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We present a coordinated study of the paramagnetic-to-antiferromagnetic, rhombohedral-to-monoclinic, and metal-to-insulator transitions in thin-film specimens of the classic Mott insulator ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ using low-energy muon spin relaxation, x-ray diffraction, and nanoscale-resolved near-field infrared spectroscopic techniques. The measurements provide a detailed characterization of the thermal evolution of the magnetic, structural, and electronic phase transitions occurring in a wide temperature range, including quantitative measurements of the high- and low-temperature phase fractions for each transition. The results reveal a stable coexistence of the high- and low-temperature phases over a broad temperature range throughout the transition. Careful comparison of temperature dependence of the different measurements, calibrated by the resistance of the sample, demonstrates that the electronic, magnetic, and structural degrees of freedom remain tightly coupled to each other during the transition process. We also find evidence for antiferromagnetic fluctuations in the vicinity of the phase transition, highlighting the important role of the magnetic degree of freedom in the metal-insulator transition.

Using scanning near-field optical microscopy at cryogenic temperatures, we explored the first-order metal-insulator transition of exfoliated $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ microcrystals on a ${\mathrm{SiO}}_{2}/\mathrm{Si}$ substrate. We clearly observed spatially separated metallic and insulating states during the transition between commensurate and nearly commensurate charge-density-wave phases. The capability to probe electrodynamics on nanometer length scales revealed temperature-dependent electronic properties of the insulating and metallic regions near the transition temperature. At fixed temperature, a remarkably broad spatial boundary between insulating and metallic regions was observed, across which the nano-optical signal smoothly evolved over a length scale of several hundred nanometers. To understand these observations, we performed Ginzburg-Landau calculations to determine the charge-density-wave structure of the domain boundary, which revealed the existence of an intermediate electronic phase with unique properties distinct from the bulk thermodynamic phases.

Infrared spectroscopy of VO${}_{2}$ thin films at high spatial resolution shows new electronic and lattice states due to epitaxial strain that differ fundamentally from those in the bulk. This is the first ultra-broadband infrared near-field study of a correlated electron material, made possible by the newly developed synchrotron infrared near-field spectroscopy method (SINS) on the Advanced Light Source at Lawrence Berkeley National Laboratory.