Magnetic Skyrmion

Skyrmions are topologically protected spin textures: vortex-like configurations where the spin winds from +z at the periphery to −z at the center (or vice versa). The topological charge Q = (1/4π)∫ m·(∂ₓm × ∂ᵧm) dA = ±1 is an integer that cannot change continuously — the skyrmion cannot be unwound without a phase transition. When driven by a current, they undergo a Skyrmion Hall effect: the Magnus force from Q deflects them transversely (like a ball with spin), creating a Hall angle that could scatter skyrmions into edges. This is a key challenge for skyrmion- based racetrack memory.