Microscopic nature of the asymmetric hysteresis in the insulator-metal transition of VO$_2$ revealed by spectroscopic ellipsometry

Systematic spectroscopic ellipsometry investigations have been performed in order to elucidate the asymmetric insulator-to-metal transition in thin VO$_2$ films. The comprehensive analysis of the obtained macroscopic optical response yields a hysteretic behavior, and in particular its asymmetry, when performed in the framework of an anisotropic effective medium approximation taking into account the volume fraction of the metal inclusions as well as their shape. We reveal microscopic details of the percolation transition, namely that the shape of the metal inclusions goes through several plateaus, as seen in the evolution of the shape factor on both sides of the transition region and resulting in different critical volume fractions at the transition for the heating and cooling cycles.