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The recent detection of the singular diamagnetism of Dirac electrons in a single graphene layer paved a new way of probing 2D quantum materials through the measurement of equilibrium orbital currents which cannot be accessed in usual transport experiments. Among the theoretical predictions is an intriguing orbital paramagnetism at saddle points of the dispersion relation. Here we present magnetisation measurements in graphene monolayers aligned on hexagonal boron nitride (hBN)crystals. Beside the sharp diamagnetic McClure response at the Dirac point, we detect extra diamagnetic singularities at the satellite Dirac points (sDP) of the moir\'e lattice. Surrounding these diamagnetic satellite peaks, we also observe paramagnetic peaks located at the chemical potential of the saddle points of the Graphene moir\'e band structure and relate them to the presence of van Hove logarithmic singularities in the density of states. These findings reveal the long ago predicted anomalous paramagnetic orbital response in 2D systems when the Fermi energy is tuned to the vicinity of saddle points., Comment: main paper 6 pages 5 figures and supplementaray materials 18 pages and 14 figures

In this letter, we present a study of optimized TMR magnetic field sensors as a function of voltage bias. The 1/f low-frequency noise is quantified by the Hooge-like parameter {\alpha} which allows to compare the low-frequency behavior of various TMR sensors. The sensitivity as well as the detectivity of the sensor are characterized in the parallel state and at 0 mT. We observe that the sensitivity shows a strong voltage dependence and the noise presents an unexpected decrease, not anticipated by the Hooge's law. Moreover, surprisingly, an almost stable detectivity (140-200 nT/sqrt(Hz) at 10 Hz and 15-20 nT/sqrt(Hz) at 1 kHz) as a function of the bias voltage is observed, tending to highlight that the variation of sensitivity and noise are correlated. Even if the I-V curves are strongly non-linear and reflect the different symmetries of the conduction bands channels, the variations in sensitivity and noise seems to depend mainly on the distortion of the MgO barrier due to bias voltage. With a simple model where the normal noise and sensitivity of the TMR sensors are modified by an element having no noise and a parabolic conductance with voltage, we describe the behavior of noise and sensitivity from mV to V.

In this manuscript we propose a theoretical model where the magneto-resistive elements are modelled as fluctuating resistances to correct the output voltage noise of tunnel magnetic junction (MTJ) from standard electronic circuits. This model is validated on single elements, partial and full Wheatstone bridge circuits, giving rise to a correction factor affecting the output noise voltage as well as sensitivity values. Combining the correction factor and a normalization by the number of MTJs pillars and the pillar surface, we show that the performances extracted by this method allow universal comparison between any results from literature.

The electronic properties of graphene have been intensively investigated over the last decade, and signatures of the remarkable features of its linear Dirac spectrum have been displayed using transport and spectroscopy experiments. In contrast, the orbital magnetism of graphene, which is one of the most fundamental signature of the characteristic Berry phase of graphene's electronic wave functions, has not yet been measured in a single flake. In particular, the striking prediction of a divergent diamagnetic response at zero doping calls for an experimental test. Using a highly sensitive Giant Magnetoresistance sensor (GMR) we have measured the gate voltage-dependent magnetization of a single graphene monolayer encapsulated between boron nitride crystals. The signal exhibits a diamagnetic peak at the Dirac point whose magnetic field and temperature dependences agree with theoretical predictions starting from the work of Mc Clure \cite{McClure1956}. Our measurements open a new field of investigation of orbital currents in graphene and 2D topological materials, offering a new means to monitor Berry phase singularities and explore correlated states generated by combined effects of Coulomb interactions, strain or moir\'e potentials., Comment: 6 pages 5 figures and supplemental material

Vertical packaging of multiple Giant Magnetoresistance (multi-GMR) stacks is a very interesting noise reduction strategy for local magnetic sensor measurements, which has not been reported experimentally so far. Here, we have fabricated multi-GMR sensors (up to 12 repetitions) keeping good GMR ratio, linearity and low roughness. From magnetotransport measurements, two different resistance responses have been observed with a crossover around 5 GMR repetitions: step-like (N<5) and linear (N>5) behavior, respectively. With the help of micromagnetic simulations, we have analyzed in detail the two main magnetic mechanisms: the Neel coupling distribution induced by the roughness propagation and the additive dipolar coupling between the N free layers. Furthermore we have correlated the dipolar coupling mechanism, controlled by the number of GMRs (N) and lateral dimensions (width), to the sensor performance (sensitivity, noise and detectivity) in good agreement with analytical theory. The noise roughly decreases in multi-GMRs as 1/\sqrt{N} in both regimes (low frequency 1/f and thermal noise). The sensitivity is even stronger reduced, scaling as 1/N, in the strong dipolar regime (narrow devices) while converges to a constant value in the weak dipolar regime (wide devices). Very interestingly, they are more robust against undesirable RTN noise than single GMRs at high voltages and the linearity can be extended towards much larger magnetic field range without dealing with the size and the reduction of GMR ratio. Finally, we have identified the optimal conditions for which multi-GMRs exhibit lower magnetic field detectivity than single GMRs: wide devices operating in the thermal regime where much higher voltage can be applied without generating remarkable magnetic noise.

The presence of magnetic noise in magnetoresistive-based magnetic sensors degrades their detection limit at low frequencies. In this paper, different ways of stabilizing the magnetic sensing layer to suppress magnetic noise are investigated by applying a pinning field, either by an external field, internally in the stack or by shape anisotropy. We show that these three methods are equivalent, could be combined and that there is a competition between noise suppression and sensitivity reduction, which results in an optimum total pinning field, for which the detection limit of the sensor is improved up to a factor of ten., Comment: 5 pages, 3 figures

Magneto-resistance is a physical effect of great fundamental and industrial interest since it is the basis for the magnetic field sensors used in computer read-heads and Magnetic Random Access Memories. As device dimensions are reduced, some important physical length scales for magnetism and electrical transport will soon be attained. Ultimately, there is a strong need to know if the physical phenomena responsible for magneto-resistance still hold at the atomic scale. Here, we show that the anisotropy of magneto-resistance is greatly enhanced in atomic size constrictions. We explain this physical effect by a change in the electronic density of states in the junction when the magnetization is rotated, as supported by our ab-initio calculations. This stems from the "spin-orbit coupling" mechanism linking the shape of the orbitals with the spin direction. This sensitively affects the conductance of atomic contacts which is determined by the overlap of the valence orbitals., Comment: latex AAMR.tex, 6 files, 5 figures, 4 pages (http://www-drecam.cea.fr/spec/articles/S06/011)