Magnetic Skyrmion & Topological Charge

A topologically non-trivial spin texture — the skyrmion wraps the unit sphere once, giving winding number Q = −1

Parameters

6.0
0.00
+1
28
Topological charge Q—
Skyrmion radius R—
Helicity γ—
Exchange energy—
Sz average—
Magnetic Skyrmion

The spin texture is given by the mapping 𝐧(𝐫): ℝ² → S², with topological charge:
Q = 1/(4π) ∫ 𝐧·(∂ₓ𝐧 × ∂ᵧ𝐧) d²r

A Néel-type skyrmion: spins point down at center, rotate to up at periphery. The Dzyaloshinskii-Moriya interaction (DMI) stabilizes skyrmions against collapse.

Topological protection: Q is an integer, continuously invariant under smooth deformations. A skyrmion cannot be unwound without creating a singularity — the hedgehog field on S².

Color: ● Sz≈+1 (up)   ● Sz≈0   ● Sz≈−1 (down)

Arrows show in-plane spin components (Sx, Sy). This visualization is used in spintronics/racetrack memory research.