Magnetic Skyrmion — Topology & Winding Number

Topological charge Q = (1/4π) ∫ m·(∂m/∂x × ∂m/∂y) dx dy

Skyrmion Parameters

Topological charge (integer):
Q = 1/(4π) ∫ m·(∂ₓm×∂ᵧm) dA
Néel: γ=0, Bloch: γ=π/2
Stability: topological protection
Skyrmion Hall effect: F_sk = -Q·B×v
DM interaction drives type selection
Winding number Q:
Skyrmion size:
Energy (arb.):
m_z center: