Beyond Baby Skyrmions: principle chiral model in noncollinear magnets

We discuss noncollinear magnetic phenomena whose local order parameter is characterized by more than one spin vector. By focusing on the simple cases of 2D triangular and 3D pyrochlore lattices, we demonstrate that their low-energy theories can be described by a one-parametric class of sigma models continuously interpolating between the classical Heisenberg model and the principal chiral model. A natural consequence of our derivation is that stable Skyrmion of type π₃(SO(3)) can be generically induced in noncollinear magnets.