Nonadiabatic Berry phase in nanocrystalline magnets

It is investigated how a Berry phase is created in polycrystalline nanomagnets and how the phase translates into an emergent magnetic field and into a topological Hall-effect contribution. The analysis starts directly from the spin of the conduction electrons and does not involve any adiabatic Hamiltonian. Completely random spin alignment in the nanocrystallites does not lead to a nonzero emergent field, but a modulation of the local magnetization does. As an explicit example, we consider a wire with a modulated cone angle