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We obtain the non-collinear ground states of a triangular-latticeantiferromagnet with exchange interactions up to third nearest neighbors as afunction of the single-ion anisotropy $D$. At a critical value of $D$, thecollinear $\uudd $ phase transforms into a complex non-collinear phase withodd-order harmonics of the fundamental ordering wavevector $\vQ $. The observedelastic peaks at $2\pi \vx -\vQ $ in both Al- and Ga- doped CuFeO$_2$ areexplained by a "scalene" distortion of the triangular lattice produced by therepulsion of neighboring oxygen atoms.

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