Topological Spin Texture Atlas

Explore the live atlas

An interactive atlas for learning how magnetic spin textures map onto topological charge. Explore skyrmions, antiskyrmions, merons, bimerons, skyrmionium, domain walls, and vortices; perturb their analytic fields; and compare the resulting spin lattice, charge density, and total winding.

The project pairs a React and Three.js visualization with a small Python reference implementation of the texture generators and numerical topology calculations. Everything runs locally or as a static GitHub Pages site.

Method

For radial textures, the displayed unit spin field is generated from the polar profile $\theta(r)$, vorticity $w$, helicity $\gamma$, and core polarity $p=m_z(0)$:

$$ \mathbf m = \left(\sin\theta\cos(w\phi+\gamma),; \sin\theta\sin(w\phi+\gamma),; p\cos\theta\right). $$

The continuum topological charge density and total charge are

$$ q(x,y)=\frac{1}{4\pi}\mathbf m\cdot \left(\partial_x\mathbf m\times\partial_y\mathbf m\right), \qquad Q=\int q(x,y),dx,dy. $$

The reported lattice charge uses oriented triangle solid angles for neighboring spins $\mathbf a$, $\mathbf b$, and $\mathbf c$:

$$ \Omega_\triangle = 2\ \mathrm{atan2}\left( \mathbf a\cdot(\mathbf b\times\mathbf c), 1+\mathbf a\cdot\mathbf b+\mathbf b\cdot\mathbf c+\mathbf c\cdot\mathbf a \right), \qquad Q_\Omega=\frac{1}{4\pi}\sum_\triangle\Omega_\triangle. $$

Local development

cd frontend
npm install
npm run dev