Dynamics of an Electrically Driven Phase Transition in Ca2RuO4 Thin Films: Nonequilibrium High‐Speed Resistive Switching in the Absence of an Abrupt Thermal Transition

In Mott‐type resistive switching phenomena, which are based on the metal–insulator transition in strongly correlated materials, the presence of an abrupt temperature‐driven transition in the material is considered essential for achieving high‐speed and large‐resistance‐ratio switching. However, this means that the freedom of material/device design in applications is significantly reduced for this type of switching by the strict requirement of transition abruptness. Here, high‐speed, abrupt resistive switching with a switching time of 140 ns is demonstrated in epitaxial films of Ca2RuO4/LaAlO3 (001), which is a material with a nonthermal metal–insulator transition driven by current, despite the complete absence of an abrupt thermal transition in the resistivity–temperature characteristics. Highly smooth negative‐differential‐resistance behavior, very high cycling stability, and an endurance over 106 cycles are also demonstrated in the current–voltage and current–time characteristics, which confirm the nonstochastic nature of the abrupt switching. These results suggest that strict control of the resistivity–temperature characteristics is not necessarily required in a material with a nonthermal‐type metal–insulator transition to obtain high‐speed resistive switching because of the independence of the dynamics from those of the thermal transition, and this phenomenon potentially has important advantages in resistive switching applications.


Dynamics of an Electrically Driven Phase Transition in Ca 2 RuO 4 Thin Films: Nonequilibrium High-Speed Resistive Switching in the Absence of an Abrupt Thermal Transition
Keiji Tsubaki, Atsushi Tsurumaki-Fukuchi,* Takayoshi Katase, Toshio Kamiya, Masashi Arita, and Yasuo Takahashi DOI: 10.1002/aelm.202201303 important research topic because most of the critical properties of Mott neuromorphic devices, such as the firing rate of artificial neurons [3][4][5][6][7] and the potentiation/ depression rate and temporal plasticity of artificial synapses, [5,8] directly depend on the formation/retention time of the metallic phases, as well as because of the fundamental interest in the physics of the transition pathway. [9][10][11][12][13] In previous studies, dynamics analysis and performance characterization of the metal-insulator transition have been conducted by fabricating two-terminal electrodes on a material and inducing the transition via electric field application or current injection. Using the resistance changes under fields as a probe of the formation of the metallic phase, the dynamics and speed of the transition have been investigated for a variety of strongly correlated materials, including vanadium oxides (VO 2 , V 2 O 3 , and V 3 O 5 ), [5][6][7][9][10][11][13][14][15] metal chalcogenides (AM 4 X 8 (A = Ga and Ge, M = V, Nb, and Ta, X = S and Se), [3,4,8,[16][17][18][19] Ni(S,Se) 2 , [19] and 1T-TaS 2 [20,21] ), and rare-earth perovskite manganites [22] and nickelates, [12] and high-speed resistive switching with a switching time down to <100 ns has been demonstrated in some materials. [6,11,12,17,20] Recent investigations have indicated that the electrically driven resistive switching in the strongly correlated materials is generally produced by the increase in the internal temperature due to Joule heating, and temperature-driven metal-insulator transitions that are the same as those induced by temperature In Mott-type resistive switching phenomena, which are based on the metalinsulator transition in strongly correlated materials, the presence of an abrupt temperature-driven transition in the material is considered essential for achieving high-speed and large-resistance-ratio switching. However, this means that the freedom of material/device design in applications is significantly reduced for this type of switching by the strict requirement of transition abruptness. Here, high-speed, abrupt resistive switching with a switching time of 140 ns is demonstrated in epitaxial films of Ca 2 RuO 4 / LaAlO 3 (001), which is a material with a nonthermal metal-insulator transition driven by current, despite the complete absence of an abrupt thermal transition in the resistivity-temperature characteristics. Highly smooth negative-differential-resistance behavior, very high cycling stability, and an endurance over 10 6 cycles are also demonstrated in the current-voltage and current-time characteristics, which confirm the nonstochastic nature of the abrupt switching. These results suggest that strict control of the resistivitytemperature characteristics is not necessarily required in a material with a nonthermal-type metal-insulator transition to obtain high-speed resistive switching because of the independence of the dynamics from those of the thermal transition, and this phenomenon potentially has important advantages in resistive switching applications.
