Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets

Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe_{3}Sn_{2}

It has been theoretically predicted that perturbation of the Berry curvature by electromagnetic fields gives rise to intrinsic nonlinear anomalous Hall effects that are independent of scattering. Two types of nonlinear anomalous Hall effects are expected. The electric nonlinear Hall effect has recently begun to receive attention, while very few studies are concerned with the magneto-nonlinear Hall effect. Here, we combine experiment and first-principles calculations to show that the kagome ferromagnet Fe_{3}Sn_{2} displays such a magneto-nonlinear Hall effect. By systematic field angular and temperature-dependent transport measurements, we unambiguously identify a large anomalous Hall current that is linear in both applied in-plane electric and magnetic fields, utilizing a unique in-plane configuration. We clarify its dominant orbital origin and connect it to the magneto-nonlinear Hall effect. The effect is governed by the intrinsic quantum geometric properties of Bloch electrons. Our results demonstrate the significance of the quantum geometry of electron wave functions from the orbital degree of freedom and open up a new direction in Hall transport effects.

Nonlinear Valley Hall Effect

The valley Hall effect arises from valley-contrasting Berry curvature and requires inversion symmetry breaking. Here, we propose a nonlinear mechanism to generate a valley Hall current in systems with both inversion and time-reversal symmetry, where the linear and second-order charge Hall currents vanish along with the linear valley Hall current. We show that a second-order valley Hall signal emerges from the electric field correction to the Berry curvature, provided a valley-contrasting anisotropic dispersion is engineered. We demonstrate the nonlinear valley Hall effect in tilted massless Dirac fermions in strained graphene and organic semiconductors. Our Letter opens up the possibility of controlling the valley degree of freedom in inversion symmetric systems via nonlinear valleytronics.

Odd Nonlinear Conductivity under Spatial Inversion in Chiral Tellurium

Electrical transport in noncentrosymmetric materials departs from the well-established phenomenological Ohm's law. Instead of a linear relation between current and electric field, a nonlinear conductivity emerges along specific crystallographic directions. This nonlinear transport is fundamentally related to the lack of spatial inversion symmetry. However, the experimental implications of an inversion symmetry operation on the nonlinear conductivity remain to be explored. Here, we report on a large, nonlinear conductivity in chiral tellurium. By measuring samples with opposite handedness, we demonstrate that the nonlinear transport is odd under spatial inversion. Furthermore, by applying an electrostatic gate, we modulate the nonlinear output by a factor of 300, reaching the highest reported value excluding engineered heterostructures. Our results establish chiral tellurium as an ideal compound not just to study the fundamental interplay between crystal structure, symmetry operations and nonlinear transport; but also to develop wireless rectifiers and energy-harvesting chiral devices.

Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect and nonreciprocal magnetoresistance (longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in films of the doped antiferromagnetic topological insulator MnBi_{2}Te_{4}. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

Symmetry dictionary on charge and spin nonlinear responses for all magnetic point groups with nontrivial topological nature

Recently, charge or spin nonlinear transport with nontrivial topological properties in crystal materials has attracted much attention. In this paper, we perform a comprehensive symmetry analysis for all 122 magnetic point groups (MPGs) and provide a useful dictionary for charge and spin nonlinear transport from the Berry curvature dipole, Berry connection polarizability and Drude term with nontrivial topological nature. The results are obtained by conducting a full symmetry investigation of the matrix representations of six nonlinear response tensors. We further identify every MPG that can accommodate two or three of the nonlinear tensors. The present work gives a solid theoretical basis for an overall understanding of the second-order nonlinear responses in realistic materials.

Quantum-metric-induced nonlinear transport in a topological antiferromagnet

The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

Anomalous Skew-Scattering Nonlinear Hall Effect and Chiral Photocurrents in PT-Symmetric Antiferromagnets

Berry curvature and skew scattering play central roles in determining both the linear and nonlinear anomalous Hall effects. Yet in PT-symmetric antiferromagnetic metals, Hall effects from either intrinsic Berry curvature mediated anomalous velocity or the conventional skew-scattering process individually vanish. Here we reveal an unexpected nonlinear Hall effect that relies on both Berry curvature and skew-scattering working in cooperation. This anomalous skew-scattering nonlinear Hall effect (ASN) is PT even and dominates the low-frequency nonlinear Hall effect for PT-symmetric antiferromagnetic metals. Surprisingly, we find that in addition to its Hall response, ASN produces helicity dependent photocurrents, in contrast to other known PT-even nonlinearities in metals that are helicity blind. This characteristic enables us to isolate ASN and establishes new photocurrent tools to interrogate the antiferromagnetic order of PT-symmetric metals.

