Les nouvelles technologies numériques sont très avides en capacité de stockage, ainsi qu’en efficacité (rapidité et bas coût énergétique) de transport d’information. Les dispositifs d’aujourd’hui atteignant leurs limites, la recherche de nouvelles solutions de stockage est primordiale.L’utilisation de parois magnétiques comme brique élémentaire au codage de l’information a été proposée il y a quelques années, dans l’optique de réaliser un enregistrement tridimensionnel et ainsi d’augmenter considérablement les capacités de stockage.Depuis, un nouvel objet magnétique plus robuste et moins sensible aux perturbations extérieures a été découvert : le skyrmion. Il est récemment devenu un sujet d’étude très actif et a été observé expérimentalement dans deux types de systèmes. Le premier est basé sur les matériaux hélimagnétiques, dont la structure cristalline est non centrosymétrique. Le FeGe est l’un d’eux, avec la température de transition magnétique observée la plus élevée. Le skyrmion a également été observé à l’interface entre un métal lourd à fort couplage spin-orbite et un matériau ferromagnétique. En particulier, les systèmes de multicouches à interfaces non symétriques ont montré leur fort potentiel pour la manipulation de skyrmions à température ambiante.Les deux principales difficultés rencontrées aujourd’hui sont la réalisation de systèmes avec des techniques d’élaboration intégrables à des dispositifs industriels, ainsi que la détection fiable de la présence de skyrmions. Cette thèse est donc séparée en deux problématiques, appliquées aux deux types de systèmes. Un protocole de croissance de couches minces de FeGe hélimagnétique par pulvérisation cathodique a été développé en s’appuyant principalement sur des caractérisations structurales par diffraction de rayons X. L’élaboration de multicouches à interfaces non symétriques du type [métal lourd 1/matériau ferromagnétique/métal lourd 2]n a également été étudiée. Ces deux systèmes ont ensuite été caractérisés magnétiquement par diverses techniques basées sur de l’imagerie magnétique, des mesures de magnéto-transport et de la spectroscopie magnétique. / New technology needs huge storage capacity together with high speed and low-cost transport of information. Current devices meeting their limits, research on new storage solutions is needed.One of them, proposed a few years ago, consists in using magnetic domain walls. Aligning them in nanowires and using the thickness of the layers could enable the realization of a tridimensional recording device and then improve the storage capacity.A new object more robust and less sensitive to perturbations has been discovered since. Skyrmion is now widely studied. It has been experimentally observed in two kinds of systems. The first one is helimagnet, with non centrosymmetric crystal structure. FeGe is one of them, with the highest critical temperature observed yet. Skyrmion has been observed as well at the interface between a heavy metal with strong spin-orbit coupling and a ferromagnet. In particular, multilayers with non-symmetric interfaces are very promising systems for manipulation of skyrmions at room temperature.Nevertheless, the elaboration of systems for industrial devices and reliable detection of skyrmions is still challenging. These two problematics are explored in this thesis, applied to two different systems. A protocol to grow helimagnetic FeGe thin films was first established, thanks to structural characterization mainly based on X-ray diffraction. Growth of multilayers with non symmetrical interfaces [heavy metal 1/ferromagnet/heavy metal 2]n was studied as well. These systems were then magnetically characterized, using numerous techniques such as magnetic imaging, magneto transport measurements and magnetic spectroscopy.

No description available.

