NV microscopy of thermally controlled stresses caused by Cr$_2$O$_3$ thin films
Many modern applications, including quantum computing and quantum sensing, use substrate-film interfaces. Particularly, thin films of chromium or titanium and their oxides are commonly used to bind various structures, such as resonators, masks, or microwave antennas, to a diamond surface. Due to different thermal expansions of involved materials, such films and structures could produce significant stresses, which need to be measured or predicted. In this paper, we demonstrate imaging of stresses in the top layer of diamond with deposited structures of Cr$_2$O$_3$ at temperatures 19$^{\circ}$C and 37$^{\circ}$C by using stress-sensitive optically detected magnetic resonances (ODMR) in NV centers. We also calculated stresses in the diamond-film interface by using finite-element analysis and correlated them to measured ODMR frequency shifts. As predicted by the simulation, the measured high-contrast frequency-shift patterns are only due to thermal stresses, whose spin-stress coupling constant along the NV axis is 21$\pm$1 MHz/GPa, that is in agreement with constants previously obtained from single NV centers in diamond cantilever. We demonstrate that NV microscopy is a convenient platform for optically detecting and quantifying spatial distributions of stresses in diamond-based photonic devices with micrometer precision and propose thin films as a means for local application of temperature-controlled stresses. Our results also show that thin film structures produce significant stresses in diamond substrates, which should be accounted for in NV-based applications.