In recent years an increasing number of devices and experiments are shown to be limited by mechanical thermal noise .
In particular sub-Hertz laser frequency stabilization and gravitational wave detectors , that are able to measure fluctuations of \SI { e - 18 } { m / \sqrt { Hz } } or less , are being limited by thermal noise in the dielectric coatings deposited on mirrors .
In this paper we present a new measurement of thermal noise in low absorption dielectric coatings deposited on micro-cantilevers and we compare it with the results obtained from the mechanical loss measurements .
The coating thermal noise is measured on the widest range of frequencies with the highest signal to noise ratio ever achieved .
In addition we present a novel technique to deduce the coating mechanical losses from the measurement of the mechanical quality factor which does not rely on the knowledge of the coating and substrate Young moduli .
The dielectric coatings are deposited by ion beam sputtering .
The results presented here give a frequency independent loss angle of \mathrm { ( 4.7 \pm 0.2 ) \times 10 ^ { -4 } } with a Young ’ s modulus of 118 GPa for annealed tantala from \SI { 10 } { Hz } to \SI { 20 } { kHz } .
For as-deposited silica , a weak frequency dependence ( \propto f ^ { -0.025 } ) is observed in this frequency range , with a Young ’ s modulus of 70 GPa and an internal damping of \mathrm { ( 6.0 \pm 0.3 ) \times 10 ^ { -4 } } at \SI { 16 } { kHz } , but this value decreases by one order of magnitude after annealing and the frequency dependence disappears .