Generating a Topological Anomalous Hall Effect in a Nonmagnetic Conductor: An In-Plane Magnetic Field as a Direct Probe of the Berry Curvature

Intrinsic Nonlinear Spin Hall Effect and Manipulation of Perpendicular Magnetization

We propose an intrinsic nonlinear spin Hall effect, which enables the generation of collinearly polarized spin current in a large class of nonmagnetic materials with the corresponding linear response being symmetry forbidden. This opens a new avenue for field-free switching of perpendicular magnetization, which is required for the next-generation information storage technology. We develop the microscopic theory of this effect and clarify its quantum origin in band geometric quantities which can be enhanced by topological nodal features. Combined with first-principles calculations, we predict pronounced effects at room temperature in topological metals PbTaSe_{2} and PdGa. Our work establishes a fundamental nonlinear response in spin transport and opens the door to exploring spintronic applications based on nonlinear spin Hall effect.

Antisymmetric planar Hall effect in rutile oxide films induced by the Lorentz force

The conventional Hall effect is linearly proportional to the field component or magnetization component perpendicular to a film. Despite the increasing theoretical proposals on the Hall effect to the in-plane field or magnetization in various special systems induced by the Berry curvature, such an unconventional Hall effect has only been experimentally reported in Weyl semimetals and in a heterodimensional superlattice. Here, we report an unambiguous experimental observation of the antisymmetric planar Hall effect (APHE) with respect to the in-plane magnetic field in centrosymmetric rutile RuO2 and IrO2 single-crystal films. The measured Hall resistivity is found to be linearly proportional to the component of the applied in-plane magnetic field along a particular crystal axis and to be independent of the current direction or temperature. Both the experimental observations and theoretical calculations confirm that the APHE in rutile oxide films is induced by the Lorentz force. Our findings can be generalized to ferromagnetic materials for the discovery of anomalous Hall effects and quantum anomalous Hall effects induced by in-plane magnetization. In addition to significantly expanding knowledge of the Hall effect, this work opens the door to explore new members in the Hall effect family.

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.

An ideal candidate for observing anomalous Hall effect induced by the in-plane magnetic field

The anomalous Hall effect induced by the in-plane magnetic field (anomalous planar Hall effect) has recently attracted a lot of interests due to its numerous advantages. Although several schemes have been put forward in theory, experimental observations in many materials so far are often accompanied by planar Hall effects due to other mechanisms, rather than the pure anomalous planar Hall effect (APHE). We propose the surface state of the strained topological insulator as an ideal candidate to observe this effect. The surface state exhibits a pure APHE, characterized by a linear dependence on the magnetic field and a 2πperiodicity, which remains robust against the scattering of non-magnetic and various magnetic impurities, as long as the uniaxial strain preserves mirror symmetry. Although a general strain that breaks the mirror symmetry can induce the conventional Drude Hall effect, the anomalous contribution remains dominant. Furthermore, we present a feasible scheme to distinguish between the two contributions based on their distinct magnetic field dependencies. Our work is of great significance for promoting experimental observation of the APHE and provides reference value in the search for other realistic materials.

Orbital Origin of the Intrinsic Planar Hall Effect

Recent experiments reported an antisymmetric planar Hall effect, where the Hall current is odd in the in plane magnetic field and scales linearly with both electric and magnetic fields applied. Existing theories rely exclusively on a spin origin, which requires spin-orbit coupling to take effect. Here, we develop a general theory for the intrinsic planar Hall effect (IPHE), highlighting a previously unknown orbital mechanism and connecting it to a band geometric quantity-the anomalous orbital polarizability (AOP). Importantly, the orbital mechanism does not request spin-orbit coupling, so sizable IPHE can occur and is dominated by an orbital contribution in systems with weak spin-orbit coupling. Combined with first-principles calculations, we demonstrate our theory with quantitative evaluation for bulk materials TaSb_{2}, NbAs_{2}, and SrAs_{3}. We further show that AOP and its associated orbital IPHE can be greatly enhanced at topological band crossings, offering a new way to probe topological materials.

Crystal Symmetry-Dependent In-Plane Hall Effect

The Hall effect has played a vital role in unraveling the intricate properties of electron transport in solid materials. Here, we report on a crystal symmetry-dependent in-plane Hall effect (CIHE) observed in a CuPt/CoPt ferromagnetic heterostructure. Unlike the planar Hall effect (PHE), the CIHE in CuPt/CoPt strongly depends on the current flowing direction (ϕI) with respect to the crystal structure. It reaches its maximum when the current is applied along the low crystal-symmetry axes and vanishes when applied along the high crystal-symmetry axes, exhibiting an unconventional angular dependence of cos(3ϕI). Utilizing a symmetry analysis based on the Invariant Theory, we demonstrate that the CIHE can exist in magnetic crystals possessing C3v symmetry. Using a tight-binding model and realistic first-principles calculations on the metallic heterostructure, we find that the CIHE originates from the trigonal warping of the Fermi surface. Our observations highlight the critical role of crystal symmetry in generating new types of Hall effects.

Designing spin and orbital sources of Berry curvature at oxide interfaces

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO₃/SrTiO₃ interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

Resonant Second-Harmonic Generation as a Probe of Quantum Geometry

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higher-order pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal WTe_{2} and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases

Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of four-dimensional Z_{2} topological insulator (TI) protected by CP symmetry, whose 3D boundary supports an odd number of Dirac cones. A specific perturbation splits each bulk massive Dirac cone into two valleys separated in energy-momentum space with opposite second Chern numbers, in which the 3D boundary modes become a nodal sphere or a Weyl semimetallic phase. By introducing the electromagnetic (EM) and pseudo-EM fields, exotic topological responses of our 4D system are revealed, which are found to be described by the (4+1)D mixed Chern-Simons theories in the low-energy regime. Notably, several topological phase transitions occur from a CP-broken Z_{2} TI to a Z TI when the bulk gap closes by giving rise to exotic double-nodal-line or nodal-hyper-torus gapless phases. Finally, we propose to probe experimentally these topological effects in cold atoms.

Novel /2-Periodic Planar Hall Effect Due to Orbital Magnetic Moments in MnBi2Te4

The Berry curvature and orbital magnetic moment (OMM) come from either inversion symmetry or time-reversal symmetry breaking in quantum materials. Here, we demonstrate the significance of OMMs and Berry curvature in planar Hall effect (PHE) in antiferromagnetic topological insulator MnBi₂Te₄ flakes. We observe a PHE with period of π and positive magnitude at low fields, resembling the PHE of the surface states in nonmagnetic topological insulators. Remarkably, a novel predominant PHE with period of π/2 and negative magnitude emerges below the Néel temperature with B > 10 T. Our theoretical calculations reveal that this unusual π/2-periodic PHE originates from the topological OMMs of bulk Dirac electrons. Moreover, the competition between the contributions from the bulk and the surface states leads to nontrivial evolutions of PHE and anisotropic magnetoresistance. Our results reveal intriguing electromagnetic response due to the OMMs and also provide insight into the potential applications of magnetic topological insulators in spintronics.