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The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and is related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder…

To account for the anomalous/spin Hall conductivities and spin-orbit torque in the zeroth order of electron scattering time in strongly spin-orbit coupled systems, the Boltzmann transport theory in the case of weak disorder-potentials has…

We present a study of transport in multiple-band non-interacting Fermi metallic systems based on the Keldysh formalism, taking into account the effects of Berry curvature due to spin-orbit coupling. We apply this formalism to a Rashba 2DEG…

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…

We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field…

We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows…

We revisit model calculations of the anomalous Hall effect (AHE) and show that, in isotropic Rashba-coupled two-dimensional electron gas (2DEG) with pointlike potential impurities, the full solution of the semiclassical Boltzmann equation…

We investigate the possibility of observing the anomalous Hall effect (AHE) in two dimensional paramagnetic systems. We apply the semiclassical equations of motion to carriers in the conduction and valence bands of wurtzite and zincblende…

We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many…

We describe the charge transport in ferromagnets with spin orbit coupled Bloch bands by combining the wave-packet evolution equations with the classical Boltzmann equation. This approach can be justified in the limit of smooth disorder…

The anomalous Hall effect in disordered band ferromagnets is considered in the framework of quantum transport theory. A microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling is used. The…

An anomalous Hall effect (AHE) in antiferromagnetic (AF) systems with no net magnetization is of considerable interest for both fundamental physics and spintronic applications. Of particular interest is the two-dimensional van der Waals…

A finite equilibrium current density arises in the anomalous Hall effect (AHE) as a result of time-reversal symmetry breaking, affecting both the differential current density and total current. This study illustrates the equilibrium current…

Anomalous Hall effect (AHE) is the key transport signature unlocking topological properties of magnetic materials. While AHE is usually proportional to the magnetization, the nonlinearity suggests the existence of complex magnetic and…

Non-Hermitian descriptions often model open or driven systems away from the equilibrium. Nonetheless, in equilibrium electronic systems, a non-Hermitian nature of an effective Hamiltonian manifests itself as unconventional observables such…

We evidenced unconventionnal Anomalous Hall Effects (AHE) in 3d/5d (Co0.2nm/Ni0.6nm)N multilayers grown on a thin Pt layer or thin Au:W alloy. The inversion observed on AHE originates from the opposite sign of the spin-orbit coupling of Pt…

We present the analytical description of the anomalous Hall effect (AHE) in a 2DEG ferromagnet within the Keldysh formalism. These results unify all three linear response approaches to anomalous Hall transport and close a long standing…

The understanding of the Chern insulator and anomalous quantum Hall effect (AQHE) in terms of chiral edge states in confined systems is the first aim of the paper. The model we use consists in a diatomic square lattice with hopping to the…

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 $\sigma_{xy}$ induced by the…

In model studies of the spin/anomalous Hall effect, effective Hamiltonians often serve as the starting point. However, a complete effective quantum theory contains not only the effective Hamiltonian but also the relation linking the…