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Riku Ishii, Ryo Motohashi, Keitaro Tada, Yusuke Suzuki, Takayoshi Kouchi, [Hiroshi Oike](https://orcid.org/0000-0001-6866-7774), Fumitaka Kagawa, Reizo Kato, Tetsuaki Itou

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[Volatile resistive-switched state in a bulk organic conductor with a sharp metal-insulator transition](https://mdr.nims.go.jp/datasets/fa97e4b3-2f7b-44d6-8810-e17e91cb2f58)

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Volatile resistive-switched state in a bulk organic conductor with a sharpmetal-insulator transitionRiku Ishii,1 Ryo Motohashi,1 Keitaro Tada,1 Yusuke Suzuki,1 Takayoshi Kouchi,1Hiroshi Oike,2, 3 Fumitaka Kagawa,4,5 Reizo Kato,6 and Tetsuaki Itou1, ∗1Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585, Japan2Research Center for Materials Nanoarchitechtonics (MANA),National Institute for Materials Science (NIMS), Tsukuba-shi, Ibaraki 305-0047, Japan3PRESTO, Japan Science and Technology Agency (JST), Kawaguchi-shi, Saitama 332-0012, Japan4RIKEN Center for Emergent Matter Science (CEMS), Wako-shi, Saitama 351-0198, Japan5Department of Physics, Institute of Science Tokyo, Tokyo 152-8551, Japan6RIKEN, Cluster for Pioneering Research (RIKEN-CPR), Wako-shi, Saitama 351-0198, Japan(Dated: August 20, 2026)Volatile resistive switching in correlated-electron systems, characterized by an abrupt resistancedecrease under applied current, is crucial for developing next-generation electronics. Despite its tech-nological significance, the underlying physics remains elusive. Inorganic thin films on substrates—thewidely studied platform for resistive switching—usually exhibit broad temperature-induced metal-insulator transitions (MITs) and substantial heat dissipation. These factors complicate the nonlinearthermal effect induced by Joule heating, a key contributor to resistive switching, rendering it ex-cessively complex and difficult to decipher. Here we investigate a resistive-switched state in thebulk organic conductor (d7-DMe-DCNQI)2Cu, which undergoes an extremely sharp first-order MITand exhibits weak heat dissipation, using resistance and 1H-NMR measurements. These extremeconditions make the Joule heating effect vivid, allowing us to observe peculiar phenomena, includ-ing temperature locking to the MIT and ‘inverse Ohm’s law’—an inverse proportionality betweenvoltage and current. These findings provide fundamental insights into the nonlinear thermal effectin resistive switching, offering a pathway to efficient resistive-switching technologies.I. INTRODUCTIONMetal-insulator transitions (MITs) in electron systems,induced by electronic correlations and often intertwinedby low dimensionality, have been central issues in funda-mental physics. Over the course of a century of extensiveresearch, both theoretical and experimental physicistshave established a solid foundational understanding ofthese MITs—namely, the Mott and Peierls transitions—typically triggered by changes in temperature or pres-sure [1]. In the insulating phases near the transitions,it has also been empirically observed that applying anelectric field/current can sometimes cause a significantdrop in resistance, almost certainly related to the tran-sitions, a phenomenon known as ‘resistive switching’.This phenomenon is the focus of intense research in ap-plied physics, because it holds promise as a candidate forvarious innovative applications, such as resistive memo-ries [2–6], optoelectronics [7–19] and neuromorphic com-puting [20–37].Despite the intensive interest and numerous experi-mental studies, however, the fundamental understandingof the mechanism behind volatile resistive switching re-mains incomplete over the long term. Although Jouleheating has been considered to play invariably a signif-icant role, it is sometimes nontrivial whether resistiveswitching is solely triggered by Joule heating [38–46] or∗ tetsuaki.itou@rs.tus.ac.jpinfluenced also by electronic effects [47–49]. One rea-son for this uncertainty is that resistive switching hasbeen studied mainly in inorganic thin films with complexparameters, which complicate the Joule heating effect,making it difficult to accurately interpret experimentalobservations in such systems. For example, while thesharpness of the MIT has been identified as a criticalparameter in resistive switching caused by Joule heat-ing [41, 43, 45, 46, 50], most of the inorganic thin filmsstudied so far exhibit resistance ratios (Rins/Rmetal) ofno more than five orders of magnitude, as well as distri-butions of the transition temperature (∆Tc) [38, 39, 41–46, 48, 50–53]. In addition, it has been proposed thatsmaller heat dissipation makes resistive switching eas-ier to achieve [43, 46], and also that excessively strongheat dissipation makes the switching phenomena stochas-tic and thus unpredictable [43]. Therefore, it is desiredto study the switching phenomena in systems with lowheat dissipation. However, most investigations to datehave been conducted on thin films on substrates, wherestrong dissipation to the substrate is inevitable.Under these circumstances, we present an experimen-tal elucidation of the volatile