We review the mechanism of spin-lattice coupling in relieving the geometrical
frustration of pyrochlore antiferromagnets, in particular spinel oxides. The
tetrahedral unit, which is the building block of the pyrochlore lattice,
undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom
are coupled to the antiferromagnetism. By restricting our considerations to
distortions which preserve the translational symmetries of the lattice, we
present a general theory of the collective spin-Jahn-Teller effect in the
pyrochlore lattice. One of the predicted lattice distortions breaks the
inversion symmetry and gives rise to a chiral pyrochlore lattice, in which
frustrated bonds form helices with a definite handedness. The chirality is
transferred to the spin system through spin-orbit coupling, resulting in a
long-period spiral state, as observed in spinel CdCr2O4. We discuss explicit
models of spin-lattice coupling using local phonon modes, and their
applications in other frustrated magnets.Comment: 23 pages, 6 figures. Lecture notes for Trieste Summer School, August
2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C.
Lacroix, P. Mendels, F. Mil
