Structure and morphology of low mechanical loss TiO$_2$-doped Ta$_2$O$_5$

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.