Hall Bar Research Articles

The physical properties of the Hall current

We study the stationary state of Hall devices composed of a load circuit connected to the lateral edges of a Hall bar. We follow the approach developed in a previous work [Creff et al., J. Appl. Phys. 128, 054501 (2020)] in which the stationary state of an ideal Hall bar is defined by the minimum power dissipation principle. The presence of both the lateral circuit and the magnetic field induces the injection of a current: the so-called Hall current. Analytical expressions for the longitudinal and transverse currents are derived. It is shown that the efficiency of the power injection into the lateral circuit is quadratic in the Hall angle and obeys to the maximum transfer theorem. For usual values of the Hall angle, the main contribution of this power injection provides from the longitudinal current flowing along the edges instead of the transverse current crossing the Hall bar.

Correlation between electronic micro-roughness and surface topography in two-dimensional surface conducting hydrogen-terminated diamond

The influence of surface topography on phase coherent transport in the two-dimensional (2D) hole band of surface transfer doped hydrogen-terminated (100) diamond is investigated. Low-temperature magneto-conductance measurements were carried out with an applied in-plane magnetic field to quantify the effect of electronic micro-roughness on spin dephasing in the 2D hole band for Hall bar devices with similar transport characteristics, but significantly different topographic roughness. The electronic micro-roughness of the 2D hole band, described by the parameter d2L, where d is the root-mean-square (rms) fluctuation in the width of the quantum well and L is the correlation length of the fluctuations, is found to increase for surfaces with increased roughness. Fluctuations in the well width likely arise from a locally varying hole carrier density, arising for example from a local variation in the concentration of ionic components in the surface water layer.

Voltage controlled N\xe9el vector rotation in zero magnetic field

Multi-functional thin films of boron (B) doped Cr2O3 exhibit voltage-controlled and nonvolatile Néel vector reorientation in the absence of an applied magnetic field, H. Toggling of antiferromagnetic states is demonstrated in prototype device structures at CMOS compatible temperatures between 300 and 400 K. The boundary magnetization associated with the Néel vector orientation serves as state variable which is read via magnetoresistive detection in a Pt Hall bar adjacent to the B:Cr2O3 film. Switching of the Hall voltage between zero and non-zero values implies Néel vector rotation by 90 degrees. Combined magnetometry, spin resolved inverse photoemission, electric transport and scanning probe microscopy measurements reveal B-dependent TN and resistivity enhancement, spin-canting, anisotropy reduction, dynamic polarization hysteresis and gate voltage dependent orientation of boundary magnetization. The combined effect enables H = 0, voltage controlled, nonvolatile Néel vector rotation at high-temperature. Theoretical modeling estimates switching speeds of about 100 ps making B:Cr2O3 a promising multifunctional single-phase material for energy efficient nonvolatile CMOS compatible memory applications.

Low-Temperature 2D/2D Ohmic Contacts in WSe2 Field-Effect Transistors as a Platform for the 2D Metal-Insulator Transition.

We report the fabrication of hexagonal-boron-nitride (hBN) encapsulated multiterminal WSe2 Hall bars with 2D/2D low-temperature Ohmic contacts as a platform for investigating the two-dimensional (2D) metal-insulator transition. We demonstrate that the WSe2 devices exhibit Ohmic behavior down to 0.25 K and at low enough excitation voltages to avoid current-heating effects. Additionally, the high-quality hBN-encapsulated WSe2 devices in ideal Hall-bar geometry enable us to accurately determine the carrier density. Measurements of the temperature (T) and density (ns) dependence of the conductivity σ(T, ns) demonstrate scaling behavior consistent with a metal-insulator quantum phase transition driven by electron-electron interactions but where disorder-induced local magnetic moments are also present. Our findings pave the way for further studies of the fundamental quantum mechanical properties of 2D transition metal dichalcogenides using the same contact engineering.

