Starting with a microscopic model based on the Kohn-Luttinger Hamiltonian and kinetic p-d exchange combined with Boltzmann formula for conductivity we identify the scattering from magnetic Mn combined with the strong spin-orbit interaction of the GaAs valence band as the dominant mechanism of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As. This fact allows to construct a simple analytical model of the AMR consisting of two heavy-hole bands whose charge carriers are scattered on the impurity potential of the Mn atoms. The model predicts the correct sign of the AMR (resistivity parallel to magnetization is smaller than perpendicular to magnetization) and identifies its origin arising from the destructive interference between electric and magnetic part of the scattering potential of magnetic ionized Mn acceptors when the carriers move parallel to the magnetization.
We have grown high-quality single crystals of the colossal-magnetoresistance (CMR) material La0.7Ca0.3MnO3 by using the laser heated pedestal growth (LHPG) method. Samples were grown as fibers of different diameters, and with lengths of the order of centimeters. Their composition and structure were verified through X-ray diffraction, scanning electron microcopy with EDX (Energy Dispersive X-ray Analysis) and by Rietveld analysis. The quality of the crystalline fibers was confirmed by Laue and EBSD (Electron Backscatter Diffraction) patterns. Rocking curves performed along the fiber axis reveal…
Recent research works have shown that the magnetic order in some antiferromagnetic materials can be manipulated and detected electrically, due to two physical mechanisms: Neel-order spin-orbit torques and anisotropic magnetoresistance. While these observations open up opportunities to use antiferromagnets for magnetic memory devices, different physical characterization methods are required for a better understanding of those mechanisms. Here we report a magnetic field induced rotation of the antiferromagnetic Neel vector in epitaxial tetragonal CuMnAs thin films. Using soft x-ray magnetic line…
We have investigated the anisotropic magnetoresistance (AMR) of (In,Fe)As ferromagnetic semiconductor (FMS) layers grown on semi-insulating GaAs substrates. In a 10 nm-thick (In,Fe)As layer which is insulating at low temperature, we observed crystalline AMR with two-fold and eight-fold symmetries. In a metallic 100 nm-thick (In,Fe)As layer with higher electron concentration, only two-fold symmetric crystalline AMR was observed. Our results demonstrate the macroscopic ferromagnetism in (In,Fe)As with magnetic anisotropy that depends on the electron concentration. Non-crystalline AMR is also obs…
We report a comprehensive magneto-transport study on single crystalline p-type topological crystalline insulator (TCI) SnTe, across the cubic-to-rhombohedral (R3m) transition which occurs as a function of temperature. The electrical resistivity of a well-characterized SnTe crystal shows evidence for the cubic-to-rhombohedral structural transition at T$_s$ $\sim$64,K and a carrier density of $\sim$1.8$\times$10$^{20}$ at 77,K. As a function of applied magnetic field perpendicular to the (100) plane, SnTe exhibits a large unsaturated linear magnetoresistance (LMR) reaching a value of 42% at 5K a…
It has been demonstrated that magnetocrystalline anisotropies in (Ga,Mn)As are sensitive to lattice strains as small as 10^-4 and that strain can be controlled by lattice parameter engineering during growth, through post growth lithography, and electrically by bonding the (Ga,Mn)As sample to a piezoelectric transducer. In this work we show that analogous effects are observed in crystalline components of the anisotropic magnetoresistance (AMR). Lithographically or electrically induced strain variations can produce crystalline AMR components which are larger than the crystalline AMR and a signif…
Angular magnetotransport measurements have been performed to tackle the origin of the magnetoresistance in the quasi-1D Hollandite Ba1.2Rh8O16. Three samples of different impurities amount were measured. We observe that the low temperature resistivity upturn is not due to a charge density wave transition, and a dominant role of impurities scattering for low temperature transport properties is instead demonstrated. The components of magnetoresistance were separated by using the Kohler plot and the angular dependency of the resistance under magnetic field. It shows the major contribution of an i…
The chalcogenide Bi$_2$Se$_3$ can attain the three dimensional (3D) Dirac semimetal state under the influence of strain and microstrain. Here we report the presnece of large linear magnetoresistance in such a Bi$_2$Se$_3$ crystal. The magnetoresistance has quadratic form at low fields which crossovers to linear above 4 T. The temperature dependence of magnetoresistance scales with carrier mobility and the crossover field scales with inverse of mobility. Our analysis suggest that the linear magnetoresistance in our system has a classical origin and arises from the scattering of high mobility 3D…
