Linear Hall Effect Research Articles

Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems

Abstract The nonlinear Hall effect (NLHE) has been detected in various of condensed matter systems. Unlike linear Hall effect, NLHE may exist in physical systems with broken inversion symmetry in the crystal. On the other hand, real space spin texture may also break inversion symmetry and result in NLHE. In this letter, we employ the Feynman diagrammatic technique to calculate nonlinear Hall conductivity (NLHC) in three-dimensional magnetic systems. The results connect NLHE with the physical quantity of emergent electrodynamics which originates from the magnetic texture. The leading order contribution of NLHC $\chi_{abb}$ is proportional to the emergent toroidal moment $\mathcal{T}_{a}^{e}$ which reflects how the spin textures wind in three dimension.

Picosecond Trajectory of Two-Dimensional Vortex Motion in FeSe_{0.5}Te_{0.5} Visualized by Terahertz Second Harmonic Generation.

We have investigated the vortex dynamics in a thin film of an iron-based superconductor FeSe_{0.5}Te_{0.5} by observing second-harmonic generation (SHG) in the terahertz frequency range. We visualized the picosecond trajectory of two-dimensional vortex motion in a pinning potential tilted by Meissner shielding current. The SHG perpendicular to the driving field is observed, corresponding to the nonreciprocal nonlinear Hall effect under the current-induced inversion symmetry breaking, whereas the linear Hall effect is negligible. The estimated vortex mass, as light as a bare electron, suggests that the vortex core moves independently from quasiparticles at such a high frequency and large velocity ≈300 km/s.

Quadrupole anomalous Hall effect in magnetically induced electron nematic state

Berry phases in both momentum and real space cause transverse motion in itinerant electrons, manifesting various off-diagonal transport effect such anomalous and topological Hall effects. Although these Hall effects are isotropic within the plane perpendicular to the fictitious magnetic field, here, we report the manifestation of the anisotropic linear anomalous Hall effect (AHE) in the spinel oxide NiCo2O4 epitaxial film. The unconventional Hall effect indicates a quadrupole dependence on the in-plane current direction being added to the uniform AHE. Moreover, its sign can be manipulated just by magnetic-field cooling. The anisotropic effect is attributed to an electron nematic state originating from a deformed electronic state owing to an extended magnetic toroidal quadrupole and ferrimagnetic order.

Tungsten and fluorine co-doping induced morphology change and textured growth of spray-pyrolyzed SnO2 thin films viable for photocatalytic application

Physicochemical aspects of numerous metal oxide based thin films are crucial for various optoelectronic applications. Cationic (W) and anionic (F) co-doping strategy into SnO2 thin film has been adapted in order to tune the optoelectronic parameters. X-ray diffraction pattern reveals successful doping of ‘W’ and ‘F’ into the SnO2 lattice and textured growth along (111) plane direction at the expense of suppression of the (211) plane. X-ray photoelectron spectroscopy confirmed the charge states of Sn4+, W6+, O2− and F1− elements present in the films. Scanning electron microscopy shows that tetragonal morphology of pure and F-doped SnO2 changes to a network-like feature upon ‘W’ co-doping and the elemental composition is also ensured. The contact angle measurement gives the surface wettability nature, which indicates all the films are hydrophilic. The 10 wt.% F-doped SnO2 shows a maximum transmittance of 89.36 % at 550 nm with a direct band gap of 3.82 eV. Electrical transport parameters are measured using linear four-probe and Hall effect techniques. Photocatalytic activity of methylene blue dye degradation showing a maximum efficiency for pure and solely F-doped SnO2 thin films are explained based on the obtained optoelectronic parameters.

Linear and nonlinear photonic spin Hall effect induced by analog circular birefringence of Bessel-like beams

The spin Hall effect of a light beam is essentially a product of circular birefringence but is rarely demonstrated. Here, we provide a scheme for initiating off-axis circular birefringence based on the spin-dependent wave vector bifurcation of Bessel beams via a single liquid crystal Pancharatnam–Berry phase element. The tilted Bessel beam shows a detectable photonic spin Hall effect. By introducing the nonlinear propagation trajectories, the spin Hall effect is greatly enhanced. More surprisingly, the two spin states exactly propagate along the scaled trajectories, enabling flexible control of the spin separation. This phenomenon is also applicable to other Bessel-like beams with nonlinear trajectories, which have been already reported.

