Interplay between ferroelastic and metal-insulator domains in quasi-2D VO$_{2}$ nanoplatelets*

Significant effort has been spent to date to investigate behavior of VO$_{2}$ nanostructures in the vicinity of the metal-insulator transition (MIT). However, one important aspect of this material---the fact that low temperature VO$_{2}$ phase is ferroelastic---has been almost completely left out of consideration. Using variable temperature scanning microwave microscopy (SMM) and polarized-light microscopy, we imaged development of domains of metallic and semiconducting phases during the MIT in single crystalline quasi-2D nanoplatelets and observed non-trivial strain-driven phenomena. Ferroelastic domains in VO$_{2}$ nanosystems can significantly affect local strain distributions, and hence couple to the strongly strain-dependent MIT. In contrast to quasi-1D nanobeams, the presence of the second dimension results in emergence of several possible families of ferroelastic domains in NPls, thus allowing systematic studies of strain-controlled transitions in the presence of geometrical frustration.