Optical Mapping and On-Demand Selection of Local Hysteresis Properties in VO₂

Abstract

Quantum materials have tremendous potential for disruptive applications. However, scaling devices down has been challenging due to electronic inhomogeneities in many of these materials. Understanding and controlling these electronic patterns on a local scale has thus become crucial to further new applications. To address this issue, we have developed a new optical microscopy method that allows for the precise quasi-continuous filming of the insulator-to-metal transition in VO${\phantom{­}}_2$ with fine temperature steps. This enables us to track metal and insulator domains over thousands of images and quantify, for the first time, the local hysteresis properties of VO${\phantom{­}}_2$ thin films. The analysis of the maps has allowed us to quantify cycle-to-cycle reproducibility of the local transitions and reveals a positive correlation between the local insulator–metal transition temperatures T${\phantom{­}}_c$ and the local hysteresis widths $\Delta {\mathrm{T}}_c$. These maps also enable the optical selection of regions of high or low transition temperature in combination with large or nearly absent local hysteresis. These maps pave the way to understand and use stochasticity to advantage in these materials by picking on-demand transition properties, allowing the scaling down of devices such as optical switches, infrared microbolometers and spiking neural networks.

1. Introduction

Electronic phase separation commonly emerges in a wide variety of quantum materials [1] such as high-T${\phantom{­}}_c$ superconductors [2], colossal magnetoresistance manganites [3], insulator–metal transition (IMT) materials [4], multilayer rhombohedral graphene [5], etc. An archetypal example of a phase-separated material is vanadium dioxide, VO${\phantom{­}}_2$, which undergoes a first order IMT at a transition temperature T${\phantom{­}}_c$∼68 °C [6] (i.e., just above room temperature) accompanied by an abrupt several-order-of-magnitude resistivity decrease and monoclinic-to-tetragonal structural change. The exact nature of the transition, whether it is a Peierls transition driven by electron-phonon interactions or a Mott–Hubbard transition driven by electron–electron interactions, is still under debate [7].

In the vicinity of the transition, VO${\phantom{­}}_2$ exhibits a spatial coexistence of metal and insulator domains that form intricate patterns due to local variations in the IMT transition temperatures [8]. As a result, stochastic transitions have been seen as step-like/avalanche responses [9]. The impact of this stochasticity only increases when scaling down, hindering VO${\phantom{­}}_2$-based applications, such as optical switches, nanophotonics [10], infrared microbolometers [11] and coupled oscillators [12,13]. Understanding and controlling the electronic phase-separated state in this quantum material has therefore become a major research field in recent years [14].

Over the years, the most successful approaches to map out electronic phase separation in this material have been scattering scanning near-field infrared microscopy (s-SNIM) [8], conductive atomic force microscopy (c-AFM) [15], and scanning photoemission microscopy [16] (for the closely related material V${\phantom{­}}_2$O${\phantom{­}}_3$). Scanning X-ray microscopy, which is sensitive to the structural transition [17], has also been reported to be able to track electronic phase separation, but so far only with 1D scans [18]. Scanning tunneling microscopy, which has been very successful in tracking clusters in quantum materials [2,3], is limited in VO${\phantom{­}}_2$ for various reasons (STM lacks energy resolution at room temperature; non-cleavable samples; and loss of spatial registry when ramping the temperature through the full phase transition [19]). While all of these scanning methods have very high spatial resolution, fine temporal resolution remains hard to implement since scanning probes are very time-consuming. Over the course of a few hours to days, local probe measuring campaigns can take typically 6 to 28 scans [8,15,20,21,22]), but this is still not enough to systematically track the growth and evolution of electronic clusters in order to generate transition temperature maps, i.e., T${\phantom{­}}_c$ maps.

In order to achieve a technique that can track fine electronic cluster changes, we have developed a new optical full-field microscopy method that is able to map out in-focus, stabilized, highly contrasted 2D images of the electronic phases on the sample surface during the IMT. This insulator–metal domain imaging could be viewed as the equivalent of magnetic domain imaging techniques [23]. This method has already proven to be vital for tracking and understanding the encoding of memory in VO${\phantom{­}}_2$ using ramp reversal temperature protocols [24], as well as for tracking criticality when analyzing fractal patterns through machine learning [25].