Some single-crystalline materials present an electrical resistivity which decreases between room temperature and low temperatures at zero magnetic field as in a good metal and switches to a nearly semiconductinglike behavior at low temperatures with the application of a magnetic field. Often, this is accompanied by a huge and nonsaturating linear magnetoresistance which remains difficult to explain. Here we present a systematic study of the magnetoresistance in single-crystal $γ$-PtBi$_2$. We observe that the angle between the magnetic field and the crystalline $c$ axis fundamentally changes t…
We investigated the relationship between the tunnel magnetoresistance (TMR) ratio and the electrode structure in MgO-barrier magnetic tunnel junctions (MTJs). The TMR ratio in a MTJ with Co40Fe40B20 reference and free layers reached 355% at the post-deposition annealing temperature of Ta=400 degree C. When Co50Fe50 or Co90Fe10 is used for the reference layer material, no high TMR ratio was observed. The key to have high TMR ratio is to have highly oriented (001) MgO barrier/CoFeB crystalline electrodes. The highest TMR ratio obtained so far is 450% at Ta = 450 degree C in a pseudo spin-valve M…
The magnetic properties of perovskite CaVO3 single crystals have been studied by means of magnetoresistance r(T, H) and magnetization M(H) measurements in fields to 18T. At 2 K, the magnetoresistance is positive and a maximum value of Dr(18T)/r(0) = 16.5% is found for H//a. The magnetization exhibits a smooth increase at 2 K, reaching values of M(18T) = 0.03, 0.05, 0.17 mB/f.u. for H//a, H//b, and H//c, respectively. This anisotropy found in M(H) is consistent with that observed for Dr(H//a) > Dr(H//b) > Dr(H//c). These results can be interpreted in terms of the field-dependent scattering mech…
The consequences of several microscopic interactions on the photoemission spectra of crystalline organic semiconductors (OSC) are studied theoretically. It is argued that their relative roles can be disentangled by analyzing both their temperature and their momentum/energy dependence. Our analysis shows that the polaronic thermal band narrowing, that is the foundation of most theories of electrical transport in OSC, is inconsistent in the range of microscopic parameters appropriate for these materials. An alternative scenario is proposed to explain the experimental trends.
The magnetoresistance in a series of Ga1-xMnxAs samples with 0.2 =< x =< 0.8 have been measured for three mutually orthogonal orientations of the external magnetic field. The anisotropy magnetoresistance decreases with increasing of the Mn content, which means that the magnetic disorder or defects scattering increases with increasing of Mn content. And also the magneto-crystalline anisotropy increases with increasing of Mn concentration.
Topological insulators with their topological protected surface states are highly promising quantum materials. In this article the micro-flakes of single-crystalline topological insulators Bi2Te3 and Sb2Te3 are explored through physical parameter measurement at low temperatures and thereby the charge carrier dynamics are investigated at 5K to study the various optical transitions related to these surface states. The magnetoresistance is experimentally investigated at temperatures of 5K and 100K for a field range of 1Tesla. The occurrence of the weak anti-localization effect predicts the presen…
Magnetic topological semimetals, the latest member of topological quantum materials, are attracting extensive attention as they may lead to topologically-driven spintronics. Currently, magnetotransport investigations on these materials are focused on anomalous Hall effect. Here, we report on the magnetoresistance anisotropy of topological semimetal CeBi, which has tunable magnetic structures arising from localized Ce 4f electrons and exhibits both negative and positive magnetoresistances, depending on the temperature. We found that the angle dependence of the negative magnetoresistance, regard…
The integration of ferromagnetic Mn5Ge3 with the Ge matrix is promising for spin injection in a silicon-compatible geometry. In this paper, we report the preparation of magnetic Mn5Ge3 nanocrystals embedded inside the Ge matrix by Mn ions implantation at elevated temperature. By X-ray diffraction and transmission electron microscopy, we observe crystalline Mn5Ge3 with variable size depending on the Mn ion fluence. The electronic structure of Mn in Mn5Ge3 nanocrystals is 3d6 configuration, the same as in bulk Mn5Ge3. A large positive magnetoresistance has been observed at low temperatures. It c…
