Nonlinear Anomalous Hall Effect Research Articles

Two-Dimensional Os2Se3 Nanosheet: A Ferroelectric Metal with Room-Temperature Ferromagnetism.

Two-dimensional (2D) ferroelectric metals (FEMs) possess intriguing characteristics, such as unconventional superconductivity and the nonlinear anomalous Hall effect. However, their occurrence is exceedingly rare due to mutual repulsion between ferroelectricity and metallicity. In addition, further incorporating other features like ferromagnetism into FEMs to enhance their functionalities poses a significantly greater challenge. Here, via first-principles calculations, we demonstrate a case of an FEM that features a coexistence of room-temperature ferromagnetism, ferroelectricity, and metallicity in a thermodynamically stable 2D Os2Se3. It presents a vertical electric polarization of 3.00 pC/m that exceeds those of most FEMs and a moderate polarization switching barrier of 0.22 eV per formula unit. Moreover, 2D Os2Se3 exhibits robust ferromagnetism (Curie temperature TC ≈ 527 K) and a sizable magnetic anisotropy energy (-30.87 meV per formula unit). Furthermore, highly magnetization-dependent electrical conductivity is revealed, indicative of strong magnetoelectric coupling. Berry curvature calculation suggests that the FEM might exhibit nontrivial band topology.

Magnetochiral tunneling in paramagnetic Co1/3NbS2

Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co1/3NbS2, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up an avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.

Terahertz linear/non-linear anomalous Hall conductivity of moiré TMD hetero-nanoribbons as topological valleytronics materials

Twisted moiré van der Waals heterostructures hold promise to provide a robust quantum simulation platform for strongly correlated materials and realize elusive states of matter such as topological states in the laboratory. We demonstrated that the moiré bands of twisted transition metal dichalcogenide (TMD) hetero-nanoribbons exhibit non-trivial topological order due to the tendency of valence and conduction band states in K valleys to form giant band gaps when spin-orbit coupling (SOC) is taken into account. Among the features of twisted WS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}/MoS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and WSe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}/MoSe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}, we found that the heavy fermions associated with the topological flat bands and the presence of strongly correlated states, enhance anomalous Hall conductivity (AHC) away from the magic angle. By band analysis, we showed that the topmost conduction bands from the ± K-valleys are perfectly flat and carry a spin/valley Chern number. Moreover, we showed that the non-linear anomalous Hall effect in moiré TMD hetero-nanoribbons can be used to manipulate terahertz (THz) radiation. Our findings establish twisted heterostructures of group-VI TMD nanoribbons as a tunable platform for engineering topological valley quantum phases and THz non-linear Hall conductivity.

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.

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.

Twisted chiral superconductivity in photodoped frustrated Mott insulators

Recent advances in ultrafast pump-probe spectroscopy provide access to hidden phases of correlated matter, including light-induced superconducting states, but the theoretical understanding of these nonequilibrium phases remains limited. Here we report how a new type of chiral superconducting phase can be stabilized in photodoped frustrated Mott insulators. The metastable phase features a spatially varying order parameter with a $120^\circ$ phase twist which breaks both time-reversal and inversion symmetry. Under an external electric pulse, the $120^\circ$ chiral superconducting state can exhibit a second-order supercurrent perpendicular to the field in addition to a first-order parallel response, similar to a nonlinear anomalous Hall effect. This phase can be tuned by artificial gauge fields when the system is dressed by high-frequency periodic driving. The mechanism revealed in this study applies to Mott insulators on various frustrated lattices and the hidden superconducting phase can be realized in both cold-atom quantum simulators and correlated solids.

Switchable moiré potentials in ferroelectric WTe2/WSe2 superlattices.

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect. This is achieved in a ferroelectric WTe2 bilayer of the Td structure with a centred-rectangular moiré superlattice induced by interfacing with a WSe2 monolayer of the H structure. The results can be understood in terms of polarization-dependent charge transfer between two WTe2 monolayers, in which the interfacial layer has a much stronger moiré potential depth; ferroelectric switching thus turns on and off the moiré insulating states. Our study demonstrates the potential for creating new functional moiré materials by incorporating intrinsic symmetry-breaking orders.

