  We report an investigation of the phonon thermal Hall effect in single
crystal samples of Y$_2$Ti$_2$O$_7$, Dy$_2$Ti$_2$O$_7$, and DyYTi$_2$O$_7$. We
measured the field-linear thermal Hall effect in all three samples. The
temperature dependence of thermal Hall conductivities shows a peak around 15 K,
which coincides with the peak positions of the longitudinal thermal
conductivities. The temperature-dependent longitudinal thermal conductivities
indicates that phonons dominate thermal transport in all three samples.
However, the presence of Dy$^{3+}$ magnetic ions introduces significant effects
on the field dependence of longitudinal thermal conductivities. The thermal
Hall ratio is sizeable in all three samples and consistent with the values
reported for other insulating materials exhibiting a phononic thermal Hall
effect, though their exact underlying mechanism remains yet to be identified.
The thermal Hall ratio is nearly the same for $\rm Y_2Ti_2O_7$ and
DyYTi$_2$O$_7$, and slightly larger for Dy$_2$Ti$_2$O$_7$, suggesting that
magnetic impurities are less significant in generating the phononic thermal
Hall effect. Our observations of the phononic thermal Hall effect support an
intrinsic origin in Y$_2$Ti$_2$O$_7$, but suggest a combination of intrinsic
and extrinsic effects in Dy$_2$Ti$_2$O$_7$ and DyYTi$_2$O$_7$.
