In-plane orientation-dependent metal-insulator transition in vanadium dioxide induced by sublattice strain engineering

Selectively modulating the sublattices in 3D transition metal oxides via strains could tailor the electronic con ﬁ gurations with emerging anomalous properties, which provides new platforms for fundamental researches as well as designs of devices. Here, we report tailoring the oxygen octahedral sublattices in vanadium dioxide (VO 2 ) thin ﬁ lms by anisotropic in-plane strains, and the observation of in-plane orientation-dependent metal – insulator transition. Through multimodal characterizations based on high-resolution X-ray diffraction, electrical transport measurements, and polarization-dependent X-ray absorption spectroscopy at different temperatures, we demonstrate that nonequal strains were successfully induced along A and B oxygen octahedral chains in VO 2 ﬁ lms via a special design of epitaxial growth on vicinal substrates. The V 3 d 1 orbital con ﬁ gurations are modulated in the two oxygen octahedral chains, resulting in in-plane orientation-dependent metal – insulator transition behaviors such as reduced hysteresis width and anisotropic phase transition temperature. This work provides new fundamental insights on metal – insulator transitions, and more importantly, opens up new opportunities for material and device developments phase transition temperature T c , as well as the signi ﬁ cant reduction of the hysteresis width Δ T c , have been observed. Our experimental results demonstrate the feasibility of tailoring the sublattices in the 3D transition metal oxides for modulating their electronic con ﬁ gure using anisotropic strains. This demonstration presents a unique platform in the material genetic design for exploring both fundamental physical properties and practical applications.


INTRODUCTION
Exploring exotic physical properties in 3D transition metal oxide films by using epitaxial elastic strains is a popular way in materials science. 1,2 Strain, as a tool of modifying the crystal lattice of the oxide films, can simultaneously modify the interaction between charge, orbital and spin degrees of freedom, which are strongly related to the physical properties of materials. [2][3][4][5] For some 3D transition metal oxides, sublattices with different spatial symmetries often coexist in their crystal lattices, such as in Fe 3 O 4 , CoFe 2 O 4 , Vanadium dioxide (VO 2 ), and some superconductor cuprates crystal lattices. 3,6,7 These sublattices, including oxygen octahedral, oxygen tetrahedron, and oxygen dodecahedron, are fundamental functional unit cells of oxides. Although strain engineering techniques have been developed for decades, 8 controllably manipulating the sublattices of the 3D transition metal oxides still needs deep and systematical investigations. Especially, knowledge on correlation between the spatial symmetries of the sublattice unit cells and the symmetries of the charge, orbital and spin degrees of freedom of the 3D electrons inhabited in them, can provide a knob to tailor the sublattice of the 3D transition metal oxides using strain and thus to explore novel physical properties for practical applications. VO 2 , a classical strong-correlated oxide that has a sharp metal-insulator transition (MIT) near 341 K, is a typical 3D transition metal oxide consisting of two types of sublattices, i.e., two types of edge-shared oxygen octahedral chains. 2,3,9,10 The MIT properties of VO 2 mainly originate from the V-V dimers inhabited in these two distinguishable edge-shared oxygen octahedral sublattices, which are called A octahedral chain and B octahedral chain. The A octahedral chain and the B octahedral chain are arranged alternatively with a relative 90°rotation around c R axial, as seen in Fig. 1a, b (a simplify structure depicture can be accessed in Fig. S1). During the MIT, VO 2 transfers from a rutile structure into a monoclinic structure, meanwhile the V ions shift and form the V-V dimers. 2,3,9,10 More exact to say, there is a shifting component along the VO 2 [001] R direction for both V ions of the A octahedral chain and the B octahedral chain. Besides, they have different shifting components in the VO 2 (001) R lattice plane. As shown in Fig. 1b Fig. 1c) of VO 2 , which influences the overlap of V 3d and oxygen 2p orbitals, hence changes the electronic configuration of VO 2 and its MIT properties. 2,3 The V ions inhabit in the center of oxygen-octahedral cage and the crystal field of the oxygen octahedral splits the 3d orbital into twofold degenerate e g orbitals and triple fold degenerate t 2g orbitals. The e g orbitals contain d x 2 þy 2 and d z 2 which directly point toward the oxygen ions, hence lifting up their energy levels relative to the t 2g orbitals. In this case, the V d 1 electron would occupy the t 2g orbital rather than the e g orbital. 