Microscopic mechanism for intrinsic nonlinear anomalous Hall conductivity in noncollinear antiferromagnetic metals

We theoretically investigate an intrinsic nonlinear anomalous Hall effect (INAHE) in space-time ($\mathcal{PT}$) symmetric antiferromagnetic metals. The INAHE is characterized by an asymmetric and nondissipative part of the second-order electric conductivity tensor in the clean limit in contrast to the Drude-type symmetric conductivity tensor with dissipation. By introducing a multipole description, we show that the emergence of the INAHE is due to active odd-parity magnetic quadrupoles or magnetic toroidal dipoles under magnetic orderings. In order to clarify the microscopic origin of the INAHE, we specifically consider a fundamental tight-binding model of a three-dimensional tetragonal system. We demonstrate that the INAHE arises from the effective coupling between magnetic ordering and antisymmetric spin-orbit interaction. We also discuss essential electron hopping paths driving the INAHE.

Anisotropic magneto-transport behavior in a hexagonal ferromagnetic EuCuP single crystal

In this study, the magnetism, transport properties, and electronic structure of ferromagnetic EuCuP single crystals were investigated using magnetic and transport measurements and first-principles calculations. The magneto-transport behavior of EuCuP exhibits a large anisotropy for H // c and H // ab. There is an anomalous Hall effect (AHE) and a nonlinear AHE for H // c. However, there is only a normal Hall effect for H // ab, in which the system shows strong ferromagnetism, which is contradictory to the understanding of AHE in conventional ferromagnetic materials. Theoretical calculations showed that there is a small anomalous Hall conductivity (AHC) platform near the Fermi level for M // c state. However, the AHC is almost zero near the Fermi level for M // ab state, which is consistent with experimental measurements. These results indicate that the transverse transport behavior in EuCuP is dominated by an intrinsic mechanism related to electron band structures.

Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene

Nonlinear anomalous (NLA) Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference induced by a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time-reversal symmetric systems. These band-geometry induced responses in recently realized twistronic platforms can probe their novel electronic band structure and topology. Here, we investigate the family (electrical, thermoelectric, and thermal) of second-order NLA Hall effects in the moiré system of twisted double bilayer graphene (TDBG). We combine the semiclassical transport framework with the continuum model of TDBG to demonstrate that the NLA Hall signals can probe topological phase transitions in moiré systems. We show that the whole family of NLA Hall responses undergo a sign reversal across a topological phase transition. Our study establishes a deeper connection between valley topology and nonlinear Hall effects in time-reversal symmetric systems.

Orbital polarization and third-order anomalous Hall effect in WTe2

The anomalous Hall effect (AHE) has been extended into the nonlinear regime, where the Hall voltage shows higher-order response to the applied current. Nevertheless, the microscopic mechanism of the nonlinear AHE remains unclear. Here we report the orbital polarization and its induced third-order AHE in few-layer WTe2 flakes. Through angle-dependent electric measurements, it is found that the third-order AHE is quite consistent with the electric field induced polarization of orbital magnetic moment caused by the Berry connection polarizability tensor, which is further directly detected by polar reflective magnetic circular dichroism spectroscopy. The microscopic mechanisms of third-order AHE are analyzed through the scaling law, that is, the opposite orbital magnetic moments (up or down) deflect to opposite directions driven by electric field induced Berry curvature, forming the intrinsic contribution; driven by the Magnus effect of the self-rotating Bloch electrons, the opposite orbital magnetic moments are scattered towards opposite transverse directions, resulting in the skew scattering.

