Spin-Phonon coupling in frustrated magnet CdCr$_2$O$_4$

Strongly frustrated magnetic materials resist magnetic ordering down to very low temperatures. The existence of order in some of these systems involves the occurrence of a spin-driven lattice distortion. The Cr spinels, with non-Janh-Teller active ions, are excellent examples of such frustrated systems where magneto-elastic coupling causes the ordering of the spins. The distinct distortions in these Cr spinels couple to different spin orders. This is the case in ZnCr$_2$O$_4$ and CdCr$_2$O$_4$, where the unit cell contracts and elongates along the \textit{c} axis, respectively. The contraction in ZnCr$_2$O$_4$ splits a triply degenerate infrared (IR) active phonon\footnote{A.B. Sushkov, et al. PRL \textbf{94} 137202 (2005)}. The magnitude of the splitting and the redistribution of spectral weight gives a sensitive measure of the spin correlations in this system. We report the temperature dependence of the IR active phonons in CdCr$_2$O$_4$. The phonon splitting is similar to ZnCr$_2$O$_4$, but with opposite spectral weight distribution. We discuss these effects in light of recent theoretical models\footnote{G-W.Chern, et al. PRB \textbf{74} 060405 (2006)}.