Spin phonon induced collinear order and magnetization plateaus in triangular and kagome antiferromagnets:: Applications to CuFeO2

We study the effect of spin-lattice coupling on triangular and kagome antiferromagnets and find that even moderate couplings can induce complex collinear orders. On coupling classical Heisenberg spins on the triangular lattice to Einstein phonons, a rich variety of phases emerge including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magnetoelectric material CuFeO(2). Also, we predict magnetization plateaus at 1/3, 3/7, 1/2, 3/5, and 5/7 at these couplings. Strong spin-lattice couplings induce a striped collinear state, seen in alpha-NaFeO(2) and MnBr(2). On the kagome lattice, moderate spin-lattice couplings induce collinear order, but an extensive degeneracy remains.