Berry curvature-induced local spin polarisation in gated graphene/WTe2 heterostructures

Experimental control of local spin-charge interconversion is of primary interest for spintronics. Van der Waals (vdW) heterostructures combining graphene with a strongly spin-orbit coupled two-dimensional (2D) material enable such functionality by design. Electric spin valve experiments have thus far provided global information on such devices, while leaving the local interplay between symmetry breaking, charge flow across the heterointerface and aspects of topology unexplored. Here, we probe the gate-tunable local spin polarisation in current-driven graphene/WTe2 heterostructures through magneto-optical Kerr microscopy. Even for a nominal in-plane transport, substantial out-of-plane spin accumulation is induced by a corresponding out-of-plane current flow. We present a theoretical model which fully explains the gate- and bias-dependent onset and spatial distribution of the intense Kerr signal as a result of a non-linear anomalous Hall effect in the heterostructure, which is enabled by its reduced point group symmetry. Our findings unravel the potential of 2D heterostructure engineering for harnessing topological phenomena for spintronics, and constitute an important step toward nanoscale, electrical spin control.

Giant nonlinear anomalous Hall effect induced by spin-dependent band structure evolution

The anomalous Hall effect (AHE) is a key transport signature revealing the topological properties of magnetic compounds. In quantum materials, the classical linear dependence of the AHE on magnetization often breaks down, which is typically ascribed to the presence of topological magnetic or electronic textures. However, the complex electronic structure of these compounds may offer alternative, unexplored mechanisms. Here, we show that a giant nonlinear AHE can originate from a series of magnetic-field-induced Lifshitz transitions in the spin-dependent band structure. In our experiments on ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$ the AHE contributes to 97% of the total Hall response, corresponding to a record anomalous Hall angle of 21%. Our scaling analysis and first-principles calculations demonstrate that the electronic structure is extremely sensitive to spin canting, with the magnetic field causing band crossing and band inversion and introducing a band gap when oriented along specific directions. Our results not only provide an ideal platform for Berry curvature engineering but reveal a general effect that may be applied to other material systems.

Anisotropy of the magnetic and transport properties of EuZn2As2

Several recent studies have shown that the anisotropy in the magnetic structure of \ECA\ plays a significant role in stabilizing the Weyl nodes. To investigate the relationship between magnetic anisotropy and Weyl physics, we present a comparative study between EuZn$_2$As$_2$ and EuCd$_2$As$_2$ that are isostructural but with different magnetic anisotropy. We performed structural analysis, electronic transport, and magnetization experiments on millimeter-sized single crystals of EuZn$_2$As$_2$, and compared the results to those of EuCd$_2$As$_2$. By combining the first principle calculations and neutron diffraction experiment, we identify the magnetic ground state of EuZn$_2$As$_2$ as A-type antiferromagnetic order with a transition temperature ($T_\mathrm{N}$ = 19.6 K) twice that of EuCd$_2$As$_2$. Like EuCd$_2$As$_2$, the negative magnetoresistance of EuZn$_2$As$_2$ is observed after suppressing the resistivity peak at $T_\mathrm{N}$ with increasing fields. However, the anisotropy in both transport and magnetization are much reduced in EuZn$_2$As$_2$. The difference could be ascribed to the weaker spin-orbit coupling, more localized $d$-orbitals, and a larger contribution from the Eu $s$-orbitals in the zinc compound, as suggested by the electronic band calculations. The same band structure effect could be also responsible for the observation of a smaller non-linear anomalous Hall effect in EuZn$_2$As$_2$ compared to EuCd$_2$As$_2$.

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.

Observation of possible nonlinear anomalous Hall effect in organic two-dimensional Dirac fermion system

We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor α-(BEDT-TTF)2I3 in the charge order (CO) insulating phase just under the critical pressure for transition into two-dimensional (2D) massless Dirac fermion (DF) phase. We successfully extracted the finite nonlinear Hall voltage proportional to square current at zero magnetic field. The observed NLAHE features, current direction dependence and correlation with CO, are consistent with the previous estimation assuming 2D massive DF with a pair of tilted Dirac cones. This is the first observation of topological transport in organic conductors, and also the first example of NLAHE in the electronic phase with spontaneous symmetry breaking.

