Gigantic Maximum of Nanoscale Noncontact Friction

We report measurements of noncontact friction between surfaces of ${\mathrm{NbSe}}_2$ and ${\mathrm{SrTiO}}_3$ and a sharp Pt-Ir tip that is oscillated laterally by a quartz tuning fork cantilever. At 4.2 K, the friction coefficients on both the metallic and insulating materials show a giant maximum at the tip-surface distance of several nanometers. The maximum is strongly correlated with an increase in the spring constant of the cantilever. These features can be understood phenomenologically by a distance-dependent relaxation mechanism with distributed time scales.

Figure 1

(a) Experimental setup. The QTF with the Pt-Ir tip oscillates parallel to the sample surface at its resonance frequency with constant amplitude under the control of a commercial FM-AFM controller EasyPLL. The frequency shift $\Delta f$, the dissipation $g$, and the tunneling current $I$ are measured as a function of the tip-sample distance. (b) A photograph of the QTF. The tip is electrically isolated from the QTF and is connected to the ground port by a gold wire.

Figure 2

The noncontact friction coefficient ${\Gamma }_{\mathrm{int}}$ and the friction-induced spring constant $k_{\mathrm{int}}$ of ${\mathrm{NbSe}}_2$ as a function of the tip-sample distance $d$. (a) Data at 4.2 K and under $\sim {10}^{-4}\mathrm{Pa}$. Lower panel: The tunneling current $I$. (b) Data at room temperature and under $\sim {10}^{-3}\mathrm{Pa}$. Note the different scales for ${\Gamma }_{\mathrm{int}}$ and $k_{\mathrm{int}}$ in the two graphs.

Figure 3

(a) ${\Gamma }_{\mathrm{int}}$ and $k_{\mathrm{int}}$ as a function of $d$ for the ${\mathrm{SrTiO}}_3$ sample at 4.2 K. Note that both ${\Gamma }_{\mathrm{int}}$ and $k_{\mathrm{int}}$ vary over a wider distance range (about 25 nm) than those of ${\mathrm{NbSe}}_2$. (b) ${\Gamma }_{\mathrm{int}}$ and $k_{\mathrm{int}}$ for ${\mathrm{NbSe}}_2$ at 4.2 K measured by a QTF oscillating at 300 kHz. ${\Gamma }_{\mathrm{int}}$ and $k_{\mathrm{int}}$ are 2 and 1 order of magnitude smaller, respectively, than those taken at 32 kHz.

Figure 4

The $k_{\mathrm{int}}-{\omega }_0{\Gamma }_{\mathrm{int}}$ plots: (a) ${\mathrm{NbSe}}_2$ data of Fig. 2a. (b) ${\mathrm{SrTiO}}_3$ data from Fig. 3a. Note that the ellipse of the ${\mathrm{SrTiO}}_3$ data is more squeezed in the vertical direction by an order of magnitude than that for ${\mathrm{NbSe}}_2$. Red lines are a part of arbitral semicircles.