Asymmetrically sandwiched ferromagnetic thin films display a large number of spin-orbit effects, including the Dzyaloschinsii-Moriya interaction (DMI), spin-orbit torques (SOT) and magnetoresistance (MR) effects. Their concurrence promises the implementation of interesting magnetic structures like skyrmions in future memory and logic devices. The complex interplay of various effects originating from the spin-orbit coupling and their dependencies on the microstructural details of the material system mandates a holistic characterization of its properties. In this PhD thesis, a comprehensive study of the spin-orbit effects in a chromium oxide/cobalt/platinum trilayer sample series is presented. The determination of the complete micromagnetic parameter set is based on a developed measurement routine that utilizes quasistatic methods. The unambiguous quantification of all relevant constants is crucial for the modeling of the details of magnetic structures in the system. In this context the necessity of a strict distinction of magnetic objects, that are stabilized by magnetostatics or the DMI, was revealed. Furthermore, a sample layout was developed to allow for the simultaneous quantification of the magnitudes of SOTs and MR effects from nonlinear magnetotransport measurements. In conjunction with a structural characterization, the dominating dependence of the effect magnitudes on microstructural details of the systems is concluded. Precisely characterized systems establish a solid groundwork for further investigations that are needed for viable skyrmion-based devices.

In the present work, the magnetotransport measurement technique was developed and various materials, exhibiting resistances from 1 mOhm up to several tens of kOhm, were investigated in pulsed magnetic fields of up to 60 T. Phase diagrams of irreversibility and upper critical fields for pure and Zn-doped YBa2Cu3O_7-x high-temperature superconductors were measured. A high-field study of the electronic properties of the two semimetals LaBiPt and CeBiPt were presented. Magnetoresistance of La0.7Sr0.3MnO3 and La0.7Ca0.3MnO3 thin films were investigated.

Asymmetrically sandwiched ferromagnetic thin films display a large number of spin-orbit effects, including the Dzyaloschinsii-Moriya interaction (DMI), spin-orbit torques (SOT) and magnetoresistance (MR) effects. Their concurrence promises the implementation of interesting magnetic structures like skyrmions in future memory and logic devices. The complex interplay of various effects originating from the spin-orbit coupling and their dependencies on the microstructural details of the material system mandates a holistic characterization of its properties. In this PhD thesis, a comprehensive study of the spin-orbit effects in a chromium oxide/cobalt/platinum trilayer sample series is presented. The determination of the complete micromagnetic parameter set is based on a developed measurement routine that utilizes quasistatic methods. The unambiguous quantification of all relevant constants is crucial for the modeling of the details of magnetic structures in the system. In this context the necessity of a strict distinction of magnetic objects, that are stabilized by magnetostatics or the DMI, was revealed. Furthermore, a sample layout was developed to allow for the simultaneous quantification of the magnitudes of SOTs and MR effects from nonlinear magnetotransport measurements. In conjunction with a structural characterization, the dominating dependence of the effect magnitudes on microstructural details of the systems is concluded. Precisely characterized systems establish a solid groundwork for further investigations that are needed for viable skyrmion-based devices.:1 Introduction 2 Fundamentals 2.1 Towards new devices 2.2 Spin-orbit effects 2.2.1 Spin-current sources 2.2.2 Magnetoresistanceeffects 2.2.3 Spin-orbit torques 2.2.4 Harmonic analysis 2.3 Micromagnetic model 2.3.1 Dzyaloshinskii-Moriya interaction (DMI) 2.3.2 Consequences of the DMI for magnetic structures 2.3.3 Interface-induced DMI in asymmetrically stacked ferromagnets 2.3.4 Quantification of the interface-induced DMI 2.3.5 Levy-Fert three-site model including roughness 3 The CrOx/Co/Pt sample system 3.1 Experimental techniques 3.2 Structural characterization 4 Complete micromagnetic characterization 4.1 Magnetometry 4.1.1 Static investigation 4.1.2 Ferromagnetic resonance 4.2 DMI quantification 4.2.1 Field-driven domain wall creep motion 4.2.2 Asymmetric domain growth 4.2.3 Winding pair stability 4.3 Determination of the exchange parameter 4.3.1 Generation of circular magnetic objects 4.3.2 Homochiral magnetic bubble domains 4.4 Results 5 Magnetotransport measurements 5.1 Measurement setup 5.2 Magnetoresistance effects 5.3 Spin-orbit torque quantification 5.4 Results 6 Discussion 6.1 Structural predomination of the DMI strength 6.2 Ultra-thin limit exchange parameter reduction 6.3 Magnetotransport properties 6.4 Magneticstructures in //CrOx/Co/Pttrilayers 7 Conclusion and Outlook A Appendix A.1 Calculation of the skyrmion diameter A.2 Micromagnetic simulation of the winding pair stability Bibliography Acknowledgements

