Magnetic Skyrmion — Topological Soliton

Skyrmions are topologically protected spin textures with integer winding number Q = ±1. The Dzyaloshinskii–Moriya interaction (DMI) stabilizes them against collapse. Current drives skyrmion Hall drift at ~40°.

Parameters

Topological charge Q
Skyrmion radius R
Hall angle θ_H
~40°
n(r) = (sin f(r)cosφ, sin f(r)sinφ, cos f(r))
f(r): π at center → 0 at edge

Q = (1/4π)∫n·(∂_x n × ∂_y n) dA = ±1

DMI: H_DMI ~ D(m × ∂m/∂r)
Skyrmion Hall effect: J→m drift at angle arctan(α/1)