We studied the angular dependence of anisotropic magnetoresistance (AMR) and Planar Hall effect (PHE) at various temperatures in high quality epitaxial Fe3O4 films grown on MgO(001) substrates. The PHE contains only a twofold angular dependence, but the AMR below 200K is constituted with both twofold and fourfold symmetric terms. A quantitative fitting based on a phenomenological model indicates the nonmonotonics temperature dependence of the twofold component of AMR can be ascribed to the competition between the term and the term. A unidirectional component was observed in the angular depende…
Many conductors, including recently studied Dirac materials, show saturation of coherence length on decreasing temperature. This surprising phenomenon is assigned to external noise, residual magnetic impurities or two-level systems specific to non-crystalline solids. Here, by considering the SnTe-class of compounds as an example, we show theoretically that breaking of mirror symmetry deteriorates Berry's phase quantization, leading to additional dephasing in weak-antilocalization magnetoresistance (WAL-MR). Our experimental studies of WAL-MR corroborate these theoretical expectations in (111) …
We report the observation of colossal positive magnetoresistance (MR) in single crystalline, high mobility TaAs2 semimetal. The excellent fit of MR by a single quadratic function of the magnetic field B over a wide temperature range (T = 2-300 K) suggests the semiclassical nature of the MR. The measurements of Hall effect and Shubnikov-de Haas oscillations, as well as band structure calculations suggest that the giant MR originates from the nearly perfectly compensated electrons and holes in TaAs2. The quadratic MR can even exceed 1,200,000% at B = 9 T and T = 2 K, which is one of the largest …
By carrying out density functional theory analysis within the Keldysh non-equilibrium Green's functional formalism, we have calculated the nonlinear and non-equilibrium quantum transport properties of Fe/MgO/Fe trilayer structures as a function of external bias voltage. For well relaxed atomic structures of the trilayer, the equilibrium tunnel magnetoresistance ratio (TMR) is found to be very large and also fairly stable against small variations in the atomic structure. As a function of external bias voltage, the TMR reduces monotonically to zero with a voltage scale of about 1V, in agreement …
We report point-contact measurements of anisotropic magnetoresistance (AMR) in a single crystal of antiferromagnetic (AFM) Mott insulator Sr2IrO4. The point-contact technique is used here as a local probe of magnetotransport properties on the nanoscale. The measurements at liquid nitrogen temperature revealed negative magnetoresistances (MRs) (up to 28%) for modest magnetic fields (250 mT) applied within the IrO2 a-b plane and electric currents flowing perpendicular to the plane. The angular dependence of MR shows a crossover from four-fold to two-fold symmetry in response to an increasing mag…
We have performed a systematic investigation of magnetotransport of a series of as-grown and annealed Ga1-xMnxAs samples with 0.011 <= x <= 0.09. We find that the anisotropic magnetoresistance (AMR) generally decreases with increasing magnetic anisotropy, with increasing Mn concentration and on low temperature annealing. We show that the uniaxial magnetic anisotropy can be clearly observed from AMR for the samples with x >= 0.02. This becomes the dominant anisotropy at elevated temperatures, and is shown to rotate by 90o on annealing. We find that the in-plane longitudinal resistivity depends …
Unsaturated magnetoresistance (MR) has been reported in WTe2, and remains irrepressible up to very high field. Intense optimization of the crystalline quality causes a squarely-increasing MR, as interpreted by perfect compensation of opposite carriers. Herein we report our observation of linear MR (LMR) in WTe2 crystals, the onset of which is first identified by constructing the mobility spectra of the MR at low fields. The LMR further intensifies and predominates at fields higher than 20 Tesla while the parabolic MR gradually decays. The LMR remains unsaturated up to a high field of 60 Tesla …
Given renewed interest in the electronic properties of semimetallic compounds with varying degrees of spin orbit coupling we have grown single crystals of SrAgSb and SrAuSb, measured their temperature and field dependent electrical resistivity and magnetization and performed density functional theory (DFT) band structure calculations. Magnetization measurements are consistent with a diamagnetic host with a small amount of local moment bearing impurities. Although the residual resistivity ratio (RRR) for all samples studied was relatively low, ranging between 2.4 and 3.4, the compounds had non-…
