Topological magnetism in correlated insulators and Weyl semimetals

Spin-orbit interaction is the driving force in many topological materials. Its effect on the spins of localized electrons is seen through the short-range Dzyaloshinskii-Moriya (DM) and chiral interactions. Additional itinerant electrons that interact with local moments can further mediate RRKY interactions (Heisenberg, Kitaev and DM) as well as multi-spin chiral interactions among the moments. When induced by Weyl electrons, these spin interactions can be oscillatory on both short and intermediate length scales, and feature an algebraic envelope dependence on the spatial separation between the spins. After outlining the theory behind these conclusions, I will discuss the observable implications: magnetic orders with skyrmions and hedgehogs, spin-momentum locking of magnetic excitations, transport properties, and the prospects for 3D quantum spin liquids with topological order. I will also propose a neutron scattering method for characterizing the spectrum of Weyl electrons from the damping of spin waves.