5 For the t 2g orbitals (d xy , d xz , and d yz ), the structural distortion of VO 2 further splits the orbitals into d ∥ (d xy ) and π * (d xz and d yz ). 2,4 The V 3d 1 electron occupies d ∥ orbital in the insulating state of VO 2 . However, in the metallic VO 2 , the electrons normally redistribute and occupy both the d ∥ and π * orbitals (as shown in Fig. S2). The redistribution of V 3D electrons is very sensitive to the energy levels of d ∥ and π * orbitals, which are strongly influenced by the apical V-O bond length. 3 If we observe along the c R direction, the d xy , d xz , and d yz orbitals extend to different directions in VO 2 (001) R plane (as shown in Fig. 1f-h). 4,5 The A octahedral chain and the B octahedral chain have a relative 90°rotation around c R axis, so their apical V-O bond and orbitals also rotate. Since the energy level of π * is sensitive to the apical V-O bond length, the energy levels of π * of 3d 1 electrons in A octahedral chain and the B octahedral chain would be influenced by strains with a relative 90°r otation, respectively. When isotropic biaxial strains are loaded along VO 2 [110] R and ½110 R directions(as the case of Fig. 1d), the apical V-O bond lengths of both the A octahedral chain and the B octahedral chain would be tuned to the same degree simultaneously, as reported by Aetukuri et.al. 3 The isotropic biaxial strains loaded along VO 2 [110] R and ½110 R directions can modulate the electronic configurations of V 3D electrons, consequently significantly tune the MIT temperature. Since the strains along VO 2 [110] R and ½110 R directions can selectively influence the apical V-O bond lengths of the A octahedral chain and the B octahedral chain, their sublattices could be tuned separately with nonequal strains along VO 2 [110] R and ½110 R directions. In other words, the orbital configurations of the A octahedral chain and the B octahedral chain can be tailored separately by the anisotropic strains(as the case of Fig. 1e). High-quality works on tailoring the MIT properties of VO 2 in virtue of thickness effects on the epitaxial strain, 11,12 thermal strain, 13 and interface facet effect 14 were reported. However, researches on the effect of anisotropic strains are still rare. Although the experiments of loading uniaxial strain along the [110] R direction have been demonstrated in VO 2 nanowire system, 10,15 the impact of the applied strain on the physical properties was hardly determined due to the dimension limitation. Furthermore, there is few data available on the anisotropic electron transport properties and the electronic Fig. 1 The schematic of lattice and electronic structures for VO 2 : a the VO 2 lattice constructed with A and B oxygen octahedral chains which are edge-shared oxygen octahedral chains with V ions located inside the oxygen octahedral; b the details of A and B octahedral chains of VO 2 ; c the definition of V-O apical bonds and equatorial bonds of oxygen octahedral in VO 2 ; d the lattice of VO 2 grown on a normal TiO 2 (001) substrate, which undergoes symmetric biaxial strains along VO 2 [110] R and ½110 R directions; e the lattice of VO 2 grown on a vicinal TiO 2 (001) substrate with asymmetric biaxial strains along VO 2 [110] R and ½110 R directions, in which the VO 2 [110] R direction is the vicinal direction and bares a smaller strain compared with VO 2 ½110 R direction; (f-h) the schematic of the d xy , d xz , and d yz molecular orbitals of VO 2 observed from VO 2 [001] R direction, respectively configurations under the anisotropic strains. On the other hand, it has been demonstrated that substrates with small miscutting angles can induce designable strains in the films by virtue of the mismatching between the surface-step-terrace of the substrate and lattice unit cells of the films. [16][17][18][19] For the substrates with miscutting angles, the surface-step-terrace can be formed after being annealed at a high temperature and its width can be adjusted by tuning the miscutting angles. When the films are grown on such substrates, the lattice unit cells of the films have to accommodate the width of surface-step-terrace, consequently strain is induced. (more details can be accessed in Supplementary Figs. S3 and S4). Herein, we induce nonequal strains in a VO 2 film via high-quality epitaxial growth on a designed vicinal TiO 2 (001) substrate with a small miscutting angle along VO 2 [110] R direction and directly observe an in-plane orientation-dependent MIT behavior of the as-grown VO 2 film.
It is found that by high-quality epitaxial growth through sophisticated experimental control, anisotropic biaxial in-plane strains are induced in A and B oxygen octahedral chains in the VO 2 film, resulting in an in-plane orientation-dependent MIT in VO 2 film, e.g., obvious anisotropy in conductivity, crystal-orientation dependency of phase transition temperature T c , and reduction of phase transition hysteresis width.

RESULTS
The VO 2 films were grown using a polymer-assisted deposition technique. 20 More details can be accessed in our previous reports. 21,22 The epitaxial relationship between the films and the substrates is VO 2 (001) R ∥ TiO 2 (001) and VO 2 Supplementary Fig. S5). And the thickness of the films is about 17 nm. An ordinary TiO 2 (001) substrate with no intentional miscut and a vicinal TiO 2 (001) substrate with a 1°miscutting angle along TiO 2 [110] direction were used for comparative study. The anisotropic in-plane strains were successfully induced in the VO 2 film on the vicinal TiO 2 (001) substrate as manifested by the highresolution reciprocal space mapping (RSM) (Fig. 2). For the film grown on the normal TiO 2 (001) substrate, equal strain of σ a was found along both VO 2 [110] R and ½110 R directions in the VO 2 film (Fig. 1d). However, the case was found to be different for the VO 2 film grown on the vicinal TiO 2 (001) substrate. We denoted the strain in the film grown on the vicinal substrate along the VO 2 [110] R direction as σ0 a and along the VO 2 ½110 R direction as σ b (Fig. 1e). It was found that the strain σ0 a is very close to σ a but the strain σ b is different from the strain σ a . Obviously, the strain along the VO 2 [110] R direction was modulated by the surface-step-terraces on the vicinal substrate, as what it can be expected. Figure 2 show the RSMs for the nonvicinal and vicinal samples in both the metallic and insulating states, measured at 298 and 373 K, respectively. Lattice parameters of the VO 2 thin films are calculated based on the RSM data and listed in Table 1  The change of the apical V-O bond length by strain would affect the overlap of V 3d and O 2p orbitals. A shorter apical V-O bond length increases the overlap of V 3d and O 2p orbitals, which would increase the energy level of π * orbitals relative to those of the d ∥ orbitals, hence decrease the electron occupancy of π * orbitals. Since the d ∥ and π * orbitals are both partially occupied in the metallic state, as shown in Fig. S2, the electron occupancy of d ∥ orbitals will increase correspondingly. 3 In other words, the nonequal strains in the VO 2 film along VO 2 [110] R and ½110 R directions result in nonequal apical V-O bond lengths in A and B octahedral chains, leading to different energy levels of π * orbitals and different electronic configurations of the A and B octahedral chains.
To verify the electronic state configurations described above, synchrotron-based linear-polarization-dependent X-ray absorption spectroscopy (XAS) was tested at the V L 2,3 edges of both VO 2 thin films epitaxially grown on non-vicinal and vicinal substrates. The experiments were performed using total electron yield (TEY) detection with a typical probe depth of about 10 nm. Linearly polarized X-rays with the electric-field orientation parallel (E ⊥ c R ) and perpendicular (E ⊥ c R ) to the rutile VO 2 c-axis are measured to probe the vacant d ∥ and π * valence-electron states, respectively. 3 To investigate the anisotropic in-plane strain effect, the measurements perpendicular to the rutile c-axis (E ⊥ c R ) were performed along VO 2 [110] R and ½110 R directions, respectively. Based on previous studies on the valence-electron states, 3 we particularly focus on the excitonic features of the XAS spectra with 512-516 eV photon energies. Figure 3 shows the polarization-dependent V L-edge XAS spectra in the metallic and insulating states of the nonvicinal and vicinal samples. The intensity differences I ∥ − I ⊥ , which are respectively defined as I CR À I ½110 and I CR À I ½110 along the VO 2 [110] R and ½110 R directions, are also plotted. In the insulating state, the dichroic signals I CR À I ½110 and I CR À I ½110 (Fig. 3a, b) of both nonvicinal and vicinal samples show negligible difference. That is expected and consistent with the previous report, 3 because the 3d 1 electron occupies the d ∥ orbitals while the π * orbitals located above the Fermi level are empty in the insulating state. However, the orbital occupancy in the metallic state, which is believed to set the energy scale for the MIT of VO 2 , 3 shows remarkable distinctions between the two samples, as reflected by the XAS data. It is found that the XAS dichroic signals, I CR À I ½110 and I CR À I ½110 , of the nonvicinal sample in the energy region of 512-516 eV show negligible difference in the metallic state (Fig. 3c), which is as expected due to the equal strains along VO 2 [110] R and ½110 R directions. On the other hand, the XAS dichroic signals I CR À I ½110 and I CR À I ½110 of the vicinal sample in the metallic state (Fig. 3d), show obvious difference in this energy region, which should be attributed to the nonequal strains along VO 2 [110] R and ½110 R directions. For the vicinal sample, the apical V-O bond length of the B octahedral chain (1.9208 Å) was shorter than the A octahedral chain (1.9538 Å), suggesting that the difference in the XAS dichroic signals I CR À I ½110 and I CR À I ½110 is due to the redistribution of the orbital occupation. As mentioned ahead, the shorter apical V-O bond length increases the p-d overlap, hence raises the energy level of π * orbital and consequently reduces their orbital occupancy, resulting in the increase of the orbital occupancy of d ∥ orbitals. Since the XAS data correspond to the unoccupied states of the orbitals, the increase of the occupancy of d ∥ orbitals will reduce the signal I CR . For the π * orbitals, the d yz orbitals extend to [100] R and [010] R directions (Fig. 1h). Thus, the related XAS signals display no difference with the X-ray electric field along either [110] R or ½110 R directions. However, the d xz orbitals of B octahedral chain extend along [110] R direction (Fig. 1g) while the d xz orbitals of A octahedral chain extend along ½110 R direction. The anisotropic in-plane strain effect, i.e., a shorter lattice parameter along the [110] R , would increase the energy level and decrease the orbital occupancy of the d xz orbitals in the B octahedral chain, compared with those in the A octahedral chain. Such an effect is directly shown in the XAS raw data plot in Fig. 3d, with stronger I ½110 R signals comparing with I ½110 R , leading to smaller I CR À I ½110 than I CR À I ½110 . Therefore, the XAS data in the metallic states clearly prove that the anisotropic in-plane strains have effectively changed the orbital occupancy of the two sublattices.
Since the nonequal apical V-O bonds of the A octahedral chain and the B octahedral chain change the electronic configurations of the VO 2 film on the vicinal substrate, it can significantly modulate the MIT behaviors of the film. Temperature-dependent resistances of both the nonvicinal and the vicinal samples were tested. In-plane orientation-dependent MIT behavior attributed to the anisotropic inplane strains were observed in the vicinal sample.
The nonvicinal sample exhibits a normal MIT behavior (Fig. 4a, c). The resistance-temperature (R − T) curves tested along VO 2 [110] R and ½110 R directions show weak directional dependency, as shown in the direction-dependent resistance in metallic state is shown in Fig. 4e. Its phase transition temperature (T c ) for heating was determined to be 324 K in both VO 2 [110] R and ½110 R directions (derived from the dlnR/dT-T curves in Fig. 4c), and the hysteresis width (ΔT c , defined as the difference of T c for heating and cooling) is about 3.5 K. These results are very similar to previous reports. 23,24 However, for the vicinal sample, the MIT behavior has been obviously altered (Fig. 4b, d).The R − T curves tested along VO 2 [110] R and ½110 R directions show obvious directional dependency. The film in the metallic state has a much larger resistance along the VO 2 [110] R direction (vicinal direction) than that along the VO 2 ½110 R direction. The direction-dependent resistance in metallic state is shown in Fig. 4f, which can be fitted by: where R ½110 R =R ½110 R ¼ 17:3. The phase transition temperature exhibits anisotropy as well. The T c values measured along [110] R and ½110 R directions are determined to be 333 and 326 K, respectively. From Table 1, we observe that the vicinal sample

DISCUSSION
A possible mechanism for the conductivity anisotropy is the striplike phase domain structure generated by the phase separation during the phase transition in the film. 25 Clearly, mixture of the metallic and insulating phases would occur in the temperature range near the phase transition temperature. This mixing phase domains would form anisotropic percolation hence lead to anisotropic carrier transport behavior. Anisotropy of the conductivity induced by this mechanism will disappear beyond the phase transition temperature range, since the phase transition has completed and the metallic and insulating domains no longer coexist. However, our vicinal sample shows obvious anisotropic conductivity even at a high (373 K) and a low (298 K) temperature beyond the phase transition temperature. Other mechanisms need to be proposed to understand the phenomenon. We suggest that the anisotropic in-plane strains play a key role.  Fig. 4 The electrical properties. a Temperature-dependent resistance and c dlnR/dT-T curves of the nonvicinal sample, respectively; b temperature-dependent resistance and d dlnR/dT-T curves of the vicinal sample, respectively; e, f the experimental and fitting results of direction-dependent resistance for the nonvicinal and vicinal sample in metallic state, respectively octahedral chain, leading to different energy scales for the MIT along ½110 R and [110] R directions. Since the apical V-O bond length expands when VO 2 transfers from a low temperature monoclinic phase to a rutile phase, a longer apical V-O bond length would make the phase transition easier, therefore yielding a lower transition T c along ½110 R than [110] R .
