Spinristor: A Spin‐Filtering Memristor

In this paper, an in silico proof of concept of a spinristor is proposed and provided; a new electronic component that combines a spin‐filter and a memristor in a single molecule, useful for in‐memory processing. It builds on the idea of an open‐shell transition metal ion enclosed within an elliptical fullerene connected to a pair of electrodes. The spin‐ and electronic‐polarization induced by the enclosed open‐shell metallic ion leads to differential rectification of the electrons at low voltages applied between the source–drain electrodes, VSD. The position of the encapsulated ion can be switched by a high VSD which leads to a change in the direction of the rectification and the spin‐filtering ratio. The system can thus be used as a switching rectifier, that is, a memristor and a spin‐filter; therefore, a spinristor. The effect of different linkers on the function of the proposed device is further analyzed to show that linkers reduce the overall conductivity by an order of magnitude, but improve the spin‐filtering ratio. The computations suggest that nitrile and isocyanide linkers enhance the rectification, too. To the best of the authors’ knowledge, spinristor has no macroscopic counterpart in electronics, so far.


Introduction
The holy grail of molecular electronics [1][2][3][4][5][6] is the miniaturization of electronic circuits by replacing macroscopic circuit components with single molecules featuring similar functions. After the insightful lecture of Richard Feynman, "There is plenty of room at the bottom," [7] Aviram and Ratner introduced the first examples of molecular devices; molecular diodes. [8] In subsequent years, various molecular devices from simple wires, [9] rectifiers, [8,10] and switches [11,12] to more complicated DOI: 10.1002/aelm.202300360 transistors [13] and memristors [14][15][16][17][18][19] have been proposed, fabricated, and some already commercialized. [20] So far, the general trend in the realm of molecular electronics has been replicating macroscopic circuit components on the nanoscale level. However, molecular electronics can do better. Here, we use in silico multiscale modeling to propose the first example of a molecular circuit component, that so far has no equivalent in the macroscopic world; we coin it spinristor. The spinristor is a circuit component that combines the functions of a memristor [21,22] and a spin-filter. Alternatively, considering the memristor as a combination of a resistor/switch and a rectifier as proposed by Abraham, [23] the spinristor can be defined as a circuit component combining the functionalities of a switch, a rectifier, and a spinfilter. We foresee a spinristor in spintronics as a counterpart to a memristor in ordinary electronics, that is, a spinristor is an active circuit element that can control spin conductivity in a spintronic circuit.  To choose the ideal computational level (see Supporting Information) the performance of BLYP, [25][26][27] B3LYP, [25][26][27][28] PBE, [29,30] PBE0, [29][30][31] TPSS, [32] TPSSH, [32,33] and B97D3 [34,35] density functional theory (DFT) functionals together with def2-SVP or def2-TZVP [36,37] basis sets and Grimme's empirical dispersion (D3) correction was evaluated, [34] Figure S1, Supporting Information. Spin state ordering was further evaluated using the CASSCF, [38] CASPT2, [39] and MC-pDFT [40] results obtained using the Open-Molcas 22.10 [41] software, Table S1, Supporting Information. Based on the calibration, the calculations presented in this paper were done at PBE0-D3/def2-SVP level. The most abundant isolated-pentagon rule D 5h (1)-C 70 cage was used in studies. The effect of the oriented external electric field (EF) on the energy and structures of the species was studied by applying uniform EF along the main D 5 axis of symmetry of C 70 . A second EF perpendicular to the initial EF, as it was implemented under the Field option of the Gaussian 16 software, was applied to model a gate voltage effect on the energy and geometry. Energy profiles corresponding to the translation of titanium ion inside C 70 were studied both by minimum/transition state computations and also by relaxed PES scan approaches to catch all possible minima, Figure  S10, Supporting Information.
To perform NEGF computations the systems were dissected into three regions, which consisted of a scattering region and two semi-infinite electrodes (Figure 1). No direct interaction between the electrodes was considered. The Au (001) surface of a bulk gold structure was selected to utilize the electrodes. Each electrode consisted of five and four gold layers in sequence, and a single Au atom as the tip of the electrode. The optimized system was embedded between two gold atoms at the tips of the electrodes via the -carbon atoms of the fullerene. Five possible connection modes were considered; see Figure S4, Supporting Information. The distance between the tip and the -C was fixed to 2.33 Å which was the optimized bond length of -C-Au at the PBE [29] /DZP [42] computational level as described elsewhere. [15] DFT-coupled non-equilibrium Green's function (DFT-NEGF) computations using generalized gradient approximation (GGA) functional developed by Perdew, Burke, and Ernzerhof (PBE) [29,42] combined with double-polarized basis set as implemented in SIESTA suite of programs were used for all electron transport computations. [43] The energy cut-off was set to 300 Ry for the real space grid. Γ points for sampling were used for the first Brillouin zone in the molecular region and 10 × 10 × 100 Monkhorst-Pack k-point grid for the nanowire electrodes. [44,45] All the transport properties were carried out for the applied voltage in the range of ±1 V.

