dimensions B.2.1. General formula B.2.2. Three-dimensional electron gas B.2.3. Three-dimensional Weyl semimetal C. Heusler database tables D. Details on the NbP strain calculations E. Details on the geometrical matching procedure References List of abbreviations List of Figures List of Tables Acknowledgements Eigenständigkeitserklärung

The work presented in this thesis encompasses the design, development, realization and testing of novel magnetoelectric thin film elements that do not rely on ferromagnets, but are based entirely on magnetoelectric antiferromagnets such as Cr2O3. Thin film spintronic elements, and in particular magnetoelectric transducers, are crucial building blocks of high efficiency data processing schemes that could complement conventional electronic data processing in the future. Recent developments in magnetoelectrics have revealed, that exchange biased systems are ill-suited to electric field induced switching of magnetization due to the strong coupling of their ferromagnetic layer to magnetic fields. Therefore, ferromagnet-free magnetoelectric elements are proposed here in an effort to mitigate the practical problems associated with existing exchange biased magnetoelectric elements. This goal is achieved by establishing an all-electric read-out method for the antiferromagnetic order parameter of thin films, which allows to omit the ferromagnet from conventional exchange biased magnetoelectric elements. The resulting ferromagnet-free magnetoelectric elements show greatly reduced writing thresholds, enabled operation at room temperature and do not require a pulsed magnetic field, all of which is in contrast to state-of-the-art exchange biased magnetoelectric systems. The novel all-electric read-out method of the magnetic field-invariant magnetization of antiferromagnets, so-called spinning-current anomalous Hall magnetometry, can be widely employed in other areas of thin film magnetism. Its high precision and its sensitivity to previously invisible phenomena make it a promising tool for various aspects of thin solid films. Based on this technique, a deep understanding could be generated as to what physical mechanisms drive the antiferromagnetic ordering in thin films of magnetoelectric antiferromagnets. As spinning-current anomalous Hall magnetometry is an integral probe of the magnetic properties in thin films, it offers no intrinsic scale sensitivity. In order to harness its great precision for scale related information, a statistical framework was developed, which links macroscopic measurements with microscopic properties such as the antiferromagnetic domain size.

Cette thèse est consacrée à la description de la physique à une particule ainsi qu'à celle de fluides quantiques bosoniques dans des systèmes topologiques. Les deux premiers chapitres sont introductifs. Dans le premier, nous introduisons des éléments de théorie des bandes et les quantités géométriques et topologiques associées : tenseur métrique quantique, courbure de Berry, nombre de Chern. Nous discutons différents modèles et réalisations expérimentales donnant lieu à des effets topologiques. Dans le second chapitre, nous introduisons les condensats de Bose-Einstein ainsi que les excitons-polaritons de cavité.La première partie des résultats originaux discute des phénomènes topologiques à une particule dans des réseaux en nid d'abeilles. Cela permet de comparer deux modèles théoriques qui mènent à l'effet Hall quantique anormal pour les électrons et les photons dû à la présence d'un couplage spin-orbite et d'un champ Zeeman. Nous étudions aussi l'effet Hall quantique de vallée photonique à l'interface entre deux réseaux de cavités avec potentiels alternés opposés.Dans une seconde partie, nous discutons de nouveaux effets qui émergent due à la présence d'un fluide quantique interagissant décrit par l’équation de Gross-Pitaevskii dans ces systèmes. Premièrement, il est montré que les interactions spin anisotropes donnent lieu à des transitions topologiques gouvernées par la densité de particules pour les excitations élémentaires d’un condensat spineur d’exciton-polaritons.Ensuite, nous montrons que les tourbillons quantifiés d'un condensat scalaire dans un système avec effet Hall quantique de vallée, manifestent une propagation chirale le long de l'interface contrairement aux paquets d'ondes linéaires. La direction de propagation de ces derniers est donnée par leur sens de rotation donnant lieu à un transport de pseudospin de vallée protégé topologiquement, analogue à l’effet Hall quantique de spin.Enfin, revenant aux effets géométriques linéaires, nous nous sommes concentrés sur l’effet Hall anormal. Dans ce contexte, nous présentons une correction non-adiabatique aux équations semi-classiques décrivant le mouvement d’un paquet d’ondes qui s’exprime en termes du tenseur géométrique quantique. Nous proposons un protocole expérimental pour mesurer cette quantité dans des systèmes photonique radiatifs. / This thesis is dedicated to the description of both single-particle and bosonic quantum fluid Physics in topological systems. After introductory chapters on these subjects, I first discuss single-particle topological phenomena in honeycomb lattices. This allows to compare two theoretical models leading to quantum anomalous Hall effect for electrons and photons and to discuss the photonic quantum valley Hall effect at the interface between opposite staggered cavity lattices.In a second part, I present some phenomena which emerge due to the interplay of the linear topological effects with the presence of interacting bosonic quantum fluid described by mean-field Gross-Pitaevskii equation. First, I show that the spin-anisotropic interactions lead to density-driven topological transitions for elementary excitations of a condensate loaded in the polariton quantum anomalous Hall model (thermal equilibrium and out-of-equilibrium quasi-resonant excitation configurations). Then, I show that the vortex excitations of a scalar condensate in a quantum valley Hall system, contrary to linear wavepackets, can exhibit a robust chiral propagation along the interface, with direction given by their winding in real space, leading to an analog of quantum spin Hall effect for these non-linear excitations. Finally, coming back to linear geometrical effects, I will focus on the anomalous Hall effect exhibited by an accelerated wavepacket in a two-band system. In this context, I present a non-adiabatic correction to the known semiclassical equations of motion which can be expressed in terms of the quantum geometric tensor elements. We also propose a protocol to directly measure the tensor components in radiative photonic systems.

