The ordinary Hall effect is driven by the Lorentz force, while its anomalous counterpart occurs in ferromagnets. Here we show that the Berry curvature monopole of non-magnetic 2D spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B_x. There is no Lorentz force hence no ordinary Hall effect, while all disorder contributions vanish to leading order in B_x. This intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a non-quantized footprint of topological transport directly accessible in p-type semiconductors.
This is a theoretical review of the quantum Hall effect observed in quasi-one-dimensional organic conductors such as (TMTSF)2X. It is written for a book "Physics of Organic Superconductors and Conductors" to be published by Springer and edited by A. G. Lebed.
Shot noise is not normally evident in bulk solid-state conductors, since it is strongly attenuated by inelastic collisions. The ``anomalous'' emergence of macroscopic shot noise is discussed in G. Gomila and L. Reggiani, Phys. Rev. B 62, 8068 (2000). We remark on the consistency of this linear diffusive model at the large voltages and currents needed to see the effect.
We studied the insulator-quantum Hall conductor transition which separates the low-field insulator from the quantum Hall state of the filling factor $ν=4$ on a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. To enter the $ν=4$ quantum Hall state directly from the low-field insulator, the two-dimensional system undergoes a crossover from the low-field localization to Landau quantization. The crossover, in fact, covers a wide range with respect to the magnetic field rather than only a small region near the critical point of the insulator-quantum Hall condu…
The dynamic coupling between spin and charge currents in non-magnetic conductors is considered. As a consequence of this coupling, the spin dynamics is directly reflected in the electrical impedance of the sample, with a relevant frequency scale defined by spin relaxation and spin diffusion. This allows the observation of the electron spin resonance by purely electrical measurements.
There has been renewed interest in the physics of the so-called crossover for current fluctuations in mesoscopic conductors, most recently involving the possibility of its appearance in the passage to the macroscopic limit. Shot noise is normally absent from solid-state conductors in the large, and its anomalous resurgence there has been ascribed to a rich interplay of drift, diffusion, and Coulomb screening. We demonstrate that essentially the same rise in shot noise occurs in a much less complex system: the Boltzmann-Drude-Lorentz model of a macroscopic, uniform gas of strictly noninteractin…
We derive the effective action for a moving magnetic-field-induced spin-density wave (FISDW) in quasi-one-dimensional conductors at zero and nonzero temperatures by taking the functional integral over the electron field. The effective action consists of the (2+1)D Chern-Simons term and the (1+1)D chiral anomaly term, both written for a sum of the electromagnetic field and the chiral field associated with the FISDW phase. The calculated frequency dependence of Hall conductivity interpolates between the quantum Hall effect at low frequencies and zero Hall effect at high frequencies, where the co…
Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance ($Z_0 \approx 50 Ω$) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the quantum of resistance ($R_K \approx 25 k Ω$), offering the possibility of an enhanced coupling to low-dimensional quantum conductors. By applying a combination of dc and ac drives to a quantum point con…
We report a simple route to generate magnetotransport data that results in fractional quantum Hall plateaus in the conductance. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that th…
The electric conductivity of Dirac electrons in the organic conductor $α$-(BEDT-TTF)$_2$I$_3$ [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene] under pressure has been examined using a two-dimensional tight-binding (TB) model with both impurity and electron--phonon (e--p) scatterings. We study an anomalous temperature dependence of the conductivity, which shows a crossover from $σ_{x} < σ_{y}$ at low temperatures [region (I)] to $σ_{x} > σ_{y}$ at high temperatures [region (II)]. $σ_y$ and $σ_x$ are diagonal conductivities parallel and perpendicular to a stacking axis of molecules, respective…
We study the low frequency admittance of a quantum Hall bar of size much larger than the electronic coherence length. We find that this macroscopic conductor behaves as an ideal quantum conductor with vanishing longitudinal resistance and purely inductive behavior up to f<1MHz. Using several measurement configurations, we study the dependence of this inductance on the length of the edge channel and on the integer quantum Hall filling fraction. The experimental data are well described by a scattering model for edge magnetoplasmons taking into account effective long range Coulomb interactions wi…
We predict the existence of an anomalous crossover between thermal and shot noise in macroscopic diffusive conductors. We first show that, besides thermal noise, these systems may also exhibit shot noise due to fluctuations of the total number of carriers in the system. Then we show that at increasing currents the crossover between the two noise behaviors is anomalous, in the sense that the low frequency current spectral density displays a region with a superlinear dependence on the current up to a cubic law. The anomaly is due to the non-trivial coupling in the presence of the long range Coul…
Spin Hall effect and its inverse provide essential means to convert charge to spin currents and vice versa, which serve as a primary function for spintronic phenomena such as the spin-torque ferromagnetic resonance and the spin Seebeck effect. These effects can oscillate magnetization or detect a thermally generated spin splitting in the chemical potential. Importantly this conversion process occurs via the spin-orbit interaction, and requires neither magnetic materials nor external magnetic fields. However, the spin Hall angle, i.e., the conversion yield between the charge and spin currents, …
We investigate magnetic-field asymmetries in the linear transport of a mesoscopic conductor interacting with its environment. Interestingly, we find that the interaction between the two systems causes an asymmetry only when the environment is out of equilibrium. We elucidate our general result with the help of a quantum dot capacitively coupled to a quantum Hall conductor and discuss the asymmetry dependence on the environment bias and induced dephasing.
