Metastability Phenomena in VO2 Thin Films

VO2 is a transition metal oxide in which complex electronic phases appear near the metal-to-insulator transition due to electron correlation and electron–lattice interactions. This system is characterized by a metal-to-insulator transition (MIT) at around 341 K. The metal (high T) phase is tetragonal while the insulator (low T) phase is monoclinic and the resistivity changes at the MIT by about five orders of magnitude. Here, we report investigations of the MIT in a thin VO2 film deposited on a sapphire substrate showing hysteresis. The MIT has been characterized by resistance measurements versus temperature and a DC magnetic field. The thin sample shows different final resistance values in both the insulating and metallic state after different temperature cycles. Moreover, some cycles do not close in the insulating phase. An unexpected magnetic dependence of the temperature cycle in the sample was also observed. The results show that the MIT of VO2 can be controlled by reducing the thickness below 40 nm in micron-sized ribbons since MIT is associated with the emergence of coexisting metastable conformations controlled by the thickness-dependent misfit strain and stress distributions induced by the mismatch between thin ribbon film and the substrate.


Introduction
Vanadium dioxide (VO 2 ) is a transition metal oxide which exhibits unique complex phases where both electronic correlation, local lattice fluctuations, orbital ordering and charge ordering play a key role. These competing interactions are at the origin of the complex electronic and structural metal-to-insulator transition (MIT) observed around 341 K [1][2][3]. The MIT in VO 2 is highly sensitive to chemical and physical local perturbations, e.g., strain/stress [1,4,5] affects the temperature transition and the final resistance in the insulating phase is affected by the distribution of the M1 and M2 phases where the latter is three times more resistive than M1. The metallic and insulating phases and the transition changes across the MIT in VO 2 thin films, are controlled by the electronic orbital occupation tuned by the local strain [3]. This effect has been confirmed and further demonstrated to be reversible by the incorporation of hydrogen into VO 2 thin films [6]. The hysteresis cycle indicates the emergence of an arrested nanoscale phase separation during the transition, and structural defects and the quenched disorder at nano/micro-scale contribute to a complex landscape with multiple domains where different phases coexist [4]. For a single domain, the hysteretic cycle temperature width, ∆T, is around 5 K [4], while in multi-domains the temperature width, ∆T, of the phase transition increases [7]. The low dimensionality of the film structure and the lattice mismatch (misfit) with the substrate contribute to a nanoscale inhomogeneity. The aim of this work is to investigate this complex scenario in VO 2 thin films since the control of the quenched disorder superstructures at the nanoscale is technologically important to make VO 2 a functional material [8,9]. Indeed, we will show that low dimensionality VO 2 thin films show a non-conventional resistance behavior with metastable resistance states in both the insulating and the metallic phase. Moreover, some cycles show an initial insulating resistive state that is different from the final one, i.e., the hysteresis loop remains open. This condition points out the coexistence of two insulating phases: M1 and M2, where M2 is about three times more resistive than M1, or the presence of metal domains embedded in the insulating matrix [10,11]. Finally, in the thin VO 2 sample, by increasing the magnetic field, the temperature loop width (∆T(K)) increases, in clear disagreement with the well-known independent behavior from the magnetic field of the bulk VO 2 [12].

Results
We report low dimensionality effects on the MIT of a VO 2 thin ribbon film of d a = 40 nm height, of width W a = 514 µm and length L a = 4541 µm. The thin film is sensitive to the substrate surface microstructure and misfit strain. We have measured the resistance as a function of temperature and high magnetic field, of the VO 2 thin film. The characteristics of this sample are representative of a series of thin films realized with different thickness and width, which exhibited similar hysteresis cycles. In Figure 1a, we compare the hysteretic resistance cycles for different magnetic field amplitudes. The resistance values depend on both the time evolution during the cycle, called τ c , and the "waiting time" among cycles, called τ w .
Condens. Matter 2017, 2, 10 2 of 6 hysteresis cycle indicates the emergence of an arrested nanoscale phase separation during the transition, and structural defects and the quenched disorder at nano/micro-scale contribute to a complex landscape with multiple domains where different phases coexist [4]. For a single domain, the hysteretic cycle temperature width, ΔT, is around 5 K [4], while in multi-domains the temperature width, ΔT, of the phase transition increases [7]. The low dimensionality of the film structure and the lattice mismatch (misfit) with the substrate contribute to a nanoscale inhomogeneity. The aim of this work is to investigate this complex scenario in VO2 thin films since the control of the quenched disorder superstructures at the nanoscale is technologically important to make VO2 a functional material [8,9]. Indeed, we will show that low dimensionality VO2 thin films show a non-conventional resistance behavior with metastable resistance states in both the insulating and the metallic phase. Moreover, some cycles show an initial insulating resistive state that is different from the final one, i.e., the hysteresis loop remains open. This condition points out the coexistence of two insulating phases: M1 and M2, where M2 is about three times more resistive than M1, or the presence of metal domains embedded in the insulating matrix [10,11]. Finally, in the thin VO2 sample, by increasing the magnetic field, the temperature loop width (ΔT(K)) increases, in clear disagreement with the well-known independent behavior from the magnetic field of the bulk VO2 [12].