The work presented in this thesis encompasses the design, development, realization and testing of novel magnetoelectric thin film elements that do not rely on ferromagnets, but are based entirely on magnetoelectric antiferromagnets such as Cr2O3. Thin film spintronic elements, and in particular magnetoelectric transducers, are crucial building blocks of high efficiency data processing schemes that could complement conventional electronic data processing in the future. Recent developments in magnetoelectrics have revealed, that exchange biased systems are ill-suited to electric field induced switching of magnetization due to the strong coupling of their ferromagnetic layer to magnetic fields. Therefore, ferromagnet-free magnetoelectric elements are proposed here in an effort to mitigate the practical problems associated with existing exchange biased magnetoelectric elements. This goal is achieved by establishing an all-electric read-out method for the antiferromagnetic order parameter of thin films, which allows to omit the ferromagnet from conventional exchange biased magnetoelectric elements. The resulting ferromagnet-free magnetoelectric elements show greatly reduced writing thresholds, enabled operation at room temperature and do not require a pulsed magnetic field, all of which is in contrast to state-of-the-art exchange biased magnetoelectric systems. The novel all-electric read-out method of the magnetic field-invariant magnetization of antiferromagnets, so-called spinning-current anomalous Hall magnetometry, can be widely employed in other areas of thin film magnetism. Its high precision and its sensitivity to previously invisible phenomena make it a promising tool for various aspects of thin solid films. Based on this technique, a deep understanding could be generated as to what physical mechanisms drive the antiferromagnetic ordering in thin films of magnetoelectric antiferromagnets. As spinning-current anomalous Hall magnetometry is an integral probe of the magnetic properties in thin films, it offers no intrinsic scale sensitivity. In order to harness its great precision for scale related information, a statistical framework was developed, which links macroscopic measurements with microscopic properties such as the antiferromagnetic domain size.:TABLE OF CONTENTS Abbreviations 9 1 Introduction 11 1.1 Motivation 11 1.2 Objectives 12 1.3 Organization of the thesis 13 2 Background 15 2.1 History of magnetoelectric coupling 15 2.2 Long range magnetic ordering 16 2.2.1 Magnetic order parameter and field susceptibility 17 2.2.2 Magnetic proximity effect 19 2.2.3 Exchange bias 20 2.3 Phenomenology of magnetoelectric coupling 21 2.3.1 The linear magnetoelectric effect 21 2.3.2 Magnetoelectric pressure on the antiferromagnetic order parameter 22 2.3.3 Switching the antiferromagnetic order parameter 23 2.4 Realized magnetoelectric thin film elements 24 2.4.1 BiFeO3/CoFe system 24 2.4.2 Cr2O3/Co/Pt system 25 3 Experimental methods 27 3.1 Development of ferromagnet free magnetoelectric elements 28 3.1.1 The substrate 29 3.1.2 The Cr2O3 bulk and top surface 31 3.1.3 The V2O3 or Pt bottom electrodes 33 3.1.4 Epitaxial relationships 34 3.1.5 The Cr2O3 bottom interface 39 3.1.6 Twinning of Cr2O3 39 3.1.7 Hall crosses and patterning processes 43 3.2 Magnetotransport measurements 44 3.2.1 Hall effects 45 3.2.2 Anomalous Hall effect 46 3.2.3 Magnetoelectric writing 47 3.2.4 All electric read out 49 3.3 The experimental setup 50 3.3.1 Temperature control 50 3.3.2 Magnetic field control 51 4 Spinning-current anomalous Hall magnetometry 53 4.1 Characteristics of the technique 53 4.1.1 Operational principle 53 4.1.2 Advantages 55 4.1.3 Magnetic hysteresis loops and field-invariant magnetization 55 4.1.4 Measurement of field-invariant magnetization 56 4.1.5 Limitations 58 4.2 Application of SCAHM to Cr2O3(0001) thin films 59 4.2.1 Criticality and distribution of the antiferromagnetic phase transition 61 4.2.2 Evaluation of the magnetic proximity effect 64 4.3 SCAHM with thin metallic antiferromagnetic IrMn films 65 4.3.1 [Pt/Co]4/IrMn exchange bias system 65 4.3.2 Isolated antiferromagnetic IrMn thin films 67 5 Magnetoelectric performance 69 5.1 Magnetoelectric field cooling 69 5.2 The gate bias voltage 71 5.3 Isothermal binary magnetoelectric writing in Cr2O3 72 6 Order parameter selection in magnetoelectric antiferromagnets 77 6.1 Uncompensated magnetic moment 77 6.2 Extrinsic causes for broken sublattice equivalence 81 6.3 The V2O3 gate electrode 83 7 Measurement of microscopic properties with an integral probe 87 7.1 Interentity magnetic exchange coupling 87 7.2 Ensemble formalism for the entity size determination 90 7.3 Estimation of the entity sizes 94 7.4 Microscopic confirmation of the ensemble model 97 8 Summary and Outlook 101 8.1 Goal-related achievements 101 8.1.1 All-electric read-out of the AF order parameter 101 8.1.2 Electric field induced writing of the AF order parameter 102 8.2 Further achievements 103 8.2.1 Foreseen impact of SCAHM on thin film magnetism 103 8.2.2 Practical optimization routes of magnetoelectric Cr2O3 systems 104 8.2.3 Theoretical work 105 8.3 Future directions 105 8.3.1 Development of Cr2O3-based magnetoelectric systems 105 8.3.2 Applications of SCAHM 106 References 107 Erklärung 113 Acknowledgements 115 Curriculum Vitae 117 Scientific publications, contributions, patents 119