Systems that exhibit the extraordinary magnetoresistance (EMR) effect and other more disordered semiconductor-metal hybrid structures have been investigated numerically with the use of the finite element method (FEM). Initially, modelling focused on circular geometry EMR devices where a single metallic droplet is embedded concentrically into a larger semiconducting disk. The dependence of the magnetoresistance of such systems on the transverse magnetic field (0 5T) and filling factor (1/16 15/16) are reported and generally show a very good agreement with existing experimental data. The influence of the geometry of the conducting region of these EMR systems was then investigated. The EMR effect was found to be highly sensitive to the shape of the conducting region with a multi-branched geometry producing a four order of magnitude enhancement of the magnetoresistance over a circular geometry device of the same filling factor. Conformal mapping has previously been shown to transform a circular EMR device into an equivalent linear geometry. Such a linear EMR device has been modelled with the EMR mechanism clearly observed. The magnetoresistive response of a circular EMR device upon changes to: the mobility of the semiconducting region; the ratio of metal to semiconductor conductivity; and the introduction of a finite resistance at the semiconductor-metal interface, have also been investigated. In order for a large EMR effect to be observed the system requires: the semiconductor mobility to be large; the conductivity of the metal to be greater than two orders of magnitude larger than that of the semiconductor; and a very low interface resistance. This modelling procedure has been extended to include inhomogeneous semiconductor-metal hybrids with a more complex and disordered structure. Two models are presented, both based upon the random distribution of a small proportion of metal inside a semiconducting material. The resultant magnetoresistance in each case is found to have a quasi-linear dependence on magnetic field, similar to that observed in the silver chalcogenides.

Dans le régime de l'effet Hall quantique, les porteurs de charge se propagent le long de canaux unidimensionnels situés au bords d'un gaz d'électron bidimensionel (2D electron gas, 2DEG). Un contact ponctuel quantique (quantum point contact, QPC) - une constriction étroite confinant spatialement le gaz électronique - permet de contrôler la transmission de ces canaux de bords. Dans un 2DEG conventionnel, une tension négative appliquée sur les grilles électrostatiques du QPC engendre la déplétion locale du gaz électronique sous la grille, forçant les électrons à se propager au travers de la constriction. Cependant, dans le graphène, du fait de l'absence de bande interdite, une tension négative provoque la transition continue du dopage d'électrons à trous. Dans le régime de l'effet Hall quantique, électrons et trous se propagent le long de l'interface p-n dans la même direction, et la diffusion inélastique induit un transfert de charge et du mélange entre eux.Au cours de cette thèse, nous avons fabriqué des dispositifs à base de graphène encapsulé dans deux feuillets de hBN, et munis de grilles électrostatiques définissant un QPC. Nous avons étudié l'effet du QPC sur la propagation des canaux de bords entiers et fractionnaires de l'effet Hall quantique, et sur le mélange entre eux. Dans l'effet Hall quantique, nous avons démontré que les canaux entiers et fractionnaires peuvent être contrôlés et sélectivement transmis au travers de la constriction. Du fait de la haute mobilité de nos structures, et de la levée de dégénérescence complète des niveaux de Landau qui en résulte à fort champ magnétique, l'équilibrage à l'interface p-n est réduit aux sous-niveaux de même spin et au niveau de Landau N=0.Un QPC dans le régime de l'effet Hall quantique constitue également un système idéal pour l'étude de l'effet tunnel des porteurs de charge entre canaux de bords fractionnaires, unidimensionnels et fortement corrélés, se propageant dans des directions opposées, décrits par la théorie de Tomonaga-Luttinger. Nous avons étudié l'effet tunnel entre canaux de bords fractionnaires dans notre structure muni un QPC, en nous concentrant