Design Strategy
To design a functional spinristor, one may employ known molecular memristors and tune them to sustain spin-filtering properties. Thus far known molecular devices with memristive properties can be classified under three main groups: 1) organic molecules which undergo bond-breaking/forming processes, [12,17,46] 2) transition metal complexes (TMCs) whose conductivity changes upon spin-crossover or redox processes, [14,18,19] and 3) endohedral fullerenes. [15,16,47] While the relevant organic systems have a closed-shell electronic structure that rules out spin-filtering properties, the TMCs can, hypothetically, enable spin-filtering, if the employed transition metals have an open-shell electronic structure. However, to the best of our knowledge, the spin-filtering properties for experimentally studied TMC memristors have neither been reported experimentally nor predicted theoretically. This might be the result of the conductivity of the reported devices being measured by gold, not by magnetically active electrodes. In the present study, we simulate our model systems in between gold electrodes to verify their intrinsic spin-filtering properties.
The endohedral metallofullerenes seem to offer the functionalities needed for molecular spinristors. Our idea of a molecular spinristor consists of a transition metal ion enclosed in a fullerene cage, here D 5h (1)-C 70 , that is connected to two or four electrodes, Figure 2. The primary function of the proposed spinristor is spin-filtering at low temperatures, where spin flipping does not occur and when a low potential between source and drain electrodes, V SD , is applied, Figure 2a,b. The spinfiltering arises from the spin-polarized electronic structure of the M@D 5h (1)-C 70 , vide infra. When the V SD and/or the gate voltage, V G , increase to certain values, the energy barrier for the relocation of the enclosed metal atom reduces (Figure 2c,d) while the energy barrier for the reverse process remains substantially high. Switching leads to an abrupt change in the overall conductivity of the system similar to a memristor, [15] but in the spinristor the spin-filtering ratio also changes. Overall, the proposed system should function as a switching diode and a spin-filter or a spinfiltering memristor, or a spinristor for short.
The so-far experimentally reported EMF-based switching molecular components typically remain functional at temperatures near absolute zero because their switching barri- ers are rather low. [16,48,49] This stems mainly from the quasiisotropic nature of the fullerene interior and the largely ionic (i.e., non-directional) character of the metal-cage bonding. [50,51] For example, the Gd@C 82 molecular electret operates with a barrier of ≈0.25 kcal mol −1 (11 meV) at 1.6 K, [16] and Li@C 60 , a multistate molecular switch in STM experiments, works at 5 K. [52] A recent EMF-based memristor, fabricated by Sc 2 C 2 @C s (hept)-C 88 proved to be functional at room tempera-ture, but long-time storage of data via EMFs is not achieved yet. [47] A functional switch should ideally have an energy barrier equal to or higher than 50 k b T in its operational temperature. This value at the working temperature of present-day computers translates to a comparatively large switching barrier of about 35-38 kcal mol −1 . [53,54] If the energy barrier halves, the year-long stability reaches the day-long range. [54] Nevertheless, a low-barrier species can still be used for operations that do not require the long-term stability of the states as proved recently. [47] To ensure a sufficiently large switching barrier in the proposed spinristor, we arrived at two model EMFs, Ti@D 5h (1)-C 70 and Zr@D 5h (1)-C 70 , with respective 13.9 and 32.8 kcal mol −1 fieldfree (intrinsic) switching barriers according to PBE0/def2-SVP computations [55] (see Experimental Section). We utilized the facts that group 4 to 6 elements are known to form strong polarcovalent bonds to carbon atoms [56,57] and that D 5h (1)-C 70 fullerene has an elliptical non-isotropic shape with distinct binding sites for the selected metal atoms (Figure 2f). The proposed systems should combine reasonable switching barriers with spinpolarized electronic structures because of the enclosed metal, which brings in the spin-filtering function. For Zr@D 5h (1)-C 70 , our computations suggest that this system is not suitable for becoming a spinristor, as the ground state is a closed-shell singlet. Therefore, here we keep the discussion in the main text limited to the Ti@D 5h (1)-C 70 system while all data regarding the Zr@D 5h (1)-C 70 are collected in Supporting Information.
We should emphasize that the proposed molecules have not been synthesized so far and serve as models here. However, a few analogous systems from group 4 of the periodic table have been experimentally observed. In particular, Hf@C 84 has been isolated [58] and Ti@C n (n = 28, 80, 90), as well as Zr@C28, have been detected in mass-spectroscopy experiments. [59,60] As a general guide to fullerene chemists, we propose that any elliptical or asymmetric fullerene with an endohedral metal possessing an open-shell electronic configuration and at least two interconvertible geometric isomers could serve as a spinristor. The D 5h (1)-C 70 cage here is chosen as the smallest energetically stable model of elliptical systems.