We start by describing the key experimental steps to acquire accurate spatial maps of transition temperatures, from which the phase separation patterns can be easily obtained at any given temperature, and T${\phantom{­}}_c$ maps constructed [24]. Using these maps, we first quantify the cycle-to-cycle reproducibility of the transition. We then analyze the presence of global correlations between local IMT transitions T${\phantom{­}}_c$, local hysteresis widths $\Delta$T${\phantom{­}}_c$, and local transitions widths $\delta$T${\phantom{­}}_c$. Finally, we identify places on the sample surface with unique transition signatures.

2. Materials and Methods

VO${\phantom{­}}_2$ thin films were prepared by reactive RF magnetron sputtering on sapphire substrates (see SI Section S1.1). IMT properties of the films were characterized electrically with a T${\phantom{­}}_c$ of 68 °C. The thin film samples were placed on a temperature stage inside an optical microscope with visible lamp illumination. The surface images of the sample are measured using a high magnification, high numerical aperture objective lens allowing a final resolution of ≈400 nm (see SI Section S2.1). The temperature, resistance and images were recorded around the IMT while performing temperature sweeps (see Figure 1). Translation $xy$ thermal drifts were first compensated using coarse in situ translation motors beneath the sample during the temperature sweep, and subsequently corrected using fine post-experiment auto-correlation drift correction [26] (see SI Section S2.2). To compensate for the height z thermal drift, the sample was kept in focus using a piezoelectric stage under the sample or on the microscope objective and a gradient-based metric to evaluate the best focus (see SI Section S2.2). This focusing stack technique allows the recording of one fully focused image per 10 s. Using the in-focus aligned surface sample quasi-continuous movie, each pixel intensity is tracked over the temperature sweeps. High-frequency noise in each time trace was reduced using a smoothing procedure (see SI Section S2.5). Each single pixel intensity time trace was first normalized to generate scaled images (see SI Section S2.4). In this process, spurious optical effects due to surface height variations from sample warping, variations in film thickness, minor surface defects, shadows cast from the gold leads and pixel sensitivity in the camera were mostly eliminated (see Figure S8). Finally, a midpoint threshold was used on the smoothed time traces to produce black and white (metallic/insulating domains) for each temperature (see SI Section S2.4). The pair connectivity correlation length was calculated to justify the midpoint threshold (see SI Section S2.4.1). The optical setup and post-measurement image processing steps are detailed in Figure 1 and Figure 2. This curated data set was used to produce all the results presented in Section 3.

Sample Characteristics Making This Study Possible

The key steps that have allowed us to complete this study come from the unique properties of VO${\phantom{­}}_2$: (1) The IMT is just above room temperature, which allows close optical microscopy (using a strong objective ×150 with a high numerical aperture 0.9 brought to 1 mm focus above the sample surface). This setup would be much harder to achieve if cryogenic cooling (i.e., a cryostat with a window between the sample and objective) were needed. (2) Phase separation was observed by s-SNIM at sub-micron scales in this material [8]. We find that this phase separation extends to at least 30 µm (see Figure 3a). (3) In the visible range, a relative 27% drop in the thin film reflectivity is found in the metallic state (described in SI Section S1.2). (4) Measuring in the visible range gave us results with a 400 nm resolution. In the infrared, the contrast between metal and insulator is much larger, as expected, but only allows optical resolution up to the IR wavelength, i.e., 1–10 µm. Note that this optical microscopy method is sensitive to changes in the local reflectivity of the sample, which is proportional to its electronic conductivity, and it does not directly probe structural changes in the thin film.