sur l'état fractionnaire 7/3 et la dépendance en température de ses propriétés tunnels. / In the quantum Hall regime, the charge carriers are conducted within one-dimensional channels propagating at the edge of a two-dimensional electron gas (2DEG). A quantum point contact (QPC) – a narrow constriction confining spatially electron transport – can control the transmission of these quantum Hall edge channels. In conventional 2DEG systems, a negative voltage applied on the electrostatic split gates depletes locally the electrons underneath them forcing the electrons to pass through the constriction. In contrast, due to the absence of a band gap in graphene, a negative gate voltage induces a continuous shift of the doping from electrons to holes. In the quantum Hall regime, electron and hole edge channels propagate along the pn-interface in the same direction while inelastic scattering induces charge transfer and mixing between them.In this PhD thesis, we have fabricated ballistic graphene devices made by van der Waals stacking of hBN/Gr/hBN heterostructures, and equipped with split gates forming a quantum point contact (QPC) constriction. We have studied the effect of the QPC on the propagation of integer and fractional quantum Hall edge channels and the mixing among them. In the quantum Hall regime, we demonstrate that the integer and fractional quantum Hall edge channels can be controlled and selectively transmitted by the QPC. Due to the high mobility of our devices and the resultant full lifting of the degeneracies of the Landau levels in strong magnetic field, equilibration at the pn-interface is restricted to sublevels of identical spins of the N=0 Landau level.A QPC in the quantum Hall regime offers also an ideal system to study the tunnelling of charge carriers between counter-propagating fractional edge channels of highly correlated, one-dimensional fermions described by the theory of Tomonaga-Luttinger. We study the tunnelling between fractional quantum Hall edge channels in our QPC device in graphene and focus on the 7/3-fractional state to explore the temperature dependence of tunnelling characteristics.

This thesis describes studies on two-dimensional electron gases (2DEG) in graphene and related 2D systems. Magnetotransport investigations specifically in graphene and its bilayer system are demonstrated in detail, while the experimental techniques presented in this thesis are widely applicable to a large variety of other 2D materials. Chapter 1 gives an introduction and motivation for the principal topic presented in this thesis, with a general introduction to carbon nano-materials and an overview of the current state of graphene-related research and technological development (RTD). Chapter 2 establishes a basic theoretical framework which is essential for interpreting the results presented in this thesis, starting with the crystal and electronic band structures of graphene and its bilayer, followed by high magnetic fields effects on transport properties in these 2D systems. Chapter 3 details the experimental methods directly related to the presented work. The next three chapters report experimental results of three specific magnetotransport studies. Chapter 4 reports the disorder effects on epitaxial graphene in the vicinity of the Dirac point. Quadratic increases of carrier densities with temperature are found to be due to intrinsic thermal excitation combined with electron-hole puddles induced by charged impurities. It is also shown that the minimum conductivity increases with increasing disorder strength, in good agreement with quantum-mechanical numerical calculations. Chapter 5 reports measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to a magnetic field dependent charge transfer process from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels this process is modelled in excellent agreement with experimental results. In Chapter 6, energy relaxation of hot carriers in graphene bilayer systems is investigated from measurements on Shubnikovde Haas oscillations and weak localisation. The hot-electron energy loss rate follows the predicted T⁴ power-law at carrier temperatures from 1.4 up to about 100 K, due to electron-acoustic phonon interactions. Comparisons are made between graphene monolayer and bilayer systems and a much stronger carrier density dependence of the energy loss rate is found in the bilayer system. This thesis concludes with a summary of the most important findings of the topics that have been discussed. The significance and limitations of the present research are listed. Some suggestions and outlook are given for possible improvements and interesting areas of future research and development.

