Random number generation can be based on physical events with probabilistic character, or on algorithms that use complex or one-way functions, alternatively on both of these approaches. A magnetic vortex is a basic state of magnetization that forms in magnetic micro- and nanostructures of an appropriate shape, dimensions and material. Quantities of the magnetic vortex form randomly if ambient conditions are chosen eligibly. A concept of a true random number generator using a random switching of states of the magnetic vortex is presented in this thesis. This concept is realized and random numbers were experimentally generated and numbers were statistically analysed.

Nanoelectronics and spintronics are concerned with writing, transporting, and reading information stored in electronic charge and spin degrees of freedom at the nanoscale. Past few years have shown that two spintronics effects discovered in the 19th century, namely anisotropic magnetoresistance and anomalous Hall effect, can be used also for sensing antiferromagnetism which opened the field of antiferromagnetic spintronics. The more than a century of controversial studies of these effects have shown their relativistic spin-orbit coupling and spin-polarisation symmetry breaking origin. However, a complete understanding of these effects and a fully predictive theory capable of identifying novel suitable antiferromagnetic materials are still lacking. Here, by extending modern symmetry and topology concepts in condensed matter physics, we have further developed the theory of anisotropic magnetoresistance and spontaneous Hall effect. Our approach is based on magnetic symmetry and topology analysis of antiferromagnetic energy bands, Bloch spectral functions, and Berry curvatures calculated from the state-of-the- art first-principle theory. This guided us to the prediction of two novel, previously unanticipated effects: relativistic metal-insulator transition from antiferromagnetic Dirac fermions, and crystal Hall...

Perovskit-Oxide weisen eine große Bandbreite an physikalischen Eigenschaften bei gleichzeitig hoher struktureller Qualität in kleinsten Dimensionen auf. Die dramatischen Veränderungen ihrer Eigenschaften bei nur geringer Variation der stöchiometrischen Zusammensetzung sind sowohl für ein tieferes physikalisches Verständnis als auch für mögliche Anwendungsperspektiven interessant. In der vorliegenden Arbeit wurde der Einfluss von Ladungsübertragung an Grenz- flächen, Anisotropiemodifikation durch Verspannung und Oberflächeneffekte sowie magnetische und strukturelle Kopplung untersucht. Aufgrund ihrer kontrastierenden Eigenschaften im Hinblick auf Ferromagnetismus und Ladungstransport wurden dotiertes Lanthanmanganat und Strontiumruthenat (SRO) für die Untersuchungen ausgewählt. Durch ihre hervorragenden Wachstumseigenschaften mit fehlerlosen Grenzflächen auf atomarer Ebene erlauben sie als Modellsystem die Untersuchung elektronischer, magnetischer und struktureller Kopplung in Perovskit-Oxiden – mit folgenden Ergebnissen: Durch Ladungsübertragung an Grenzflächen wird Ferromagnetismus in Schichten von weniger als vier Einheitszellen in Manganaten stabilisiert. Die mikroskopische Struktur der Systeme kann aus der Analyse der durch die Anisotropie bedingten Symmetrie der winkelabhängigen Magnetotransport- messungen erschlossen werden. Bei abnehmender Schichtdicke verringert sich die intrinsische orthorhombische Symmetrie in SRO zugunsten einer tetragonalen aufgrund der Symmetriebrechung an der Grenzfläche. Die Untersuchungen des anormalen Hall Effekts unterstreichen seine Tensor-Natur und zeigen eine Abhängigkeit des Vorzeichens sowohl von der magnetischen Anisotropie als auch der mikroskopischen Schichtqualität. Die Beobachtung einer Anisotropie oberhalb der Übergangstemperatur von SRO in Manganatschichten einer Dicke von zwei bis sechs Einheitszellen weist auf eine strukturelle Kopplung über die Sauerstoffoktaederrotationen hin. Die komplexe Wechselwirkung zwischen antiferromagnetischer Kopplung und schichtdickenabhängiger Anisotropie und dem magnetischen Moment werden in einem 2-Schichten-Modell beschrieben. Übergitter mit Einzelschichten von weniger als drei Einheitszellen lassen sich nicht mehr mit individuellen Einzelschichten beschreiben sondern stellen einen künstlichen Ferrimagneten dar. / Perovskite oxides show a range of physical properties in combination with high structural quality in small dimensions. The dramatic change of their properties upon small variation in stoichiometry or external influences as pressure/strain are interesting for both a deeper understanding of fundamental condensed matter physics as well as electronic applications. In the present thesis the influence of charge transfer at interfaces, modification of the magnetic anisotropy by strain and surface effects, as well as magnetic and structural coupling was studied. In virtue of their contrasting ferromagnetic and transport properties, charge doped lanthanum manganite and strontium ruthenate (SRO) were chosen for this study. Their superior growth properties allowing atomically flat defect free interfaces make them a model system to study electronic magnetic and structural coupling phenomena in perovskite oxides − with the following findings: Charge transfer at interfaces stabilizes ferromagnetism in