resistive-switched state in-duced by an applied electric current in a bulk systemexhibiting an extremely sharp MIT, aiming to establish arobust foundation for understanding resistive switchingcaused by Joule heating and to re-evaluate the underly-ing behavior of the resistive-switched state under a sharpMIT and low heat dissipation. The material of focus isthe quasi-one-dimensional organic conductor (d7-DMe-DCNQI)2Cu (Fig. 1(a)-(d)), which exhibits an extremelyarXiv:2608.19864v1  [cond-mat.str-el]  20 Aug 2026https://arxiv.org/abs/2608.19864v121 mmDHCD3CD3ND CD3CD3CCNNHNcabbca(e) (f)(d)(a) (b) (c)(d7-DMe-DCNQI)2CuVO2 thin filmV2O3 thin film-20 -10 0 10 2010-310-210-1100101102103T-Tc (K)Normalized RVO2, 320 KV2O3, 135 K0 41 2 310-210-1100101102103104105106107SdownSdownSdownSup(d7-DMe-DCNQI)2Cu9.62 K(d7-DMe-DCNQI)2Cu66.1 KP/ Ω (W mm-3)I (mA)FIG. 1. Structure and transport properties of (d7-DMe-DCNQI)2Cu. (a) Molecular structure of (d7-DMe-DCNQI)2Cu. The d7means that the seven 1H sites are substituted with deuterons. (b) (d7-DMe-DCNQI)2Cu structure viewed down the c-axis. Thespace group is I41/a, and the structure consists of planar DCNQI molecules stacked along the c-axis. (c) (d7-DMe-DCNQI)2Custructure viewed down the a-axis. In the insulating phase, the threefold superlattice occurs along the stacking axis. The chargeordering at the Cu sites follows a Cu+ Cu+ Cu2+ pattern. (d) Photograph of needlelike crystals of (d7-DMe-DCNQI)2Cu.(e) T − Tc dependence of the normalized resistance for VO2 and V2O3 thin films and (d7-DMe-DCNQI)2Cu. The normalizedresistance represents the sample resistance divided by the center value of the hysteresis loop, and T −Tc denotes the differencebetween the sample temperature and the hysteresis midpoint temperature. (f) Current dependence of power (I × V ) dividedby volume, representing Joule heating per unit volume, for VO2 and V2O3 thin films and (d7-DMe-DCNQI)2Cu. Sdown andSup represent the switching points when the current is decreased and increased, respectively. The data in panels (e) and (f) forthe VO2 and V2O3 thin films were obtained by extracting values from Ref. [50].sharp 1st-order MIT at 79 K [54–56]. In addition, thesample used in this study is a bulk crystal rather than athin film on a substrate.The family of DCNQI (N,N′-dicyanoquinonediimine)compounds provides a wide platform for studying suchMITs in organic conductors. Their electronic statesare highly tunable by chemical substitution or exter-nal pressure. For instance, the non-deuterated (DMe-DCNQI)2Cu remains metallic down to low temperatures,whereas deuteration of the DCNQI molecule or the ap-plication of slight pressure induces a sharp first-orderMIT [54–56], which is considered to be caused by a syn-ergetic mechanism involving both the Mott and Peierlstransition natures [57, 58]. This sensitivity to isotopicsubstitution and pressure reflects the delicate balancebetween electron correlation and lattice effects in thismolecular system, making the DCNQI family an idealframework for exploring correlation-driven transitions.In this study, we focused on (d7-DMe-DCNQI)2Cu, inwhich seven of the eight 1H sites in the DCNQI moleculeare replaced by deuterons, as shown in Fig. 1(a).The sample in this study exhibits a metallic phaseabove 79 K with a two-wire resistance of ∼10 Ω, andan insulating phase below 78 K, where the resistance ex-ceeds the measurement limit of 1 MΩ, showing an enor-mous ratio Rins/Rmetal > 105. More importantly, thetransitions on heating and cooling occur within ±0.5 Ktemperature range, and the hysteresis loop is approxi-mately ±1 K (Fig. 1(e)). This sharp transition contrastswith transitions observed in inorganic thin films in whichresistive switching has been studied so far. For exam-ple, VO2 and V2O3 thin films typically have a transi-tion temperature distribution ∆Tc ranging between ±20K [38, 43, 46, 48, 50, 51, 53]. A more significant pointis that the sample in this study is a bulk crystal withouta substrate. In this situation, heat dissipation outside3the sample occurs through the surrounding He gas fortemperature control and through the wiring for electriccurrent application. Consequently, the dissipation is sig-nificantly lower, much weaker than that in thin films onsubstrates. Indeed, Joule heating per unit volume in theresistive-switched state of this study, which balances heatdissipation, is more than five orders of magnitude smallerthan that in the resistive-switched states of VO2 andV2O3 thin films, as shown in Fig. 1(f). The present studyseeks a paradigm shift to uncover phenomena occurringunder low heat generation/dissipation, in which resistiveswitching takes place under minimal current density andthe Joule heating is unequivocally responsible for the re-sistive switching.From the perspective of fundamental physics, the low-resistance state under an electric current after resis-tive switching is nothing but a ‘dissipative structure’,where the strong nonlinearity in the relationships be-tween flows and forces (corresponding to negative dif-ferential resistance in the context of resistive switching)induces spinodal-like decomposition in nonequilibriumsteady states [59–61]. In the field of resistive switching,this phenomenon has been discussed in terms of spon-taneous ‘filament configuration’ or ‘current constriction’,where metallic current filament forms within an insulat-ing background [38, 40–46, 48, 50, 51, 53, 60–62]. Wedemonstrate that such spatial self-organization is indeedrealized even in the present bulk sample under appliedelectric current, using NMR techniques, which can pro-vide microscopic information throughout the bulk sam-ple and also can measure the internal temperature of thesample.II. RESULTSA. Experimental setupDue to the sharp MIT and low heat dissipation in thepresent sample, the spatial self-organized state can beachieved with a relatively small current density. Con-sequently, the self-organized state is stabilized in thepresent sample down to an ambient temperature of ab-solute zero with an application of only a 2.0 mA current(corresponding to a current density of ∼10 A/cm2). Thissmall current density ensures that the electronic effect isnot active and that the resistive switching is governedby the Joule heating mechanism. Note that, due to thenearly infinite Rins, this state cannot be realized exper-imentally by applying an electric voltage (up to 210 Vin our experimental setup) to the insulating state. In-stead, we achieved the state by cooling the sample witha constant current applied, from temperatures above thetransition temperature of 79 K, where the metallic stateis realized. We later show through microscopic NMR re-sults that the state obtained in this process is indeed aspatially self-organized state, which can be considered aresistive-switched state, similar to those obtained by ap-～～ ～～VHe gasGold wirePTFE tubeSampleCurrent source Load resistorVolt multimeter78 kΩCoilCarbon pasteMagnetic fieldcabFIG. 2. Schematic of the experimental setup for resis-tance and 1H-NMR measurements on a bulk single crys-tal of (d7-DMe-DCNQI)2Cu. The crystal dimensions are0.13 × 0.13 × 6.3 mm3. The sample was placed in a Teflontube, around which an NMR coil was wound, and a mag-netic field of 2.62 T was applied approximately perpendicularto the c-axis. To apply an electric current, two gold wires(φ 15 µm) were attached to the crystal edges using carbonpaste. The measurements were performed using a currentsource (Keithley 2450) with a 78 kΩ resistor to stabilize thenegative differential resistance state.plying an electric voltage under constant ambient tem-peratures in previous studies.Figure 2 illustrates the setup for resistance and 1H-NMR measurements on a bulk needlelike single crystalof (d7-DMe-DCNQI)2Cu (see the Appendix for details).In this configuration, the sample was not mounted on asubstrate, and heat dissipation occurred through the goldwires and He gas (∼ 0.7 atm) filling the sample cham-ber, resulting in minimal heat dissipation. The ambi-ent temperature was measured using a resistance sensor(Cernox), located a few centimeters from the sample.B. Resistance under applied currentFigure 3(a) shows the ambient temperature depen-dence of the two-wire sample resistance (defined as sam-ple voltage divided by applied current, V/I) under theinfinitesimal current limit (equilibrium conditions, 0.001mA and 0.01 mA below and above the transition temper-ature, respectively) and with constant currents applied(current values: 0.3 mA, 0.5 mA, and 2.0 mA). The dataunder equilibrium conditions were collected during bothheating and cooling processes, while the data under con-stant currents were obtained only during cooling process.Under equilibrium conditions, a sharp and significantresistive jump was observed, as reported in earlier stud-ies [54–56]. As stated in the introduction, the resistance42.0 mA0.5 mA0.3 mAEquilibrium conditions50 60 70 80 90 100100101102103104105106R (W)10-310-210-1100101102ρ (W cm)Tambient (K)10-310-210-1100101102ρ (W cm)0 50 100 150 200Tambient (K)100101102103104105106R (W)SdownSdown(d7-DMe-DCNQI)2Cu9.62 K(d7-DMe-DCNQI)2Cu66.1 K0.0 2.00.5 1.0 1.50255075100125150V (V)I (mA)(a) (b)FIG. 3. Transport properties of (d7-DMe-DCNQI)2Cu. (a)Ambient temperature dependence of the resistance of (d7-DMe-DCNQI)2Cu. The black plot shows the two-wire resis-tance under equilibrium conditions, while the other plots showthe two-wire resistance under applied constant currents (0.3mA, 0.5 mA, 2.0 mA). The inset shows the behavior of the re-sistance around the transition temperature. The data underequilibrium conditions are the same as the black data shownin Fig. 1(e). (b) Two-probe I(current)–V (voltage) character-istics at 9.62 K and 66.1 K for (d7-DMe-DCNQI)2Cu. Sdownindicates the switching points when the current is decreased.These data yield the current dependence of power (I×V ) perunit volume shown in Fig. 1(f).ratio between a metal and an insulator under equilibriumconditions is generally regarded as a critical parameter inresistive switching. As shown in Fig. 1(e), in the presentsystem (d7-DMe-DCNQI)2Cu, the resistance ratio is no-tably large, and the transition is much sharper comparedto those in VO2 and V2O3 thin films. (We note thatthe comparison in Fig. 1 is made with thin-film data ofVO2 and V2O3, whose transitions are generally broaderthan those of bulk