The study of the co-existence of singlet superconductivity and ferromagnetism in bulk materials has been a long standing and intriguing problem in condensed matter physics since the superconductivity and ferromagnetism are quantum mechanically antagonistic to each other (i.e. parallel alignment of spins in the ferromagnet and Cooper pairs with oppositely aligned spins in the superconductor).Though it is incompatible to have the coexistence of singlet superconductivity and ferromagnetism in bulk compound, it is highly possible to artificially fabricate superconductor (S)/ferromagnet (F) heterostructures using various thin film deposition techniques and to study the interplay between the two antagonistic quantum phases over their characteristic length scales. The mutual interaction between the two competing order parameters at the interface in hybrid S/F heterostructures give rise to a variety of novel exotic physical phenomena. Moreover, the spin polarized transport and tunneling experiments in S/F heterostructures seem to be very much useful for providing important information on the spin dependent electronic properties of high Tc superconductors below and above the transition temperature. This can help a lot to understand the long debated unusual electronic properties and pairing mechanism of high Tc superconductors. In addition to the rich fundamental aspects buried in the study of S/F heterostructures, one can also use the spin dependent properties of high Tc superconductors in S/F heterostructures to design new spintronics devices from the application point of view. In this thesis an attempt is made to understand the spin polarized electron transport across S/F heterostructures where the superconductor used is YBa2Cu3O7-δand the ferromagnets are La0.5Sr0.5CoO3, La0.7Sr0.3MnO3, and La0.7Ca0.3MnO3. In addition, the magnetic properties of the La1-x SrxCoO3 system is also investigated in detail. The thesis is organized in six chapters and a brief summary of each chapter is given below. Chapter1 gives a brief introduction to the superconductivity, ferromagnetism and the interplay between superconductivity and ferromagnetism at the interface of S/F heterostructures. It also describes various exotic phenomena and the proximity effect that emerges at the S/F interface due to competing interactions. In addition, it also includes a discussion on various types of indirect magnetic interactions and basic idea about the spin glass ordering in magnetic materials. Chapter 2 outlines the basic principles of various experimental techniques employed for the work presented in this thesis. Chapter 3 describes an extensive magnetic and magnetotransport study of the La1-xSrxCoO3 system to understand the manifestation of various magnetic phases associated with it. The first section of this chapter aims at understanding the phase separation scenario in La0.85Sr0.15CoO3. Since the magnetic behavior of La0.85Sr0.15CoO3 is in the border area of spin glass (SG) and ferromagnetic (F) region in the x-T phase diagram; it has been subjected to a controversial debate for the last several years; while some groups show evidence for magnetic phase separation (PS), others show SG behavior. However, the experimental results presented in this thesis clearly demonstrate that the instability towards PS with inhomogeneous states or competing phases in La0.85Sr0.15CoO3 is not inherent or intrinsic to this compound; rather it is a consequence of the heat treatment condition during the preparation method. It is realized that low temperature annealed sample shows PS whereas the high temperature annealed sample shows the characteristics of canonical SG behavior. The second section of this chapter deals with a detailed study about the possible existence of various magnetic phases of La1-xSrxCoO3 in the range 0 ≤x ≤0.5. The dc magnetization study for x ≥0.18 exhibits the characteristic of ferromagnetic like behavior and for x<0.18, the SG behavior. More strikingly, the dc magnetization studies for x<0.18 rules out the existence of any ferromagnetic correlation that gives rise to irreversible line in the spin glass regime. The ac susceptibility study for x<0.18, exhibits a considerable frequency dependent peak shift, time-dependent memory effect, and the characteristic spin relaxation time scale τo ~10-13s, all pointing towards the characteristics of SG behavior. On the other hand, the ac susceptibility study in the higher doping ferromagnetic side exhibits the coexistence of glassy and ferromagnetic behavior. The glassiness is interpreted in terms of inter-cluster interaction. The reciprocal susceptibility vs. T plot in the paramagnetic side adheres strictly to Curie-Weis behavior and does not provide any signature for the pre-formation of ferromagnetic clusters well above the Curie temperature. The magnetotransport study reveals a cross over from metallic behavior to semiconducting like