A path integral (Lagrangian formalism) is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2π\hbar/T$, where $T$ is the typical time scale of the slower system and $E_{n}$ is the energy level of the fast system.
In the conventional definition of the adiabatic condition with $T\rightarrow {\rm large}$ and fixed energy eigenvalues, no commutation relations are defined for slower variables by the Bjorken-Johnson-Low prescription except for the starting canonical commutators. On the other hand, in a singular limit $|E_{n\pm1}-E_{n}|\rightarrow \infty$ with specific $E_{n}$ kept fixed for which any motions of the slower variables $X_{k}$ can be treated to be adiabatic, the non-canonical dynamical system with deformed commutators and the Nernst effect appear. In the Born-Oppenheimer approximation based on the canonical commutation relations, the equations of motion of the anomalous Hall effect is obtained if one uses an auxiliary variable $X_{k}^{(n)}=X_{k}+{\cal A}^{(n)}_{k}$ with Berry's connection ${\cal A}^{(n)}_{k}$ in the absence of the electromagnetic vector potential $eA_{k}(X)$ and thus without the Nernst effect. It is shown that the gauge symmetries associated with Berry's connection and the electromagnetic vector potential $eA_{k}(X)$ are incompatible in the canonical Hamiltonian formalism. The appearance of the non-canonical dynamical system with the Nernst effect is a consequence of the deformation of the quantum principle to incorporate the two incompatible gauge symmetries.
We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the emergence of the phase current in a system where the interlayer phase coherence develops spontaneously. The phase current arranges itself to minimize the total energy of the system, as induces certain anomalous behaviors in the Hall current in the counterflow geometry and also in the drag experiment. They explain the recent experimental data for anomalous Hall resi…
An anomalous Hall insulator without magnetic long-range ordering is theoretically reported in the absence of the relativistic spin-orbit coupling. It is realized in itinerant electrons coupled with the Ising spins on a <111> kagome plane of pyrochlore spin ice in applied magnetic field. We find that the kagome-ice type local spin correlation in the magnetization plateau state opens a charge gap without magnetic ordering, which results in quantization of the Hall conductivity. By Monte Carlo simulation, we identify the anomalous Hall insulating region in the magnetic phase diagram, in addition …
It is shown that topological insulating phases driven by interactions can be realized without the need for spin-orbit coupling or large intersite interaction in a two-dimensional system of spin-1/2 fermions with a single pair of parabolically touching bands. Using a weak-coupling, Wilsonian renormalization group procedure, we show that a quantum anomalous Hall phase is realized for Hubbard interaction, while a quantum spin Hall phase is favored for longer-ranged interactions.
It is well established that the anomalous Hall effect that a ferromagnet displays scales with its magnetization. Therefore, an antiferromagnet that has no net magnetization should exhibit no anomalous Hall effect. Here we show that the non-collinear triangular antiferromagnet Mn3Ge exhibits a large anomalous Hall effect comparable to that of ferromagnetic metals; the magnitude of the anomalous conductivity is 500 per ohm per cm at 2 K and 50 per ohm per cm at room temperature. The angular dependence of the anomalous Hall effect measurements confirm that the small residual in-plane magnetic mom…
Analytic Formulas for the Anomalous Hall Effect in Itinerant Magnets
French American Center for Theoretical Science, CNRS（法美理论科学中心，法国国家科学研究中心）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（卡弗里理论物理研究所，加州大学圣塔芭芭拉分校）；École Normale Supérieure de Lyon, CNRS, Laboratoire de physique（里昂高等师范学校，法国国家科学研究中心，物理实验室）
We demonstrate an electric field control of anomalous Hall effect emerging in CaIrO$_3$/CaMnO$_3$ heterostructures. We fabricate both electron-type and hole-type carrier samples by tuning epitaxial strain and then control the carrier density in CaIrO$_3$ layer via electric double layer gating technique. As the Fermi energy of CaIrO$_3$ is tuned close to the Dirac line node, anomalous Hall conductivity is enlarged in both carrier-type samples. This result reveals that the anomalous Hall effect comes from the intrinsic origin reflecting the Dirac like dispersion in CaIrO$_3$. We propose that ban…
We perform Monte Carlo simulations to obtain quantitative results for the anomalous Hall resistance, R_A, observed in colossal magnetoresistance manganites. R_A arises from the interaction between the spin magnetization and topological defects via spin-orbit coupling. We study these defects and how they are affected by the spin-orbit coupling within the framework of the double exchange model. The obtained anomalous Hall resistance is, in sign, order of magnitude and shape, in agreement with experimental data.