Results
We report low dimensionality effects on the MIT of a VO2 thin ribbon film of da = 40 nm height, of width Wa = 514 µm and length La = 4541 µm. The thin film is sensitive to the substrate surface microstructure and misfit strain. We have measured the resistance as a function of temperature and high magnetic field, of the VO2 thin film. The characteristics of this sample are representative of a series of thin films realized with different thickness and width, which exhibited similar hysteresis cycles. In Figure 1a, we compare the hysteretic resistance cycles for different magnetic field amplitudes. The resistance values depend on both the time evolution during the cycle, called τc, and the "waiting time" among cycles, called τw. The sample shows the MIT transition while heating at around 340 K, and in the cooling procedure at ~330 K. These values have been calculated from the peaks of the plots of dR(Ω)/dT versus T. The VO2 sample exhibits, in the same run, small differences in the resistance values in the final insulating and metallic states after temperature cycles, while differences increase among different runs (Figure 1a,b). These effects can be explained considering the waiting time (τw) among runs, which is longer by about one order of magnitude compared to τc in the same run. In this context, the electrical resistance values are dominated by the comparison between the experimental The sample shows the MIT transition while heating at around 340 K, and in the cooling procedure at~330 K. These values have been calculated from the peaks of the plots of dR(Ω)/dT versus T. The VO 2 sample exhibits, in the same run, small differences in the resistance values in the final insulating and metallic states after temperature cycles, while differences increase among different runs (Figure 1a,b). These effects can be explained considering the waiting time (τ w ) among runs, which is longer by about one order of magnitude compared to τ c in the same run. In this context, the electrical resistance values are dominated by the comparison between the experimental time to measure the hysteresis cycles (τ c ) and the waiting time (τ w ) between two hysteresis cycles. The latter have to be compared with the characteristic times of formation of the insulating and metallic phase in the VO 2 sample, called τ i and τ m . In particular, these characteristic times (τ i , τ m ) depend on the structure of the material at the nanoscale, since local stress/strain may increase these characteristic times. Actually, if τ c and τ w are shorter than τ i and τ m , then the VO 2 system may reach metastable states which will evolve over time. In this framework, open cycles in the insulating phase can be observed ( Figure 2). This behavior underlines history dependence.
Condens. Matter 2017, 2, 10 3 of 6 time to measure the hysteresis cycles (τc) and the waiting time (τw) between two hysteresis cycles. The latter have to be compared with the characteristic times of formation of the insulating and metallic phase in the VO2 sample, called τi and τm. In particular, these characteristic times (τi, τm) depend on the structure of the material at the nanoscale, since local stress/strain may increase these characteristic times. Actually, if τc and τw are shorter than τi and τm, then the VO2 system may reach metastable states which will evolve over time. In this framework, open cycles in the insulating phase can be observed (Figure 2). This behavior underlines history dependence. Regarding the application of high magnetic fields, the VO2 resistance shows an "unexpected weak magnetic dependence" that points out a different behavior with respect to the well-recognized invariance of the resistance versus the magnetic field observed in bulk VO2 samples [10]. To clarify this issue, we show the temperature variation (ΔT(K)) of the hysteresis loop width as a function of the magnetic field. We analyzed the behavior of the derivative of the resistance dR(Ω)/dT(K).
In Figure 3a, we show the behaviors for two magnetic fields: 0 T and 30 T. The comparison highlights changes in the shape of the hysteresis cycle, possibly related to the structure of the VO2 film and, in particular, to internal stresses at the nanoscale. In Figure 3b, we show the dependence of ΔT(K) as a function of the magnetic field. Samples showing the occurrence of open cycles or different values of the resistance in the two phases while a high magnetic field and the temperature are changed, show "metastable" conformations that depend on the time history and on the local structure of the sample. At first approximation, they are not affected by the presence of the strong magnetic field. Actually, we may Regarding the application of high magnetic fields, the VO 2 resistance shows an "unexpected weak magnetic dependence" that points out a different behavior with respect to the well-recognized invariance of the resistance versus the magnetic field observed in bulk VO 2 samples [10]. To clarify this issue, we show the temperature variation (∆T(K)) of the hysteresis loop width as a function of the magnetic field. We analyzed the behavior of the derivative of the resistance dR(Ω)/dT(K).
In Figure 3a, we show the behaviors for two magnetic fields: 0 T and 30 T. The comparison highlights changes in the shape of the hysteresis cycle, possibly related to the structure of the VO 2 film and, in particular, to internal stresses at the nanoscale. In Figure 3b, we show the dependence of ∆T(K) as a function of the magnetic field.
Condens. Matter 2017, 2, 10 3 of 6 time to measure the hysteresis cycles (τc) and the waiting time (τw) between two hysteresis cycles. The latter have to be compared with the characteristic times of formation of the insulating and metallic phase in the VO2 sample, called τi and τm. In particular, these characteristic times (τi, τm) depend on the structure of the material at the nanoscale, since local stress/strain may increase these characteristic times. Actually, if τc and τw are shorter than τi and τm, then the VO2 system may reach metastable states which will evolve over time. In this framework, open cycles in the insulating phase can be observed (Figure 2). This behavior underlines history dependence. Regarding the application of high magnetic fields, the VO2 resistance shows an "unexpected weak magnetic dependence" that points out a different behavior with respect to the well-recognized invariance of the resistance versus the magnetic field observed in bulk VO2 samples [10]. To clarify this issue, we show the temperature variation (ΔT(K)) of the hysteresis loop width as a function of the magnetic field. We analyzed the behavior of the derivative of the resistance dR(Ω)/dT(K).
In Figure 3a, we show the behaviors for two magnetic fields: 0 T and 30 T. The comparison highlights changes in the shape of the hysteresis cycle, possibly related to the structure of the VO2 film and, in particular, to internal stresses at the nanoscale. In Figure 3b, we show the dependence of ΔT(K) as a function of the magnetic field.  Samples showing the occurrence of open cycles or different values of the resistance in the two phases while a high magnetic field and the temperature are changed, show "metastable" conformations that depend on the time history and on the local structure of the sample. At first approximation, they are not affected by the presence of the strong magnetic field. Actually, we may Samples showing the occurrence of open cycles or different values of the resistance in the two phases while a high magnetic field and the temperature are changed, show "metastable" conformations that depend on the time history and on the local structure of the sample. At first approximation, they are not affected by the presence of the strong magnetic field. Actually, we may claim that the magnetic field alone is not sufficient to induce metastable conformations in thin films of VO 2 .

