Magnetic Skyrmion — Spin Texture & Topological Hall Effect

Real-space spin winding · Berry phase · emergent magnetic field
2.50
π/2
1
0.50
A magnetic skyrmion is a topologically protected spin texture with winding number Q = (1/4π)∫n·(∂ₓn×∂ᵧn)d²r. The non-trivial topology creates an emergent magnetic field b_z = Φ₀·Q acting on conduction electrons. The topological Hall resistivity: ρ_THE = R₀·b_eff = R₀·Φ₀·n_sk·Q where n_sk is the skyrmion density. Bloch skyrmion (γ=π/2) vs Néel skyrmion (γ=0) differ by spin rotation — same Q, different emergent field sign.