Damping in high-frequency metallic nanomechanical resonators

We have studied damping in polycrystalline Al nanomechanical resonators by measuring the temperature dependence of their resonance frequency and quality factor over a temperature range of 0.1–4 K. Two regimes are clearly distinguished with a crossover temperature of 1 K. Below 1 K we observe a logarithmic temperature dependence of the frequency and linear dependence of damping that cannot be explained by the existing standard models. We attribute these phenomena to the effect of the two-level systems characterized by the unexpectedly long (at least two orders of magnitude longer) relaxation times and discuss possible microscopic models for such systems. We conclude that the dynamics of the two-level systems is dominated by their interaction with one-dimensional phonon modes of the resonators.

Figure 1

(Color online) Amplitude of the induced electromotive force of the $5\mu \text{m}$ beam at $B=0.5\text{T}$ for different temperatures (symbols). The solid lines are Lorentzian fits. The right inset shows damping $1/Q$ of the same beam as a function of the magnetic field (black squares). The $B^2$ dependence expected from magnetomotive damping is shown as a fit (red [gray] line) to the experimental data. The left inset presents a layout of the beams studied.

Figure 2

(Color online) Relative shift of the resonance frequency as a function of the temperature for different resonators (symbols). For each device the frequency shift is normalized to the maximum resonance frequency $f_0^{\text{max}}$. The dotted lines are logarithmic fits to the measured data used to determine the values for $C$ in Table . The inset shows the temperature dependence of $f_0$ measured from room temperature (black squares). The red (gray) circles are a fit using thermal-expansion coefficients from Ref. 15.

Figure 3

(Color online) Damping $1/Q_{\text{int}}$ as a function of temperature for four resonators of different lengths (symbols). Damping increases linearly up to 0.7–1.5 K followed by a weaker temperature dependence above this temperature. The dotted lines are linear fits to the measured data used to determine the values for ${\nu }_{F}U$.