single crystals. Single-crystal VO2 andV2O3 exhibit much sharper transitions [63].)The data under constant currents exhibit gradual in-creases in resistance below the transition temperature (79K), which sharply contrasts to the high resistance in theinsulating state under equilibrium conditions. The re-sistance then abruptly switches to the insulating state at67.8 K under 0.3 mA, and 12.0 K under 0.5 mA. Notably,the intermediate resistance is stabilized down to zero am-bient temperature under 2.0 mA. This intermediate re-sistance indicates that a non-equilibrium steady state isrealized in the sample under these currents, analogousto the resistive-switched states discussed in prior stud-ies investigating the effects of current/voltage applica-tion under constant ambient temperatures. Indeed, whenthe current is reduced under a constant ambient tem-perature, drastic resistive switching behavior is observedin the I(current)–V (voltage) characteristics, as shown inFig. 3(b). Note that, once the resistance switches to theinsulating state, the intermediate resistance state can-not be re-established by increasing the voltage, even upto 210 V. However, after heating the sample above thetransition temperature and subsequently cooling it downfollowing the same procedure, the same intermediate re-sistance state can be reproduced. In the present sample(b)(a)0.0 0.5 1.0 1.5 2.0 2.5 3.00.11.01-M(t)/ M(∞)Metallic state79.3 K, under 0 mA Insulating state 69.9 K, under 0 mAIntermediate resistance state66.1 K, under 2.0 mAEquilibrium conditions, under 0 mANon-equilibrium conditions, under 2.0 mAIntermediate resistance state0 50 100 150 200Tambient (K)10-1100101102T1-1 (s-1)t (s)FIG. 4. 1H-NMR relaxation curves and relaxation rate (T−11 )of (d7-DMe-DCNQI)2Cu. (a) 1H-NMR relaxation curves forthe metallic and insulating states under 0 mA, and the inter-mediate resistance state under 2.0 mA. The black solid curvesrepresent fits to single-exponential functions for the metallicand insulating states, while the red solid curve represents afit to a double-exponential function for the intermediate re-sistance state under 2.0 mA. The excellent fit of the double-exponential function provides evidence for the coexistence ofthe metallic and insulating phases in the intermediate resis-tance state. (b) Ambient temperature dependence of T−11 un-der 0 mA (equilibrium conditions) and under 2.0 mA (inter-mediate resistance state). T−11 under 2.0 mA is decomposedinto two relaxation components via the double-exponentialfitting shown in (a). The dashed black line indicates the Kor-ringa relation (T−11 ∝ Tambient) expected for the metallic stateunder equilibrium conditions.geometry, the maximum applied voltage of 210 V cor-responds to an electric field of ∼300 V/cm, under whichswitching from the insulating state back to the intermedi-ate resistance state could not be achieved. Reducing thecrystal size allows access to higher electric fields and mayenable switching from the insulating to the intermediate-resistance state.C. 1H-NMR under applied currentTo discuss whether the intermediate resistance stateunder current is indeed a spatially self-organized statethat can be considered a volatile resistive-switched state,we performed 1H-NMR measurements, which provide mi-croscopic information on the bulk sample.Figure 4(a) illustrates the 1H-NMR relaxation curvefor the intermediate resistance state realized under 2.0mA at 66.1 K. For comparative analysis, the figure alsopresents the relaxation curves for the metallic (79.3 K)and insulating (69.9 K) phases under equilibrium condi-tions. In the metallic and insulating phases, the relax-ation curves exhibit nearly single-exponential behaviors,ensuring that the system is indeed in a single uniformphase. The relaxation time (T1) in the insulating phaseis more than an order of magnitude faster than that inthe metallic phase, which is due to localized spins as-sociated with the Mott nature [64]. In the intermedi-50-100 10050-50Fast relaxationcomponentSlow relaxationcomponentShift from 111.755 MHz (kHz)0.10.0 0.5 1.0 1.5 2.5 3.02.0t (s)1-M(t) / M(∞)0-100 10050-50Metallic state79.3 K,  under 0 mAInsulating state69.9 K,  under 0 mAIntermediate resistancestate66.1 K,  under 2.0 mAShift from 111.755 MHz (kHz)(a) (b)1.0Intensity (arb. units)Intensity  (arb. units)FIG. 5. 1H-NMR spectra of (d7-DMe-DCNQI)2Cu. (a) 1H-NMR spectra of the metallic and insulating states under 0mA, and the intermediate resistance state under 2.0 mA. (b)Decomposed 1H-NMR spectra of the intermediate resistancestate. The fast relaxation component corresponds to the spec-trum that recovers within 0.25 s after the saturation combpulses, while the slow relaxation component corresponds tothe spectrum that recovers after 0.25 s.ate resistance state, contrastingly, the relaxation curveis not a single exponential but is described by a double-exponential function, wherein the slow and fast relax-ation times align with those of the metallic and insulat-ing phases, respectively. This result suggests that, in theintermediate resistance state, spatial coexistence of themetallic and insulating phases occurs. Figure 4(b) illus-trates the ambient temperature