sweeping are caused in the resistive switching. [10][11][12][13][14] In some materials, however, nonthermal, purely electronic mechanisms have also been proposed and demonstrated for electrically driven metal-insulator transitions and resistive switching, such as carrier-mediated (band-filling-controlled) transitions in vanadium-oxide nanowires [23] and metal chalcogenides, [17][18][19][20] which are caused by field-assisted dynamic carrier generation in the materials, but the distinction of the involved metallic phases from those in the temperature-driven transitions remain elusive (i.e., the metallic phases in these nonthermal transitions may be the same as those in the thermal transitions). Due to the expected involvement of thermally induced metallic phases, the abruptness of the temperature-driven metal-insulator transition has been regarded as a critical parameter of the resistive switching based on the metal-insulator transition for both the thermal and nonthermal mechanisms, which directly determines the switching behavior, [24][25][26] and the resistive switching has been believed to be caused by the abrupt state change that is observed in the resistivity-temperature characteristics. In materials with the metal-insulator transition, the abruptness of the temperature-driven transition has been estimated from the temperature coefficient of resistivity (TCR) defined as |(1/ρ) (dρ/dT)|, where ρ is the resistivity and T is the temperature of the material, [27,28] and a large TCR of >100% K −1 (as a discontinuity in the resistivity-temperature curve) has been generally required for the resistivity-temperature characteristics to induce high-speed switching as Mott switching devices [14,21,[24][25][26] and sharp firing as Mott neurons. [5][6][7]15] However, to obtain a high TCR, highly controlled stoichiometry and crystallinity is essentially required for the switching material, [27][28][29][30][31] and severe restrictions have been imposed on the selection of the switching and substrate materials in the thin film fabrication. [27][28][29]31] Device applications of materials with the metalinsulator transition have therefore been complicated thus far due to the requirement of the transition abruptness.
The 4d layered perovskite ruthenate Ca 2 RuO 4 is known as a Mott insulator in which the temperature-induced metal-insulator transition appears at 357 K in bulk crystals, [32] and the nonthermal, purely electronic insulator-to-metal transition driven by current has also been demonstrated in bulk crystals [33][34][35][36][37][38][39][40][41][42][43] and epitaxial thin films. [44] Unlike other materials with nonthermal-type transitions, remarkably, the presence of nonequilibrium metallic and insulating phases (called L* and S*), which are distinctive from the phases in the temperature-driven transition under electronic equilibrium, has been observed for bulk Ca 2 RuO 4 under current densities of >4 A cm −2 in structural characterizations [37,38,40] and Raman spectroscopy measurements. [36] From the viewpoint of resistive switching, these observations in bulk Ca 2 RuO 4 suggest that the thermal transition abruptness requirement may no longer be valid for resistive switching in a material with such nonequilibrium phases, and abrupt resistive switching may be electronically induced therein independent of the equilibrium phases and resistivitytemperature characteristics. In some recent studies, abrupt resistive switching has been demonstrated in materials with less abruptness of the temperature-driven transition, such as V 3 O 5 [11,13] and SmNiO 3 , [12] in which the temperature-driven transition is second order and has relatively gradual behavior, and AM 4 X 8 chalcogenides, whose resistivity-temperature characteristics are seemingly gradual but are abruptly irreversibly changed after applying a voltage. [16,17] The possibility of independence of electrically driven resistive switching from the resistivity-temperature characteristics has also been suggested in these materials, and thus, detailed dynamics investigations of resistive switching are currently required for materials with the nonthermal-type metal-insulator transition toward electronics applications.
Here, we demonstrate that discontinuous, abrupt resistive switching is induced in the nonthermal transition system of a Ca 2 RuO 4 epitaxial thin film by current injection despite the complete absence of an abrupt temperature-driven transition and a resistive anomaly in the resistivity-temperature characteristics. This directly indicates that the dynamics of the electrically driven transition and resistive switching in the Ca 2 RuO 4 thin films are basically independent of those of the temperature-driven transition under electronic equilibrium. In the current-voltage measurements obtained under DC current sweeping, a continuous resistance decrease with a negative differential resistance (NDR) behavior, which resembles that in bulk Ca 2 RuO 4 , [34,35,38,40,42] was observed in thin films with high stability, and formation of a nonequilibrium low-resistivity phase was suggested. By conducting time-resolved currentvoltage measurements for the thin films under pulsed voltage application, a significant discontinuity in the resistance state and a short switching time of 140 ns were demonstrated by the resistive switching despite the complete absence of a discontinuity in the resistivity-temperature characteristics. High reproducibility of the switching characteristics and an endurance of over 10 6 cycles were also demonstrated by the abrupt switching phenomenon. These results suggest that the technical restrictions imposed on the switching materials to increase the thermal transition abruptness may be significantly reduced in the resistive switching induced by a nonthermal-type metalinsulator transition and will provide important insights into device applications and the mechanism understanding.

