Topological Hall effect from strong to weak coupling

Abstract

Topological Hall effect (THE) of electrons coupled to a noncoplanar spin texture has been studied so far for the strong- and weak-coupling regimes separately; the former in terms of the Berry phase and the latter by perturbation theory. In this letter, we present a unified treatment in terms of spin gauge field by considering not only the adiabatic (Berry phase) component of the gauge field but also the nonadiabatic component. While only the adiabatic contribution is important in the strong-coupling regime, it is completely canceled by a part of the nonadiabatic contribution in the weak-coupling regime, where the THE is governed by the rest of the nonadiabatic terms. We found a new weak-coupling region that cannot be accessed by a simple perturbation theory, where the Hall conductivity is proportional to M, with 2M being the exchange splitting of the electron spectrum.

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• Triple-$\mathcal{Q}$ partial magnetic orders induced by quadrupolar interactions: Triforce order scenario for UNi${}_4$B
• Theory of Magnetic-Texture-Induced Anomalous Hall Effect on the Surface of Topological Insulators
• Coherent backscattering in the topological Hall effect
• Interband contributions to nonlinear transport in semiconductor nanostructures
• Theory of an electron asymmetric scattering on skyrmion textures in two-dimensional systems
• Weak Localization in Systems with Chiral Spin Textures and Skyrmion Crystals
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• Topological spin Hall effect in antiferromagnets driven by vector Néel chirality
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Theory of magnetic vortex crystals induced by electric dipole interactions
• Magnetic Bloch-point hopping in multilayer skyrmions and associated emergent electromagnetic signatures
• Robustness of real-space topology in moiré systems
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals