  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 V$_2$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.
