Role of 1-D finite size Heisenberg chain in increasing metal to insulator transition temperature in hole rich VO2
VO2 samples are grown with different oxygen concentrations leading to different monoclinic, M1 and triclinic, T insulating phases which undergo a first order metal to insulator transition (MIT) followed by a structural phase transition (SPT) to rutile tetragonal phase. The metal insulator transition temperature (Tc) was found to be increased with increasing native defects. Vanadium vacancy (VV) is envisaged to create local strains in the lattice which prevents twisting of the V-V dimers promoting metastable monoclinic, M2 and T phases at intermediate temperatures. It is argued that MIT is driven by strong electronic correlation. The low temperature insulating phase can be considered as a collection of one-dimensional (1-D) half-filled band, which undergoes Mott transition to 1-D infinitely long Heisenberg spin ½ chains leading to structural distortion due to spin-phonon coupling. Presence of VV creates localized holes (d0) in the nearest neighbor, thereby fragmenting the spin ½ chains at nanoscale, which in turn increase the Tc value more than that of an infinitely long one. The Tc value scales inversely with the average size of fragmented Heisenberg spin ½ chains following a critical exponent of ⅔, which is exactly the same predicted theoretically for Heisenberg spin ½ chain at nanoscale undergoing SPT (spin-Peierls transition). Thus, the observation of MIT and SPT at the same time in VO2 can be explained from our phenomenological model of reduced 1-D Heisenberg spin ½ chains. The reported increase (decrease) in Tc value of VO2 by doping with metal having valency less (more) than four, can also be understood easily with our unified model, for the first time, considering finite size scaling of Heisenberg chains.