Results and Discussion
As explained in Introduction, bulk single crystals of Ca 2 RuO 4 show a sharp metal-insulator transition around 357 K. Meanwhile, we observed that the Ca 2 RuO 4 thin films grown by the solid phase epitaxy under nonvacuum conditions do not show an abrupt temperature-driven metal-insulator transition in their resistivity-temperature characteristics in our previous work. [44] We have also observed that the resistivity of the nonvacuum grown Ca 2 RuO 4 /LaAlO 3 (001) thin films is more than one order of magnitude higher than that of Ca 2 RuO 4 /LaAlO 3 (001) thin films grown under vacuum conditions. [45 -47] The upper panel of Figure 1a shows the resistivity-temperature characteristics of a Ca 2 RuO 4 (100 nm)/LaAlO 3 (001) thin film grown in this study, measured by the four-probe method for a rectangular bar shaped sample with a dimension of 2.3 mm × 1.0 cm. The characteristics showed a semiconductor-like behavior over the whole measurement range of 50-400 K, and no discontinuity nor anomaly were detected therein, as further confirmed from the TCR profiles (bottom panel of Figure 1a). Note that below 50 K, reliable data were not obtained in the measurements because www.advelectronicmat.de of the voltage limit = 95 mV. The monotonous and smooth temperature dependences shown by the resistivity and TCR are considered to be a result of broadening of the temperaturedriven metal-insulator transition due to the compressive epitaxial strain from the LaAlO 3 (001) substrate, as also observed in other materials with the metal-insulator transition, [29][30][31] and the broadened temperature-driven transition will influence the characteristics below the transition temperature of 240 K, as discussed in our previous study. [44] Because an abrupt first-or second-order temperature-driven transition is clearly absent in the characteristics, the occurrence of bias-driven abrupt resistive switching cannot be supposed in the Ca 2 RuO 4 (100 nm)/ LaAlO 3 (001) thin films, if the mechanisms previously considered for materials with thermal-type metal-insulator transitions (such as vanadium oxides [6,7,11,13,14,24] and perovskite nickelate [12] ) are considered for the films. When the resistance-temperature characteristics were measured under constant DC currents, large decreases in the resistance were caused for the Ca 2 RuO 4 thin films by current injection for T < 240 K through the current-driven insulator-to-metal transition ( Figure S1, Supporting Information and ref. [44] ). However, the measurements indicated that the DC-current-dependent changes in the resistance were highly continuous, [44] and the reduced resistance state in the Ca 2 RuO 4 thin films was only stabilized under a steady current (i.e., only in the nonequilibrium steady state; [41] Figure S1, Supporting Information). Therefore, unlike the field-driven transition in AM 4 X 8 chalcogenides, in which abrupt nonvolatile changes are caused in the resistance-temperature characteristics by voltage application (through the pressure-based stabilization of the equilibrium metallic phases), [16,17] the occurrence of abrupt resistive switching is not expected for the present Ca 2 RuO 4 thin films from the smooth continuous currentdependent resistance-temperature characteristics.
Because the details of the switching behaviors and the switching dynamics were not revealed for the Ca 2 RuO 4 thin films in our previous study, [44] to understand them, we conducted thorough current-voltage and current-time (timeresolved current-voltage) measurements of the resistive switching in the present work. To investigate the resistive switching characteristics, we fabricated two types of in-plane metal electrodes for the Ca 2 RuO 4 thin films (Figure 1b To induce the current-driven transition by applying short, pulsed voltages from a function generator (Tektronix AFG 3102 with a voltage pulse height of ≤20 V) and measure the dynamic characteristics, the electrode with a smaller gap was fabricated in the configuration of electrode B, and the width was set as 10 µm to apply a sufficient current density to the Ca 2 RuO 4 thin films. An oscilloscope with an internal resistance of 50 Ω was used as a current meter in the measurements with electrode B, and the flowing currents were derived from the voltage readings and internal resistance.
