We analyze a classical Heisenberg spin model on the simple cubic lattice which is invariant under time reversal and contains multiple chiral spin interactions. The modeled dynamics is appropriate either for local moments coupled to itinerant Weyl electrons or localized electrons with a strong spin-orbit coupling that would produce a Weyl spectrum away from half filling. Using a Monte Carlo method, we find a robust $4Q$ bipartite lattice of hedgehogs and antihedgehogs which melts through a first order phase transition at a critical temperature in certain segments of the phase diagram. The density of hedgehogs is a nonlinear function of the Dzyaloshinskii-Moriya interaction and a linear function of the multiple-spin chiral interaction which plays the fundamental role of a “magnetic flux” or a hedgehog chemical potential. These findings are related to the observations of hedgehog lattices in MnGe, ${\mathrm{MnSi}}_{1-x}{\mathrm{Ge}}_x$, and ${\mathrm{SrFeO}}_3$ and indirectly support the possible existence of incompressible quantum-disordered hedgehog liquids.

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• Magnetic phase transitions
• Spin texture
• Topological phase transition
• Chiral magnets
• Monte Carlo methods