Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice

Abstract

The hallmark of a skyrmion crystal (SkX) is the topological Hall effect (THE). In this Article, we predict and explain an unconventional behavior of the topological Hall conductivity in SkXs. In simple terms, the spin texture of the skyrmions causes an inhomogeneous emergent magnetic field whose associated Lorentz force acts on the electrons. By making the emergent field homogeneous, the THE is mapped onto the quantum Hall effect (QHE). Consequently, each electronic band of the SkX is assigned to a Landau level. This correspondence of THE and QHE allows to explain the unconventional behavior of the THE of electrons in SkXs. For example, a skyrmion crystal on a triangular lattice exhibits a quantized topological Hall conductivity with steps of $2\cdot e^2/h$ below and with steps of $1\cdot e^2/h$ above the van Hove singularity. On top of this, the conductivity shows a prominent sign change at the van Hove singularity. These unconventional features are deeply connected to the topology of the structural lattice.

5 pages, 4 figures

References in corpus (5)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Interface-driven topological Hall effect in SrRuO${}_3$-SrIrO${}_3$ bilayer
• Robust formation of skyrmions and topological Hall effect in epitaxial thin films of MnSi
• Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
• Real-Space Berry Phases - Skyrmion Soccer

Cited by in corpus (24)

• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions
• Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk
• Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry
• Skyrmion-size dependence of the topological Hall effect: A real-space calculation
• Transverse Transport in Two-Dimensional Relativistic Systems with Non-Trivial Spin Textures
• Skyrmion Crystals in the Triangular Kondo Lattice Model
• Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents
• Magnetic skyrmion crystal at a topological insulator surface
• Tunable large spin Nernst effect in a two-dimensional magnetic bilayer
• Topological orbital Hall effect caused by skyrmions and antiferromagnetic skyrmions
• Resonant optical topological Hall conductivity from skyrmions
• Machine learning assisted derivation of effective low energy models for metallic magnets
• From chiral spin liquids to skyrmion fluids and crystals, and their interplay with itinerant electrons
• Topological magnon-polarons in honeycomb antiferromagnets with spin-flop transition
• Skyrmion-driven topological Hall effect in a Shastry-Sutherland magnet
• Chiral Stoner magnetism in Dirac bands
• Electric control of two-dimensional Van Hove singularity in oxide ultra-thin films
• Insights into the orbital magnetism of noncollinear magnetic systems
• Chern insulating state with double-$Q$ ordering wave vectors at the Brillouin zone boundary
• Klein tunneling of the electronic states in the gate voltage modulated skyrmion crystal
• Three-dimensional topological orbital Hall effect caused by magnetic hopfions
• Double-$Q$ and quadruple-$Q$ instabilities at low-symmetric ordering wave vectors under tetragonal symmetry
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals