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 Tr(∂aU∂aU†) for all USU(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 SO(3)×SO(3)→SO(3).
Bibliographical noteFunding Information:
M. S. is grateful to Andrei Losev and Paul Wiegmann for useful discussions. The work of M. S. is supported in part by Department of Energy Grant No. DE-SC0011842. C. D. B., Z. W., and S.-S. Z. are supported by funding from the Lincoln Chair of Excellence in Physics.
© 2018 American Physical Society.