Spin-Driven Jahn-Teller Distortion in a Pyrochlore System

The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the corner-sharing tetrahedra, the pyrochlore lattice, are investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin-1 spinel compounds ${\mathrm{ZnV}}_2{\mathrm{O}}_4$ and ${\mathrm{MgV}}_2{\mathrm{O}}_4$.