Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals

Abstract

Magnetic skyrmion crystals with zero net skyrmion charge and zero topological Hall response are interesting candidate phases which can occur at a vanishing magnetic field in centrosymmetric systems. We study a minimal bilayer model of skyrmion crystals having opposite chirality and topological charge in the two layers, and show that it can host nearly flat electronic bands with quasi-uniform Berry curvature and quantum metric. Using Hartree-Fock theory, we show that weak to moderate short-range electron interactions induce two distinct types of symmetry breaking patterns depending on the band dispersion: an intra-unit-cell charge density modulation from Chern band mixing or a layer-imbalanced phase with a nonzero ferroelectric polarization. Both phases break inversion symmetry leading to a spontaneous and large net topological Hall effect, with the phase diagram tunable by external electric fields. Our results may be relevant to centrosymmetric skyrmion materials such as Gd${}_2$PdSi${}_3$ and Gd${}_3$Ru${}_4$Al${}_{12}$ as well as artificially engineered heterostructures. We also discuss its relation to recent work on twisted transition metal dichalcogenide bilayers.

References in corpus (23)

• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Observation of Fractionally Quantized Anomalous Hall Effect
• Skyrmions in Magnetic Multilayers
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Interface-driven topological Hall effect in SrRuO${}_3$-SrIrO${}_3$ bilayer
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
• Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings
• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Theory of helical spin crystals: phases, textures and properties
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Non-Abelian fractionalization in topological minibands
• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
• Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures
• Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
• Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems
• Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field