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterizat…
When conduction electrons are forced to follow the local spin texture, the resulting Berry phase can induce an anomalous Hall effect (AHE). In gadolinium, as in double-exchange magnets, the exchange interaction is mediated by the conduction electrons and the AHE may therefore resemble that of chromium dioxide and other metallic double-exchange ferromagnets. The Hall resistivity, magnetoresistance, and magnetization of single crystal gadolinium were measured in fields up to 30 T. Measurements between 2 K and 400 K are consistent with previously reported data. A scaling analysis for the Hall res…
Motived by time-reversal symmetry breaking and giant anomalous Hall effect in kagome superconductor \textit{A}V$_3$Sb$_5$ (\textit{A} = Cs, K, Rb), we carried out the thermal transport measurements on CsV$_3$Sb$_5$. In addition to the anomalous Hall effect, the anomalous Nernst effect and the anomalous thermal Hall effect emerge. Interestingly, the longitudinal thermal conductivity $κ_{xx}$ largely deviates from the electronic contribution obtained from the longitudinal conductivity $σ_{xx}$ by the Wiedemann-Franz law. In contrast, the thermal Hall conductivity $κ_{xy}$ is roughly consistent w…
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…
Working with epitaxial films of Fe, we succeeded in independent control of different scattering processes in the anomalous Hall effect. The result appropriately accounted for the role of phonons, thereby clearly exposing the fundamental flaws of the standard plot of the anomalous Hall resistivity versus longitudinal resistivity. A new scaling has been thus established that allows an unambiguous identification of the intrinsic Berry curvature mechanism as well as the extrinsic skew scattering and side-jump mechanisms of the anomalous Hall effect.
The Berry phase due to the spin wavefunction gives rise to the orbital ferromagnetism and anomalous Hall effect in the non-coplanar antiferromagnetic ordered state on face centered cubic (fcc) lattice once the crystal is distorted perpendicular to (1,1,1) or (1,1,0)- plane. The relevance to the real systems $γ$-FeMn and NiS$_2$ is also discussed.
The Hall resistivity and magnetization have been investigated in the ferromagnetic state of the bilayered manganite La(2-2x)Sr(1+2x)Mn2O7 (x=0.36). The Hall resistivity shows an increase in both the ordinary and anomalous Hall coefficients at low temperatures below 50K, a region in which experimental evidence for the spin glass state has been found in a low magnetic field of 1mT. The origin of the anomalous behavior of the Hall resistivity relevant to magnetic states may lie in the intrinsic microscopic inhomogeneity in a quasi-two-dimensional electron system.
We study the anomalous Hall effect on the antiferromagnetic coloring-triangular lattice with a coplanar magnetic configuration in presence of a spin-orbit interaction. The effect of the spin-orbit coupling is included at effective level as a rotation of the electronic spin as the electrons hop from site to site. Our result reveals that a finite Hall conductivity in the planar 120$^{\circ}$ structure takes place if a finite spin-orbit coupling is present. A quantized Hall conductivity occurs at global band gaps resulting from the topologically non-trivial band structure.
In a heavy fermion system, there exists the anomalous Hall effect caused by localized $f$-orbital freedom, in addition to the normal Hall effect due to the Lorentz force. In 1994, we found that the Hall coefficient caused by the anomalous Hall effect ($R_H^{AHE}$) is predominant and the relation $R_H^{AHE} \propto ρ^2$ ($ρ$ is the electrical resistivity) holds at low temperatures in many compounds. In this work, we study the system where the magnetic susceptibility is highly anisotropic due to the strong crystalline electric field on $f$-orbitals. Interestingly, we find that $R_H^{AHE}$ is nea…
We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.
The geometric ideas underlying the Berry phase and the modern viewpoint of Karplus and Luttinger's theory of the anomalous Hall effect are discussed in an elementary way. We briefly review recent Hall and Nernst experiments which support the dominant role of the KL velocity term in ferromagnets.
Motivated by work on the bulk topological proximity effect and the topological bootstrap, we consider two coupled layers of quantum anomalous Hall (QAH) insulators with opposite signs of time-reversal breaking, which leads to a trivial band insulator at half-filling. We study the impact of interactions in this model within slave rotor theory, which leads to a layer-selective Mott transition, resulting in a fractionalized quantum anomalous Hall insulator QAH$^*$ where a Chern band insulator coexists with a chiral spin liquid. We also compute the edge electron spectral function in the vicinity o…
We demonstrate that a distinct high-disorder anomalous Hall effect phase emerges at the correlated insulator threshold of ultra-thin, amorphous, ferromagnetic CNi3 films. In the weak localization regime, where the sheet conductance G >> e^2/h, the anomalous Hall resistance of the films increases with increasing disorder and the Hall conductance scales as Gxy ~ G^1.6. However, at sufficiently high disorder the system begins to enter the 2D correlated insulator regime, at which point the Hall resistance Rxy abruptly saturates and the scaling exponent becomes 2. Tunneling measurements show that t…
The anomalous Hall effect (AHE) around the flux state in square Kondo lattice is investigated. By introducing the lattice distortion and local chirality, the square Kondo lattice can break the parity symmetry and time reversal symmetry spontaneously, and thus generate a topological nontriviality in the band structure associated with the AHE. Moreover, a possible realization of this AHE in multiferroic TbMnO$_3$ is discussed.
We report anomalous Hall effect (AHE) and transport properties of trigonal Cr$_5$Te$_8$ (tr-Cr$_5$Te$_8$) single crystals. The electrical resistivity as well as the Seebeck coefficient shows a clear kink at the paramagnetic-ferromagnetic transition of tr-Cr$_5$Te$_8$, which is also confirmed by the heat capacity measurement. The scaling behavior between anomalous Hall resistivity $ρ^A_{xy}$ and longitudinal resistivity $ρ_{xx}$ is linear below $T_c$. Further analysis suggests that the AHE in tr-Cr$_5$Te$_8$ is dominated by the skew-scattering mechanism rather than the intrinsic or extrinsic si…
The Hall effect on selected samples of the dilution series Nb1-yFe2+y is studied. Normal and anomalous contributions are observed, with positive normal Hall effect dominating at high temperatures. Consistent analysis of the anomalous contribution is only possible for Fe-rich Nb0.985Fe2.015 featuring a ferromagnetic ground state. Here, a positive normal Hall coefficient is found at all temperatures with a moderate maximum at the spin-density-wave transition. The anomalous Hall effect is consistent with an intrinsic (Berry-phase) contribution which is constant below the ordering temperature TC a…
We engineer quantum anomalous Hall effect in silicene via doping 3d transition metals. We show that there exists a stable quantum anomalous Hall effect in Vanadium doped silicene using both analytical model and Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our finding provides new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states.
We argue that the scaling of the anomalous Hall effect (AHE) by Mathieu et al. [Phys. Rev. Lett. 93, 016602 (2004)] does not provide support to the interpretation of the AHE in SrRuO3 as an intrinsic effect due to Berry phase monopoles in k-space.
The anomalous Hall coefficient Rs has been studied for the reentrant spin glass system Fe0.7Al0.3 by measuring the magnetization M and the Hall resistivity r_H. We have found that R_s exhibits anomalous temperature dependence at the spin-glass transition temperature T_G, indicating that an additional term appears along with the beginning of the spin glass phase. The result is discussed in relation to the recent proposal of the chirality mechanism of the Hall effect in the spin glass phase.
We report on the experimental observation of an anomalous Hall effect (AHE) in highly oriented pyrolytic graphite samples. The overall data indicate that the AHE in graphite can be self-consistently understood within the frameworks of the magnetic-field-driven excitonic pairing models.
Anomalous Hall effect (AHE) of a ferromagnetic semiconductor anatase \cotio thin film is studied from 10K to 300K. Magnetic field dependence of anomalous Hall resistance is coincident with that of magnetization, while the anomalous Hall resistance decreases at low temperature in spite of nearly temperature-independent magnetization. Anomalous Hall conductivity sigma_AHE is found to be proportional to the square of Hall mobility, suggesting that charge scattering strongly affects the AHE in this system. The anatase Ti1-xCoxO2 also follows a scaling relationship to conductivity sigma_xx as sigma…
We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin Hall insulators and quantum anomalous Hall insulators. Employing the variational cluster approximation to obtain the single-particle Green's function of the interacting many-body system, we characterize different phases by direct calculation of the recently proposed topological order parameter for interacting systems. We pinpoint the influence of quantum fluctuations on the quantum spin Hall to Mott insulator transition in several models. Furthermore, we propose a general mechanism by which…
The Hall effect has been studied in a series of AuFe samples in the re-entrant concentration range, as well as in the spin glass range. The data demonstrate that the degree of canting of the local spins strongly modifies the anomalous Hall effect, in agreement with theoretical predictions associating canting, chirality and a real space Berry phase. The canonical parametrization of the Hall signal for magnetic conductors becomes inappropriate when local spins are canted.
