Noncollinear magnetic phases of a triangular-lattice antiferromagnet and of doped CuFeO₂

We obtain the noncollinear ground states of a triangular-lattice antiferromagnet with exchange interactions up to third nearest neighbors as a function of the single-ion anisotropy D. At a critical value of D, the collinear ↑↑↓↓ phase transforms into a complex noncollinear phase with odd-order harmonics of the fundamental ordering wavevector Q. The observed elastic peaks at 2πx-Q in both Al- and Ga-doped CuFeO₂ are explained by a "scalene" distortion of the triangular-lattice produced by the repulsion of neighboring oxygen atoms.