Chiral Stoner magnetism in Dirac bands

Stoner magnetism in bands endowed with Berry curvature is shown to be profoundly influenced by the coupling between spin chirality density $\vec s\cdot(\partial_x\vec s\times\partial_y\vec s)$ and Berry's orbital magnetization. The key effect is that carriers moving in the presence of a spin texture see it as a source of a geometric magnetic field coupled to the carrier's orbital motion through a spin-dependent Aharonov-Bohm effect. This emergent spin-orbit interaction effect was recently predicted to enable chiral magnons propagating along system boundaries. Here we show that it also favors chiral spin textures such as skyrmions -- the topologically protected objects with particle-like properties, stabilized in the ground state. The threshold for Stoner instability is found to soften, rendering chiral spin-ordered phases accessible under realistic conditions. We present a detailed analysis of the chiral effect for Bernal bilayer graphene and discuss the unique properties of skyrmion textures in graphene multilayers.