The anomalous Hall effect, a hallmark of broken time-reversal symmetry and spin-orbit coupling, is frequently observed in magnetically polarized systems. Its realization in non-magnetic systems, however, remains elusive. Here, we report on the observation of anomalous Hall effect in nominally non-magnetic KTaO3. Anomalous Hall effect emerges in reduced KTaO3 and shows an extrinsic to intrinsic crossover. A paramagnetic behavior is observed in reduced samples using first principles calculations and quantitative magnetometry. The observed anomalous Hall effect follows the oxygen vacancy-induced …
We report a detailed characterization of quantum Hall effect (QHE) influence on the linear and non-linear resistivity tensor in FISDW phases of the organic conductor (TMTSF)2PF6. We show that the behavior at low electric fields, observed for nominally pure single crystals with different values of the resistivity ratio, is fully consistent with a theoretical model, which takes QHE nature of FISDW and residual quasi-particle density associated with different crystal imperfection levels into account. The non-linearity in longitudinal and diagonal resistivity tensor components observed at large el…
We demonstrate a new quantum state of matter---valley-polarized quantum anomalous Hall effect in monolayer silicene. In the presence of extrinsic Rashba spin-orbit coupling and exchange field, monolayer silicene can host a quantum anomalous-Hall state with Chern number C=2. We find that through tuning Rashba spin-orbit coupling, a topological phase transition gives rise to a valley polarized quantum anomalous Hall state, i.e. a quantum state which exhibits electronic properties of both quantum valley-Hall effect (valley Chern number C_V=3) and quantum anomalous Hall effect with C=-1.
In this paper, we study topological properties and Hall conductivities in PbC/MnSe heterostructure under the illumination of a circularly polarized light. At high frequency regime, energy gap, Chern numbers, and Hall conductivities are studied based on the Floquet theory and Green's function formalism, respectively. The interplay between spin orbit coupling and light leads to topological phase transition between anomalous Hall states and spin Hall states, which is related to the emission and absorption of two virtual photons. The anomalous Hall conductivities are dependent on polarization of l…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. In recent years, quantum anomalous Hall effect has been proposed theoretically and realized experimentally. In this review article, we provide a systematic overview of the theoretical and experimental developments in this field.
Nonlinear anomalous Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference in response to a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time reversal symmetric systems. Here, we investigate the family of second-order nonlinear anomalous Hall effects, the electrical, thermoelectric and thermal nonlinear Hall effects in the moiré system of twisted double bilayer graphene. We demonstrate that the nonlinear anomalous Hall signals can be used to probe the topological phase-transitions in moiré systems,…
Both quantum spin Hall and quantum anomalous Hall states are novel states of quantum matter with promising applications. We propose junction quantum wells comprising II-VI, III-V or IV semiconductors as a large class of new materials realizing the quantum spin Hall state. Especially, we find that the bulk band gap for the quantum spin Hall state can be as large as 0.1 eV. Further more, magnetic doping would induce the ferromagnetism in these junction quantum wells due to band edge singularities in the band-inversion regime and to realize the quantum anomalous Hall state.