behavior for x ≤0.18 and the system exhibits a peak in MR in the vicinity of Tc on the metallic side and a large value of MR at low temperature on the semiconducting side. Such high value of MR in the semiconducting spin glass regime is strongly believed due to spin dependent part of random potential distribution. Based on the present experimental findings, a revised phase diagram has been constructed and each phase has been characterized with its associated properties. Chapter 4 deals with a comprehensive study of thickness dependent structural, magnetic and magnetotransport properties of oriented La0.5Sr0.5CoO3 thin films grown on LaAlO3 by pulsed laser deposition. The films are found to undergo a reduction in Curie temperature with decrease in film thicknesses and it is primarily caused by the finite size effect since the finite scaling law holds good over the studied thickness range. The contribution from strain induced suppression of the Curie temperature with decreasing film thickness is ruled out since all the films exhibit a constant out of plane tensile strain (0.5%) irrespective of their thickness. The coercivity of the films is observed to be an order of magnitude higher than that of the bulk. This is attributed to the local variation of the internal strain that introduces strong pinning sites (via. magnetoelastic interaction) for the magnetization reversal. In addition, an increase in the electrical resistivity and coercivity is observed with decrease in film thickness and it is strongly believed to be due to the interface effect. Chapter5 reports on the investigation of the effect of ferromagnetic layer on (i) pair breaking effect and (ii) vortex dynamics in different superconducting(S)/ ferromagnetic (F) bi-layers grown by pulsed laser deposition. The current (I) dependent electrical transport studies in the S/F bi-layers exhibit a significant reduction in the superconducting transition temperature with the increase in applied current as compared to single YBa2Cu3O7-δlayer and it follows I2/3 dependence in accordance with the pair breaking effect. Moreover, the superconducting transition temperature in YBa2Cu3O7-δ/ La0.7Sr0.3MnO3 bilayer is surprisingly found to be much larger than the YBa2Cu3O7-δ/La0.5Sr0.5CoO3. It appears that the current driven from a material with low spin polarization (-11%) like La0.5Sr0.5CoO3 can also suppress the superconductivity to a larger extent. This indicates that the degree of spin polarization of the ferromagnetic electrode is not the only criteria to determine the suppression of superconductivity by pair breaking effect in superconductor/ferromagnet hybrid structures; rather the transparency of the interface for the spin polarization, the formation of vortex state due to the stray field of ferromagnetic layer and the ferromagnetic domain patterns might play significant roles to determine such effect. More interestingly, the spin diffusion length in YBa2Cu3O7-δis found have a much longer length scale than that reported earlier in the study of F/ S heterostructures. The activation energy (U) for the vortex motion in S/F bilayers is reduced remarkably by the presence of the F layers. In addition, the U exhibits a logarithmic dependence on the applied magnetic field in the S/F bilayers suggesting the existence of decoupled 2D pancake vortices. This result is discussed in terms of the reduction in the effective S layer thickness and the weakening of the S coherence length due to the presence of F layers. Chapter 6 deals with the magnetotransport study on two different kind of F/S/F trilayers viz. La0.7Sr0.3MnO3/YBa2Cu3O7-δ/La0.7Sr0.3MnO3 and La0.5Sr0.5CoO3/YBa2Cu3O7-δ/La0.7Ca0.3MnO3 with changes in superconducting and ferromagnetic layer thickness. The activation energy for the vortex motion in F/S/F trilayer is found to decrease considerably as compared to S/F bilayer and it also exhibits a logarithmic dependence on magnetic field which gives the signature of existence of decoupled 2D pancake vortices. The magnetotransport study reveals that a much lower magnetic field is required to suppress the superconductivity in trilayer as compared to single YBCO layer. Moreover, the transport study also reveals that a threshold thickness of YBCO is required for the onset of superconductivity in trilayer structure and the onset of superconducting Tc increases with increase in YBCO thickness. More strikingly, a remarkable unconventional anisotropic superconducting Tc (Tc H║c-axis<Tc H⊥c-axis) is observed in La0.5Sr0.5CoO3/YBa2Cu3O7-δ/La0.7Ca0.3MnO3 trilayer for the magnetic field applied parallel and perpendicular to c-axis. The trilayer system also exhibits a huge positive magnetoresistance (MR) below superconducting Tc and it could arise due to vortex dissipation in liquid state of superconductor in the tri-layer structure. Finally, the thesis concludes with a general conclusion and an outlook in this area of research.

