An experimental demonstration of the memristor test
000 (2021) 1–4
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An experimental demonstration of the memristor test
Yuriy V. Pershin a, ∗ , Jinsun Kim a , Timir Datta a , Massimiliano Di Ventra b a Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA b Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
Abstract
A simple and unambiguous test has been recently suggested [J. Phys. D: Applied Physics, , 01LT01 (2018)] to check experimentally if a resistorwith memory is indeed a memristor, namely a resistor whose resistance depends only on the charge that flows through it, or on the history of thevoltage across it. However, although such a test would represent the litmus test for claims about memristors (in the ideal sense), it has yet to beapplied widely to actual physical devices. In this paper, we experimentally apply it to a current-carrying wire interacting with a magnetic core,which was recently claimed to be a memristor (so-called ‘ Φ memristor’) [J. Appl. Phys. , 054504 (2019)]. The results of our experimentdemonstrate unambiguously that this ‘ Φ memristor’ is not a memristor: it is simply an inductor with memory. This demonstration casts furtherdoubts that ideal memristors do actually exist in nature or may be easily created in the lab. Keywords:
Memristor, memristive system, resistance switching memory, inductor, magnetic core
1. Introduction
The question of whether or not the resistance switching cellsare memristors [1, 2] has intrigued the scientific communitysince the early days of the modern ‘memristor era’ [3, 4, 5, 6,7, 8]. By ‘memristor’ it is meant here one whose resistancedepends only on the the charge that flows through it, or on thehistory of the voltage across it [1]. It is then clear that claimsabout the existence and nature of these devices have to rely ona direct and experimental verification of the functional depen-dence of the resistance on either the charge or the flux linkage(time integral of the voltage). However, such a verification hasbeen missing for a long time, thus depriving the scientific com-munity of reliable means to ascertain whether actual physicaldevices are memristors or not.Very recently, two of us (YVP and MD) have allayed this is-sue by introducing a simple memristor test [9]. Moreover, thepresent authors have applied the test experimentally to Cu-SiO electrochemical metallization cells and commercially availableelectrochemical metallization cells (Knowm, Inc.) [10]. Ourexperimental work [10] provides a solid and unambiguous proof that the resistance switching memories are not memris-tors. ∗ Corresponding author
Email addresses: [email protected] (Yuriy V. Pershin), [email protected] (Massimiliano Di Ventra)
However, despite the existence of such an easy experimentaltest, several claims still plague the scientific literature regardingthe ‘discovery’ of ideal memristors. For instance, very recently,an alleged experimental realization of a ‘memristor’ was pro-posed by a group of authors [11]. In that work, it was suggestedthat a current-carrying wire interacting with a magnetic core isa ‘real’ memristor, which the authors called the ‘ Φ memristor’.It is worth noting that in a comment on that paper written bytwo of the present authors (YVP and MD) [12], the claims ofWang et al. [11] were questioned, and serious concerns wereraised about the validity of their results. This resulted in the re-traction of Ref. [11] from the Journal of Applied Physics basedon technical grounds [13]. Such an unfortunate outcome couldhave been easily avoided if the authors of Ref. [11] would availthemselves of the test we had previously suggested. It alsoshows that such a test has yet to be fully appreciated by theresearchers working in the field.The purpose of the present paper is then twofold. First, wewant to implement the memristor test [9] experimentally to clar-ify both how the test can be administered in practice, and, mostimportantly, its simplicity. Second, we apply it directly to theso-called ‘ Φ memristor’ and provide a definitive experimentalproof that the latter is not a memristor. We thus hope our presentpaper may serve as a starting point to carefully apply the sug-gested test, before claims of ‘discoveries’ of such devices aremade. Indeed, the present experimental demonstration, is yet1 a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b
00 (2021) 1–4 another confirmation that memristors, as defined in Ref. [1],may not actually exist in nature, or cannot be built easily inhardware. This paper is organized as follows. In the next Section 2.1 weprovide the description of the memristor test as formulated inRef. [9]. The goal is to apply it to the ‘ Φ memristor’, which wedescribe in Sec. 2.2. In Sec. 2.3, we introduce the electric circuitused in our experiments. Section 3.1 presents the dynamics ofa ‘ Φ memristor’ driven periodically. In Sec. 3.2 we perform thememristor test. In Sec. 4 we o ff er our conclusions.
