Magnetic Skyrmion — Topological Charge & DM Interaction

Spin texture on a 2D lattice with Dzyaloshinskii-Moriya interaction. Topological charge Q = ±1 protects the skyrmion.

Parameters

Q = —
Topological charge:
Q = (1/4π) ∫ m·(∂ₓm × ∂ᵧm) d²r

DM interaction favors spin canting, stabilizing skyrmions. Q is an integer invariant — the skyrmion cannot unwind without crossing an energy barrier.