Topological Defect — Skyrmion Nucleation

Magnetic skyrmions: topologically protected spin vortices with integer winding number Q

Skyrmions

A skyrmion is a topological soliton in a 2D magnetic system — a vortex-like spin texture with a quantized topological charge (winding number).

Q = (1/4π) ∫ m·(∂m/∂x × ∂m/∂y) dx dy
Q ∈ ℤ (integer — topological!)

Skyrmions are stabilized by competing interactions: Heisenberg exchange (J), Dzyaloshinskii-Moriya interaction (D), and external magnetic field (B). The DM interaction arises from broken inversion symmetry and cants neighboring spins.

H = -J Σ Sᵢ·Sⱼ - D Σ (ẑ×rᵢⱼ)·(Sᵢ×Sⱼ)
- B Σ Sᵢᶻ

Skyrmions are topologically protected: Q cannot change continuously — annihilation requires an energy barrier. They are candidates for spintronic memory bits.

Topological charge Q: 0
Skyrmions: 0