Topological Charge & Skyrmions

Visualize spin textures on a 2D lattice. Skyrmions are localized spin whirlpools with integer topological charge Q — stable against smooth deformations.

Topological charge Q: - Exchange energy: - Mode: Skyrmion
Each arrow is a unit spin vector projected onto the plane (color = z-component: red=up, blue=down). The topological charge Q = (1/4π) ∫ n·(∂xn × ∂yn) d²r counts how many times the spin texture wraps the unit sphere. Integer Q cannot change without creating a discontinuity — topological protection.