Discussion
The resistance measurements, as a function of the temperatures for the VO 2 film, show the presence of metastable final states (Figures 1 and 2). This metastability is present for both insulating and metallic states. Moreover, some resistance measurements have shown that the initial insulating metastable phase has a different value with respect to the final value in the same resistive hysteresis loop. These observations, together with a broad MIT transition, indicate the co-existence of multi-domains that nucleate and grow and/or shrink during the transition. These domain patterns are formed spontaneously and result from the competition between the strain/stress misfit energy in the VO 2 film and the substrate, together with the wall energy of the same domains [4]. The metastable state resistance is also associated with the time and thermal history of the VO 2 film (Figures 1 and 2). In fact, there is also an interplay between the characteristic time scale, τ i and τ M associated to the insulating and the metallic phase; and the changing time of the measure, such as the experimental time to measure the hysteresis cycle, τ c , and the waiting time, τ w , between two hysteresis cycles [13]. In this framework, the metastability during the MIT in VO 2 is driven by defects, non-homogeneities, quenched disorder and symmetries at the nano/micrometer-scale, influenced by local stress/strain due to the misfit between the film and the substrate. This aspect is present not only in VO 2 , but in all "transition metal oxide" materials, such as high temperature superconductor (HTSC) materials (HTSC), for which the critical temperature and the "magnetic flux pinnings" depend on the self-assembling of the quenched disorder in the structure [8,9]. The metastability in this VO 2 thin film is assigned to the competition between the two insulating phases (M1 and M2) with different resistance values [4] and/or the possible presence of persistent metallic domains in the final insulating phase [10]. Surprisingly, the dependence on the magnetic field is also observed in other similar low-dimensional systems such as self-assembly VO x nanotubes [14] or in defective VO 2 thin films [15]. This is an indication that in the VO 2 sample, the magnetic field modulates the formation of multi-domains that in turn regulate the gradual variation of the phase during the MIT transition in a wide range of temperatures [1].