Electrical transport in materials is typically diffusive, due to dominant momentum-relaxing scattering of carriers with the phonons or defects. In ultraclean material systems such as GaAs/AlGaAs or graphene/hBN heterostructures, momentum-relaxing can be suppressed, leading to the onset of non-diffusive transport regimes, where Ohm's law is no longer valid. Within these non-diffusive regimes, the hydrodynamic regime occurs when momentum-conserving electron-electron scattering length scale is smaller than the device length scale (usually at intermediate temperatures). On the other hand, weak electron-electron scattering (at low temperatures) results in ballistic transport, commonly understood using the familiar single-particle framework of injected carriers travelling in straight line trajectories with intermittent reflections off device boundaries. Both the ballistic and hydrodynamic regimes can exhibit a emph{negative} nonlocal resistance, and collective behaviour such as the formation of current vortices. In this work, we study nonlocal current-voltage characteristics in mesoscopic devices fabricated from a GaAs/AlGaAs heterostructure that hosts a two-dimensional electron system in a GaAs quantum well. First, we report a quadratic non-linearity in the nonlocal current-voltage characteristics that manifests in any device where a nonlocal voltage measurement is possible. Using measurements at low temperatures ($sim$ 4 K) across multiple devices and considering various contact configurations for each device, we show that the non-linearity is universal. We apply the non-linearity to rectification and frequency multiplication. We also report on a periodic peaks in the nonlocal voltage vs. magnetic field, in an enclosed mesoscopic geometry in which transverse magnetic focusing (TMF) is typically studied. These peaks occur at weak magnetic fields, are independent of the source-detector separation and are distinct from TMF. Our experimental findings are backed by an extensive set of simulations using in both the semiclassical as well as quantum-coherent transport models. / Master of Science / Current is made up of charged particles such as electrons moving through a material. Typically, current is proportional to the applied voltage and flows from higher to lower potential within the device with the potential decreasing monotonically as we move from the source contact to the drain contact irrespective of the path taken through the device. This is commonly known as Ohm's law, and is followed in most materials we come across. The motion of electrons carrying this current is akin to the motion of balls inside a pinball machine, their momentum randomized by intermittent collisions due to lattice vibrations, defects and impurities present in the material. In ultraclean two-dimensional materials at low-intermediate temperatures (where lattice vibration is weak), these collisions become sparse. Collisions of electrons with other electrons now become important. When electron-electron collisions are frequent, the electrons collectively behave like a fluid, giving rise to so called hydrodynamic transport. On the other hand, when electron-electron collisions are sparse as well, electrons move unhindered in ballistic straight line trajectories until they reflect off the device boundaries. This is known as ballistic transport. Under both these transport regimes, Ohm's law breaks down, leading to interesting physical phenomena such as the formation of current whirlpools. In this work, we study the voltage measured at a point in the device which is distinct from the point where current is injected or extracted. This is commonly known as the nonlocal voltage. We explore the relationship between the nonlocal voltage and the injected current and find it to be significantly different from predictions made by Ohm's law. We use this novel current-voltage relationship to build a rectifier and frequency multiplier - two devices commonly used in high-frequency detection, radar systems and telecommunications. We also report previously unseen periodic oscillations in the nonlocal voltage when the magnetic field perpendicular to the device is varied. Using high-resolution simulations, we show the these oscillations can not be explained by looking at individual electron paths, and arise due to contribution from all electrons that travel through the device.