Although the list above may seem restrictive, VO${\phantom{­}}_2$ is not the only material that can be observed using this technique. For example, manganites (e.g., LaO${\phantom{­}}_{2/3}$CaO${\phantom{­}}_{1/3}$MnO${\phantom{­}}_3$), nickelate (NdNiO${\phantom{­}}_3$), and other vanadates (V${\phantom{­}}_2$O${\phantom{­}}_3$) all present a metal-to-insulator transition accompanied by a change in reflectivity in the visible range. A drawback of such samples is their lower transition temperature, forcing the use of a cryostat. In this case, an objective with a longer working distance is necessary, which would typically bring the numerical aperture to 0.8, resulting in a 10% loss in spatial resolution (≈440 nm). Finally, this technique could also be used with polarized light, which would complicate the analyses but could reveal anisotropies in the thin films.

3. Results

Having introduced the basic steps to obtain single pixel time traces in Figure 1 and Figure 2, we now present the detailed spatially resolved study of the IMT in VO${\phantom{­}}_2$ films using our new optical mapping method.

Local Transition Temperature T${\phantom{­}}_c$ Maps: In a macroscopic hysteresis loop, T${\phantom{­}}_c$ is typically defined as the inflection point of the hysteresis loop, whether upon warming or upon cooling. In the microscopic hysteresis loops measured, we have defined the local transition T${\phantom{­}}_c$ in a similar way (consistently with Refs. [15,24,25]) as the temperature at which a pixel has a step-function like change in its local reflectivity. Figure 3c reports the local transition temperature T${\phantom{­}}_c$ map in VO${\phantom{­}}_2$ sample. These maps show a large spatial variation in T${\phantom{­}}_c$, with rich pattern formation over tens of microns. These spatial variations have been previously reported using s-SNIM [8]. This local probe technique offers much higher resolution than the optical maps presented here (limited by the AFM tip radius ∼15 nm). However, the stabilized optical images offer the advantage of the full field of view faster acquisition, allowing for finer time and temperature resolution. Note that both optical and scanning s-SNIM are resolution-limited (400 nm and 15 nm, respectively), meaning that any “subpixel” metal–insulator structures below the experimental resolution will be averaged in each pixel signal much like would be carried out in a real space block renormalization procedure. Moreover, in any technique, if the pixel size is chosen to be lower than the spatial resolution, this will lead to signal convolution from adjacent pixels. In the optical measurements presented here, the local transition ${\mathrm{T}}_c$ within a single pixel should thus be considered to be the temperature at which 50% of the subpixels and adjacent pixels, within the experimental resolution, have switched. Within these limitations, this detailed spatial and temporal knowledge of the location of these variations in insulator-to-metal transition has recently been exploited to determine the fractal nature of clusters [25,27] and to track memory in the cluster patterns [24].

Reproducibility of T${\phantom{­}}_c$ Maps: Previous reports on avalanches in this material showed jumps in resistivity randomly appearing during the transition in macroscopic transport measurements [9]. This suggested that the metal–insulator patterns could appear randomly during each temperature sweep. At first glance, this appears to be at odds with the optical data reported in this study, where we find that the metal and insulator patterns are highly repeatable globally (occurring at the same location and with the same shape) during successive temperature sweeps (see Figure 4). The repeatability suggests that the patterns are strongly influenced by an underlying random field present in the thin film or its substrate [27]. This has been confirmed recently by showing, using a convolutional neural network, that the underlying model best describing the black and white cluster images was a 2D random field Ising model [25]. The observed stochasticity of resistance jumps in transport measurements [9] could arise from small variations in the exact time at which avalanches are triggered. In addition, small changes in local T${\phantom{­}}_c$’s can potentially create large changes in resistance, when tiny “shorts” connect pre-existing larger metallic clusters (further discussion on this is presented in SI Section S2.6).

Transition Width $\delta$T${\phantom{­}}_c$ Maps: The transition width $\delta$T${\phantom{­}}_c$ of each pixel can be accessed by fitting single pixel scaled intensity time traces to a hyperbolic tangent: $-{\displaystyle \frac{1}{2}}(tanh$(${\displaystyle \frac{{\mathrm{T}-\mathrm{T}}_c}{\delta {\mathrm{T}}_c}}$)−1). Because T${\phantom{­}}_c$ is known from our time trace analysis, there is only one fitting parameter. The map of $\delta$T${\phantom{­}}_c$ distribution is shown in Figure 3e. The average transition width of the pixels as measured in optics is $2.8\pm 1.1$ °C with extremes from 0 °C to 8 °C. Moreover, a small number of pixels show more than one step during a transition (see, for example, pixel F in Figure 6). This case could arise from structures that are smaller than the pixel size. Indeed, s-SNIM has clearly observed inhomogeneities on smaller length scales than the resolution of the optical maps presented here [8]. Interestingly, the standard deviation of local T${\phantom{­}}_c$’s across the sample, ${\sigma }_{{\mathrm{T}}_c}$(1.2 °C), is smaller than the average transition width of pixels $\delta$T${\phantom{­}}_c$ (2.8 °C). It remains an open question whether the self-similar metal–insulator domain patterns [8] could be the source of this difference.

This double-step case could also arise from an overlap between multiple metal or insulator domains affecting a single pixel. Indeed as mentioned above, the optical resolution averages over 400 nm (approximately 10 pixels), and here, pixel F is surrounded by two very different adjacent regions—one with a T${\phantom{­}}_c$ of 68 °C (green) and another with a T${\phantom{­}}_c$ of 72 °C (red). This spatial averaging scenario is supported by the fact that the two steps in the time trace Figure 6F occur specifically at these two adjacent T${\phantom{­}}_c$ values, and the fact that the double-step transition can be traced over 10 pixels around the location, matching the optical resolution. Note that this double-step transition should also be observed at the edges of highly contrasted domains in local probes. The fact that it is clearly observed here is most likely due to our fine interval between temperature steps. Interestingly, in time traces where double steps are observed, this occurs during the warming cycle and very rarely during the cooling cycle. This asymmetry has already been reported in macroscopic transport measurements [28] and was attributed to differential thermal strain build-up in the films upon heating and cooling. In the future, these two-step pixels could potentially be detected in an automated way from their anomalously high error on the fit to the hyperbolic tangent function.

Hysteresis Width $\Delta$T${\phantom{­}}_c$ Maps: For each pixel analyzed, note that local transition temperature T${\phantom{­}}_c$ (upon warming) is not equal to T${\phantom{­}}_c$ (upon cooling) because there is hysteresis $\Delta$T${\phantom{­}}_c$ (analyzed below). By subtracting T${\phantom{­}}_c$${\phantom{­}}^{up}$ − T${\phantom{­}}_c$${\phantom{­}}^{down}$ (see the caption of Figure 3b for the definition), one can construct a hysteresis width $\Delta$T${\phantom{­}}_c$ map. The hysteresis width $\Delta$T${\phantom{­}}_c$ map is shown in Figure 3d. The average width is found to be $4.3\pm 1.1$ °C as seen in macroscopic transport measurements. However, certain small regions have small $\Delta$T${\phantom{­}}_c$, in the range [0 °C–1 °C] (small blue clusters in Figure 3d). Probing this region with other local probes could shed light on whether this is an intrinsic property of these regions. These hysteresis-free patches could be very useful in multiple switching applications such as optical electronic devices. Indeed it has been shown that the presence of a large hysteresis in VO${\phantom{­}}_2$ greatly complicates using it as an optical sensor [29]. These $\Delta$T${\phantom{­}}_c$ maps will also stimulate theoretical models to develop predictions about local hysteresis properties (hysterons) [30], and their spatial interrelation.

4. Discussion

4.1. Correlations Between Maps

With these three maps above, we quantify correlations among these quantities. Figure 5 plots T${\phantom{­}}_c$ vs. $\Delta {\mathrm{T}}_c$, $\Delta {\mathrm{T}}_c$ vs. $\delta {\mathrm{T}}_c$ and T${\phantom{­}}_c$ vs. $\delta {\mathrm{T}}_c$ for each pixel. Among the three correlation maps, no trend is seen in the last two, but T${\phantom{­}}_c$ vs. $\Delta {\mathrm{T}}_c$ shows a slightly positive correlation. This means that pixels with low T${\phantom{­}}_c$ tend to have low $\Delta {\mathrm{T}}_c$ (i.e., close to zero) and vice versa. This relationship had previously only been observed via macroscopic measurements of irradiated or doped samples using multiple samples [31,32]. Here, all the correlated data are taken on the same sample surface. Note that the positive correlation in Figure 5a is not to be confused with the few diagonal/horizontal lines present. These come from multiple pixels (spatially close by) switching at the same temperature upon cooling and warming, respectively. This is typically what one would expect from avalanches, but further analysis is needed to extract the full dynamics occurring.