single layers of manganites down to one unit cell thickness similar to finite size scaling in ordinary transition metal ferromagnets. The microscopic structure of crystalline layers can be obtained from an analysis of the symmetries present in angle dependent magnetotransport measurements, which are determined by the anisotropy. Upon thickness reduction, the intrinsic orthorhombic symmetry in SRO is reduced in favour of a tetragonal one owing to the symmetry breaking at the interface. Studies on the anomalous Hall effect underline its tensorial nature and show a sign dependence on both magnetic anisotropy and microstructural quality. The observation of an in-plane anisotropy in manganite layers in the thickness range of two to six unit cells indicates a structural coupling via the oxygen octahedra. The complex interplay of antiferromagnetic coupling and layer thickness dependent anisotropy and magnetic moment are described in a bilayer model. Superlattices with individual layers of less than three unit cells cannot be described by the individual layer properties but represent an artificial ferrimagnet.

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This work presents the successful development of micro-origami sensorics by 3D self-assembling and reconfiguring in space integrated thin-film magnetic sensors, which rely on anisotropic (AMR) and giant magnetoresistance (GMR). Stimuli responsive polymeric materials able to reshape into mesoscale 3D “Swiss-roll” and polygonal architectures accomplish a strain driven parallel spatial realignment of magnetic sensors from the in-plane state. High performance 3D magnetic vector angular encoders demonstrates the successful realization of complex sensor configurations. The proposed concepts rely on parallel wafer scale processes, which allow for a monolithic fabrication of 3D sensor arrays and pave the way towards active sensory matrix circuits. As a proof of this concept, magneto-resistive Wheatstone bridge sensors are developed and integrated in the self-assembling platform at predefined rigid regions and integrated with an active matrix backplane circuit. This circuit, based on a-IGZO TFT technology, is specially designed for the operation with the Wheatstone bridge differential sensors and optimized to be compatible with the micro-origami self-folding technology. Such an active sensory matrix system with integrated 3D self-assembled pixels is called Integrated Micro-Origami Sensors or in short IMOS. IMOS is capable for static and dynamic mapping of magnetic fields enabling spatiotemporal mapping of artificial magnetic hair arrays embedded in an elastic skin layer. The presented results offer a fresh strategy for large area integration of microscale 3D electronic devices with various vector functionalities in active matrix circuits, which are of great interest in novel robotics, bioelectronics and diagnostic systems.

Magnetic nanorings are the object of increasing scientific interest because they possess the vortex (stray field free) state which ensures lower magnetostatic interactions between adjacent ring elements in high packing density memory devices. In addition, they have other potential applications such as single magnetic nanoparticle sensors, microwave-frequency oscillators and data processing. The stabilization of magnetization state, types of domains and domain wall structures depends on the competing energies such as magnetostatic, exchange and anisotropy. The nucleation/ pinning of domain walls depends on the local inhomogeneity in shape such as roughness, notches etc, which play an important role in stabilizing domain configurations that can be controlled by magnetic field/spin polarized current etc. The information gained by the study of magnetization reversal in the nanoring devices could help in understanding the possible stable magnetization states, which can be incorporated into the development of magnetic logic and recording devices in a NR-based architecture. The magnetization reversal and the stable states in the symmetric cobalt nanorings (NRs) attached with nanowires (NWs) (at diametrically opposite points), is studied through magnetoresistance (MR) measurements by application of in-plane magnetic field (H). Here, a strong in-plane shape anisotropy is introduced in cobalt thin films by patterning them into NR and NWs. The presence or absence of a DW in the device is detected utilizing the AMR property of the material, where the presence of DW leads to a decrease in the resistance of the probed section of the device. It is demonstrated that the magnetization reversal of the device with smaller width, proceeds through four distinct magnetization states, one of these is the stabilized vortex state that persists over a field range of 0.730 kOe. The effect of width (from 70 nm to 1 µm) and diameter (from 2 µm to 6 µm) on the switching behavior is demonstrated. The magnetization states observed in the MR measurements are well supported by micromagnetic simulations. A statistical analysis of switching fields in these devices was demonstrated by histogram plot (of switching counts) to understand the repeatability and reproducibility of switching characteristics. In addition, the magnetization reversal of permalloy NR is also studied by MR experiment when two NWs are attached to it