Nonuniform spin-Peierls distortion in the ``pyrochlore'' antiferromagnet ZnCr$_2$O$_4$

The cubic spinel ZnCr$_2$O$_4$ is a nice realization of the Heisenberg antiferromagnet on the ``pyrochlore lattice'' with spins $S = 3/2$. A high degree of geometrical frustration creates a strongly correlated paramagnetic regime at low temperatures where spins remain liquid and move in a highly coordinated fashion. The frustration is eventually lifted through a spin-Peierls-like transition at 12.5 K [1]. A basic physical picture of the transition has been developed by Yamashita and Ueda [2] and Tchernyshyov, Moessner and Sondhi [3] for the cases of a uniform lattice distortion. However, accumulating experimental evidence points to the dominance of a nonuniform lattice distortion that enlarges the structural unit cell [4]. The lattice modes most likely involved in the transition are the four phonon doublets with the wavevectors $\langle \frac{1}{2} \frac{1}{2} \frac{1}{2} \rangle$. We discuss the symmetry aspects of the appropriate spin-Peierls order parameter and ways of measuring it. [1] S.-H. Lee {\em et al.}, Phys. Rev. Lett. {\bf 84,} 3718 (2000). [2] Y. Yamashita and K. Ueda, Phys. Rev. Lett. {\bf 85,} 4960 (2000). [3] O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Phys. Rev. B {\bf 66,} 064403 (2002). [4] H. Ueda {\em et al.}, Bull. Amer. Phys. Soc. {\bf 48,} 826 (2003).