  In this work, we investigate the local structural distortion of the double
perovskite Ba$_2$YMoO$_6$ by means of infrared transmission spectroscopy. At
300 K, three bands are observed at $\sim$ 255.1 cm$^{-1}$, $\sim$ 343.4
cm$^{-1}$, and $\sim$ 561.5 cm$^{-1}$, which are related to the motion between
the cation Ba$^{2+}$ and the anion YMO$_6^{-2}$, the Y-O stretching motion and
the stretching vibration of the MoO$_6$ octahedron, respectively. These modes
continue to harden upon cooling owing to the shrink of the lattice constant.
When the temperature decreases to $T \leq$ 130 K around which the spin singlet
dimer begins to form, an additional phonon mode appears at $\sim$ 611
cm$^{-1}$, suggesting the occurrence of local distortion of MoO$_6$ octahedra.
With further decrease of the temperature, its intensity enhances and its peak
position keeps unchanged. These results indicate that the formation of the spin
singlet dimers is accompanied with the occurrence of the local structure
distortion of MoO$_6$ octahedra, providing evidence for the strong spin-phonon
coupling in the double perovskite Ba$_2$YMoO$_6$.