2. Methods
Let us first introduce the reader the memristor test that wassuggested in Ref. [9]. According to it, to prove or disprove thata given device is an ideal memristor or not, the fundamentalmemristor relation [1] R = R ( q ) (1)needs to be verified. For this purpose, the tested device is con-nected in-series with a capacitor, and the circuit is subjectedto an arbitrary voltage waveform such that the final capacitorcharge equals its initial value (in practice, it is convenient touse the initially discharged capacitor).According to Eq. (1), memristors would return to their ini-tial state, each time the capacitor charge returns to the initialvalue (this is the so-called duality in the memristor-capacitorcircuit [9]). In actual experiments, a su ffi ciently wide range ofvoltage amplitudes and initial states of memristors are neces-sary to prove that the tested device is a memristor. To prove theopposite, a single measurement, in principle, is enough (withinthe operational range of the device).In the next Section, we apply this test to the ‘ Φ memristor’.The only distinctive feature of the present implementation ofthe test is that we will consider the dynamics of magnetiza-tion instead of resistance, since the magnetization is the internalstate variable in the so-called ‘ Φ memristor’. Φ memristor’ To fabricate the ‘ Φ memristor’, one lot of ferrite cores (madeby VEB Elektronik Gera, German Democratic Republic inearly eighties) was purchased on ebay. Scanning electron mi-croscopy (SEM) imaging and energy dispersive X-ray (EDS)analysis were carried out using a TESCAN Vega-3 scanningelectron microscope at the Electron Microscopy Center at theUniversity of South Carolina. Fig. 1(a) presents an SEM imageof the core. The EDS analysis was performed at three di ff erentpoints on the surface with 4.5 kV accelerating voltage. It wasfound that the core is composed of ferrite doped by Mg and Mnatoms (about 4 and 8 atomic percent, respectively). In fact, the closest physical realization of this concept, we are aware of, isthe phase-dependent conductance of a Josephson junction, which is, however,just a component of the junction’s total current [14]. (a)(b) R Φ C AmplifierPulse generator Digitaloscilloscope sw Figure 1. (a) SEM image of the magnetic core. (b) Experimental setup formeasuring the response of the ‘ Φ memristor’. The initial design of the ‘ Φ memristor’ [11] was slightlymodified by increasing the coupling between the magnetic coreand current-carrying wire, and adding a pick-up coil. For thispurpose, two similar coils of three turns each were woundaround the magnetic core using 0.1mm enameled copper wire.The pick-up coil facilitates the reading of the device state: themagnetization reversal events appear as voltage peaks acrossthe pick-up coil. The peak polarity indicates the direction ofreversal. The basic electrical circuit used in our measurements isshown in Fig. 1(b). Here, the standard and arbitrary waveformsare generated by the arbitrary waveform generator (SiglentSDG1025) and amplified by a power amplifier (HP 467A). The‘ Φ memristor’ is connected to the amplifier with the help of acurrent-limiting resistor (47 Ω ) and a capacitor necessary forthe test (0.2 µ F). Two channels of digital oscilloscope (Agi-lent DSO1012A) measure the voltage across the pick-up coiland applied voltage. To simplify the measurements, the test se-quence is applied to the ‘ Φ memristor’ periodically. Some ofour measurements were performed at shunted capacitor (closedstate of the switch, indicated as SW in Fig. 1(b)).We emphasize that the use of current-limiting resistor doesnot undermine the test. As the in-series connected resistor doesnot open any additional charge / discharge channels for the ca-pacitor, the duality between the memristor state and capacitorcharge [9] is conserved. As an alternative argument we notethat the in-series connected resistor and memristor can alwaysbe considered as an e ff ective memristor.2
00 (2021) 1–4 (a) V o lt a g e ( V ) Time ( μ s) x10 (b) V =7 V V =5 V V =4 V V o lt a g e ( m V ) Time (ms) V =3 V Figure 2. (a) Voltage across the pick-up coil (red) for the ‘ Φ memristor’ sub-jected to a triangular voltage waveform (dark green). To perform this measure-ment, the capacitor in Fig. 1(b) was shunted (by closing the switch SW). (b)Voltage across the pick-up coil for several amplitudes, V , of a 5 kHz sinu-soidal voltage waveform.
