Spin-lattice interaction effect in frustrated antiferromagnets

Lattice-coupled antiferromagnetic spin model is analyzed for a number of frustrated lattices. In the pyrochlore lattice, a uniform hexagon contraction can take place and reduce the exchange energy within the hexagonal cluster. In the triangular and kagomé lattice, the mean-field theory predicts lack of lattice displacement. However, after considering the possibility of valence-bond formation, we argue that a type of valence-bond-solid order can be stabilized through spin-lattice interaction and leads to lattice deformation in the triangular structure. Excitation spectrum for the lattice-deformed ground state is worked out, which differs from the conventional spin waves and is in principle observable in neutron scattering.