The Hall effect in SrRuO$_3$ thin-films near the thickness limit for ferromagnetism shows an extra peak in addition to the ordinary and anomalous Hall effects. This extra peak has been attributed to a topological Hall effect due to two-dimensional skyrmions in the film around the coercive field; however, the sign of the anomalous Hall effect in SrRuO$_3$ can change as a function of saturation magnetization. Here we report Hall peaks in SrRuO$_3$ in which volumetric magnetometry measurements and magnetic force microscopy indicate that the peaks result from the superposition of two anomalous Hal…
Topological phases typically encode topology at the level of the single particle band structure. But a remarkable class of models shows that quantum anomalous Hall effects can be driven exclusively by interactions, while the parent non-interacting band structure is topologically trivial. Unfortunately, these models have so far relied on interactions that do not spatially decay and are therefore unphysical. We study a model of spinless fermions on a decorated honeycomb lattice. Using complementary methods, mean-field theory and exact diagonalization, we find a robust quantum anomalous Hall phas…
We investigate the pressure evolution of the anomalous Hall effect in magnetic topological semimetal Co3Sn2S2 in diamond anvil cells with pressures up to 44.9-50.9 GPa. No evident trace of structural phase transition is detected through synchrotron x-ray diffraction over the measured pressure range of 0.2-50.9 GPa. We find that the anomalous Hall resistivity and the ferromagnetism are monotonically suppressed as increasing pressure and almost vanish around 22 GPa. The anomalous Hall conductivity varies non-monotonically against pressure at low temperatures, involving competition between origin…
This article reviews the main contributions to the anomalous Hall effect and its resurgence in the past three decades, which has been accompanied by the rise of topological phenomena and topological materials. I will show that the anomalous Hall effect stems from the interplay of magnetism, spin-orbit coupling, disorder scattering and driving electric fields, it spans the classical, quantum and relativistic worlds, and has generated controversy for nearly one and a half centuries. It has become the smoking gun for detecting magnetic order and, extraordinarily, it continues to reveal new physic…
In transition metals and their compounds, the orbital degrees of freedom gives rise to an orbital current, in addition to the ordinary spin and charge currents. We reveal that considerably large spin and anomalous Hall effects (SHE and AHE) observed in transition metals originate from an orbital Hall effect (OHE). To elucidate the origin of these novel Hall effects, a simple periodic s-d hybridization model is proposed as a generic model. The giant positive OHE originates from the orbital Aharonov-Bohm phase factor, and induces spin Hall conductivity that is proportional to the spin-orbit pola…
The anomalous Hall effect is investigated for ferromagnetic Fe3Sn2 single crystal with geometrically frustrated kagome bilayer of Fe. The scaling behavior between anomalous Hall resistivity rho_{xy}^{A} and longitudinal resistivity rho_{xx} is quadratic and further analysis implies that the AHE in Fe3Sn2 single crystal should be dominated by the intrinsic Karplus-Luttinger mechanism rather than extrinsic skew-scattering or side-jump mechanisms. Moreover, there is a sudden jump of anomalous Hall conductivity sigma_{xy}^{A} appearing at about 100 K where the spin-reorientation transition from th…
Observation of anomalous thermal Hall effect in altermagnets
Fudan University（复旦大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与创新中心）；ShanghaiTech University（上海科技大学）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Advanced Microstructures（先进微结构协同创新中心）
Orthorhombic CuMnAs has been proposed as an antiferromagnetic semimetal hosting nodal line and Dirac points around the Fermi level. We investigate relations between the topological bands and transport phenomena, i.e. spin Hall effect and anomalous Hall effect, in orthorhombic CuMnAs with first-principles calculations combined with symmetry analysis of magnetic structures and of (spin) Berry curvature. We show the nodal line gapped with spin-orbit coupling in CuMnAs dominantly generates large spin Hall conductivity in the ground state. Although the magnetic symmetry in the ground state of CuMnA…
Ab initio prediction of anomalous Hall effect in antiferromagnetic CaCrO$_3$
Institute of Scientific and Industrial Research, Osaka University（大阪大学科学工业研究所）；Department of Precision Engineering, Graduate School of Engineering, Osaka University（大阪大学大学院工学研究科精密工程专攻）
