The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach

Abstract

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-interpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.

arXiv comment14 pages, 5 figures

References in corpus (34)

• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• String Theory and Noncommutative Geometry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• Noncommutative Field Theory
• Observation of room temperature magnetic skyrmions and their current-driven dynamics in ultrathin Co films
• Quantum Field Theory on Noncommutative Spaces
• Topological Hall effect in the A-phase of MnSi
• Direct Observation of the Skyrmion Hall Effect
• Large anomalous Hall effect driven by non-vanishing Berry curvature in non-collinear antiferromagnetic Mn3Ge
• Skyrmion Hall Effect Revealed by Direct Time-Resolved X-Ray Microscopy
• Berry phase correction to electron density of states in solids
• The Non-Commutative Geometry of the Quantum Hall Effect
• Topological Hall effect and Berry phase in magnetic nanostructures
• Interface-driven topological Hall effect in SrRuO${}_3$-SrIrO${}_3$ bilayer
• Non-collinear Antiferromagnets and the Anomalous Hall Effect
• Electrical signature of individual magnetic skyrmions in multilayered systems
• Spirit: Multifunctional Framework for Atomistic Spin Simulations
• Electric-field control of anomalous and topological Hall effects in oxide bilayer thin films
• Giant topological Hall effect in correlated oxide thin films
• Topological Hall effect at above room temperature in heterostructures composed of a magnetic insulator and a heavy metal
• Chiral magnetic textures in Ir/Fe/Co/Pt multilayers: Evolution and topological Hall signature
• Real-Space and Reciprocal-Space Berry Phases in the Hall Effect of Mn${}_{1-\mathrm{x}}$Fe${}_{\mathrm{x}}$Si
• Topological Invariants of Metals and Related Physical Effects
• Discrete Hall resistivity contribution from Néel skyrmions in multilayer nanodiscs
• Spin-Hall Topological Hall Effect in Highly Tunable Pt/Ferrimagnetic-Insulator Bilayers
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• General theory of topological Hall effect in systems with chiral spin textures
• Purely electrical detection of a skyrmion in constricted geometry
• Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism
• A Note on Noncommutative Chern-Simons Theories
• Engineering Chiral and Topological Orbital Magnetism of Domain Walls and Skyrmions
• Rashba-induced spin electromagnetic fields in a strong sd coupling regime

Cited by in corpus (29)

• Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles
• The 2020 Skyrmionics Roadmap
• Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling
• Topological response of the anomalous Hall effect in MnBi2Te4 due to magnetic canting
• The chiral Hall effect in canted ferromagnets and antiferromagnets
• Transverse Transport in Two-Dimensional Relativistic Systems with Non-Trivial Spin Textures
• Spin-orbit enabled all-electrical readout of chiral spin-textures
• Geometrical Hall effect and momentum-space Berry curvature from spin-reversed band pairs
• Spin-chirality-driven second-harmonic generation in two-dimensional magnet CrSBr
• Role of magnetic exchange interactions in chiral-type Hall effects of epitaxial Mn${}_x$PtSn films
• Resonant optical topological Hall conductivity from skyrmions
• Theory of Magnetic-Texture-Induced Anomalous Hall Effect on the Surface of Topological Insulators
• Antiskyrmions and their electrical footprint in crystalline mesoscale structures of Mn${}_{1.4}$PtSn
• Tailoring the anomalous Hall effect of SrRuO${}_3$ thin films by strain: a first principles study
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Topological Hall effect induced by classical large-spin background: $su(2)$ path-integral approach
• Experimental progress in Eu(Al,Ga)${}_4$ topological antiferromagnets
• Wigner-Weyl calculus in Keldysh technique
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Activation of anomalous Hall effect and orbital magnetization by domain walls in altermagnets
• Higher-order Hall response arises from octupole order and scalar spin chirality in a noncollinear antiferromagnet
• Electric field effect on electron gas spins in two-dimensional magnets with strong spin-orbit coupling
• Mixed topology ring states for Hall effect and orbital magnetism in skyrmions of Weyl semimetals
• Skew scattering by magnetic monopoles and anomalous Hall effect in spin-orbit coupled systems
• Robust noncoplanar magnetism in band filling-tuned (Nd${}_{1-x}$Ca${}_x$)${}_2$Mo${}_2$O${}_7$
• Fingerprints of the electron skew-scattering on paramagnetic impurities in semiconductor systems
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions
• Structure and magnetism of MnGe thin films grown with a nonmagnetic CrSi template
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals