Temperature dependent Raman and x-ray studies of spin-ice pyrochlore $Dy_2Ti_2O_7$ and non-magnetic pyrochlore $Lu_2Ti_2O_7$

We present here temperature-dependent Raman, x-ray diffraction and specific heat studies between room temperature and 12 K on single crystals of spin-ice pyrochlore compound $Dy_2Ti_2O_7$ and its non-magnetic analogue $Lu_2Ti_2O_7$. Raman data show a new band not predicted by factor group analysis of Raman-active modes for the pyrochlore structure in $Dy_2Ti_2O_7$, appearing below a temperature of $T_c=$110 K with a concomitant contraction of the cubic unit cell volume as determined from the powder x-ray diffraction analysis. Low temperature Raman experiments on O$^{18}$-isotope substituted $Dy_2Ti_2O_7$ confirm the phonon origin of the new mode. These findings, absent in $Lu_2Ti_2O_7$, suggest that the room temperature cubic lattice of the pyrochlore $Dy_2Ti_2O_7$ undergoes a subtle structural transformation near $T_c$. We find anomalous textit{red-shift} of some of the phonon modes in both the $Dy_2Ti_2O_7$ and the $Lu_2Ti_2O_7$ as the temperature decreases, which is attributed to strong phonon-phonon anharmonic interactions.