in two different configurations. It has been demonstrated that a vortex state can be stabilized if the NWs are attached in a way that they are at an obtuse angle with respect to each other (type-II device) which is not the case if the NWs are attached at diametrically opposite points (type-I device). This occurs because the NWs reverse at different fields as they are asymmetric with respect to applied magnetic field at every angle. The angular dependence study of the magnetization states indicates that the vortex state could be always stabilized in the type-II device irrespective of the direction of in-plane applied magnetic field while it is not the case in type-I device. The experimental observations are in good agreement with micromagnetic simulations performed on similar device structures. Further, in the last part of the thesis, the magnetization reversal of geometrically engineered cobalt NR (of width 80 nm) devices are studied by application of H. Two types of cobalt nanoring devices were fabricated. In type-1 devices the NR is attached with two nanowires (NWs) at diametrically opposite positions. In type-2 devices the NR is attached with one NW, whose other end is attached to a 5 µm x 5 µm square pad. In type-2 device, the pad reverses first, thus causing the generation of a DW at the junction of the nucleation pad and the NW. The device type-2 possesses five distinct magnetization states, one of these is the vortex state. Easy nucleation of domain walls (DWs) results in a decrease of switching field corresponding to the reversal of the nanowire. This leads to an increase in the range of fields, where the vortex state exists. In addition, angular dependence of the switching behavior indicates that the vortex state can be stabilized at all in-plane orientations of H. This occurs because of the fact that symmetry was broken due to the presence of single domain wall pinning center which was the junction of the NR and NW. The results of our micromagnetic simulations are in a good agreement with the experimental results. These results are important to understand the role of NWs which allows the formation of vortex state at every angle of the in-plane H. In type-1 device, the simulation shows that when the field is applied at any angle away from the axis of the NW, the vortex state cannot be stabilized. The width dependent study of switching fields indicates, that the switching fields decrease with increasing the width of NR devices due to a reduction of the demagnetization field.

This dissertation presents a substantial contribution to a new field of material science, the investigation of the magnetic properties of 3D curved surfaces, achieved by using a self-assembled geometrical transformation of an initially planar membrane. Essential magnetic properties of thin films can be modified by the process of transforming them from a 2D planar film to a 3D curved surface. By investigating and controlling the reasons that influence the properties, it is possible to improve the functionality of existing devices in addition to laying the foundation for the future development of microelectronic devices based on curved magnetic structures. To accomplish this, it is necessary both to fabricate high-quality 3D curved objects and to establish reliable characterization methods based on commonly available technology. The primary objective of this dissertation is to develop techniques for characterizing the static and dynamic magnetic properties of self-assembled rolled 3D geometries. The second objective is to examine the origin of shape-, size- and strain/curvature-induced effects. The developed approach based on anisotropic magnetoresistance (AMR) measurement can quantitatively define the rolling-induced static magnetic changes, namely the induced magnetoelastic anisotropy, thus eliminating the need for microscopic imaging to characterize the structures. The interpretation of the AMR signal obtained on curved stripes is enabled by simultaneous visualization of the domain patterns and micromagnetic simulations. The developed approach is used to examine the effect of sign and magnitude of curvature on the induced anisotropies by altering the rolling direction and diameter of the 'Swiss-roll'. Furthermore, a time-averaged imaging technique based on conventional microscopies (magnetic force microscopy and Kerr microscopy) offers a novel strategy for investigating nanoscale periodic domain wall oscillations and hence dynamic magnetic characteristics of flat and curved structures. This method exploits the benefit of a position-dependent dwell time of periodically oscillating DWs and can determine the trajectory and amplitude of DW oscillation with sub-100 nm resolution. The uniqueness of this technique resides in the ease of the imaging procedure, unlike other DW dynamics imaging methods. The combined understanding of rolling-induced anisotropy and imaging DW oscillation is utilized to examine the dependence of DW dynamics on external stimuli and the structure's physical properties, such as lateral size, film thickness, and curvature-induced anisotropy. The presented methods and fundamental studies help to comprehend the rapidly expanding field of 3-dimensional nanomagnetism and advance high-performance magneto-electronic devices based on self-assembly rolling.