The DC current-voltage characteristics of a Ca 2 RuO 4 (100 nm)/LaAlO 3 (001) thin film measured with electrode A are shown in Figure 2 for current-sweeping and voltage-sweeping cases. The current-sweeping characteristics showed clear NDR behavior for stage temperature T s ≤ 80 K (top panel of Figure 2), similar to that observed in bulk Ca 2 RuO 4 , [34,35,38,40,42] though much smoother current-voltage profiles were obtained in the present film for the NDR process. For T s ≤ 80 K, the film initially showed a gradual decrease in the resistance in low current regions (e.g., < 5.9 mA at T s = 40 K), and then, NDR behavior started to appear upon further increasing the current. When the measurements were conducted under voltage-sweeping conditions (middle panel of Figure 2), the large decrease in the differential resistance due to the occurrence of NDR was observed as an abrupt jump of the current. Such two-stage (from gradual to abrupt) decreases in the resistance have been recently demonstrated in many materials that exhibit nonthermal-type metalinsulator transitions [3,4,8,18,19,23,34,35,38,40,42] and are considered a universal behavior of the resistive switching based on the nonthermal metal-insulator transitions. The origin of the initial www.advelectronicmat.de gradual decrease in the resistance is not clear yet but has been explained by supposing gradual growth of the metallic domains in AM 4 X 8 chalcogenides [3,4,8,18,19] and field-driven gradual carrier generation in vanadium-oxide nanowires. [23] For bulk Ca 2 RuO 4 , the involvement of carrier-driven energy-gap suppression [34,39] in the gradual decrease in the resistance has also been noted, in addition to the contributions from carrier generation itself. An abrupt nonthermal-type transition to the metallic phase has been considered to occur with the NDR behavior in the current-voltage characteristics in vanadium-oxide nanowires. [23] In bulk Ca 2 RuO 4 , more directly, the occurrence of a current-driven first-order transition between the nonequilibrium phases of S* and L* has been experimentally observed for the NDR regions of the current-voltage characteristics through optical microscopy measurements [35] and structural characterizations. [37,38,40] If we consider that the Ca 2 RuO 4 films have a nonthermal transition pathway analogous to that in vanadium-oxide nanowires and bulk Ca 2 RuO 4 , then the highly smooth NDR behavior indicates that the growth of the low-resistivity phase more uniformly progresses in the thin film structure with the increase of the current density compared with the transition in bulk Ca 2 RuO 4 (as discussed later). The correspondence of the two patterns of current-voltage characteristics measured in the current-and voltage-sweeping conditions is shown in the bottom panel of Figure 2. As shown in this figure, in the actual profiles, the measurement points in the voltage-sweeping characteristics experience an abrupt jump of the state after reaching the NDR region (to the uppermost point in the current-sweeping characteristics) because of the voltage-feedback operation of a Keysight 4156C analyzer in compliance current (CC) control. From these current-voltage profiles under voltage sweeping, the Ca 2 RuO 4 thin films are suggested to possibly show significant abruptness in the resistive switching when a nongradual increase in the flowing current is permitted in the electrical measurement circuit.
The dynamic behavior of the resistive switching in the Ca 2 RuO 4 thin films investigated by pulsed voltage application using electrode B at T s = 70 K is shown in Figure 3. The measurements were conducted under voltage-sweeping conditions and triangular/rectangular waveforms of the applied voltages for various maximum amplitudes (V max s) (as monitored in the top panels of Figure 3a-c). Despite the voltage-sweeping operation of the function generator, finite voltage feedback effects were still present in the measurements due to the internal resistance of the oscilloscope (50 Ω, which is comparable to the resistance of the Ca 2 RuO 4 films in the low-resistance state), as demonstrated by the sudden voltage drops in the characteristics with V max = 9 and 10 V (upper panel of Figure 3b). Rapid runaway of flowing currents was thus partially suppressed in these measurements by the load resistance, partially similar to a measurement under current sweeping (which corresponds to a measurement with an infinitely large load resistance [20,42] ). In the pulsed-voltage measurements with a triangular waveform with a duration of 5.0 ms (Figure 3a), the occurrence of a nonlinear transport phenomenon was observed in the Ca 2 RuO 4 thin film for V max = 2-8 V as a gradual increase in the current, and the amount of resistance change significantly depended on V max . By further increasing V max to ≥9 V, remarkably, abrupt resistive switching was observed in the currenttime characteristics (Figure 3b). In the characteristics with V max = 9 and 10 V, the film showed a discontinuous increase in the current after reaching the lower threshold current (I th1 ) of 6.0 mA, and the rapid current increase