dependence of the fastand slow relaxation rates (1/T1) in the intermediate re-sistance state realized under 2.0 mA, in comparison tothose in the metallic and insulating phases under equi-librium conditions. The two values of 1/T1 in the in-termediate resistance state are virtually independent ofambient temperature over the entire temperature range,corresponding to the 1/T1 values for the metallic and in-sulating phases near the transition temperature.Figure 5(a) shows the 1H-NMR spectra of the interme-diate resistance state under 2.0 mA, as well as those ofthe metallic and insulating phases (detailed data on theambient temperature dependence of the spectra are pre-sented in the Supplemental Material [65]). The spectrumof the intermediate resistance state combines characteris-tics of both the metallic and insulating phases. As shownin Fig. 5(b), the fast relaxation component matches thatof the insulating phase, whereas the slow relaxation com-ponent coincides with the metallic phase. This resultfurther provides clear support for the spatial coexistenceof the metallic and insulating phases in the intermediateresistance state under current; taking into account theintermediate resistance, metallic current filament formswithin an insulating background.D. Effect of the Joule heatingTo investigate the effect of Joule heating, we measuredthe sample temperature influenced by the applied cur-Equilibrium conditions, under 0 mANon-equilibrium conditions, under 2.0 mA0 20015050 100Tambient (K)050100150200Tsample (K)0 20015050 100Tambient (K)0.00.20.41.00.80.6Intensity (arb. units)TMIIntermediateresistance stateFIG. 6. Ambient temperature dependence of the 1H-NMRsignal intensity, which is inversely proportional to the sampletemperature. The black closed circles represent the intensityunder 0 mA, while the open red circles represent the intensityunder 2.0 mA. The intensity under 0 mA exhibits inverse pro-portionality with ambient temperature (black dashed line),demonstrating that the sample temperature is equal to theambient temperature. In the region where Tambient > 79 K(TMI), the intensity under 2.0 mA is the same as that un-der 0 mA, indicating that the sample temperature is equalto the ambient temperature even under 2.0 mA. However, itremains nearly constant in the region where Tambient < 79 K(red dashed line), demonstrating that the sample temperaturein the intermediate resistance state is kept nearly constant.The inset shows the ambient temperature dependence of thesample temperature, estimated from the NMR signal inten-sity.rent as a function of ambient temperature. The sampletemperature was estimated not through optical surfaceimaging, often used in thin-film research, but rather via1H-NMR signal intensity, which reflects the average tem-perature across the bulk sample, as it is essential to ac-quire temperature information for the entire bulk.Figure 6 illustrates the ambient temperature depen-dence of the 1H-NMR signal intensity, defined as theintegral of the Fourier-transform spectrum over the en-tire frequency range. In general, NMR signal intensityis proportional to the inverse of the sample temperature,as described by Curie’s law, independent of whether thesystem is metallic or insulating. Thus, the NMR inten-sity can serve as a probe of the sample temperature. Asshown in the figure, the intensity under equilibrium con-ditions is proportional to the inverse of the ambient tem-perature. This result demonstrates that the sample tem-perature under equilibrium conditions is identical to theambient temperature, as expected. Above the transi-tion temperature (79 K), the intensity under a currentof 2.0 mA also follows this proportionality, indicatingnegligible Joule heating. However, below the transitiontemperature, the intensity remains almost constant, re-69.62 K17.9 K27.3 K36.8 K46.5 K57.6 K66.1 K(a) (b)(c)0.0 2.00.5 1.0 1.5020406080100I (mA)P (mW)9.62 K17.9 K27.3 K36.8 K46.5 K57.6 K66.1 K0.0 2.00.5 1.0 1.50255075100125150I (mA)V (V)P (mW)020406080Tambient (K)0 8020 40 60FIG. 7. Transport characteristics at different ambient temper-atures. (a) I(current)–V (voltage) characteristics at differentambient temperatures. The data were measured by decreas-ing the current in 0.01 mA steps. The abrupt increases involtage upon decreasing the current correspond to switchingto the insulating state. (b) I–P (calculated as I × V ) char-acteristics at different ambient temperatures. (c) Ambienttemperature dependence of P in the intermediate resistancestate. The dashed line serves as a guide to the eye, represent-ing P ∝ (79 K−Tambient)gardless of the cooling of the ambient temperature. Thisresult clearly demonstrates that, in the intermediate re-sistance state, the average sample temperature is sig-nificantly increased from the ambient temperature byJoule heating. The average sample temperature, thoughslightly reduced at low ambient temperatures (details arediscussed in the Supplemental Material [65]), is almostlocked to the transition temperature, as shown in theinset of Fig. 6.E. Applied current dependence of the sampletemperatureTo explore phenomena caused by the temperature lock-ing effect discussed in the previous