  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 ${\rm Tr} \,\left( \partial_a U \partial_a
U^\dagger\right)$ for all $U\in \text{SU}(2)$. The target space can be viewed
as a U$(1)$ fibration over the $CP(1)$ space. The 3D version of our model is
further generalized to break spatial and spin rotation symmetry $\text{SO}(3)
\times \text{SO}(3) \to \text{SO}(3)$.