suddenly ceased at the higher threshold current (I th2 ) of 9.2 mA. Abrupt resistive www.advelectronicmat.de switching was also observed in the voltage-decreasing operation of the measurements at the same I th1 and I th2 . The presence of a discontinuous resistive switching phenomenon was directly demonstrated in the current-time characteristics of the Ca 2 RuO 4 thin films despite the complete absence of a discontinuity in the resistivity-temperature characteristics. The assumption that the nonlinear transport and abrupt resistive switching in the pulsed-voltage measurements correspond to the gradual behavior and NDR behavior in the static currentvoltage characteristics (Figure 2), respectively, can be reasonably made. The measurements under rectangular-waveform pulsed voltages indicated that a finite incubation time (t inc ) was required before the occurrence of the abrupt switching, and t inc = 2.57 µs was obtained at V max = 9 V (Figure 3c). The occurrence of finite t inc has generally been observed in resistive switching phenomena based on the metal-insulator transition for both the thermal [7,[10][11][12]14] and nonthermal mechanisms. [3,4,8,[17][18][19]40,41] In the present Ca 2 RuO 4 thin films, however, the origin of t inc cannot be directly attributed to the gradual increase in the internal temperature, which has been widely assumed for the resistive switching in epitaxial thin films of vanadium oxides [10,11,14] and perovskite nickelate, [12] since a nonthermal origin of the switching is strongly suggested, as discussed below. The current-time measurements under rectangular pulses also indicated that the abrupt switching in the Ca 2 RuO 4 thin film has a short switching time (t sw ) of 140 ns at V max = 9 V (Figure 3d). Additionally, finite retention times (t re s) of the low-resistance states were observed in the Ca 2 RuO 4 thin film after removal of the switching voltages, and t re = 1.85 µs was observed at V max = 9 V (Figure 3e). From numerical simulations of the internal temperatures ( Figure S2, Supporting Information), we confirmed that the t re of the resistance state is significantly shorter than the thermal relaxation time of the Ca 2 RuO 4 thin film under resistive switching.
The single-step abrupt switching observed at T s = 70 K tended to be divided into multiple steps of small abrupt switching when T s was decreased to ≤50 K ( Figure S3, Supporting Information). In the measurements shown in Figure 4a, the occur-rence of abrupt resistive switching was detected twice (from I th1 = 6.54 mA to I th2 = 9.52 mA and from I th1 ' = 11.0 mA to I th2 ' = 12.4 mA) in the voltage-increasing sweeps at T s = 50 K. In addition, the switching behavior in the voltage-decreasing sweeps became different from that in the voltage-increasing sweeps in the measurements at T s = 50 K, and single abrupt switching was detected in the decreasing sweeps between the shifted higher and lower threshold currents of I th2 * = 7.04 mA and I th1 * = 2.60 mA. Even with the occurrence of such multistep abrupt resistive switching, interestingly, the Ca 2 RuO 4 thin film showed very stable current-time characteristics in cycling operations, and very small (<0.7 mA) distributions of I th1 , I th2 , I th1 ', I th2 ', I th1 *, and I th2 * were observed for the 50 measurement cycles (Figure 4a), indicating the intrinsically high reliability of the switching mechanism. I th1 was also shown to be independent of the measurement time. Figure 4b shows the current-time characteristics of a Ca 2 RuO 4 thin film measured under triangular waveform applied voltages with durations (t p s) of 5.0 µs-500 ms at T s = 30 K. The abrupt resistive switching of the film was observed at the same I th1 of 2.40 mA in all the  When the number of measurements was further increased, the Ca 2 RuO 4 thin films showed a notable difference in the endurance characteristics of the switching depending on the occurrence of the abrupt-type switching behavior. Figure 5a shows the current-time characteristics of a Ca 2 RuO 4 (100 nm)/ LaAlO 3 (001) thin film measured under triangular-waveform applied voltages for 10 6 cycles at T s = 50 K and V max = 6.2 V, in which only gradual-type resistance changes were induced in the film. At this stage of switching, the resistance changes were reproduced in the film with no observable change in the characteristics over the 10 6 cycles. The current-time characteristics of the same Ca 2 RuO 4 thin film measured at T s = 50 K and V max = 10 V for 10 6 cycles with induction of the abrupt-type switching behavior are shown in Figure 5b. With the induction of the abrupt-type switching, progressive changes in the switching characteristics became observable in the Ca 2 RuO 4 thin film. Figure 5c plots the cycle number dependences of I th1 and the maximum current (I max ) in the switching obtained from the current-time characteristics shown in Figure 5a,b. This figure indicates that the I th1 and I max in the abrupt-type resistive switching have a clear tendency to decrease with cycling in a rather systematic manner, in contrast to the very stable I max in the gradual-type switching.