The Rashba interaction induced when inversion symmetry is broken in solids is a key interaction connecting spin and charge for realizing novel magnetoelectric cross-correlation effects. Here, we theoretically explore the optical properties of a bulk Rashba conductor by calculating the transport coefficients at finite frequencies. It is demonstrated that the combination of direct and inverse Edelstein effects leads to a softening of the plasma frequency for the electric field perpendicular to the Rashba field, resulting in a hyperbolic electromagnetic metamaterial. In the presence of magnetizat…
The Moore-Read Pfaffian $ν=5/2$ quantum Hall state is a p-wave super-conductor of composite fermions. Small deviations from $ν=5/2$ result in the formation of an array of vortices within this super-conductor, each supporting a Majorana zero mode near its core. Here we consider how tunneling between these cores is reflected in the electronic response to an electric field of non-zero wave vector $\bf q$ and frequency $ω$. We find a mechanism for dissipative transport at frequencies below the $ν=5/2$ gap, and calculate the ${\bf q},ω$ dependence of the dissipative conductivity. The contributions …
A key step towards dissipationless transport devices is the quantum anomalous Hall effect, which is characterized by an integer quantized Hall conductance in a ferromagnetic insulator with strong spin-orbit coupling. In this work, the anomalous Hall effect due to the impurity scattering, namely the extrinsic anomalous Hall effect, is studied when the Fermi energy crosses with the topologically nontrivial conduction band of a quantum anomalous Hall system. Two major extrinsic contributions, the side-jump and skew-scattering Hall conductivities, are calculated using the diagrammatic techniques i…
We study theoretically the anomalous Hall effect due to the vector spin chirality carried by the local spins in the $s$-$d$ model. We will show that the vector spin chirality indeed induces local Hall effect in the presence of the electron spin polarization, while the global Hall effect vanishes if electron transport is homogeneous. This anomalous Hall effect can be interpreted in terms of the rotational component of the spin current associated with the vector chirality.
Silicene have been proposed to host multiple topological phases depending on the environmental parameters such as gated voltage and proximity induced exchange field. Two typical topological phase are quantum spin Hall phase and quantum anomalous Hall phase. We found that in the presence of antiferromagnetic exchange field and (or) gated voltage, the bilayer silicene host a topological phase that the Chern numbers of the two spin are different in both sign and magnitude, .i.e the anomalous Hall effects of the two spins are imbalanced. The topological phase is generated by triple band inversion …
We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse s…
We present a theory of the anomalous Hall effect in ferromagnetic (Mn,III)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired by a quasiparticle wavefunction upon traversing closed paths on the spin-split Fermi surface of a ferromagnetic state. It can be applied equally well to any itinerant electron ferromagnet. The quantitative agreement between our theory and experimental data in both (In,Mn)As and (Ga,Mn)As systems suggests that this disorder independent contribution to the anomalous Hall conductivity dominates in dil…
We develop a hydrodynamic theory for an electron system exhibiting the anomalous Hall effect, and show that an additional anomalous Hall effect is induced by a vorticity generated near boundaries. We calculate the momentum flux and force proportional to the electric field using linear response theory. The hydrodynamic equation is obtained by replacing the local electric field with the electric current, focusing on a scale that is sufficiently larger than the mean free path. It is demonstrated that there is a coupling between a vorticity of an electric current and a magnetization which generate…
Anomalous Hall effect arising from non-trivial spin configuration (chirality) is studied based on the $s$-$d$ model. Considering a weak coupling case, the interaction is treated perturbatively. Scattering by normal impurities is included. Chirality is shown to drive locally Hall current and leads to overall Hall effect if there is a finite uniform chirality. This contribution is independent of the conventional spin-orbit contribution and shows distinct low temperature behavior. In mesoscopic spin glasses, chirality-induced anomalous Hall effect is expected below the spin-glass transition tempe…
We predict a spin anomalous-Hall unidirectional magnetoresistance (AH-UMR) in conducting bilayers composed of a ferromagnetic layer and a nonmagnetic layer, which does $\textit{not}$ rely on the spin Hall effect in the normal metal layer$-$in stark contrast to the well-studied unidirectional spin-Hall magnetoresistance$-$but, instead, arises from the spin anomalous Hall effect in the ferromagnetic layer. Physically, it is the charge-spin conversion induced by the spin anomalous Hall effect that conspires with the structural inversion asymmetry to generate a net nonequilibrium spin density in t…
A static electric field generates circulating currents at the surfaces of a magnetoelectric insulator. The anomalous Hall part of the surface conductivity tensor describing such bound currents can change by multiples of $e^2/h$ depending on the insulating surface preparation, and a bulk calculation does not fix its quantized part. To resolve this ambiguity, we develop a formalism for calculating the full surface anomalous Hall conductivity in a slab geometry. We identify a Berry-curvature term, closely related to the expression for the bulk anomalous Hall conductivity, whose value can change b…
A theory of the anomalous and spin Hall effects, based on the space distribution of the current densities, is presented. Spin-orbit coupling gives rise to a space separation of the mass centers, as well as a current density separation of the quasiparticle states having opposite group velocities. It is shown that this microscopic property is essential for existence of both Hall effects.
