Incommensurate single-angle spiral ordering of classical Heisenberg spins on zigzag ladder lattices

Exact and rigorous solutions of the ground-state problem for the classical Heisenberg model with nearest-neighbor interactions on two-and three-dimensional lattices composed of zigzag (triangular) ladders are obtained in a very simple way, with the use of a cluster method. It is shown how the geometrical frustration due to the presence of triangles as structural units leads to the emergence of incommensurate spiral orderings and their frustrated collinear limits which become nonfrustrated if the interaction along ladder legs changes the sign (becoming ferromagnetic). Interestingly, these orderings are determined by a single angle (along with the signs of the interactions between neighboring spins); therefore, the term "single-angle spiral ordering" is proposed. A hypothesis about the origin of a puzzling spin ordering in a zigzag ladder compound beta-CaCr2O4 is made.