The transport properties of magnetic tunnel junctions (MTJs) are very sensitive to interface modifications. In this work we investigate both experimentally and theoretically the effect of asymmetric barrier modifications on the bias dependence of tunneling magnetoresistance (TMR) in single crystal Fe/MgO-based MTJs with (i) one crystalline and one rough interface and (ii) with a monolayer of O deposited at the crystalline interface. In both cases we observe an asymmetric bias dependence of TMR and a reversal of its sign at large bias. We propose a general model to explain the bias dependence i…
Negative longitudinal magnetoresistances (NLMRs) have been recently observed in a variety of topological materials and often considered to be associated with Weyl fermions that have a defined chirality. Here we report NLMRs in non-Weyl GaAs quantum wells. In the absence of a magnetic field the quantum wells show a transition from semiconducting-like to metallic behaviour with decreasing temperature. We observed pronounced NLMRs up to 9 Tesla at temperatures above the transition and weak NLMRs in low magnetic fields at temperatures close to the transition and below 5 K. The observed NLMRs show …
Temperature and crystallographic orientation dependence of the anisotropic magnetoresistance in epitaxial Fe65Co35 thin films
Universidad Nacional de Ingeniería（国立工程学院）；Universidad Católica San Pablo（圣保罗天主教大学）；Instituto Balseiro, Universidad Nacional de Cuyo, Comisión Nacional de Energía Atómica（巴尔塞罗研究所，门多萨国立大学，国家原子能委员会）；Instituto de Nanociencia y Nanotecnología (CNEA - CONICET)（纳米科学与技术研究所（国家原子能委员会-国家科学研究和技术委员会））；Comisión Nacional de Energía Atómica（国家原子能委员会）
GeMn granular thin films are a unique and promising material for spintronics applications due to large positive magnetoresistance (MR). Previous studies on GeMn have suggested that the large MR is related to nanospinodal decomposition of GeMn into Mn-rich ferromagnetic nanoparticles and Mn-poor paramagnetic matrix. However, its microscopic origin of the MR has not been clarified yet. Here, using X-ray magnetic circular dichroism (XMCD), which is extremely sensitive to the local magnetic state of each atom, we investigate the magnetic properties of the nanoparticles and the matrix in GeMn separ…
This paper proposes a new model for Giant Magnetoresistance (GMR) and calculates its typical graph qualitatively. The model foundation is the microscopic mechanism in GMR, where the GMR effect can be explained by intrinsic and extrinsic potential. The potentials are spin-dependent. The potentials determine the transmission probability then it will give conductance value. Here, the multiple barrier potential model is proposed as the new GMR model. The transmission probability is determined using transfer matrix method. It was found that this model is fit qualitatively with the typical GMR graph…
We investigated the dependence of giant tunnel magnetoresistance (TMR) on the thickness of an MgO barrier and on the annealing temperature of sputtered CoFeB/MgO/CoFeB magnetic tunnel junctions deposited on SiO2/Si wafers. The resistance-area product exponentially increases with MgO thickness, indicating that the quality of MgO barriers is high in the investigated thickness range of 1.15-2.4 nm. High-resolution transmission electron microscope images show that annealing at 375 C results in the formation of crystalline CoFeB/MgO/CoFeB structures, even though CoFeB electrodes are amorphous in th…
We report a metal-insulator like transition in single crystalline 3D topological insulator Bi2Te3 at a temperature of 230K in presence of an external magnetic field applied normal to the surface. This transition becomes more prominent at larger magnetic field strength with the residual resistance value increasing linearly with the magnetic field. At low temperature, the magnetic field dependence of the magnetoresistance shows a transition from logarithmic to linear behavior and the onset magnetic field value for this transition decreases with increasing temperature. The logarithmic magnetoresi…
Magnetic layered van der Waals crystals are an emerging class of materials giving access to new physical phenomena, as illustrated by the recent observation of 2D ferromagnetism in Cr2Ge2Te6 and CrI3. Of particular interest in semiconductors is the interplay between magnetism and transport, which has remained unexplored. Here we report first magneto-transport measurements on exfoliated CrI3 crystals. We find that tunneling conduction in the direction perpendicular to the crystalline planes exhibits a magnetoresistance as large as 10 000 %. The evolution of the magnetoresistance with magnetic f…
