Frustrated Topological Orbital Magnetism

By studying the interplay of geometric frustration with Aharonov-Bohm fluxes in three dimensions, we unveil a rich playground exhibiting topological semimetallic ground states with orbital magnetic dipole, quadrupole and ferrotoroidic orders, akin to spin patterns in classical spin ices - a class of phenomena which we dub frustrated topological orbital magnetism. We demonstrate that the ground-state toroidizations underpinned by non-Abelian topological nodal lines induce measurable current-induced Hall phenomena. We further find that distinct 2-in-2-out and 3-in-1-out frustrated orbital current patterns can be associated with topological Weyl node charges, and corresponding anisotropic linear and nonlinear Hall effects. We propose signatures for experimental validation of distinct frustrated topological orbital magnetic orders in candidate materials.