Intrinsic Nonlinear Hall Detection of the Néel Vector for Two-Dimensional Antiferromagnetic Spintronics

The respective unique merit of antiferromagnets and two-dimensional (2D) materials in spintronic applications inspires us to exploit 2D antiferromagnetic spintronics. However, the detection of the Néel vector in 2D antiferromagnets remains a great challenge because the measured signals usually decrease significantly in the 2D limit. Here we propose that the Néel vector of 2D antiferromagnets can be efficiently detected by the intrinsic nonlinear Hall (INH) effect which exhibits unexpected significant signals. As a specific example, we show that the INH conductivity of the monolayer manganese chalcogenides MnX (X=S, Se, Te) can reach the order of nm·mA/V^{2}, which is orders of magnitude larger than experimental values of paradigmatic antiferromagnetic spintronic materials. The INH effect can be accurately controlled by shifting the chemical potential around the band edge, which is experimentally feasible via electric gating or charge doping. Moreover, we explicitly demonstrate its 2π-periodic dependence on the Néel vector orientation based on an effective k·p model. Our findings enable flexible design schemes and promising material platforms for spintronic memory device applications based on 2D antiferromagnets.

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure

Quantum geometry in condensed matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi₂Te₄ with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

Néel Spin Currents in Antiferromagnets

Ferromagnets are known to support spin-polarized currents that control various spin-dependent transport phenomena useful for spintronics. On the contrary, fully compensated antiferromagnets are expected to support only globally spin-neutral currents. Here, we demonstrate that these globally spin-neutral currents can represent the Néel spin currents, i.e., staggered spin currents flowing through different magnetic sublattices. The Néel spin currents emerge in antiferromagnets with strong intrasublattice coupling (hopping) and drive the spin-dependent transport phenomena such as tunneling magnetoresistance (TMR) and spin-transfer torque (STT) in antiferromagnetic tunnel junctions (AFMTJs). Using RuO_{2} and Fe_{4}GeTe_{2} as representative antiferromagnets, we predict that the Néel spin currents with a strong staggered spin polarization produce a sizable fieldlike STT capable of the deterministic switching of the Néel vector in the associated AFMTJs. Our work uncovers the previously unexplored potential of fully compensated antiferromagnets and paves a new route to realize the efficient writing and reading of information for antiferromagnetic spintronics.

In-Plane Anomalous Hall Effect in PT-Symmetric Antiferromagnetic Materials

The anomalous Hall effect (AHE), a protocol of various low-power dissipation quantum phenomena and a fundamental precursor of intriguing topological phases of matter, is usually observed in ferromagnetic materials with an orthogonal configuration between the electric field, magnetization, and the Hall current. Here, based on the symmetry analysis, we find an unconventional AHE induced by the in-plane magnetic field (IPAHE) via the spin-canting effect in PT-symmetric antiferromagnetic (AFM) systems, featuring a linear dependence of magnetic field and 2π angle periodicity with a comparable magnitude to conventional AHE. We demonstrate the key findings in the known AFM Dirac semimetal CuMnAs and a new kind of AFM heterodimensional VS_{2}-VS superlattice with a nodal-line Fermi surface and, also, briefly discuss the experimental detection. Our Letter provides an efficient pathway for searching and/or designing realistic materials for a novel IPAHE that could greatly facilitate their application in AFM spintronic devices. National Science Foundation.

Time-Reversal-Even Nonlinear Current Induced Spin Polarization

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe_{2}, and in ferromagnetic monolayer MnSe_{2}, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems.

Intrinsic Nonlinear Planar Hall Effect

We propose an intrinsic nonlinear planar Hall effect, which is of band geometric origin, independent of scattering, and scales with the second order of electric field and first order of magnetic field. We show that this effect is less symmetry constrained compared with other nonlinear transport effects and is supported in a large class of nonmagnetic polar and chiral crystals. Its characteristic angular dependence provides an effective way to control the nonlinear output. Combined with first-principles calculations, we evaluate this effect in the Janus monolayer MoSSe and report experimentally measurable results. Our work reveals an intrinsic transport effect, which offers a new tool for material characterization and a new mechanism for nonlinear device application.