We investigate electromagnetic properties of a topological crystalline insulator (TCI) thin film under external electromagnetic fields. The TCI thin film is a topological insulator indexed by the mirror-Chern number. It is demonstrated that the gap closes together with the emergence of a pair of gapless cones carrying opposite chirarities by applying in-plane magnetic field. A pair of gapless points have opposite vortex numbers. This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. We thus present an a magnetic-field induced semimetal-semiconductor transition in 2D material. Thi…
Controlling the stacking of van der Waals (vdW) materials is found to produce exciting new findings, since hetero- or homo- structures have added the diverse possibility of assembly and manipulated functionalities. However, so far, the homostructure with a twisted angle based on the magnetic vdW materials remains unexplored. Here, we achieved a twisted magnetic vdW Fe3GeTe2/Fe3GeTe2 junction with broken crystalline symmetry. A clean and metallic vdW junction is evidenced by the temperature-dependent resistance and the linear I-V curve. Unlike the pristine FGT, a plateau-like magnetoresistance …
Tungsten ditelluride is a layered transition metal dichalcogenide (TMD) that has attracted increasing research interest in recent years. WTe2 has demonstrated large non-saturating magnetoresistance, potential for spintronic applications and promise as a type-II Weyl semimetal. The majority of works on WTe2 have relied on mechanically-exfoliated flakes from chemical vapour transport (CVT) grown crystals for their investigations. While producing high-quality samples, this method is hindered by several disadvantages including long synthesis times, high-temperature anneals and an inherent lack of …
Helical magnets are emerging as a novel class of materials for spintronics and sensor applications; however, research on their charge and spin transport properties in a thin film form is less explored. Herein, we report the temperature and magnetic field dependent charge transport properties of a highly crystalline MnP nanorod thin film over a wide temperature range (2-350 K). The MnP nanorod films of 100 nm thickness were grown on Si substrates at 500 oC using molecular beam epitaxy. The temperature dependent resistivity data exhibits a metallic behavior over the entire measured temperature r…
We present a detailed study on domain imaging, Kerr effect magnetometry (MOKE) and magnetoresistance (MR), for a series of 20 nm Co$_{73.8}$Fe$_{16.2}$B$_{10}$ thin films, both as-deposited (amorphous) and annealed (crystalline). By considering the two different (orthogonal) in-plane magnetization components, obtained by MOKE measurements, we were able to study the uniaxial anisotropy induced during CoFeB-deposition and to discriminate the magnetization processes under a magnetic field parallel and perpendicular to such axis. MOKE magnetic imaging enabled us to observe the dominant magnetizati…
We present electrical transport data for single-crystalline Co$_2$FeSi which provide clear-cut evidence that this Heusler compound is truly a half-metallic ferromagnet, i.e. it possesses perfect spin-polarization. More specifically, the temperature dependence of $ρ$ is governed by electron scattering off magnons which are thermally excited over a sizeable gap $Δ\approx 100 K$ ($\sim 9 meV$) separating the electronic majority states at the Fermi level from the unoccupied minority states. As a consequence, electron-magnon scattering is only relevant at $T\gtrsimΔ$ but freezes out at lower temper…
Thin films of perovskite manganite La_{0.7}Ca_{0.3}MnO_{3} were grown epitaxially on SrTiO_3(100), MgO(100) and LaAlO_3(100) substrates by the pulsed laser deposition method. Microscopic structures of these thin film samples as well as a bulk sample were fully determined by x-ray diffraction measurements. The unit cells of the three films have different shapes, i.e., contracted tetragonal, cubic, and elongated tetragonal for SrTiO_3, MgO, and LaAlO_3 cases, respectively, while the unit cell of the bulk is cubic. It is found that the samples with cubic unit cell show smaller peak magnetoresista…
A new class of materials termed topological insulators have been intensively investigated due to their unique Dirac surface state carrying dissipationless edge spin currents. Recently, it has been theoretically proposed that the three dimensional analogue of this type of band structure, the Weyl Semimetal phase, is materialized in pyrochlore oxides with strong spin-orbit coupling, accompanied by all-in-all-out spin ordering. Here, we report on the fabrication and magnetotransport of Eu2Ir2O7 single crystalline thin films. We reveal that one of the two degenerate all-in-all-out domain structure…