Time-reversal even charge hall effect from twisted interface coupling

Under time-reversal symmetry, a linear charge Hall response is usually deemed to be forbidden by the Onsager relation. In this work, we discover a scenario for realizing a time-reversal even linear charge Hall effect in a non-isolated two-dimensional crystal allowed by time reversal symmetry. The restriction by Onsager relation is lifted by interfacial coupling with an adjacent layer, where the overall chiral symmetry requirement is fulfilled by a twisted stacking. We reveal the underlying band geometric quantity as the momentum-space vorticity of layer current. The effect is demonstrated in twisted bilayer graphene and twisted homobilayer transition metal dichalcogenides with a wide range of twist angles, which exhibit giant Hall ratios under experimentally practical conditions, with gate voltage controlled on-off switch. This work reveals intriguing Hall physics in chiral structures, and opens up a research direction of layertronics that exploits the quantum nature of layer degree of freedom to uncover exciting effects.

Even-Odd-Layer-Dependent Ferromagnetism in 2D Non-van-der-Waals CrCuSe2.

Van der Waals (vdW) layered materials with strong magnetocrystalline anisotropy have attracted significant interest as the long-range magnetic order in these systems can survive even when their thicknesses is reduced to the 2D limit. Even though the interlayer coupling between the neighboring magnetic layers is very weak, it has a determining effect on the magnetism of these atomic-thickness materials. Herein, a new 2D ferromagnetic material, namely, non-vdW CuCrSe2 nanosheets with even-odd-layer-dependent ferromagnetism when laminated from an antiferromagnetic bulk is reported. Monolayer and even-layer CuCrSe2 exhibit the anomalous Hall effect and a significantly enhanced magnetic ordering temperature of more than 125 K. In contrast, the linear Hall effect exists in the odd-layer samples. Theoretical calculations indicate that the layer-dependent magnetic coupling is attributable to the orbital shift of the Cr atoms in the CrSe2 layers owing to the Cu-induced breaking of the centrosymmetry. Thus, this work sheds light on the exotic magnetic properties of layered materials that exhibit phenomena beyond weak interlayer interactions.

Synthesis of Two-Dimensional MoO2 Nanoplates with Large Linear Magnetoresistance and Nonlinear Hall Effect.

Two-dimensional (2D) materials with large linear magnetoresistance (LMR) are very interesting owing to their potential application in magnetic storage or sensor devices. Here, we report the synthesis of 2D MoO2 nanoplates grown by a chemical vapor deposition (CVD) method and observe large LMR and nonlinear Hall behavior in MoO2 nanoplates. As-obtained MoO2 nanoplates exhibit rhombic shapes and high crystallinity. Electrical studies indicate that MoO2 nanoplates feature a metallic nature with an excellent conductivity of up to 3.7 × 107 S m-1 at 2.5 K. MoO2 nanoplates display a large LMR of up to 455% at 3 K and -9 T. A thickness-dependent LMR analysis suggests that LMR values increase upon increasing the thickness of nanoplates. Besides, nonlinearity has been found in the magnetic-field-dependent Hall resistance, which decreases with increasing temperatures. Our studies highlight that MoO2 nanoplates are promising materials for fundamental studies and potential applications in magnetic storage devices.

Third-order intrinsic anomalous Hall effect with generalized semiclassical theory

The linear intrinsic anomalous Hall effect (IAHE) and second-order IAHE have been intensively investigated in time-reversal broken systems. However, as one of the important members of the nonlinear Hall family, the investigation of third-order IAHE remains absent due to the lack of an appropriate theoretical approach, although the third-order extrinsic AHE has been studied within the framework of first- and second-order semiclassical theory. Herein, we generalize the semiclassical theory for Bloch electrons under the uniform electric field up to the third-order using wavepacket method and based on which we predict that the third-order IAHE can also occur in time-reversal broken systems. Same as the second-order IAHE, we find the band geometric quantity, the second-order field-dependent Berry curvature arising from the second-order field-induced positional shift, plays a pivotal role to observe this effect. Moreover, with symmetry analysis, we find that the third-order IAHE, as the leading contribution, is supported by 15 time-reversal broken 3D magnetic point groups (MPGs), corresponding to a wide class of antiferromagnetic (AFM) materials. Guided by the symmetry arguments, a two-band model is chosen to demonstrate the generalized theory. Furthermore, the generalized third-order semiclassical theory depends only on the properties of Bloch bands, implying that it can also be employed to explore the IAHE in realistic AFM materials, by combining with first-principles calculations.