From the fact that the abrupt-type resistive switching in the Ca 2 RuO 4 thin films occurred in the absence of an abrupt thermal metal-insulator transition (Figure 1a), the origin is strongly suggested to be based on the nonthermal-type metalinsulator (or resistive) transition driven by current. [44] The twostage behavior of the resistance change (i.e., the initial gradual and subsequent abrupt switching observed in the films), which is directly analogous to the nonthermal-transition-based switching in VO 2 nanowires [23] and bulk Ca 2 RuO 4 , [34,35,38,40,42] also supports this assumption, in addition to the very high cycling stability of the switching characteristics (Figure 4). To discuss the involvement of the nonthermal metal-insulator transition in the resistive switching in more detail, we conducted finite element thermal analysis for the Ca 2 RuO 4 (100 nm)/LaAlO 3 (001) thin films under the resistive switching measurement (Figure 6). The Ca 2 RuO 4 thin film with electrode B under the application of a triangular-waveform pulsed voltage with t p = 5.0 µs and V max = 10 V at T s = 30 K (Figure 6a), which showed the two-stage resistive switching behavior in Figure 4b, was assumed in the analysis model, and the internal temperature distributions were numerically simulated from the experimental voltage-time and current-time characteristics. First, we conducted the analysis by assuming that no phase transition was caused by the voltage application (Figure 6b,c). Under this assumption, the maximum temperature in the Ca 2 RuO 4 film (T max , which is induced by Joule heating) was estimated as 40.2 K at the starting time of the abrupt switching (2.20 µs), which is 10.2 K higher than T s , and the highest T max in the measurements was 66.7 K (Figure 6c). Because the Ca 2 RuO 4 thin film has no discontinuity in the resistivity-temperature characteristics for the temperature range of 30.0-66.7 K (Figure 1a and ref. [44] ), the occurrence of abrupt resistive switching cannot be assumed for the Ca 2 RuO 4 thin film in this situation. The analysis therefore indicated that the occurrence of a certain kind of phase separation needs to be considered in the films to explain the occurrence of the abrupt-type switching. Previous studies have shown that the current-driven nonthermal transition in bulk Ca 2 RuO 4 occurs with phase separation between the nonequilibrium phases of S* and L*, and domain boundary direction is transverse to the current direction (due to carrier accumulation on the negative electrode). [35,42] Furthermore, the current-driven transition in bulk Ca 2 RuO 4 has been reported to be a first-order transition, which is accompanied by abrupt changes in the electronic states and crystal structures. [37,38] If the current-driven transition in the Ca 2 RuO 4 thin films has a similar first-order mechanism to that in the bulk, as suggested in our previous study, [44] then the occurrence of the abrupt resistive switching is reasonably explained by the transition, but further experimental investigations are necessary to confirm the mechanism. From the viewpoint of the characteristics, the systematic fatigue caused by the abrupt resistive switching (Figure 5b,c) also suggests the occurrence of phase separation in the abrupt switching since structural domains formed by a first-order transition will inevitably cause progressive changes in the crystallinity and composition distribution of the thin films. In Figure S4, Supporting Information, we illustrated this possible mechanism of the abrupt resistive switching of the Ca 2 RuO 4 thin films, in which the occurrence of a nonthermal carrier-mediated transition was assumed in the same way with bulk Ca 2 RuO 4 . Figure 6d,e shows the temperature distributions in the Ca 2 RuO 4 thin film and time profiles of T max obtained by www.advelectronicmat.de assuming the occurrence of such current-driven phase transition in the abrupt resistive switching. In the simulations, we assumed that a metallic domain with a resistivity of 0.04 Ω cm began to grow at 2.20 µs (the time when the current reached I th1 ) and increased in size until 2.25 µs (the time when the current reached I th2 ), and the direction of the domain boundaries (depicted by the magenta ellipses in Figure 6d) was transverse to the current direction, as observed in bulk Ca 2 RuO 4 . [35,42] In the out-of-plane direction, we assumed that the metallic domain formed no domain boundary in the thickness of 100 nm. Based on separate simulations, we have confirmed that the formation of a domain boundary in the out-of-plane direction (like previous observations in bulk Ca 2 RuO 4 [35] ) hardly affects the results of the temperature