Figure 1

(a) Optical image of the fiber, the lever with sphere and the sample with a visible reflection of the sphere and the fiber. (b) SEM image of the sphere. (c) Scans of the involved surfaces. For the sphere the peak height varies from place to place and can be as high as 200 nm.Reuse & Permissions

Figure 2

(a) Measured deflection-distance curves (piezo calibration is applied) for the two glass samples at $\Delta T=0\mathrm{K}$. They are attributed to a torque $d\times F_{\parallel }$, which results in $F_{\mathrm{Tor}}$ because $F_L$ and $F_{\parallel }$ do not coincide at the lever axis (1a inset). (b) FF curves (at $40\mu \mathrm{m}$) RHT as function of $\Delta T$, the standard deviation denotes variation from place to place on the surface (c) NF RHT theory in the plate-sphere setup for a sphere diameter of $40\mu \mathrm{m}$. (d) Deflection-distance curves for the ${\mathrm{SiO}}_2$ thin film sample at different $\Delta T$, from which the electrostatic contribution in Fig. 2a at $\Delta T=0\mathrm{K}$ is subtracted. The curves are fitted to theory (lines) to calibrate the contact point $d_0$ and lever sensitivity $S_h$. Each curve is an average of six curves taken at the same place where the standard deviation is shown for the $\Delta T=75\mathrm{K}$ curve. The inset in (d) shows values and standard deviation of $S_h$ as obtained for different places (number of places are indicated for each $\Delta T$).Reuse & Permissions

Figure 3

(a) Measured FF RHT versus $\Delta T$ for the 50 and 100 nm ${\mathrm{VO}}_2$ films on a sapphire substrate. The inset shows theory in FF versus ${\mathrm{VO}}_2$ film thickness (b) Parallel plane theory of NF RHT at 300 K between ${\mathrm{SiO}}_2$ and ${\mathrm{VO}}_2$ (50 nm on sapphire). Results for two sets of dielectric data for insulating ${\mathrm{VO}}_2$ are shown. (c) Three averages of RHT measurements done at 9 different places on the surface are shown for both ${\mathrm{VO}}_2$ phases ($\Delta T=30\mathrm{K}$ minus $\Delta T=0\mathrm{K}$, open symbols, $\Delta T=75\mathrm{K}$ minus $\Delta T=50\mathrm{K}$, closed symbols). Theory is for the metallic (solid line) and insulating (dashed line) phase [see legend Fig. 3b]. The inset shows differences between the metal and insulating curves. Thin error bars depict place dependent variation in the measurements, thick error bars are standard deviations of the averages. (d) Averages of all 27 measurements obtained at different places, and theory (see legend 3b, 2 curves for metallic ${\mathrm{VO}}_2$ are shown). Fat symbols mean $\Delta T=0\mathrm{K}$ curve is not subtracted, thin symbols mean that the $\Delta T=0\mathrm{K}$ curve is subtracted.Reuse & Permissions