Magnetic Skyrmion — Topological Charge Texture

Q = 1/(4π) ∫ n·(∂ₓn × ∂ᵧn) d²r — integer topological charge, topologically protected

Skyrmion Parameters

Q = +1
Skyrmions (Skyrme 1962): Topologically non-trivial spin textures. Q is quantized — the integer winding of n:S²→S². Protected by topology: continuous deformations cannot change Q. Discovered in magnets 2009 (Mühlbauer). Promising for racetrack memory: driven by spin-transfer torque.