Sliding ferroelectricity in 2D van der Waals materials: Related physics and future opportunities

Near the 100th anniversary of the discovery of ferroelectricity, so-called sliding ferroelectricity has been proposed and confirmed recently in a series of experiments that have stimulated remarkable interest. Such ferroelectricity exists widely and exists only in two-dimensional (2D) van der Waals stacked layers, where the vertical electric polarization is switched by in-plane interlayer sliding. Reciprocally, interlayer sliding and the “ripplocation” domain wall can be driven by an external vertical electric field. The unique combination of intralayer stiffness and interlayer slipperiness of 2D van der Waals layers greatly facilitates such switching while still maintaining environmental and mechanical robustness at ambient conditions. In this perspective, we discuss the progress and future opportunities in this behavior. The origin of such ferroelectricity as well as a general rule for judging its existence are summarized, where the vertical stacking sequence is crucial for its formation. This discovery broadens 2D ferroelectrics from very few material candidates to most of the known 2D materials. Their low switching barriers enable high-speed data writing with low energy cost. Related physics like Moiré ferroelectricity, the ferroelectric nonlinear anomalous Hall effect, and multiferroic coupling are discussed. For 2D valleytronics, nontrivial band topology and superconductivity, their possible couplings with sliding ferroelectricity via certain stacking or Moiré ferroelectricity also deserve interest. We provide critical reviews on the current challenges in this emerging area.

Possible Nonlinear Anomalous Thermoelectric Effect in Organic Massive Dirac Fermion System

We propose a novel current-induced thermoelectric phenomenon, the nonlinear anomalous Ettingshausen effect (AEE), at zero magnetic field in inversion-asymmetric conductors. As an example, we discuss the weak charge ordering state in a layered organic conductor alpha-(BEDT-TTF)2I3, which is a two-dimensional massive Dirac fermion system with a pair of tilted Dirac cones. The nonlinear AEE is a thermoelectric analogue of the nonlinear anomalous Hall effect, which is recently observed in alpha-(BEDT-TTF)2I3, and these two effects generally appear simultaneously. The nonlinear AEE generates a transverse heat current, which exhibits rectifying characteristics, namely unidirectionality even under an AC current.

Giant c-axis nonlinear anomalous Hall effect in Td-MoTe2 and WTe2

While the anomalous Hall effect can manifest even without an external magnetic field, time reversal symmetry is nonetheless still broken by the internal magnetization of the sample. Recently, it has been shown that certain materials without an inversion center allow for a nonlinear type of anomalous Hall effect whilst retaining time reversal symmetry. The effect may arise from either Berry curvature or through various asymmetric scattering mechanisms. Here, we report the observation of an extremely large c-axis nonlinear anomalous Hall effect in the non-centrosymmetric Td phase of MoTe2 and WTe2 without intrinsic magnetic order. We find that the effect is dominated by skew-scattering at higher temperatures combined with another scattering process active at low temperatures. Application of higher bias yields an extremely large Hall ratio of E⊥/E|| = 2.47 and corresponding anomalous Hall conductivity of order 8 × 107 S/m.

Hall effects in artificially corrugated bilayer graphene without breaking time-reversal symmetry

The ability to engineer the electronic band structure and, more strikingly, to access new exotic phase of matter has been the cornerstone of the advance of science and technology. Twisting van der Waals materials to form moir\'e superlattice is a powerful paradigm and can drive graphene from a normal metallic state into an insulating, superconducting, or ferromagnetic states. Here, we present a new route to create non-trivial band structure and consequently an exotic phase of matter via lithographically patterned strain (lattice deformation). This method is used to realize an artificially corrugated bilayer graphene wherein the real-space and momentum-space pseudo-magnetic fields (Berry curvatures) coexist and have nontrivial properties, namely, the Berry curvature dipole. This new class of condensed-matter systems enables us to observe the so-called nonlinear anomalous Hall effect and a new type of Hall effect without breaking the time-reversal symmetry. Such artificial material system and our approach to unconventional electronic states may open an avenue of geometrical and/or topological quantum phenomena as well as that of band engineering in van der Waals crystals.