Non-Collinear Magnetic Phases of a Triangular-Lattice Antiferromagnet and Doped CuFeO$_2$

We obtain the non-collinear 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 $\uudd$ phase transforms into a complex non-collinear phase with odd-order harmonics of the fundamental ordering wavevector $\vQ$. The observed elastic peaks at $2\pi \vx -\vQ$ in both Al- and Ga- doped CuFeO$_2$ are explained by a "scalene" distortion of the triangular lattice produced by the repulsion of neighboring oxygen atoms.