Real-space Berry phase from magnetic skyrmion spin texture
Topological charge Q = —
A magnetic skyrmion is a topologically protected spin texture with winding number Q = ±1.
Conduction electrons adiabatically following the skyrmion spin accumulate a real-space Berry phase Φ_B = 4πQ per skyrmion.
This acts as an emergent magnetic flux B_eff = Φ₀·Q/A, deflecting electrons and producing a topological Hall resistivity
ρ_THE ∝ Q — measurable even without spin-orbit coupling.