Ferroelectricity-Driven Phonon Berry Curvature and Nonlinear Phonon Hall Transports.

Berry curvature (BC) governs topological phases of matter and generates anomalous transport. When a magnetic field is applied, phonons can acquire BC indirectly through spin-lattice coupling, leading to a linear phonon Hall effect. Here, we show that polar lattice distortion directly couples to a phonon BC dipole, which causes a switchable nonlinear phonon Hall effect. In a SnS monolayer, the in-plane ferroelectricity induces a phonon BC and leads to the phononic version of the nonvolatile BC memory effect. As a new type of ferroelectricity-phonon coupling, the phonon Rashba effect emerges and opens a mass gap in tilted Weyl phonon modes, resulting in a large phonon BC dipole. Furthermore, our ab initio non-equilibrium molecular dynamics simulations reveal that nonlinear phonon Hall transport occurs in a controllable manner via ferroelectric switching. The ferroelectricity-driven phonon BC and corresponding nonlinear phonon transports provide a novel scheme for constructing topological phononic transport/memory devices.

Photon-modulated linear and nonlinear anomalous Hall effects in type-II semi-Dirac semimetals

Two-dimensional semi-Dirac materials, with quadratic dispersion in one direction and linear dispersion in the orthogonal direction, provide a route to formation of the Chern-insulating states in solids. Within the framework of the Floquet theory, we investigate the photon-modulated linear and nonlinear anomalous Hall effect (AHE) in type-II semi-Dirac semimetals and find that rich topological phases, as well as interesting phenomena related to the topological transitions, can be realized and manipulated by circularly polarized light (CPL). By tuning the CPL parameters, we can control the local inverted gaps independently and switch the system between different topological phases optionally. We also demonstrate that, when the Fermi level locates outside the gap, the Drude component of the conductivity can contribute to the AHE as well, because of the anisotropy of the electronic structure. Besides, the nonlinear Hall effect due to the Berry curvature dipole can be observable when the inversion symmetry between opposite valleys is broken. Our findings are helpful to understand the topological properties of the emergent type-II semi-Dirac semimetals.

Systematic Analysis Method for Nonlinear Response Tensors

We propose a systematic analysis method for identifying essential parameters in various linear and nonlinear response tensors without which they vanish. By using the Keldysh formalism and the Chebyshev polynomial expansion method, the response tensors are decomposed into the model-independent and dependent parts, in which the latter is utilized to extract the essential parameters. An application of the method is demonstrated by analyzing the nonlinear Hall effect in the ferroelectric SnTe monolayer for example. It is shown that in this example the second-neighbor hopping is essential for the nonlinear Hall effect whereas the spin–orbit coupling is unnecessary. Moreover, by analyzing terms contributing to the essential parameters in the lowest order, the appearance of the nonlinear Hall effect can be interpreted by the subsequent two processes: the orbital magneto-current effect and the linear anomalous Hall effect by the induced orbital magnetization. In this way, the present method provides a microscopic picture of responses. By combining with computational analysis, it stimulates further discoveries of anomalous responses by filling in a missing link among hidden degrees of freedom in a wide variety of materials.

Chiral anomaly induced nonlinear Hall effect in semimetals with multiple Weyl points

After the experimental realization, the Berry curvature dipole (BCD) induced nonlinear Hall effect (NLHE) has attracted tremendous interest to the condensed matter community. Here, we investigate another family of Hall effect, namely, chiral anomaly induced nonlinear Hall effect (CNHE) in multi-Weyl semimetal (mWSM). In contrast to the BCD induced NLHE, CNHE appears because of the combination of both chiral anomaly and anomalous velocity due to non-trivial Berry curvature. Using the semiclassical Boltzmann theory within the relaxation time approximation, we show that, in contrast to the chiral anomaly induced linear Hall effect, the magnitude of CNHE decreases with the topological charge n. Interestingly, we find that unlike the case of n=1, the CNHE has different behaviors in different planes. Our prediction on the behavior of CNHE in mWSM can directly be checked in experiments.

