Magnetic skyrmions are topologically protected spin textures with integer winding number Q = ±1. They behave as quasiparticles and cannot be continuously deformed into the uniform state — they must be created or destroyed in pairs.
Topological charge: Q = (1/4π) ∫ n · (∂ₓn × ∂ᵧn) dx dy, where n is the local spin direction unit vector. For a skyrmion, Q = −1 (the spin texture wraps the unit sphere once). The Dzyaloshinskii–Moriya interaction (DMI), arising from broken inversion symmetry, stabilizes the skyrmion against collapse. Click on the canvas to place skyrmions. The color wheel shows the in-plane angle φ(x,y) of the spin field; the z-component is encoded in brightness — blue=down, red=up.