  High finesse optical cavities of current interferometric gravitational-wave
detectors are significantly limited in sensitivity by laser quantum noise and
coating thermal noise. The thermal noise is associated with internal energy
dissipation in the materials that compose the test masses of the
interferometer. Our understanding of how the internal friction is linked to the
amorphous material structure is limited due to the complexity of the problem
and the lack of studies that span over a large range of materials. We present a
systematic investigation of amorphous metal oxide and Ta$_2$O$_5$-based mixed
oxide coatings to evaluate their suitability for low Brownian noise
experiments. It is shown that the mechanical loss of metal oxides is correlated
to their amorphous morphology, with continuous random network materials such as
SiO$_2$ and GeO$_2$ featuring the lowest loss angles. We evaluated different
Ta$_2$O$_5$-based mixed oxide thin films and studied the influence of the
dopant in the optical and elastic properties of the coating. We estimated the
thermal noise associated with high-reflectance multilayer stacks that employ
each of the mixed oxides as the high index material. We concluded that the
current high index material of TiO$_2$-doped Ta$_2$O$_5$ is the optimal choice
for reduced thermal noise among Ta$_2$O$_5$-based mixed oxide coatings with low
dopant concentrations.