Topological Magnus responses in two- and three-dimensional systems

Recently, time-reversal symmetric but inversion broken systems with nontrivial Berry curvature in the presence of a built-in electric field have been proposed to exhibit a new type of linear Hall effect in ballistic regime, namely, the Magnus Hall effect. The transverse current here is caused by the Magnus velocity that is proportional to the built-in electric field enabling us to examine the Magnus responses, in particular, Magnus Hall conductivity and Magnus Nernst conductivity, with chemical potential. Starting with two-dimensional (2D) topological systems, we find that warping induced asymmetry in both the Fermi surface and Berry curvature can in general enhance the Magnus response for monolayer graphene and surface states of topological insulator. The strain alone is only responsible for Magnus valley responses in monolayer graphene, while warping leads to finite Magnus response there. Interestingly, on the other hand, strain can change the Fermi surface character substantially that further results in distinct behavior of Magnus transport coefficients as we observe in bilayer graphene. These responses there remain almost insensitive to warping unlike the case of monolayer graphene. Going beyond 2D systems, we also investigate the Magnus responses in three-dimensional multi-Weyl semimetals (mWSMs) to probe the effect of tilt and anisotropic nonlinear energy dispersion. Remarkably, Magnus responses can only survive for the WSMs with chiral tilt. In particular, our study indicates that the chiral (achiral) tilt engenders Magnus (Magnus valley) responses. Therefore, Magnus responses can be used as a tool to distinguish between the untilted and tilted WSMs in experiments. In addition, we find that the Magnus Hall responses get suppressed with increasing the nonlinearity associated with the band touching around the multi-Weyl node.

Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor.

Nonlinear responses in transport measurements are linked to material properties not accessible at linear order1 because they follow distinct symmetry requirements2-5. While the linear Hall effect indicates time-reversal symmetry breaking, the second-order nonlinear Hall effect typically requires broken inversion symmetry1. Recent experiments on ultrathin WTe2 demonstrated this connection between crystal structure and nonlinear response6,7. The observed second-order nonlinear Hall effect can probe the Berry curvature dipole, a band geometric property, in non-magnetic materials, just like the anomalous Hall effect probes the Berry curvature in magnetic materials8,9. Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor10, gives rise to higher-order signals, but it has not been probed experimentally. Here, we report a third-order nonlinear Hall effect in thick Td-MoTe2 samples. The third-order signal is found to be the dominant response over both the linear- and second-order ones. Angle-resolved measurements reveal that this feature results from crystal symmetry constraints. Temperature-dependent measurement shows that the third-order Hall response agrees with the Berry-connection polarizability contribution evaluated by first-principles calculations. The third-order nonlinear Hall effect provides a valuable probe for intriguing material properties that are not accessible at lower orders and may be employed for high-order-response electronic devices.

Theory for linear and nonlinear planar Hall effect in topological insulator thin films

Recently, the linear and nonlinear planar Hall effect (PHE) on the topological insulators (TIs) surface has been extensively studied in experiments. To explain this phenomenon, various microscopic mechanisms are proposed theoretically, and one has to employ different mechanisms to separately understand the linear and nonlinear PHE even for the same system. Here, we study the planar magnetic resistance effect in TI thin film and find that a peculiar anisotropic scattering and a spin valve structure with respect to the PHE can be caused by the tilt and shift of Dirac cones, respectively, which are induced by the combination of spin-momentum locking of surface states and an in-plane magnetic field. The tilt and shift effects can act as the origin of both the linear and nonlinear PHE by distorting the spin texture of surface states or forming the spin polarization. These two mechanisms interplay and dominate, respectively, in strong coupling (thin TI) and decoupling (thick TI) between bottom and top surfaces. For thick TI film, we show that both the linear and nonlinear PHEs induced by the tilt effect can recover the results observed in recent experiments. Our theory provides a perspective to understand the origin of both linear and nonlinear PHE observed in recent experiments.