Anodic oxidation of epitaxial superconductor-semiconductor hybrids

We demonstrate a new fabrication process for hybrid semiconductor-superconductor heterostructures based on anodic oxidation (AO), allowing controlled thinning of epitaxial Al films. Structural and transport studies of oxidized epitaxial Al films grown on insulating GaAs substrates reveal spatial non-uniformity and enhanced critical temperature and magnetic fields. Oxidation of epitaxial Al on hybrid InAs heterostructures with a conducting quantum well show similarly enhanced superconducting properties transferred to the two-dimensional electron gas (2DEG) by proximity effect, with critical perpendicular magnetic fields up to 3.5 T. An insulating AlOx film, that passivates the heterostructure from exposure to air, is obtained by complete oxidation of the Al. It simultaneously removes the need to strip Al which damages the underlying semiconductor. AO passivation yielded 2DEG mobilities two times higher than similar devices with Al removed by wet etching. An AO-passivated Hall bar showed quantum Hall features emerging at a transverse field of 2.5 T, below the critical transverse field of thinned films, eventually allowing transparent coupling of quantum Hall effect and superconductivity. AO thinning and passivation are compatible with standard lithographic techniques, giving lateral resolution below <50 nm. We demonstrate local patterning of AO by realizing a semiconductor-based Josephson junction operating up to 0.3 T perpendicular.

Sense current dependent coercivity and magnetization relaxation in Gd-Fe-Co Hall bar

The understanding of the characteristics of a magnetic layer in a different environment is crucial for any spintronics application. Before practical applications, thorough scrutiny of such devices is compulsory. Here we study such a potential Hall device of MgO-capped Hf/GdFeCo bilayer (FeCo-rich) for magnetization relaxation around nucleation fields at different voltage probe line widths and dc sensing currents. The device is characterized by anomalous Hall measurements in transverse and longitudinal Hall geometries for two different probe widths A (5 µm) and B (1 µm). The coercivities of the Hall loops (ρxy-H and Rxx-H) drop with increasing the sense current for both the probes. For probe B, the sharp and large drop in coercivity (ρxy-H loops) at comparatively lower sensing currents is observed, which is attributed to the negligible current shunting and presence of pinning site at B caused by the patterning process. The average domain wall velocities at various sensing currents for probe B are found to be smaller than probe A, from the transverse and longitudinal Hall geometry magnetization relaxation measurements, which agrees with pinning sites and Joule heating effect at probe B. The notch position in the pattern and the longitudinal Hall resistance curve peak shape suggest the domain wall propagation direction from probe B to probe A in the current channel. This study highlights the domain wall propagation at different nucleation fields, sensing currents, and the Hall probe aspect ratios.

Convenient Peierls phase choice for periodic atomistic systems under magnetic field

Peierls phase factors multiplying the hopping elements of tight-binding-like Hamiltonians conveniently describe the effect of slowly varying magnetic fields on electrons. This paper provides practical recipes to determine Peierls phase factors such that they preserve the translation symmetry of periodic two-dimensional systems and of quasi-one-dimensional systems that are periodic or with periodic subcomponents, such as Hall bars, in the presence of a homogeneous magnetic field. This allows the applicability of convenient numerical techniques based on the spatial periodicity of the Hamiltonian as demonstrated here on some examples.

Selective etching of hexagonal boron nitride by high-pressure CF4 plasma for individual one-dimensional ohmic contacts to graphene layers

We describe a technique for fabricating one-dimensional Ohmic contacts to individual graphene layers encapsulated in hexagonal boron nitride (h-BN) using CF4 and O2 plasmas. The high etch selectivity of h-BN against graphene (&amp;gt;1000) is achieved by increasing the plasma pressure, which enables etching of h-BN, while graphene acts as an etch stop to protect underlying h-BN. A low-pressure O2 plasma anisotropically etches graphene in the vertical direction, which exposes graphene edges at h-BN sidewalls. Despite the O2 plasma bombardment, the lower h-BN layer functions as an insulating layer. Thus, this method allows us to pattern metal electrodes on h-BN over a second graphene layer. Subsequent electron-beam lithography and evaporation fabricate metal contacts at the graphene edges that are active down to cryogenic temperatures. This fabrication method is demonstrated by the preparation of a graphene Hall bar with a graphite backgate and double bilayer-graphene Hall bar devices. The high flexibility of the device geometries enabled by this method creates access to a variety of experiments on electrostatically coupled graphene layers.