section, we returnto the transport properties. Figure 7(a) shows the I–V characteristics of the intermediate resistance state atseveral ambient temperatures, measured by decreasingthe applied current. At each ambient temperature, theintermediate resistance state exhibits negative differen-tial resistance and switches to the insulating state at lowcurrent.In the intermediate resistance state, remarkably, thevoltage and current exhibit an inverse proportional rela-tionship, V ∝ 1/I, which can be termed ‘inverse Ohm’slaw’. This is explicitly shown in Fig. 7(b), where thepower (I×V ) remains constant in this region, regardlessof the applied current. Here, we discuss the underlyingmechanism behind ‘inverse Ohm’s law’. When the sam-ple temperature is locked, heat dissipation outside thesample—determined by the difference between the sam-ple and ambient temperatures—remains invariant as longas the ambient temperature is unchanged, regardless ofthe applied current. In addition, since the intermediateresistance state is a steady state, the following relation-ship holds: (Joule heating) = (Heat dissipation). Thus,in the state with the sample temperature locked, Jouleheating, which balances with heat dissipation, must re-main at a fixed value to maintain the sample tempera-ture, independent of the applied current. This scenarioexplains the observation of ‘inverse Ohm’s law’ shown inFig. 7. In this regime, the current filament thickens withincreasing applied current and thins with decreasing cur-rent, as required to maintain a nearly constant level ofJoule heating.Figure 7(c) shows the ambient temperature depen-dence of P (= I×V ) in the intermediate resistance state.When the ambient temperature is decreased, the heatdissipation increases owing to the increase in the differ-ence between the ambient temperature and the sampletemperature (almost fixed around the transition tem-perature of 79 K), and consequently, Joule heating re-quired to achieve the intermediate resistance state in-evitably increases. This explains why the heat generation(P = I ×V ), or the proportionality factor of the ‘inverseOhm’s law’, systematically increases as the ambient tem-perature decreases, following P ∝ (79 K−Tambient), asshown in Fig. 7(c). This increase in the proportionalityfactor with cooling is most likely caused by the thinningof the current filament. Figure 8 illustrates the ambienttemperature dependence of the volume fraction of themetallic phase in the intermediate resistance state underan applied current of 2.0 mA, estimated from the fractionof the slow relaxation component in the 1H-NMR relax-ation curves. This figure demonstrates that decreasingthe ambient temperature reduces the volume fraction ofthe metallic phase, consistent with the scenario of currentfilament thinning.III. DISCUSSIONAs discussed in Fig. 6, the 1H-NMR intensity remainsalmost constant in the intermediate resistance state. Weinterpret this nearly constant NMR intensity as evidencethat the average sample temperature is almost lockedaround the transition temperature. Note that the NMRintensity reflects the spatially averaged temperature ofthe entire sample, and thus local variations may exist—for example, the metallic filament could be hotter than730 806040 50Tambient (K)70020406080100Volume Fraction (%)FIG. 8. Ambient temperature dependence of the volume frac-tion of the metallic phase in the intermediate resistance stateunder an applied current of 2.0 mA. The volume fraction isestimated from the fraction of the slow relaxation componentin the 1H-NMR relaxation curves.the surrounding insulating regions. However, as dis-cussed below, such temperature gradients are expectedto remain modest in the present system because of theextremely weak heat generation and dissipation per unitvolume. (In this sense, the “temperature locking” refersto the locking of the average sample temperature, ratherthan complete thermal uniformity throughout the sam-ple.)We propose that this “temperature locking” arisesfrom the two extreme conditions of the present system,as detailed below. One condition is the intense and sharpMIT—characterized by a high Rins/Rmetal > 105 withina narrow transition temperature range of ∼1 K. This en-sures that, in the intermediate resistance state, where themetallic and insulating phases coexist, the temperatureat the well-defined boundaries between the two phasesshould be precisely maintained at the transition temper-ature of 79 K. The other condition is weak heat dissipa-tion outside the sample, thereby resulting in weak heatgeneration (Joule heating) per unit volume. In princi-ple, the temperature in the metallic phase, where Jouleheating occurs due to current concentration, should behigher than the boundary temperature (79 K), while thetemperature in the insulating phase, where no Joule heat-ing occurs, should be lower than the boundary temper-ature. However, in the present bulk system in a He gasenvironment, the thermal coupling to the surroundingsis expected to be much weaker than that within the sam-ple. Thus, the heat transfer process “from the insulatingbackground to the surroundings” is much less efficientthan the process “from the metallic filament to the in-sulating background”. This results in minimal temper-ature variations across the sample. Therefore, the tem-peratures in the metallic and insulating regions do notdeviate significantly from the boundary temperature of79 K, as demonstrated by the nearly constant NMR in-tensity shown in Fig. 6. (Indeed, the metallic and in-sulating 1/T1 values in the intermediate resistance stateHighLowTMIAmbient temperatureAmbient temperatureLowHighsamplesampleHighLowTMILowHighabSchematic of conventional inorganic thin films on substrates with broad MITs Schematic of the expected 2D cross-sectional view for the present bulk organic system Current density Local temperatureCurrent density Local temperatureFIG. 