4.2. Local Selection of On-Demand Hysteretic Properties

The wide range of behaviors contained in the three maps presented in the section above (Figure 3c–e), gives us the unprecedented opportunity to locate and hand-pick individual pixels with desired properties. Figure 6 shows the T${\phantom{­}}_c$ map of the sample with six different types of pixels selected. The features put forward in these six pixels are not unique to the 37 nm square pixel location. These features usually also hold for many pixels around the $xy$ coordinates reported.

The pixel labeled “std” for standard has a rounded transition with values of T${\phantom{­}}_c$, $\Delta$T${\phantom{­}}_c$ and $\delta$T${\phantom{­}}_c$ which are close to the average values found in the distribution of these three quantities (see Figure 3f–h).

Pixels A and B show the most common type of local characteristics found in the maps: when T${\phantom{­}}_c$ is high, $\Delta$T${\phantom{­}}_c$ is high; when T${\phantom{­}}_c$ is low, $\Delta$T${\phantom{­}}_c$ is low. This positive correlation is evident at a global level in Figure 5a. However, on a local level, individual pixels can have a large deviation from the global average behavior. Indeed, pixel E shows a possibility of finding $\Delta$T${\phantom{­}}_c$ very low (0.3 °C) with a T${\phantom{­}}_c$ (66.3 °C) low but closer to the mean value of the map.

Pixels C and D illustrate the case where the width $\delta$T${\phantom{­}}_c$ of the transition is very sharp (0.5 °C) or very wide (5 °C). Pixel C shows a representative sharp pixel, where within the temperature steps of 0.17 °C, the transition occurs in a sharp, avalanche mode. Further analysis to see where and how these avalanches occur will be pursued in future work.

Finally, pixel E shows a case where $\Delta$T${\phantom{­}}_c$ is within the lower values [0 °C–1 °C]. As mentioned previously, small hysteresis could be useful in opto-electronic devices or neuromorphic devices. In the first case, small hysteresis avoids optical detectors getting stuck in subloops [29]; in the second case, small hysteresis allows lowering the voltage threshold needed for spiking [33].

5. Conclusions

We have reported the first local transition temperature T${\phantom{­}}_c$ maps derived from single pixel optical imaging on VO${\phantom{­}}_2$. Multiple new experimental steps were needed to align, focus and calibrate the raw grayscale images recorded. These experimental achievements allowed us to accurately track the spatial distribution of metal and insulator clusters. Binary black and white images, time traces, T${\phantom{­}}_c$ maps, $\Delta$T${\phantom{­}}_c$ maps, and $\delta$T${\phantom{­}}_c$ maps were plotted and discussed. The sample shows micron-sized patterns that are found to be mostly reproducible through multiple temperature sweeps. The $\Delta {\mathrm{T}}_c$ hysteresis width map exhibits, on average, the same average hysteresis width of 4.3 °C as macroscopic resistivity hysteresis, but exhibits strong variation on a local scale, down to ∼[0 °C–1 °C] in certain small regions and as large as ∼8 °C in other regions. These findings open an exciting opportunity to leverage local properties of VO${\phantom{­}}_2$ by, e.g., electrically contacting specific parts of the sample in order to select unique parameter combinations for specific applications. It also opens the path for scaling down devices for use in optical switches, nanophotonics [10], infrared microbolometers [11] and coupled oscillators [12,13]. Our results will stimulate theoretical models to develop predictions about local hysteresis properties and their spatial interrelation. Up until now, theoretical models have largely focused on predictions of macroscopic properties. Future work may even be able to extract from these datasets the local strength of the quenched disorder at sub-micron scales in the samples.