simulations for the thin film (due to fast heat conduction in the out-of-plane direction to the LaAlO 3 substrate) even when it was caused in the switching. The disappearance of the metallic domain was modeled to occur at 2.86 µs when the current decreased to I th2 in the voltage-decreasing sweep, as highlighted by the purple backgrounds in Figure 6a,e. As shown in Figure 6d,e, the analysis indicated that the T max s in the film under this type of phase formation were nearly the same as those without the phase transition (Figure 6b,c), and uniform temperature distributions were caused in the inplane junction of Pt/Ca 2 RuO 4 /Pt. The highly smooth behavior of the NDR characteristics ( Figure 2) and high reproducibility of the current-time characteristics (Figure 4a) also suggested that the temperature distributions in the Ca 2 RuO 4 thin films were spatially uniform in the measurements since the stability of the characteristics of the current-driven transition in Ca 2 RuO 4 has been shown to largely depend on the spatial uniformity of the temperature and current in bulk measurements. [42] In our thin films, the spatial uniformity of the temperature can be ascribed to the small conduction volumes (20 µm × 70 µm × 100 nm or 3.0 µm × 10 µm × 100 nm) of Ca 2 RuO 4 in the measurements when the results of the thermal analyses are considered.
In band semiconductors that do not have an electronic phase transition, the occurrence of NDR characteristics and abrupt resistive switching have been observed based on thermal/electrical runaway in the material and the spatial current confinement caused by it (i.e., spatial separation of the internal current densities). [48][49][50][51] As the resistivity-temperature characteristics of the Ca 2 RuO 4 thin films are quantitatively equivalent to the characteristics of band semiconductors, the results for band semiconductors suggest that the resistive switching in the Ca 2 RuO 4 thin films is also inducible through the occurrence of internal current confinement. However, our thermal analysis of the films indicated that the occurrence of this type of resistive switching is highly unlikely in the Ca 2 RuO 4 thin films. The www.advelectronicmat.de temperature distributions and time profiles of T max obtained by assuming the occurrence of spatial current confinement are shown in Figure 6f,g. Currents were assumed to be confined in the internal areas of the magenta solid lines, which were modeled based on the previous observations for semiconductor materials with NDR characteristics, [49,51] from 2.20 to 2.86 µs in the simulations. As this figure shows, large increases in the temperature up to 435 K were caused by the voltage application in this condition, and T max readily exceeded the chemical decomposition temperatures of ruthenium oxides (≈950 K at an oxygen partial pressure of 10 −8 Pa [52] ) when a longer t p was assumed ( Figure S5, Supporting Information). Therefore, the high stability and endurance of the resistive switching (Figures 4 and 5), which were measured in a vacuum probe station with a base pressure of 10 −8 Pa, are very unlikely to be observed under this type of current confinement. The multistep behavior of the abrupt switching (Figure 4a; and Figure S3, Supporting Information) is also inconsistent with this mechanism since thermal/electrical runaway of the Ca 2 RuO 4 thin films cannot progress in a step-by-step manner, as simulated in Figure 6g; and Figure S5a, Supporting Information.
Note that the speed of the resistive switching demonstrated in the Ca 2 RuO 4 thin films is anomalously faster than that in bulk Ca 2 RuO 4 . Previous studies have shown that both the t inc and t sw of the resistive switching in bulk Ca 2 RuO 4 are on the order of 10-100 ms, [40,41] which are 10 4 -10 5 times longer than those observed in the present Ca 2 RuO 4 thin films. In these studies, the origin of the long t inc and t sw has been explained by considering the time required to complete lattice reconstruction of Ca 2 RuO 4 , i.e., the finite time required for energy transfer from the injected carriers to the lattice, as a possible mechanism. [41] When this mechanism is applied to the Ca 2 RuO 4 thin films, the fast switching speed is basically explained by the faster energy transfer from the electron system to the lattice system, which is directly expected from the large current densities caused in the thin films (≈10 6 A cm −2 , compared to 1 A cm −2 in the bulk). For a detailed discussion of the influences of the current density, however, further in-depth measurements with micropatterning of Ca 2 RuO 4 will be necessary for the resistive switching in the Ca 2 RuO 4 thin films.