In dieser Arbeit werden das Wachstum mittels Molekularstrahlepitaxie und die Eigenschaften der Ferromagneten Fe und Fe_3Si auf niedrig-symmetirschen GaAs(113)A-Substraten studiert. Drei wichtige Aspekte werden untersucht: (i) Wachstum und strukturelle Charakterisierung, (ii) magnetische Eigenschaften und (iii) Magnetotransporteigenschaften der Fe und Fe_3Si Schichten auf GaAs(113)A-Substraten. Das Wachstum der Fe- und Fe_3Si-Schichten wurde bei einer Wachstumstemperatur von = bzw. 250 °C optimiert. Bei diesen Wachstumstemperaturen zeigen die Schichten eine hohe Kristallperfektion und glatte Grenz- und Oberflächen analog zu [001]-orientierten Schichten. Weiterhin wurde die Stabilität der Fe_(3+x)Si_(1-x) Phase über einen weiten Kompositionsbereich innerhalb der Fe_3Si-Stoichiometry demonstriert. Die Abhängigkeit der magnetischen Anisotropie innerhalb der Schichtebene von der Schichtdicke weist zwei Bereiche auf: einen Beresich mit dominanter uniaxialer Anisotropie für Fe-Schichten = 70 MLs. Weiterhin wird eine magnetische Anisotropie senkrecht zur Schichtebene in sehr dünnen Schichten gefunden. Der Grenzflächenbeitrag sowohl der uniaxialen als auch der senkrechten Anisotropiekonstanten, die aus der Dickenabhängigkeit bestimmt wurden, sind unabhängig von der [113]-Orientierung und eine inhärente Eigenschaft der Fe/GaAs-Grenzfläche. Die anisotrope Bindungskonfiguration zwischen den Fe und den As- oder Ga-Atomen an der Grenzfläche wird als Ursache für die uniaxiale magnetische Anisotropie betrachtet. Die magnetische Anisotropie der Fe_3Si-Schichten auf GaAs(113)A-Substraten zeigt ein komplexe Abhängigkeit von der Wachstumsbedingungen und der Komposition der Schichten. In den Magnetotransportuntersuchungen tritt sowohl in Fe(113)- als auch in Fe_3Si(113)-Schichten eine antisymmetrische Komponente (ASC) im planaren Hall-Effekt (PHE) auf. Ein phänomenologisches Modell, dass auf der Kristallsymmetrie basiert, liefert ein gute Beschreibung sowohl der ASC im PHE als auch des symmetrischen, anisotropen Magnetowiderstandes. Das Modell zeigt, dass die beobachtete ASC als Hall-Effekt zweiter Ordnung beschreiben werden kann. / In this work, the molecular-beam epitaxial growth and properties of ferromagnets, namely Fe and Fe_3Si are studied on low-symmetric GaAs(113)A substrates. Three important aspects are investigated: (i) growth and structural characterization, (ii) magnetic properties, and (iii) magnetotransport properties of Fe and Fe_3Si films on GaAs(113)A substrates. The growth of Fe and Fe_3Si films is optimized at growth temperatures of 0 and 250 degree Celsius, respectively, where the layers exhibit high crystal quality and a smooth interface/surface similar to the [001]-oriented films. The stability of Fe_(3+x)Si_(1-x) phase over a range of composition around the Fe_3Si stoichiometry is also demonstrated. The evolution of the in-plane magnetic anisotropy with film thickness exhibits two regions: a uniaxial magnetic anisotropy (UMA) for Fe film thicknesses = 70 MLs. The existence of an out-of-plane perpendicular magnetic anisotropy is also detected in ultrathin Fe films. The interfacial contribution of both the uniaxial and the perpendicular anisotropy constants, derived from the thickness-dependent study, are found to be independent of the [113] orientation and are hence an inherent property of the Fe/GaAs interface. The origin of the UMA is attributed to anisotropic bonding between Fe and As or Ga at the interface, similarly to Fe/GaAs(001). The magnetic anisotropy in Fe_3Si on GaAs(113)A exhibits a complex dependence on the growth conditions and composition. Magnetotransport measurements of both Fe(113) and Fe_3Si(113) films shows the striking appearance of an antisymmetric component (ASC) in the planar Hall effect (PHE). A phenomenological model based on the symmetry of the crystal provides a good explanation to both the ASC in the PHE as well as the symmetric anisotropic magnetoresistance. The model shows that the observed ASC component can be ascribed to a second-order Hall effect.