(a) (Color online) Schematic of our setup with feedback loop. Both lever and sample are put on XYZ stages of Attocube motors (ANP100 series) in vacuum. A laser (Schäfter Kirchhoff 51nanoFI-660 nm) is coupled to a 50-50 beam splitter (Schafter Kirchoff) from where a fiber goes into the vacuum chamber. The interference between the fiber and lever is sensed by a photodiode (Thorlabs DET100 A). The signal of the photodiode is amplified by a Femto DLPCA 200 amplifier and goes into a Nanonis station with RC4 and SC4 real time and signal conditioning controllers, OC4 oscillation controller with integrated Phase Lock Loop, and HVA4 Piezo Supply that controls the X-piezo on which the fiber is mounted. (b) Photo of lever and sample as taken with a microscope. The positions of the thermocouples are indicated by the circles.
(a) Motion of long term drift over several hours. (b) The measurements (use of the Peltier) induce a change in the long term drift. (c) Due to radiated heat from the sample onto its vicinity, the aluminum lever holder expands. This can be detected by placing the fiber onto the holder. The temperature and expansion of the holder are correlated. (d) After correcting for drift, and subtracting the expansion signal (Fig. 2(c)), we obtain lever motion that is well correlated with the temperature on the sample for both cooling and heating of the sample.
Measured temperature on the sample and on the lever holder, while the sample is heated. The inset shows the normalized response to highlight the different transient responses.
(a) (Color online) The sensitivity of our setup depends on position of the fiber along the length of the lever. Positions 1–3 are shown in the inset. The fiber is moved vertically over the lever with a distance corresponding to the thickness of the fiber (125 micron). The lever holder movement is also shown. (b) Here the thermocouple response is shown. Between the two dashed vertical lines one can determine the lever movement and relate it to the temperature difference between plate and sphere. (c) For small temperature differences as compared to the ambient temperature (300 K) one can do a linear calibration with the function y = ax + b, where a is the sensitivity (nm/K) and b an offset. We found b to be zero within the measured variation when repeating the measurement. Using exact theory from Ref. 15, one can estimate the sensitivity h from heat transfer in farfield (9.74 nW/K).
Measurements of lever deflection vs temperature difference between sphere and plate. The graph is similar to Fig. 4(c), but the measurement is done over a larger range of ΔT. The black line is a fit of the Stefan-Boltzmann law.
Farfield sensitivity of the lever with sphere vs the distance to the plate. The sensitivity decreases due to edge (viewpoint) effects as the distance between plate and sphere becomes similar in magnitude to the dimensions of the plate.
Motion of the lever (multiple curves) and the holder when using a gold plate instead of a glass plate. Note that both signals have significantly reduced as compared to using a glass plate. But the motion of the lever is now smaller than the motion of the holder. Note that we could heat more in this case as compared to Fig. 2, as the sample was much smaller.
Lever deflection vs temperature difference between sphere and plate for different cases. This demonstrates the sensitivity of our setup for different materials. Note that a lever without sphere above a glass plate bends more due to applied heat than a lever with sphere above a gold plate.
Multiple measurements of heat transfer between a lever with 40 micron glass sphere and a VO2 sample that undergoes a phase transition. A clear hysteresis effect is visible for the transition temperature. Once again the effect of drift becomes visible after 150 s.
The lever motion is plotted vs the applied temperature difference between the sphere and the sample. The heat transfer decreases by a factor of 5 across the phase transition. The hysteresis effect is clearly visible. Drift affects the measurement with time, which becomes more visible for the cooling part of the data. The inset shows the derivative Δdeflection/Δtemperature.
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