Materials and Methods
The VO 2 film was prepared at the University of Science and Technology of China (Hefei, China). In particular, VO 2 films were realized on Al 2 O 3 (0006) single crystal substrates by a RF-plasma assisted oxide Molecular Beam Epitaxy (MBE) instrument (assembled in house for oxide materials growth, at University of Science and Technology of China, Hefei, China) with a base pressure better than 3 × 10 −7 Pa. Prior to the VO 2 deposition, the Al 2 O 3 (0001) substrates were ultrasonically cleaned in sequence: acetone, isopropanol and deionized water, for 10 min each. After this treatment, the substrate was blown dry by N 2 flux and then rapidly transferred inside the vacuum chamber. During the deposition, the substrate temperature was kept at 530 • C and the oxygen flux was kept at 3.6 sccm. After, Au stripes were realized on the as-grown VO 2 films following this procedure: the poly(methyl methacrylate) (PMMA~1 µm thick) was first coated by spin-coating and then exposed, with an optical mask, to ultraviolet (UV) light (365 nm). After chemical removal of the exposed PMMA,~50 nm Au was deposited by electron-beam evaporation. Finally, 5 mm-length Au stripes with 100 µm and 500 µm width were obtained by removal of the extra PMMA. For the electrical transport measurement, Au stripes were connected to the external electrical circuit with Al wires of 25 µm by a wire bonding instrument (West Bond, 747677E, West-Bond, Anaheim, CA USA).
The resistance measurements at high magnetic field have been performed at the "High Field Magnet Laboratory" Institute for Molecular and Material of the Radboud University (Nijmegen, The Netherlands). For the measurements, we used a cryostat with an external normal magnet and a chip carrier with the VO 2 sample has been mounted on the cryogenic insert. The temperature cycles were controlled using the LakeShore 340 Cryogenic Temperature Controller (Lake Shore Cryotronics Inc., Westerville, OH, USA) and the temperature was measured by a cernox thermometer glued on the sample-holder. For resistance measurements, voltage and current have been measured using the Keithley Source Meter 2611 (Keithley, Solon, OH, USA). The temperature range and temperature sweep rate are 290 K < T < 370 K and R = 2 K/min, respectively, while the DC magnetic field range is 0 T < H dc < 30 T.

Conclusions
This work reports the resistivity properties of a VO 2 thin low dimensional film. The misfit between substrate/film, regulated by defects and quenched disorder, gives important contributions that dominate the MIT resistive response. By controlling the thickness and width of thin films, it is possible to change the resistive response. This sample shows a clear metastability of the final resistivity value in the insulating/metallic phase after hysteresis temperature cycles. The emerging nanoscale inhomogeneity in the vanadium dioxide at the metal-to-insulator transition is well known and makes this system similar to other complex high correlated quantum materials [8,9,[16][17][18][19][20] where the phase separation landscape depends on misfit strain [16,17]. We show that by reducing the thickness below 40 nm in micron-sized ribbons, we can control the complex nano-phase separation at MIT of VO 2 . Moreover, the VO 2 thin film ribbon shows an "unexpected high magnetic field dependence" that points out the possibility to tune magnetic ordering by controlling the multi-domain dynamics of the vanadium oxide. This behavior indicates the presence of metal localized states or a combination of "different M1, M2 insulating local phases" that affect the final insulating/metallic states. It appears evident that the possibility to control misfit, inhomogeneity and defects at the nanoscale near the metal-to-insulator transitions opens the opportunity to functionalize the VO 2 at low dimensionality and to design unique nanoscale devices.