Nanoscale Thermal Mapping of VO$_2$

We present a method for nanoscale thermal imaging of insulating thin films. We image the local temperature of the metal-insulator transition in a VO$_2$ film, and investigate the role of Joule heating in two-terminal geometry. By sweeping the voltage applied to a conducting atomic force microscope tip in contact mode, we locally trigger and detect the transition to the metallic phase. By fitting the Poole-Frenkel conduction regime immediately preceding the transition, we extract the local temperature. Finally, we find grains displaying two electronic transitions, consistent with a locally stable intermediate insulating phase.\\[4pt] We acknowledge financial support from Harvard's Nanoscale Science and Engineering Center, funded by NSF grant PHY 01-17795 and the Sloan Fellowship. Adam Pivonka acknowledges the support of the New York Community Trust--George Merck Fund. Magdalena Huefner acknowledges the support of the Deutsche Forschungsgemeinschaft (HU 1960/11).