Electrically induced breakdown of the quantum Hall effect at different Hall bar widths: Visualizing the edge- and bulk-dominated regimes within a quantum Hall plateau

We present systematic investigations of the electrically induced breakdown of the integer quantum Hall effect (QHE) in (Al,Ga)As-based Hall bars of different widths ranging from 7 to 70 $\ensuremath{\mu}\mathrm{m}$. It is striking that, for the narrow Hall bars, the threshold values for the applied voltage that induces the breakdown of the longitudinal zero-resistance state differ appreciably between the upper and lower sides of a quantum Hall (QH) plateau. When moving from the low magnetic field side of the QH plateau to higher magnetic fields, the threshold rises in a strongly superlinear manner until---at the expected integer value for the Landau level (LL) filling factor in the bulk of the two-dimensional electron system (2DES)---the threshold value abruptly drops to low values for the rest of the plateau. With increasing widths of the Hall bars, the zero-resistance state extends slightly further to higher magnetic field values. The threshold values on the low-magnetic field side are almost independent of the Hall bar width, whereas the threshold values on the high magnetic field side scale linearly with the Hall bar width. These observations correspond perfectly with the microscope picture of the QHE where the biased current flows in a dissipationless manner in electrically incompressible regions of the 2DES of locally the same LL filling factor, driven by the respective drop of the Hall voltage over the width of these incompressible regions. Owing to the self-consistent evolution of the electrically incompressible/compressible landscape within the 2DES as a function of magnetic field, a transition from an edge- to a bulk-dominated QH regime is described within a QH plateau. This microscopic picture was derived from sophisticated, long-lasting scanning probe experiments measuring Hall potential profiles on typically 15-$\ensuremath{\mu}$m-wide Hall bars. Conversely, performing systematic electrically induced breakdown measurements like those presented here would allow us to identify the presence of edge- and bulk-dominated regimes of the QHE in a wider variety of samples.

Gated two-dimensional electron gas in magnetic field: Nonlinear versus linear regime

We study the effect of magnetic field on the properties of a high mobility gated two-dimensional electron gas in a field effect transistor with the Hall bar geometry. When approaching the current saturation when the drain side of the channel becomes strongly depleted, we see a number of unusual effects related to the magnetic field induced re-distribution of the electron density in the conducting channel. The experimental results obtained in the non-linear regime have been interpreted based on the results obtained in the linear regime by a simple theoretical model, which describes quite well our observations.

Insulating SiO2 under Centimeter-Scale, Single-Crystal Graphene Enables Electronic-Device Fabrication.

Graphene on SiO2 enables fabrication of Si-technology-compatible devices, but a transfer of these devices from other substrates and direct growth have severe limitations due to a relatively small grain size or device-contamination. Here, we show an efficient, transfer-free way to integrate centimeter-scale, single-crystal graphene, of a quality suitable for electronic devices, on an insulating SiO2 film. Starting with single-crystal graphene grown epitaxially on Ru(0001), a SiO2 film is grown under the graphene by stepwise intercalation of silicon and oxygen. Thin (∼1 nm) crystalline or thicker (∼2 nm) amorphous SiO2 has been produced. The insulating nature of the thick amorphous SiO2 is verified by transport measurements. The device-quality of the corresponding graphene was confirmed by the observation of Shubnikov-de Haas oscillations, an integer quantum Hall effect, and a weak antilocalization effect within in situ fabricated Hall bar devices. This work provides a reliable platform for applications of large-scale, high-quality graphene in electronics.