An anomalous change in the phase transition hysteresis width was also observed in the vicinal sample. As shown in Fig. 4, the hysteresis width ΔT c almost disappeared in the vicinal sample, i.e, the values of ΔT c are as small as 0.2 K along both VO 2 [110] R and ½110 R directions, which are much smaller than that of the nonvicinal sample (ΔT c = 3.5 K). The reason for the dramatically reduced hysteresis width ΔT c is not clear yet. It may be related to the modification of the shearing strain in the VO 2 film during the MIT. In the previous reports, 26,27 the hysteresis width can be expressed as: where η is the domain shape parameter, G is the shear modulus, γ is the shearing strain, and ΔS is entropy change of the phase transition. The asymmetrical in-plane strains in the film may alter the shearing strain γ hence narrow the hysteresis loop. By epitaxial growth of a high-quality VO 2 thin film on a designed vicinal TiO 2 substrate, we deliberately tailored the sublattices of VO 2 crystal utilizing the nonequal biaxial in-plane strains. The anisotropic in-plane strain leads to different apical V-O bond lengths in A and B octahedral chains of the VO 2 , which modulates the orbital configurations of V 3d 1 and induces in-plane orientation-dependent MIT behaviors in the VO 2 film. Specifically, direction-dependent conductivity and phase transition temperature T c , as well as the significant reduction of the hysteresis width ΔT c , have been observed. Our experimental results demonstrate the feasibility of tailoring the sublattices in the 3D transition metal oxides for modulating their electronic configure using anisotropic strains. This demonstration presents a unique platform in the material genetic design for exploring both fundamental physical properties and practical applications.

METHODS
The vicinal TiO 2 (001) substrate and the normal TiO 2 (001) substrate were both ultrasonically cleaned in acetone and deionized water, then immersed in 5 vol% HCl solution for 5 min to remove the metal contamination on the surfaces of the substrates before being washed in deionized water. After that, the substrates were etched in 20 vol% HF solution for 2 min, and then ultrasonically cleaned in deionized water. Finally, the substrates were annealed in oxygen at 750°C for 2 h to form a surface with clear step-terrace structures. The high-resolution reciprocal space maps were tested using PANalytical XPert MRD. The temperature dependence of resistance of the films was measured using an Agilent B2900A source meter with the four-point probes method in a high-vacuum system. The anisotropic resistance of the VO 2 films was also measured with the four-point probes method by rotating the samples. The temperaturedependent polarization-dependent XAS was carried out with >99% linearly polarized X-ray beam, which was carefully aligned onto the samples mounted on an in-vacuum rotating goniometer with temperature controls. Sample current was collected as the TEY signals upon incident photons. The XAS spectra shown here have been normalized to the photon flux that was monitored by the photocurrent of a clean gold mesh simultaneously. Experimental resolution is better than 0.16 eV at V-L edges, not considering core-hole broadening.

DATA AVAILABILITY
All data supporting the findings of this study are available from the corresponding authors Y.L. and M.G. upon request.