Conclusion
The presence of an abrupt resistive switching phenomenon was demonstrated in epitaxial thin films of Ca 2 RuO 4 /LaAlO 3 (001), which is a system with a current-driven nonthermal metal-insulator transition, by time-resolved electrical transport measurements under pulsed voltage applications, whereas these films have no abrupt thermal transition in the resistivity-temperature characteristics. The results suggested that the nonthermal, electrically driven transition in a strongly correlated material has an independence of the properties from those of the thermal transition in terms of the dynamics, and abrupt resistive switching by the electrically driven transition is possible when current injection is performed without strict current compliance (e.g., in a voltage-sweeping condition). A short t sw of 140 ns and a finite t re of 1.85 µs were observed in the resistive switching phenomenon of the Ca 2 RuO 4 thin films.
These values suggested that the current-driven transition in the Ca 2 RuO 4 thin films has a high speed of the transition progress and a finite persistence time of the low-resistivity phase, similar to the electrically driven transition in a material with a sharp thermal transition. High reproducibility of the switching characteristics and an endurance of over 10 6 cycles were also observed in the abrupt resistive switching of the Ca 2 RuO 4 thin films, demonstrating the intrinsic reliability of the mechanism. The demonstration by the Ca 2 RuO 4 thin films suggests that if a material with a metal-insulator transition potentially has a nonthermal-type transition mechanism, then abrupt resistive switching, which is a key phenomenon for the development of resistive memories and electronic neurons, can be obtained in the material without increasing the abruptness (or TCR) of the thermal transition. The findings might significantly broaden the possibility of electronics applications of the metal-insulator transition and will offer important insights into understanding the nonequilibrium dynamics.

Experimental Section
c-axis oriented epitaxial thin films of Ca 2 RuO 4 with a thickness of 100 nm were grown by solid phase epitaxy on LaAlO 3 (001) single crystal substrates to measure the resistive switching characteristics. The Ca 2 RuO 4 thin films were grown at 1300 °C in an Ar (99%) + O 2 (1%) atmosphere at a pressure of 1.0 atm from amorphous precursor films deposited using a Ca 2 RuO 4 sintered ceramic target at room temperature, as reported in the previous study. [44] The crystallinity and surface morphology of the Ca 2 RuO 4 (100 nm)/LaAlO 3 (001) thin films were characterized by X-ray diffraction and atomic force microscopy measurements using a D8 Discover (Buruker AXS Inc.) and a NanoCute (Hitachi High-Tech Co.). The four-probe resistivity of the Ca 2 RuO 4 thin films was measured using the resistivity option of a physical property measurement system (PPMS, Quantum Design). Voltage and current limit for the resistivity reading was set to 95 mV and 100 µA in the four-probe measurements, respectively, and duration of the reading voltages was 0.06 s. For the measurements of the resistive switching characteristics, two types of in-plane electrodes, Au (100 nm)/Cr (5 nm) (electrode A) and Pt (65 nm) (electrode B), were fabricated on Ca 2 RuO 4 thin films via vacuum evaporation and standard photolithography processes. The DC and pulsed current-voltage characteristics of the thin films were measured in a cryogenic probe station system (Nagase, GRAIL-20-305-6-LV) using a semiconductor parameter analyzer (Keysight 4156C), a function generator (Tektronix AFG 3102), and an oscilloscope (Yokogawa DLM2022). Measurements of the two-probe resistance-temperature characteristics under constant currents ( Figure S1, Supporting Information) were conducted using a system consisting of a cryocooler, a digital multimeter (Keithley 2002), and a direct current source (Yokogawa 7651). Numerical simulations of the internal temperature distributions were conducted by the finite element method using COMSOL Multiphysics software for the Pt (65 nm)/Ca 2 RuO 4 (100 nm)/LaAlO 3 (001) in-plane junctions under resistive switching, assuming the experimental data of the current-time characteristics and literature values of the thermal conductivities and specific heats for Ca 2 RuO 4 [41] and LaAlO 3 [53] with the temperature dependences. The accuracy of the simulation results was calibrated using the experimental thermal time constant of the Ca 2 RuO 4 (30 nm)/LaAlO 3 (001) thin film with electrode A (about 10 0 s), which was suggested in the previous study. [44]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.