Skyrmion Hall Motion
Topological charge Q = ±1, Magnus force, and the Skyrmion Hall Effect
Skyrmions are topologically protected spin textures with integer topological charge Q = (1/4π)∫m·(∂_x m × ∂_y m)d²r.
Under an applied current, the Magnus/gyroscopic force F_Mag = G × v (where G = 4πQẑ) deflects the skyrmion transverse to its velocity — the Skyrmion Hall Effect.
Thiele equation: G × ṙ + D·α·ṙ = F_drive. The Hall angle θ_H = arctan(Q/α·D) can be large for small damping.
Q = +1: deflects ↑Q = −1: deflects ↓