  The chromium spinels MgCr2O4 and ZnCr2O4 are prime examples of the highly
frustrated pyrochlore lattice antiferromagnet. Experiment has carefully
established that both materials, upon cooling, distort to lower symmetry and
order magnetically. We study the nature of this process by a combination of
density-functional-theory based energy mapping and classical Monte Carlo
simulations. We first computationally establish precise Heisenberg Hamiltonian
parameters for the high temperature cubic and the low temperature tetragonal
and orthorhombic structures of both spinels. We then investigate the respective
ordering temperatures of high symmetry and low symmetry structures. We
carefully compare our results with experimental facts and find that our
simulations are remarkably consistent with a type of spin-Peierls mechanism,
adapted to three dimensions, where the structural distortion is mediated by a
magnetic energy gain due to a lower degree of frustration.
