  Amorphous oxide thin films play a fundamental role in state-of-the art
interferometry experiments, such as gravitational wave detectors where these
films compose the high reflectance mirrors of end and input masses. The
sensitivity of these detectors is affected by thermal noise in the mirrors with
its main source being the mechanical loss of the high index layers. These
thermally driven fluctuations are a fundamental limit to optical interferometry
experiments and there is a pressing need to understand the underlying processes
that lead to mechanical dissipation in materials at room temperature. Two
strategies are known to lower the mechanical loss: employing a mixture of
Ta$_2$O$_5$ with $\approx$ 20\% of TiO$_2$ and post-deposition annealing, but
the reasons behind this are not completely understood. In this work, we present
a systematic study of the structural and optical properties of ion beam
sputtered TiO$_2$-doped Ta$_2$O$_5$ films as a function of the annealing
temperature. We show for the first time that low mechanical loss is associated
with a material morphology that consists of nanometer sized Ar-rich bubbles
embedded into an atomically homogeneous mixed titanium-tantalum oxide. When the
Ti cation ratio is high, however, phase separation occurs in the film which
leads to increased mechanical loss. These results indicate that for designing
low mechanical loss mixed oxide coatings for interferometry applications it
would be beneficial to identify materials with the ability to form ternary
compounds while the dopant ratio needs to be kept low to avoid phase
separation.