In a two-dimensional electron gas, the quantized Hall conductance can be induced by a strong magnetic field, known as the quantum Hall effect, and it can also result from the strong exchange coupling of magnetic ions, dubbed as the "quantum anomalous Hall effect". The quantum Hall effect requires the out-of-plane magnetic field, and similarly, it is commonly believed that the magnetization should be out-of-plane for the quantum anomalous Hall effect. In the present work, we find this condition is not necessary and predict that the quantum anomalous Hall effect can also be induced by the purely…
Based on first-principles calculations, we demonstrate that Co decorated silicene can host a quantum anomalous Hall state. The exchange field induced by the Co atoms combined with the strong spin orbit coupling of the silicene opens a nontrivial band gap at the K-point. As compared to other transition metals, Co decorated silicene is unique in this respect, since usually hybridization and spin-polarization induced in the silicene suppress a quantum anomalous Hall state.
We have shown that the study of topological aspects of the underlying geometry in a ferromagnetic spin system gives rise to an intrinsic Berry phase. This real space Berry phase arises due to the spin rotations of conducting electrons which can be manifested as a further contribution in anomalous Hall effect.
We report on low-temperature electron transport properties of MnSb2Te4, a candidate of ferrimagnetic Weyl semimetal. Long -range magnetic order is manifested as a nearly square-shaped hysteresis loop in the anomalous Hall resistance, as well as sharp jumps in the magnetoresistance. At temperatures below 4 K, a lnT-type upturn appears in the temperature dependence of longitudinal resistance, which can be attributed to the electron-electron interaction (EEI), since the weak localization can be excluded by the temperature dependence of magnetoresistance. Although the anomalous Hall resistance exh…
Hall effect of two-dimensional holes that are spin-polarized by a strong parallel magnetic field was explored with a small tilt angle. The Hall resistivity increases nonlinearly with the magnetic field and exhibits negative corrections. The anomalous negative corrections increase with the perpendicular magnetization of the two-dimensional hole system. We attribute this to the anomalous Hall effect of spin-polarized carriers in a nonmagnetic system. The anomalous corrections to the conductivity exhibit non-monotonic dependence on the magnetic field.
We show that the quantum anomalous Hall effect almost always occurs in magnetic topological insulator thin films whenever the top and bottom surface layer magnetizations are parallel, independent of the interior layer magnetization configuration. Using this criteria we identify structures that have a quantum anomalous Hall effect even though they have collinear magnetic structures with no net magnetization, and discuss strategies for realizing these interesting magnetic states experimentally.
The magneto-transport and magnetization measurements of Sb1.90Cu0.10Te3 were performed at different temperatures and different fields. Magneto-transport measurement at high field indicates the coexistence of both bulk and surface states. The magnetization shows the induced antiferromagnetic ordering with Cu doping and the observed quantum oscillation in it indicates that magnetization in Sb1.90Cu0.10Te3 is the bulk property. The non linearity in Hall data suggests the existence of anomalous and topological Hall effect. The anomalous and topological Hall effect (THE) from measured hall data of …
A quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering d…
Recently, the semiclassical theory of the anomalous Hall effect induced by the Berry curvature in Bloch bands has been introduced. The theory operates only with gauge invariant concepts, that have a simple semiclassical interpretation and provides a clear distinction among various contributions to the Hall current. While the construction of such an approach to the anomalous Hall effect problem has been long sought, only the new semiclassical theory demonstrated the agreement with quantitative results of rigorous approaches based on the Green function techniques. The purpose of this work is to …
We theoretically investigate the anomalous Hall effect in a system of dense-packed ferromagnetic grains in the metallic regime. Using the formalism recently developed for the conventional Hall effect in granular metals, we calculate the residual anomalous Hall conductivity $σ_{xy}$ and resistivity $ρ_{xy}$ and weak localization corrections to them for both skew-scattering and side-jump mechanisms. We find that, unlike for homogeneously disordered metals, the scaling relation between $ρ_{xy}$ and the longitudinal resistivity $ρ_{xx}$ does not hold. The weak localization corrections, however, ar…
Quantum anomalous Hall state is expected to emerge in Dirac electron systems such as graphene under both sufficiently strong exchange and spin-orbit interactions. In pristine graphene, neither interaction exists; however, both interactions can be acquired by coupling graphene to a magnetic insulator (MI) as revealed by the anomalous Hall effect. Here, we show enhanced magnetic proximity coupling by sandwiching graphene between a ferrimagnetic insulator yttrium iron garnet (YIG) and hexagonal-boron nitride (h-BN) which also serves as a top gate dielectric. By sweeping the top-gate voltage, we o…
We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of $σ_{xy}$ induced by the localization except for the few extended states carrying Chern number. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore the condition for the quantized AHE is given only by the Hall conductivity $σ_{xy}$ …
We study the magnetic and transport properties of epitaxial graphene films in this letter. We predict enhanced signal of magnetic susceptibility and relate it to the intrinsic valley magnetic moments. There is also an anomalous contribution to the ordinary Hall effect, which is due to the valley dependent Berry phase or valley-orbit coupling.
