Electrical Transition in Isostructural VO2 Thin-Film Heterostructures

Control over the concurrent occurrence of structural (monoclinic to tetragonal) and electrical (insulator to the conductor) transitions presents a formidable challenge for VO2-based thin film devices. Speed, lifetime, and reliability of these devices can be significantly improved by utilizing solely electrical transition while eliminating structural transition. We design a novel strain-stabilized isostructural VO2 epitaxial thin-film system where the electrical transition occurs without any observable structural transition. The thin-film heterostructures with a completely relaxed NiO buffer layer have been synthesized allowing complete control over strains in VO2 films. The strain trapping in VO2 thin films occurs below a critical thickness by arresting the formation of misfit dislocations. We discover the structural pinning of the monoclinic phase in (10 ± 1 nm) epitaxial VO2 films due to bandgap changes throughout the whole temperature regime as the insulator-to-metal transition occurs. Using density functional theory, we calculate that the strain in monoclinic structure reduces the difference between long and short V-V bond-lengths (ΔV−V) in monoclinic structures which leads to a systematic decrease in the electronic bandgap of VO2. This decrease in bandgap is additionally attributed to ferromagnetic ordering in the monoclinic phase to facilitate a Mott insulator without going through the structural transition.

the critical thickness is calculated at 15 nm, kinetically the dislocation formation is not happening up to higher values. Figure S1. a) The HAADF image and its FFT belong to the thick VO 2 film with the zone axis of [100] monoclinic, b) the corresponding atomic alignment, and c) the indexed simulated pattern for the mentioned zone axis in the monoclinic VO 2 structure

Raman characterization
To further verify the room temperature VO2 phase formed in thick and thin films, Raman spectroscopic studies were performed, as provided in Figure S5. Both the spectra illustrate the main characteristic peaks of the monoclinic structure of VO2 at 195 cm -1 , and 225 cm -1 (assigned to V-V modes), and 618 cm -1 , and 625 cm -1 (assigned to V-O modes) 1,2 , thus confirm the stable monoclinic phase formation in thick and thin VO2 films. The peak splitting around 620 cm -1 in both samples, indicates the oxygen ions are connected to two vanadium ions with a different bondlength along the c-axis. In an interesting observation, however, the V-O peaks are shifted toward lower frequencies in the case of thin VO2 samples. These shifts are indicative of V-O shorter bond length due to oxygen octahedral distortion. Also, the intensity of V-V modes has changed in thin VO2 films compared to thick ones which can be inferred that the pairing and tilting of vanadium ions have changed attributed to the change in V-V bond length while maintaining the monoclinic structure. The presence of metallic monoclinic phase stabilized under high pressure has been shown by Raman spectroscopy previously, the result of which is consistent with the present study 3 . Figure S5. Room temperature Raman spectroscopy of thin and thick VO2 samples with the characteristic peaks belong to the monoclinic phase as indicated.

Orbital occupancy across the metal-to-insulator transition
During the metal-to-insulator transition, the V 4+ cation moves away from the center of the oxygen octahedron toward the edges and form V-V pairs and the conductivity decreases sharply.
At the high-temperature tetragonal state, V 4+ in the octahedra obstructs the free rotation of the electrons and quenches the orbital angular momentum giving rise to the splitting of the 3d 1 energies into eg (d3x 2 -r 2 , dyz) and t2g (dz 2 -y 2 , dxy, dzx) orbitals 4 . The eg wave functions are pointing toward O 2thus having higher energies, while t2g pointing between them 5 . Covalent mixing between the two electrons in dxy and dzx and pπ orbitals of the anion results in the formation of the narrow antibonding π* and a wider bonding π band. The remaining electron is nonbonding and goes into dz 2 -y 2 which is directed parallel to the c-axis. This electron is not involved in the V-O bonding and provides V-V bonding along the c-axis, also partially fills the dz 2 -y 2 which is the reason for rutile phase being metallic and reduces the c/a ratio. The relative energies and stabilities of the dz 2 -y 2 and dxy, dzx orbitals depend upon the c/a ratio as proposed by Goodenough 6 , discussed by Hearn 7 , and experimentally showed by Aetukuri 8 . We believe that the oxygen octahedra in uniformly strained thin films at high temperature are distorted which means vanadium is not stable in the center of the octahedra and thereby stabilizes the antiferroelectric distortion (the first necessary component of the transition) introduced by Goodenough 6 . According to this theory, the requirement for the insulating band structure is i) destabilizing the π* orbital and/or stabilizing the bottom half of the dz 2 -y 2 orbital by raising the π* orbital energy above the Fermi level, and ii) splitting of the dz 2 -y 2 orbital. Goodenough proposed that the distortion of the structure by displacement of V ions perpendicular to c-axis destabilizes the π* orbital (the antiferroelectric distortion) and a decrease in the c/a ratio stabilizes the bottom half of the dz 2 -y 2 orbital which fulfills the first requirement, and a homopolar V-V bonding along the c-axis split the dz 2 -y 2 and defines the energy gap 6 .
However, Zylbersztejn and Mott believed the role of distortion is to destabilize the π* orbital and to induce the transition and not to determine the electrical gap 9 . They proposed that each V 4+ has a moment and the energy to form a carrier (defined as band gap) is equal to U-1/2(B1+B2)-JH, where U is the Hubbard intra-atomic correlation energy, B1 and B2 are the bandwidth of upper and lower Hubbard bands here for the motion of electron (V 3+ ) and hole (V 5+ ), and JH is the coupling energy. Thus, the bandgap is mainly a correlation gap.