The polycrystalline form of the compound, Tb5Si3, crystallizing in Mn5Si3-type hexagonal structure, which was earlier believe to order antiferromagnetically below 69 K, has been recently reported by us to exhibit interesting magnetoresistance (MR) anomalies. In order to understand the magnetic anomalies of this compound better, we synthesized single crystals of this compound and subjected them to intense magnetization and MR studies. The results reveal that the magnetic behavior is strongly anisotropic as the easy axis is along a basal plane. There appear to be multiple magnetic features in th…
Charge-transfer excitons (CTX) at organic donor/acceptor interfaces are considered important intermediates for charge separation in photovoltaic devices. Crystalline model systems provide microscopic insights into the nature of such states as they enable microscopic structure-property investigations. Here, we use angular-resolved UV/Vis absorption spectroscopy to characterize the CTX of crystalline pentacene:perfluoro-pentacene (PEN:PFP) films allowing to determine the polarization of this state. This analysis is complemented by first-principles many-body calculations, performed on the three-d…
e report the effect of pressure on the steplike magnetostriction of single crystalline bilayered manganite (LaPr)1.2Sr1.8Mn2O8, for our understandings of the ultrasharp nature of the field-induced first-order transition from a paramagnetic insulator to a ferromagnetic metal phase. The application of pressure suppresses a steplike transformation and causes a broad change in the magnetostriction. The injection of an electric current to the crystal also weakens the steplike variation in both the magnetostriction and magnetoresistance. The stabilization of ferromagnetic interaction or the delocali…
Strain Tuning of Orbital-Driven Giant Magnetoresistance in van der Waals ferrimagnet Mn$_3$Si$_2$Te$_6$
Institute for Solid State Physics, The University of Tokyo（东京大学固体离子体研究所）；The University of Tokyo（东京大学）；Department of Physics and Astronomy, The University of Manchester（曼彻斯特大学物理与天文学系）；The University of Manchester（曼彻斯特大学）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Institute of Science Tokyo（东京科学大学）
Orbital degrees of freedom can have pronounced effects on the fundamental properties of electrons in solids. In addition to influencing bandwidths, gaps, correlation strength and dispersion, orbital effects have also been implicated in generating novel electronic and structural phases, such as Jahn-Teller effect and colossal magnetoresistance. In this work, we show for the first time how the orbital nature of bands can result in non-trivial effects of strain on the band structure. We use scanning tunneling microscopy and quasiparticle interference imaging to study the effects of strain on the …
A coarse-grained molecular dynamics model of linear polyethylene-like polymer chain system was built to investigate the responds of structure and mechanical properties during uniaxial deformation. The influence of chain length, temperature, and strain rate were studied. The molecular dynamic tests showed that yielding may governed by different mechanisms at temperatures above and below Tg. Melt-recrystallization was observed at higher temperature, and destruction of crystal structures was observed at lower temperatures beyond yield point. While the higher temperature and lower strain rate have…
Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises ultrathin insulating multiferroics, spin liquids, and ferromagnets, but new characterization methods are required to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI3 as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and inter-layer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95%,…
We present a procedure for finding the exact solution to the linear-response Boltzmann equation for two-dimensional anisotropic systems and demonstrate it on examples of non-crystalline anisotropic magnetoresistance in a system with spin-orbit interaction. We show that two decoupled integral equations must be solved in order to find the non-equilibrium distribution function up to linear order in the applied electric field. The examples are all based on the Rashba system with charged magnetic scatterers, a system where the non-equilibrium distribution function and anisotropic magnetoresistance …
Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise to a strong quasiparticle drift in the direction perpendicular to the electric current and magnetic field. This drift is responsible for a strong geometrical increase of resistance even in weak magnetic fields. Combining the Boltzmann kinetic equation with sample electrostatics, we develop a microscopic theory of magnetotransport in two and three spatial dim…