9. Schematic figures of the current density and localtemperature distributions for a current filament in volatileresistive-switched states dominated by Joule heating. (a)Schematic for conventional inorganic thin films on substrateswith broad MITs and substantial heat dissipation to the sub-strates. (b) Schematic of the expected 2D cross-sectional viewfor the present bulk organic system with a sharp MIT and lowheat dissipation outside the sample.shown in Fig. 4 appear almost constant as a function ofthe ambient temperature. Because the intrinsic temper-ature dependence of the metallic 1/T1 should obey theKorringa relation (1/T1 ∝ Tsample), the nearly constantvalue of the metallic 1/T1 implies that the metallic fila-ment is not heated far above the transition temperature.)These two characteristics keep the average sample tem-perature in the intermediate resistance state close to thetransition temperature of 79 K, as shown in the rightpanel of Fig. 9(b). Note that under these small temper-ature variations, the sharp MIT in the present systemensures drastic current-density concentration, as shownin the left panel of Fig. 9(b). This temperature lockingstands in striking contrast to the wide temperature dis-tribution (Fig. 9(a)) expected in conventional inorganicthin films with broad MITs and substantial heat dissipa-tion to substrates. As discussed previously, this distinctthermal behavior gives rise to the fundamental physicalphenomenon of ‘inverse Ohm’s law’. Our finding of tem-perature locking also provides a strategy for developingdurable resistive switching devices—namely, a directionalapproach to prevent local overheating, which can some-times destroy them.In summary, we clarified the nature of the intermedi-ate resistance state induced by applied current—regarded8as a volatile resistive-switched state—in a bulk organicMIT system under extreme conditions. This clarifica-tion was achieved through resistance measurements and1H-NMR measurements that provide information on thebulk state across the sample. The extreme conditions—the intenseness/sharpness of the MIT and weak heatgeneration/dissipation—lead to two effects: (1) lockingthe sample temperature to the transition temperatureand (2) ‘inverse Ohm’s law,’ an inverse proportional rela-tionship between V and I. These findings provide a solidfoundation for understanding resistive switching drivenby Joule heating and pave the way for developing moreefficient resistive switching technologies.ACKNOWLEDGMENTSThe authors thank T. Fusamae, Y. Sonobe, T. Sek-izawa, and H. Mori for experimental assistance and fruit-ful discussions at the early stage of this project. Thiswork was supported in part by KAKENHI (Grant Nos.22H01184, 19H01852, and 18H05225) from Japan Societyfor the Promotion of Science (JSPS), and Japan Scienceand Technology Agency (JST) CREST (Grant No. JP-MJCR23A1), Japan.Appendix: MethodsSample preparation. The single crystals of (d7-DMe-DCNQI)2Cu were prepared from d7-deuteratedDMe-DCNQI and CuI by the diffusion method in an ace-tonitrile (CH3CN) solution. A number of fine needlelikecrystals, with typical dimensions of 0.1 × 0.1 × 5 mm3,were obtained, as shown in Fig. 1(d).Details of experimental setup for resistance and1H-NMR measurements. Figure 2 illustrates thesetup for resistance and 1H-NMR measurements on abulk needlelike single crystal of (d7-DMe-DCNQI)2Cu.The crystal has dimensions of 0.13×0.13×6.3 mm3, andboth measurements were performed on the same crystalusing the same experimental setup. To perform the 1H-NMR measurements, the sample was placed in a Teflontube, around which an NMR coil was wound. A magneticfield of 2.62 T was applied approximately perpendicularto the c-axis. To apply an electric current, two gold wires(φ 15 µm) were attached to the crystal edges using carbonpaste. The current was supplied using a constant currentsource (Keithley 2450) with a voltage limit of 210 V, anda 78 kΩ resistor was connected in series with the sampleto stabilize the negative differential resistance state.1H-NMR measurements. The 1H-NMR measure-ments were conducted at a magnetic field of 2.62 T,within an ambient temperature range of 7.72–205 K. 