Probing spin correlations with phonons in the strongly frustrated magnet ZnCr$_2$O$_4$

Geometrically frustrated magnets can resist magnetic ordering and remain in a strongly correlated paramagnetic state well below the Curie-Weiss temperature. The spin-lattice coupling can play an important role in relieving the frustration in these system. In ZnCr$_2$O$_4$, an excellent realization of the Heisenberg antiferromagnet on the ``pyrochlore'' network, a lattice distortion relieves the geometrical frustration through a spin-Peierls-like phase transition at $T_c=12.5$~K. Conversely, spin correlations strongly influence the elastic properties of a frustrated magnet. By using infrared spectroscopy and published data on magnetic specific heat, we demonstrate that the frequency of an optical phonon triplet in ZnCr$_2$O$_4$ tracks the nearest-neighbor spin correlations above $T_c$. Below $T_c$, the phonon triplet splits into a singlet and a doublet, separated by 11~cm$^{-1}$. This splitting is directly proportional to the spin-Peierls order parameter. We also observed a number of weak absorption bands, arising below $T_c$, which indicates doubling of the Brillouin zone at the structural/magnetic phase transition.