Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals

TL;DR

This paper investigates a bilayer skyrmion crystal model that exhibits spontaneous topological Hall effects due to electron interactions, with potential relevance to real materials and engineered heterostructures.

Contribution

It introduces a minimal bilayer model with opposite chirality skyrmions, revealing interaction-induced phases with spontaneous Hall effects and tunability via electric fields.

Findings

Weak interactions induce charge density modulations or layer imbalance.

Both phases break inversion symmetry and produce a large net topological Hall effect.

The phase diagram can be controlled by external electric fields.

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.