Evidence of universality in the dynamical response of micromechanical diamond resonators at millikelvin temperatures

We report kelvin to millikelvin-temperature measurements of dissipation and frequency shift in megahertz-range resonators fabricated from ultra-nanocrystalline diamond. Frequency shift $\delta $f/f$_{0}$ and dissipation Q$^{-1}$ demonstrate temperature dependence in the millikelvin range similar to that predicted by the glass model of tunneling two level systems. The logarithmic temperature dependence $\delta $f/f$_{0}$ is in good agreement with such models, which include phonon relaxation and phonon resonant absorption. Dissipation shows a weak power law, Q$^{-1} \quad \sim $ T$^{1/3}$, followed by saturation at low temperature. A comparison of both the scaled frequency shift and dissipation in equivalent micromechanical structures made of single-crystal silicon and gallium arsenide indicates universality in the dynamical response.