Effects of mobile oxygen ions in top-gated synthetic antiferromagnet structure

In this work, we study the effects of mobile oxygen ions in a synthetic antiferromagnet structure gated by a sputtered SiO2 dielectric layer for memory and logic applications. Our devices utilize electrochemical reactions between dielectric reactive species and magnetic elements to create irreversible changes in magnetization. We analyzed the dependence of ion velocity on the gate dielectric properties such as the lattice parameter, oxygen migration energy barrier, and electric field (E-field). Hall bar devices were patterned and tested to determine the interlayer exchange coupling between the CoFeB and [Co/Pd]n layers. The anomalous Hall effect (AHE) of the CoFeB layer at different gate voltages (Vg) was measured to determine the Vg dependence. A sharp change in the behavior of the CoFeB layer with respect to negative Vg results in a non-reciprocal decrease in the coercivity and magnetization and an increase in exchange bias. The observed change in exchange bias field and magnetization allows us to measure the change in the effective thickness of the CoFeB layer. This led us to conclude that the source of such behavior is the negatively charged mobile oxygen ions from the SiO2 gate.

Stochastic description of the stationary Hall effect

The properties that characterize the stationary Hall effect in a Hall bar are derived from the Langevin equations describing the Brownian motion of an ensemble of interacting moving charges in a constant externally applied electromagnetic field. It is demonstrated that a non-uniform current density (a) superimposes on the injected one, (b) is confined in a boundary layer located near the edges over the Debye–Fermi length scale, (c) results from coupling between diffusion and conduction, and (d) arises because of charge accumulation at the edges. The theory can easily be transposed to describe the Hall effect in metals, semi-conductors, and plasmas and agrees with standard and previously published results.

Engineering of the spin on dopant process on silicon on insulator substrate

We report on a systematic analysis of phosphorus diffusion in silicon on insulator thin film via spin-on-dopant process (SOD). This method is used to provide an impurity source for semiconductor junction fabrication. The dopant is first spread into the substrate via SOD and then diffused by a rapid thermal annealing process. The dopant concentration and electron mobility were characterized at room and low temperature by four-probe and Hall bar electrical measurements. Time-of-flight-secondary ion mass spectroscopy was performed to estimate the diffusion profile of phosphorus for different annealing treatments. We find that a high phosphorous concentration (greater than 1020 atoms cm−3) with a limited diffusion of other chemical species and allowing to tune the electrical properties via annealing at high temperature for short time. The ease of implementation of the process, the low cost of the technique, the possibility to dope selectively and the uniform doping manufactured with statistical process control show that the methodology applied is very promising as an alternative to the conventional doping methods for the implementation of optoelectronic devices.

Quantification of interfacial spin-charge conversion in hybrid devices with a metal/insulator interface

We present and experimentally verify a universal theoretical framework for the description of spin-charge interconversion in non-magnetic metal/insulator structures with interfacial spin–orbit coupling (ISOC). Our formulation is based on drift-diffusion equations supplemented with generalized boundary conditions. The latter encode the effects of ISOC and relate the electronic transport in such systems to spin loss and spin-charge interconversion at the interface. We demonstrate that the conversion efficiency depends solely on these interfacial parameters. We apply our formalism to two typical spintronic devices that exploit ISOC: a lateral spin valve and a multilayer Hall bar, for which we calculate the non-local resistance and the spin Hall magnetoresistance, respectively. Finally, we perform measurements on these two devices with a BiOx/Cu interface and verify that transport properties related to the ISOC are quantified by the same set of interfacial parameters.

Magnetic and Magnetotransport Properties of Memory Sensors Based on Anisotropic Magnetoresistance

The magnetic and magnetoresistance properties of anisotropic magnetoresistance (AMR) sensors based on Wheatstone bridge (WB) with barber pole and conventional Hall bar structures were studied. The samples were prepared by using standard microlithography and sputter deposition techniques and then measured by magneto-optic Kerr effect and magneto transport methods. The advantages of the AMR sensor based on WB compared with Hall bar structure were discussed. It was observed that sensitivity was increased almost 15 times when sensors with the WB structures were used instead of Hall bar structures. Moreover, sensor stability was tested in various external magnetic fields with positive and negative polarities. The test results show that sensor response is stable even in various external magnetic fields up to 5000 Oe. The changes in sensitivity and output voltage were attributed to WB structure.

Negative Delta-T Noise in the Fractional Quantum Hall Effect.