Based on ab initio calculations, we predict that a monolayer of Cr-doped (Bi,Sb)2Te3 and GdI2 heterostructure is a quantum anomalous Hall insulator with a non-trivial band gap up to 38 meV. The principle behind our prediction is that the band inversion between two topologically trivial ferromagnetic insulators can result in a non-zero Chern number, which offers a better way to realize the quantum anomalous Hall state without random magnetic doping. In addition, a simple effective model is presented to describe the basic mechanism of spin polarized band inversion in this system. Moreover, we pr…
We consider DC supercurrents in SNS junctions. Spin-orbit coupling in combination with Zeeman fields can induce an effective vector potential in the normal conductor. As a consequence, an out-of-plane spin-density varying along the transverse direction causes a longitudinal phase difference between the superconducting terminals. The resulting equilibrium phase coherent supercurrent is analogue to the non-equilibrium inverse spin Hall effect in normal conductors. We explicitly compute the effect for the Rashba spin orbit coupling in a disordered two-dimensional electron gas with an inhomogeneou…
Conceptual framework behind the intrinsic spin Hall effect in three-dimensional conductors is discussed. Theory suggests how the spin Hall current should depend on symmetry and orientation of the crystal.
Most canted antiferromagnets are also anomalous Hall antiferromagnets (AHE AFMs), i.e. they have an anomalous Hall response and other responses with the same symmetry requirements. We suggest that AHE AFMs are promising materials as hosts for high-temperature quantum anomalous Hall effects. By considering models of two-dimensional (001) perovskite layers with strong spin-orbit coupling that isolates an effective total angular momentum $\tilde{j}= \frac{1}{2}$ subspace of the $t_{2g}$ manifold, we propose a strategy to engineering quantum anomalous Hall antiferromagnets.
The observation of dissipationless anomalous Hall current is one of the experimental evidences to confirm the intrinsic origin of anomalous Hall effect. To study the origin of anomalous Hall effect in iron, Fe$_{100-x}$(SiO$_{2}$)$_{x}$ granular films with volume fraction of SiO$_{2}$ 0\le x \le 40.51 were fabricated using co-sputtering. Hall and longitudinal resistivities were measured in the temperature range 5 to 350 K with magnetic fields up to 5 Tesla. As x increased from 0 to 40.51, the anomalous Hall resistivity and longitudinal resistivity increased about 4 and 3 orders in magnitude, r…
Recently, Seebeck coefficients of ferromagnetic conductors are found to be spin-dependent. However straightforward method of accurately determining its spin polarization is still to be developed. Here, we have derived a linear dependence of anomalous Nernst coefficient on anomalous Hall angle with scaling factor related to spin polarization of Seebeck coefficient, which has been experimentally verified in [Co/Pt]n superlattices. Based on the dependence, we have also evaluated spin polarization of Seebeck coefficient of some ferromagnetic conductors. Besides, we have also found a new mechanism …
We propose a new family of the d0 orbital XY (X = K, Rb, Cs; Y = N, P, As, Sb, Bi) monolayers with abundant and novel topology and valley properties. The KN, RbN, RbP, RbAs, CsP, CsAs, and CsSb monolayers possess remarkable quantum anomalous Hall effect (QAHE). CsSb monolayer also exhibits extraordinary valley QAHE with giant splitting. Moreover, the topological properties of XY monolayers can be effciently tuned by the in-plane strain, owing to the strain-induced band inversion between the px;y and pz orbitals. Our findings suggest that the d0 orbital XY monolayers can be good candidates for …
It is known that the Shubnikov--de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate that the amplitude of the Shubnikov--de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the…
We investigate anomalous Hall effect in a magnet coupled to a triplet superconductor under phase gradient. It is found that the anomalous Hall supercurrent arises from non-trivial structure of the magnetization. The magnetic structure manifested in the Hall supercurrent is characterized by even order terms of the exchange coupling, essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. We also discuss a possible candidate for magnetic structure to verify our prediction.