Discovery of a Magnetic Dirac System with a Large Intrinsic Nonlinear Hall Effect

Magnetic materials exhibiting topological Dirac fermions are attracting significant attention for their promising technological potential in spintronics. In these systems, the combined effect of the spin-orbit coupling and magnetic order enables the realization of novel topological phases with exotic transport properties, including the anomalous Hall effect and magneto-chiral phenomena. Herein, we report experimental signature of topological Dirac antiferromagnetism in TaCoTe₂ via angle-resolved photoelectron spectroscopy and first-principles density functional theory calculations. In particular, we find the existence of spin-orbit coupling-induced gaps at the Fermi level, consistent with the manifestation of a large intrinsic nonlinear Hall conductivity. Remarkably, we find that the latter is extremely sensitive to the orientation of the Néel vector, suggesting TaCoTe₂ as a suitable candidate for the realization of non-volatile spintronic devices with an unprecedented level of intrinsic tunability.

Quantum Fluctuation of the Quantum Geometric Tensor and Its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems

In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying the quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects; so do their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is purely intrinsic, and the second-order thermal Hall noise has both intrinsic and extrinsic contributions. In particular, the intrinsic part of the second-order thermal Hall noise is a manifestation of the quantum fluctuation of the quantum geometric tensor, which widely exists as long as Berry curvature is nonzero. These intrinsic thermal Hall noises provide direct measurable means to band geometric information, including Berry curvature related quantities and quantum fluctuation of quantum geometric tensor.

Role of Hidden Spin Polarization in Nonreciprocal Transport of Antiferromagnets

The discovery of hidden spin polarization (HSP) in centrosymmetric nonmagnetic crystals, i.e., spatially distributed spin polarization originated from local symmetry breaking, has promised an expanded material pool for future spintronics. However, the measurements of such exotic effects have been limited to subtle space- and momentum-resolved techniques, unfortunately, hindering their applications. Here, we theoretically predict macroscopic non-reciprocal transports induced by HSP when coupling another spatially distributed quantity, such as staggered local moments in a space-time PT-symmetric antiferromagnet. By using a four-band model Hamiltonian, we demonstrate that HSP plays a crucial role in determining the asymmetric bands with respect to opposite momenta. Such band asymmetry leads to non-reciprocal nonlinear conductivity, exemplified by tetragonal CuMnAs via first-principles calculations. We further provide the material design principles for large nonlinear conductivity, including two-dimensional nature, multiple band crossings near the Fermi level, and symmetry protected HSP. Our Letter not only reveals direct spintronic applications of HSP (such as Néel order detection), but also sheds light on finding observables of other hidden effects, such as hidden optical polarization and hidden Berry curvature.

Intrinsic Nonlinear Electric Spin Generation in Centrosymmetric Magnets

We propose an intrinsic nonlinear electric spin generation effect, which can dominate in centrosymmetric magnets. We reveal the band geometric origin of this effect and clarify its symmetry characters. As an intrinsic effect, it is determined solely by the material's band structure and represents a material characteristic. Combining our theory with first-principle calculations, we predict sizable nonlinear spin generation in single-layer MnBi_{2}Te_{4}, which can be detected in experiment. Our theory opens a new route for all-electric controlled spintronics in centrosymmetric magnets which reside outside of the current paradigm based on linear spin response.

Intrinsic Nonlinear Hall Effect in Antiferromagnetic Tetragonal CuMnAs

Detecting the orientation of the Néel vector is a major research topic in antiferromagnetic spintronics. Here we recognize the intrinsic nonlinear Hall effect, which is independent of the relaxation time, as a prominent contribution to the time-reversal-odd second order conductivity and can be used to detect the reversal of the Néel vector. In contrast, the Berry-curvature-dipole-induced nonlinear Hall effect depends linearly on relaxation time and is time-reversal even. We study the intrinsic nonlinear Hall effect in an antiferromagnetic metal: tetragonal CuMnAs, and show that its nonlinear Hall conductivity can reach the order of mA/V^{2}. The dependence on the chemical potential of such nonlinear Hall conductivity can be qualitatively explained by a tilted massive Dirac model. Moreover, we demonstrate its strong temperature dependence and briefly discuss its competition with the second order Drude conductivity. Finally, a complete survey of magnetic point groups is presented, providing guidelines for finding more antiferromagnetic materials with the intrinsic nonlinear Hall effect.