We study the current correlations of fractional quantum Hall edges at the output of a quantum point contact subjected to a temperature gradient. This out-of-equilibrium situation gives rise to a form of temperature-activated shot noise, dubbed delta-T noise. We show that the tunneling of Laughlin quasiparticles leads to a negative delta-T noise, in stark contrast with electron tunneling. Moreover, varying the transmission of the quantum point contact or applying a voltage bias across the Hall bar may flip the sign of this noise contribution, yielding signatures that can be accessed experimentally.

Single- versus Dual-Ion Conductors for Electric Double Layer Gating: Finite Element Modeling and Hall-Effect Measurements.

Electric double layer (EDL) gating using a single-ion conductor is compared to a dual-ion conductor using both finite element modeling and Hall-effect measurements. Modified Nernst-Planck Poisson (mNPP) equations are used to calculate the ion density per unit area in a parallel plate capacitor geometry with a bulk ion concentration of 215 ≤ cbulk ≤ 1782 mol/m3. With electrodes of equal size at a 2 V potential difference, the EDL ion density of the single-ion conductor is ∼7 × 1013 ions/cm2, which is approximately 50% of the ion density induced in the dual-ion conductor. However, this difference is reduced to 8% when the electrode at which the cationic EDL forms is 10 times smaller than the counter electrode. Thus, for a field-effect transistor gated by a single-ion conductor, it is especially important to have a large gate-to-channel size ratio to achieve strong ion doping. The modeled ion densities are validated by Hall-effect measurements on graphene Hall bars gated by a polyethylene oxide (PEO)-based single-ion conductor. The sheet carrier density, nS, is ∼2 × 1013 cm-2 at Vg = 2 V, which is 3.5 times smaller than the predicted value and has the same order of magnitude as the ns measured for a PEO-based, dual-ion conductor on the same graphene. The numerical modeling results can be approximated by a simple analysis of capacitors in series, where the EDLs are modeled as capacitors with thickness estimated by the sum of the Debye screening length and the Stern layer. The series of capacitor estimate agrees with the numerical modeling of the dual-ion conductor to within 10% and the single-ion conductor to within 30% from 0.25 to 2 V (cbulk = 925 mol/m3); similar agreement is observed in the concentration range of 353-1650 mol/m3 for both single- and dual-ion conductors.

Electrical readout of the antiferromagnetic state of IrMn through anomalous Hall effect

We report the electrical detection of the antiferromagnetic state of IrMn through anomalous Hall measurements in Ta/IrMn heterostructures. The magnetic state is set in the antiferromagnet through field cooling and detected electrically by transverse resistance measurements in Hall bar structures without the need for any ferromagnetic layer. The amplitude of the signal increases with the magnetic field applied during the cooling and is enhanced by the proximal interface with a Ta layer. From the temperature dependence of the effect and the comparison between Ta/IrMn and Ru/IrMn interfaces, we propose an explanation of such readouts based on the simultaneous occurrence of spin-Hall magnetoresistance and magnetic proximity in Ta. These findings highlight how interface effects could be generally employed for the investigation of antiferromagnetic materials as well as for the electrical readout of the antiferromagnetic state.

Size-dependent anomalous Hall effect in noncollinear antiferromagnetic Mn3Sn films

The coercive field of ferromagnets generally increases with decreasing the sample size to hundreds of nanometers mainly because of the (edge) defect pinning. We investigate size-dependent anomalous Hall effect (AHE) in (112¯0)-oriented noncollinear antiferromagnetic Mn3Sn films. The switching field (coercive field) of the AHE decreases abruptly when the width of the Hall bar decreases to hundreds of nanometers, giving rise to the reduced coercive field from 445 to 30 mT for Hall bar with width from 2 μm to 100 nm. This observation is in contrast to the ferromagnetic counterpart. The transition from a multidomain to single domain-like mode and the reduction of Néel temperature are proposed to explain the coercivity variation. Our finding provides a promising candidate for the device miniaturization and adds a different dimension to antiferromagnetic spintronics.