Anomalous Hall Sensors with High Sensitivity and Stability Based on Interlayer Exchange-Coupled Magnetic Thin Films

In this work, we demonstrate that interlayer exchange-coupled magnetic thin films can be employed to fabricate ultrasensitive and thermally stable magnetic sensors, taking advantage of the linear anomalous Hall effect via tuning the interlayer exchange coupling and magnetic anisotropy. We investigate the magnetotransport and noise properties of these anomalous Hall sensors. The magnetic field detectability reaches $126.1\phantom{\rule{0.1em}{0ex}}\mathrm{nT/}\sqrt{\mathrm{Hz}}$ at 1 Hz and $4.5\phantom{\rule{0.1em}{0ex}}\mathrm{nT/}\sqrt{\mathrm{Hz}}$ at 1 kHz, at room temperature. Meanwhile, the achieved dynamic reserve is 103.0 dB. The magnetic field detectability shows a good temperature stability in the 200 to 300 K range. Within the temperature range, the temperature coefficient of sensitivity is determined to be 530 ppm/K. The high temperature stability is attributed to the interlayer exchange coupling, which also improves the stability against in-plane magnetic fields, beneficial for perpendicular magnetic field sensing. The interlayer exchange-coupled magnetic thin-film-based anomalous Hall sensors solve the trade-off between the sensor size, sensing capability, and stability, which are desirable for microimaging and biomedical applications.

A NOVEL APPROACH FOR HUMAN INTENTION RECOGNITION BASED ON HALL EFFECT SENSORS AND PERMANENT MAGNETS

Human intention recognition is important for any interaction between the user and the exoskeleton. This study proposes a novel approach, based on a contactless sensory system, using linear Hall effect sensors to recognize human intentions. This contactless sensory system consists of four Hall effect sensors mounted on the exoskeleton, whilst a ring-shaped permanent magnet with diametrical magnetization consisting of two semi-rings is worn on the user's forearm. The model of the magnetic field created by the permanent magnet is also developed. Based on the developed magnetic field model and by interpreting the signals from the Hall effect sensory system received while the user's elbow and forearm move, the intention identification algorithm is derived. A lightweight elbow and forearm assistive exoskeleton is developed. The proposed approach for human intention recognition is used to assist in controlling the exoskeleton, following the wearer's intended motions. By implementing this contactless sensory system, wearers can use the exoskeleton easily and can move their forearm comfortably, while the human intention motion is recognized and used to control the exoskeleton. Moreover, achieved signals are unaffected by skin perspiration and muscle fatigue. As the sensory system is mounted on the exoskeleton, there is only indirect contact between the user's body and the sensors, leading to improved comfort. Finally, the system does not require expert knowledge to place the sensors on the body of the user. This approach can be extended to detect human intentions for the control of exoskeletons with more degrees of freedom.

Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule.

Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. We also derive a quantum rectification sum rule in time reversal invariant materials by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies. The intraband spectral weight of this sum rule is exhausted by the Berry curvature dipole Drude-like peak, and the interband weight is also entirely controlled by the Berry connection. This sum rule opens a door to search for alternative photovoltaic technologies based on the Berry geometry of bands. We also describe the rectification properties of Weyl semimetals which are a promising platform to investigate these effects.

Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2

Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials – an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a remarkable ferroelectric nonlinear anomalous Hall effect in time-reversal invariant few-layer WTe2 where nonlinear anomalous Hall current switches in odd-layer WTe2 except 1T′ monolayer while remaining invariant in even-layer WTe2 upon ferroelectric transition. This even-odd oscillation of ferroelectric nonlinear anomalous Hall effect was found to originate from the absence and presence of Berry curvature dipole reversal and shift dipole reversal due to distinct ferroelectric transformation in even and odd-layer WTe2. Our work not only treats Berry curvature dipole and shift dipole on an equal footing to account for intraband and interband contributions to nonlinear anomalous Hall effect, but also establishes Berry curvature dipole and shift dipole as new order parameters for noncentrosymmetric materials. The present findings suggest that ferroelectric metals and Weyl semimetals may offer unprecedented opportunities for the development of nonlinear quantum electronics.