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We report kelvin to millikelvin-temperature measurements of dissipation andfrequency shift in megahertz-range resonators fabricated fromultra-nanocrystalline diamond. Frequency shift $\delta f/f_0$ and dissipation$Q^{-1}$ demonstrate temperature dependence in the millikelvin range similar tothat predicted by the glass model of tunneling two level systems. Thelogarithmic temperature dependence of $\delta f/ f_0$ is in good agreement withsuch models, which include phonon relaxation and phonon resonant absorption.Dissipation shows a weak power law, $Q^{-1}\propto T^{{1/3}}$, followed bysaturation at low temperature. A comparison of both the scaled frequency shiftand dissipation in equivalent micromechanical structures made of single-crystalsilicon and gallium arsenide indicates universality in the dynamical response.

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