3. Results Φ memristor’ First of all, we verify the basic functionality of the mag-netic core and compare results to the literature. For this pur-pose, we measure the response of ‘ Φ memristor’ in the circuitof Fig. 1(b) with shunted capacitor. The circuit is driven by asawtooth waveform of V =
10 V amplitude and f =
50 kHzfrequency. Fig. 2 shows a clear magnetization reversal pattern,wherein each reversal event appears as a positive or negativevoltage peak. We note that such peaks are typical in the re-sponse of magnetic core memories (see, for instance, Ref. [15]).Moreover, at smaller voltage amplitudes ( V (cid:46) V (cid:38) q = 0 q = 0 q = 0 x 1 0 Voltage (V)
T i m e ( m s ) V ( t ) V C V p i c k - u p q = 0 Figure 3. Application of the memristor test to the ‘ Φ memristor’. The pick-upcoil curve (bottom) is shifted for clarity. V ( t ) is the applied voltage, V C is thevoltage across the capacitor, and V pick − up is the voltage across the pick-up coil. Φ memristor’ Having established that the response of the ‘ Φ memristor’is typical of magnetic core devices, we are coming now to thequestion of whether or not it is indeed a memristor. If ‘ Φ mem-ristor’ were a memristor, the core magnetization would be itsinternal state variable. Now, a di ffi culty appears: at a constantapplied voltage, the equilibrium resistance of the ‘ Φ memristor’does not depend on the core magnetization, as it is only definedby the wire resistance. This alone already disqualifies the ‘ Φ memristor’ to be a memristor. Nevertheless, we perform thetest focusing on the internal state as the resistance of memris-tors depends on their internal states.The experiment is performed at the open switch SW of Fig. 1.The test sequence consists of periodic asymmetric pulses ( V ( t )curve in Fig. 3). In fact, each pulse (either positive or negative)corresponds to a single test. We emphasize that within a half-period of the test sequence (corresponding to a single pulse)the voltage across the capacitor ( V C curve in Fig. 3) returns toits initial value (the capacitor is fully discharged right beforethe beginning of the next pulse). Therefore, all conditions ofthe memristor test are satisfied [9]. If the tested device were amemristor it should then return to its initial state before the nextpulse.However, V pick − up curve in Fig. 3 shows a dramatically dif-ferent behavior. The magnetization flips to one direction by apositive pulse, and reverses only by the application of the nega-tive one. In other words, the memristor-capacitor duality prop-erty we have mentioned in Sec. 2.1 is not satisfied. Thefore, weconclude that the ‘ Φ memristor’ fails the memristor test, and cannot be described by Eq. (1).We repeated this experiment with several other peak ampli-tudes, and the ‘ Φ memristor’ response was always the same.Therefore, our conclusion is that the ‘ Φ memristor’ is not amemristor.3
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4. Conclusion
Although it should have been evident from the start that acurrent-carrying wire interacting with a magnetic core is sim-ply an inductor, we have nonetheless applied the memristor testsuggested in Ref. [9] to the ‘ Φ memristor’ as an example andto disprove directly the claims in Ref. [11]. The test unambigu-ously demonstrates that such a device is not a memristor. Also,it is important to notice that the deviations of the ‘ Φ memristor’behavior from the memristor model in Eq. (1) are too signifi-cant to be described by small modifications of such an equation.This supports the memristor impossibility conjectures formu-lated in Ref. [10], regarding the di ffi culty of building a modelof physical resistance-switching memories based on the mem-ristor model.Finally, while in this work we have focused on a specific de-vice, the test is general. Indeed, it should be applied to all thosedevices that are declared as ’memristors’, to check the validityof such claims. Acknowledgment
This research was partially supported by an ASPIRE grantfrom the University of South Carolina.
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