Interplay of Charge Density Wave and Magnetism on the Kagomé Lattice

Motivated by the recent discovery of charge density wave (CDW) order in the magnetic kagomé metal FeGe, we study the single-orbital t-U-V₁-V₂ model on the kagomé lattice, where U, V₁, and V₂ are the onsite, nearest neighbor, and next-nearest-neighbor Coulomb interactions, respectively. When the Fermi level lies in the flat band, the instability toward ferromagnetic (FM) order gives rise to a FM half-metal at sufficiently large onsite U. Intriguingly, at band filling n = 17/24, the Fermi level crosses the van Hove singularity of the spin-minority bands of the half-metal. We show that, due to the unique geometry and sublattice interference on the kagomé lattice at van Hove singularity, the inter-site Coulomb interactions V₁ and V₂ drive a real and an imaginary bond-ordered 2a₀ × 2a₀ CDW instability, respectively. The FM loop current CDW with complex bond orders is a spin-polarized Chern insulator exhibiting the quantum anomalous Hall effect. The bond fluctuations are found to be substantially enhanced compared to the corresponding nonmagnetic kagomé metals at van Hove filling, providing a concrete model realization of the bond-ordered CDWs, including the FM loop current CDW, over the onsite charge density ordered states. When the spins are partially polarized at an intermediate U, we find that the interplay of CDW and magnetism enables the formation of real and complex bond-ordered CDWs, and the CDW transition is accompanied by a substantial enhancement in the ordered magnetic moments. These findings provide physical insights for the emergence of 2a₀ × 2a₀ CDWs and their interplay with magnetism on the kagomé lattice, and capture the essential physics observed experimentally in FeGe.