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The experimental setup is described in the Appendix of the main text.Under equilibrium conditions (Fig. S1(a)), single peak spectra were observed in the metallic phase above 79.3 Kbecause the magnetization induced by the applied magnetic field, and consequently the internal magnetic fields on the1H nuclei caused by the magnetization, are negligibly small in the metallic phase. By contrast, in the insulating phasebelow 78.3 K, the spectra show splitting because the induced magnetization and the resulting internal magnetic fieldson the 1H nuclei become pronounced owing to the appearance of localized spins. The magnetization, and consequentlythe splitting width, increase according to Curie’s law with decreasing temperature. Below 7 K, the spectrum becomesbroad due to antiferromagnetic long-range ordering. These results are consistent with a previous 1H-NMR study [64].Under non-equilibrium conditions with an applied current of 2.0 mA (Fig. S1(b)), when the ambient temperature isabove the transition temperature (79 K), the spectra show single peaks, identical to those under equilibrium conditions.By contrast, when the ambient temperature is below the transition temperature and the intermediate resistance stateis realized, the spectra deviate from those under equilibrium conditions. In this region, the spectra show broadeningowing to the appearance of the insulating phase. However, spectral splitting is ambiguous, indicating that the localsample temperature in the insulating phase is somewhat distributed. Even when the ambient temperature is decreasedto absolute zero, almost the entire spectral range remains within −30 kHz to 60 kHz, indicating that the local sampletemperature remains above ∼50 K almost everywhere, even in the region with the lowest local temperature.To investigate the distribution of the local sample temperature, we analyzed the spectrum of the intermediateresistance state at 38.5 K (Fig. S2(b)). We reconstructed the spectrum by summing the spectra of the insulating phaseunder equilibrium conditions at 75.5 K, 65.7 K, and 56.1 K (Fig. S2(a)). Overall, the spectrum of the intermediateresistance state at 38.5 K closely resembles that of the insulating phase under equilibrium conditions at 75.5 K,indicating that the local temperature over most of the sample in the intermediate resistance state is nearly fixed atthe transition temperature. However, upon closer inspection, the spectral width of the intermediate resistance stateat 38.5 K (75 kHz) is somewhat broader than that of the insulating state at 75.5 K (55 kHz), indicating the presenceof slightly lower-temperature regions than 75.5 K. Thus, we incorporated the broader spectra at 65.7 K and 56.1 Kinto the spectrum at 75.5 K to reconstruct the spectral shape of the intermediate resistance state at 38.5 K (Notethat the volume fraction of the metallic phase at 38.5 K is ∼6%, as shown in Fig. 8 of the main text; therefore, itscontribution to the spectrum is negligible.) The summed spectrum, created by adding the normalized spectra at 75.5K, 65.7 K, and 56.1 K with an integrated-intensity ratio of 2 : 1 : 1 (corresponding to a volume fraction ratio of 2.69 :1.17 : 1), successfully reproduces the spectrum of the intermediate resistance state at 38.5 K, as shown in Fig. S2(b).This result indicates that the local temperature over most of the sample is fixed around the transition temperature,but the local-temperature distribution extends slightly toward lower temperatures across the sample. This is likely thereason for the observation that the averaged sample temperature is slightly reduced from the transition temperaturewhen the ambient temperature decreases, as shown in Fig. 6 of the main text.12Intensity (arb. units)Intensity (arb. units)205 K175 K146 K126 K104 K85.1 K79.3 K78.3 K77.3 K75.5 K74.1 K71.8 K69.9 K66.1 K56.7 K38.5 K46.1 K29.6 K21.7 K11.9 K7.72 K-200 200150100500-50-100-150Shift from 111.755 MHz (kHz)(b)204 K175 K146 K126 K104 K88.0 K79.3 K78.3 K77.5 K75.5 K74.1 K71.6 K69.9 K65.7 K56.1 K36.6 K44.5 K26.8 K19.8 K9.93 K6.54 K-200 200150100500-50-100-150Shift from 111.755 MHz (kHz)(a)Equilibrium conditions, under 0 mA Non-equilibrium conditions, under 2.0 mAFIG. S1. Ambient temperature dependence of the 1H-NMR spectra of (d7-DMe-DCNQI)2Cu. The black lines represent thespectra above the transition temperature of 79 K, while the red lines represent those below the transition temperature. (a)Spectra under equilibrium conditions without an applied current. (b) Spectra under non-equilibrium conditions with an appliedcurrent of 2.0 mA.Intensity (arb. units)(a)0-100 10050-50Shift from 111.755 MHz (kHz)(b)0-100 10050-50Shift from 111.755 MHz (kHz)Insulating stateunder 0 mA75.5 K65.7 K56.1 K×2×1×1++Intermediate resistancestate38.5 K,  under 2.0 mASummed spectrum75 kHz55 kHzFIG. S2. Reconstructed 1H-NMR spectrum of the intermediate resistance state. (a) 1H-NMR spectra of the insulating phaseunder equilibrium conditions without an applied current at 75.5 K, 65.7 K, and 56.1 K. The integrated intensities are normalizedto be the same. (b) Reconstructed spectrum (red line), obtained by summing the three spectra in (a) with an integrated-intensityratio of 2 : 1 : 1 (corresponding to a volume fraction ratio of 2.69 : 1.17 : 1), and the observed spectrum (black line) of theintermediate resistance state under 2.0 mA at 38.5 K. The reconstructed spectrum well reproduces the observed spectrum.