Weak coupling theory of topological Hall effect

Abstract

Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling, $M$, of conduction electrons to the spin texture is strong (strong-coupling regime) and the adiabatic condition is satisfied. However, in the weak-coupling regime, where the coupling $M$ is smaller than the electrons' scattering rate, the adiabatic condition is not satisfied and the Berry phase picture does not hold. In such a regime, the relation of the effective magnetic field to the spin texture can be "nonlocal", in contrast to the "local" relation in the strong coupling case. Focusing on the case of continuous but general spin texture, we investigate the THE in various characteristic regions in the weak-coupling regime, namely, (1) diffusive and local, (2) diffusive and nonlocal, and (3) ballistic. In the presence of spin relaxation, there arise two more regions in the "weakest-coupling" regime: (1') diffusive and local, and (2') diffusive and nonlocal. We derived the analytic expression of the topological Hall conductivity (THC) for each region, and found that the condition for the locality of the effective field is governed by transverse spin diffusion of electrons. In region 1, where the spin relaxation is negligible and the effective field is local, the THC is found to be proportional to $M$, instead of $M^3$ of the weakest-coupling regime. In the diffusive, nonlocal regions (2 and 2'), the effective field is given by a spin chirality formed by "effective spins" that the electrons see during their diffusive motion. Applying the results to a skyrmion lattice, we found the THC decreses as the skyrmion density is increased in region 2', reflecting the nonlocality of the effective field, and shows a maximum at the boundary to the "local" region.

References in corpus (25)

• Skyrmion Lattice in a Chiral Magnet
• Anomalous Hall effect
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Topological Hall effect in the A-phase of MnSi
• Anomalous Hall effect arising from noncollinear antiferromagnetism
• Multiple-q states and skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields
• Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites
• Topological Hall effect and Berry phase in magnetic nanostructures
• Field-Dependent Size and Shape of Single Magnetic Skyrmions
• Microscopic approach to current-driven domain wall dynamics
• Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy
• Chirality driven anomalous Hall effect in weak coupling regime
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Giant topological Hall effect in correlated oxide thin films
• Microscopic Calculation of Spin Torques in Disordered Ferromagnets
• Anomalous Hall Effect and Skyrmion Number in Real- and Momentum-space
• Fluctuations and Instabilities of Ferromagnetic Domain Wall pairs in an External Magnetic Field
• Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice
• Chirality scenario of the spin-glass ordering
• General theory of topological Hall effect in systems with chiral spin textures
• Scattering on magnetic skyrmion in the non-adiabatic approximation
• Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to Non-collinearity:Significance of Orbital Aharonov-Bohm Effect
• Signatures of lattice geometry in quantum and topological Hall effect
• Phasons and excitations in skyrmion lattice
• Anomalous Hall effect driven by dipolar spin waves in uniform ferromagnets

Cited by in corpus (19)

• Oxide spin-orbitronics: spin-charge interconversion and topological spin textures
• Skyrmion-size dependence of the topological Hall effect: A real-space calculation
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Tuning skyrmion Hall effect via engineering of spin-orbit interaction
• Phase degree of freedom and topology in multiple-$Q$ spin textures
• 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
• Topological phase transitions driven by polarity change and next-nearest-neighbor hopping in skyrmion crystals
• Klein tunneling of the electronic states in the gate voltage modulated skyrmion crystal
• 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