Results and Discussion
DFT computations using hybrid-GGA PBE0 functional predict the ground-state local minimum structure (LM1/LM1´in Figure 2f) of Ti@C 70 to be an open-shell triplet. The PBE0/def2-SVP level was selected based on the method calibration discussed in the Supporting Information. This level has also been found to be an accurate and cheap option in our recent study. [55] The position of the metal can switch between LM1 and LM1′ as the metal atom passes through the cavity of the cage to the other side, Figure 2f. To switch between the local minima, the Ti atom in the C 70 cage must pass through the respective TS which is computed to be 13.9 kcal mol −1 higher than LM1, Figure 2f. An intermediate, labeled LM2, 12.7 kcal mol -1 above LM1 forms when the Ti atom is midway to the other side of the cage. The transition states between LM1/LM1′ and LM2, (TS/TS′), are all triplet ground states in the gas phase for Ti@C 70 , Figure S1, Supporting Information. Please note that while LM1 and LM1′ are identical, once they are inside an electric circuit they differ from each other because of the intrinsic polarity of the molecule with respect to the voltage polarity. The titanium is trapped in the Ti@C 70 as a Ti(IV) ion, based on the localization index computations, see Table S3, Supporting Information. [61,62] A quadruple cation strongly polarizes the fullerene cage and in practice converts it to a p-n junction inside the circuit. The polarity of this diode depends on the position of the Ti inside the cage with respect to the polarity of external voltage.
Controlling the position of metals inside EMFs by an EEF [15,63] can be realized via scanning tunneling microscopy [48,49,52] or, as recently reported, in a circuit. [16] In principle, an increasing EEF reduces the switching barrier by destabilizing the local minimum structure(s), in which the dipole moment vector of the structure(s) is parallel to and along with the polarity of the applied field, with respect to the TS energy, Figure 2c. Simultaneously, the field stabilizes the local minima with a dipole moment vector against the direction of the externally applied field. Destabilization of one local minimum and stabilization of the other local minimum connected via a TS on a PES reduces the energy barriers between them as is expected from the Hammond postulate. [63] In certain systems, such as the MX@C 70 series studied by us, a gate voltage (perpendicular to the V SD ) was found to be an efficient tool to further reduce the TS energy. [15] However, in the case of Ti@C 70 the gate voltage was found to be inefficient, even inhibitive to lowering the switching barrier, Figure S2, Supporting Information. This could be the result of the proximity of LM1 and TS structures to each other on the PES; thus, any factor that can affect the energy of the TS would also affect the energy of the LM1.
Studying the effect of an EEF on the potential energy surface of Ti@C 70 shows that the switching barrier decreases up to 1.8 V Å -1 , but further increasing the electric field strength has little to no effect on the switching barrier. The switching barrier at 1.8 V Å -1 reaches 4.9 kcal mol -1 from the intrinsic value of 13.9 kcal mol -1 , which corresponds to seven orders of magnitude increase in the switching rate at 300 K according to the Eyring equation. It is worth noting that in our study we employed a uniform electric field that is different from the electric field that is applied by sharp electrodes in a circuit or scanning tunneling spectroscopy experiments. As it has been documented before, sharp electrodes can intensify the electric field by a factor of 10-30. [64] The EEF-control of the position of the Ti atom enables writing/encoding information on the device. To read the encoded information from the device, one can measure transmission through the molecule using a low V SD applied between the source and drain electrodes, Figure 2a. The DFT-NEGF computations predict that Ti@C 70 behaves as a molecular rectifier and a spinfilter at the same time when V SD is applied, as illustrated in Figure 2b. Different connection modes of the fullerene to the electrodes, presented in Figure S3, Supporting Information, lead to moderately different transmission properties, but the resulting I/V curves share similar common features; see Figures S4 and S5, Supporting Information, for the I/V curves of each connection mode. The I/V characteristics reveal that in the studied range the Ti@C 70 -based spinristor in its LM1/LM1′ state/minima moderately (≈70%) filters the current passing through. The maximum rectification for the spin-up, spin-down, and total currents are predicted at different voltages. The rectification of the total current is controlled by the spin-up current. The maximum rectification of both the total and the spin-up currents is predicted to occur at V SD = 0.12 V (RR total Max = 1.54 and RR spin−up Max = 1.83). It is notable that at V SD = 0.12 V, the RR spin−down 0.12 is lower than one for a voltage that has the same polarity as for spin-up current (RR  computations predict that the highest rectification occurs at a low bias voltage of only 0.12 V. This is an advantage for a potential device made of Ti@C 70 because this low bias voltage will only slightly affect the relative energies of LM1/LM1′, that is, it will prevent an accidental "writing" process. The higher the reading voltage, the higher the chance of accidental writing in the memory.
The origin of the spin-filtering and rectification properties can be traced to the electronic structure of the Ti@C 70 molecule, Figure 3. The transmission spectra at selected voltages suggest that the rectification for the spin-up and spin-down electrons arise from the energy shift of both the LUMO-and the HOMOtype MOs.
Connecting Ti@C 70 to a pair of gold electrodes will be more efficient if the fullerene is functionalized by some linkers such as sulfur, cyanide, or isocyanide. [65,66] These linkers, however, can change the relative energy of molecular orbitals in the device and are thus expected to affect the transmission properties of the system. Figure 4 plots the energies of the frontier orbitals in Ti@C 70 , and the most stable isomers of , ′ di-substituted Ti@C 70 (SH) 2 , Ti@C 70 (CN) 2 , and Ti@C 70 (NC) 2 ; see Tables S4-S6, Supporting Information, for the evaluation of the most stable isomers of systems with linkers. Figure 4 reveals that substitution on the cage increases the HOMO-LUMO gap in all species by influencing the energy of singly-occupied molecular orbitals, SOMOs. In particular, the energy of the highest-energy -SOMO in Ti@C 70 falls below that of the highest energy -SOMO in Ti@C 70 (SH) 2 that suggests the latter molecule should be a spin-filter for a reverse spin compared to the unsubstituted Ti@C 70 if HOMO-type MOs participate in conductance. The band gap in nitrile and isocyanide increases further and two energy levels, -SOMO-1, and -SOMO-2, become isolated from their nearest energy levels. This suggests that these two species are more efficient spin-filters if HOMO-type MOs play a role in conductance as they do in case of unsubstituted Ti@C 70 .
Indeed, the NEGF computations confirm the conclusions drawn from our simple MO analysis. The overall conductivity of substituted systems, in particular the dicyano-and diisocyanosubstituted ones, are notably lower than the unsubstituted www.advancedsciencenews.com www.advelectronicmat.de system as a result of the increased band gap, see Figure 5 for the corresponding I/V curves. The rectification in the dicyano-and diisocyano-substituted species is enhanced substantially compared to the parent compound, Figure 2b. NEGF computations suggest that the rectification of Ti@C 70 (NC) 2 reaches a maximum of more than 140 at V SD = 0.28 V. The total current and rectification are mainly controlled by the spin-up current at this voltage. Figure 6 represents the yield of spin-filtering for spin-up electrons within different ranges of applied voltage. In a lowvoltage range, for example, ±0.1 V, where the relative energies of the MOs are not expected to change, dicyano-and diisocyano-substituted systems behave as significantly more efficient spin filters than the unsubstituted Ti@C 70 . On the other hand, Ti@C 70 (SH) 2 is not an efficient spin-filter compared to Ti@C 70 (CN) 2 and Ti@C 70 (NC) 2 .

Conclusions and Prospects: Looking for the Spinristors on a Macroscopic Scale
In summary, employing in-silico calculations we proposed, designed, and provided a proof of concept of the function of a molecular spinristor, which is-to the best of our knowledgea circuit component reported neither in the realm of molecular nor macroscopic electronics. The spinristor behaves like a combination of a spin filter and a rectifier at low voltages and low temperatures where the spin polarization of a single molecule can be conserved. At higher voltages, the "polarity" of the rectifier switches similar to a memristor by the relocation of the encapsulated metal ion, here Ti. Our design utilizes M@C 70 molecules connected to two electrodes, a source, and a drain. The spinfiltering originates from the open-shell electronic structure of the system which involves a metal ion with half-filled d-orbitals when attached to a pair of electrodes. The rectification of the molecule is the result of the metal encapsulation that polarizes the MOs of the fullerene, like a molecular memristor, [15] while here, in addition, spin-up and spin-down orbitals are polarized differently. Finally, the switching stems from the conversion between the two most stable configurations of the endohedral metallofullerene, where the metal ion is near the polar region of the elliptical C 70 cage. According to the NEGF computations, functionalization by electron-withdrawing groups such as cyano-and isocyano-improves the rectification and spin-filtering properties of the molecule significantly.
As mentioned above, the concept of spinristor, unlike other circuit components, is for the first time theoretically predicted for a single-molecule device. However, this does not rule out the possibility of finding spinristive materials on a macroscopic scale. Contemporary experimental memristors are often composed of halides or chalcogenides of metals and semi-metals. [67] Possibly, magnetic halides or chalcogenides of magnetic metals may open a way to the fabrication of macroscopic scale spinristors. Such materials may combine the ion-mobility of the memristive materials with the magnetic properties of their bulk to represent the spinristive behavior. Presently, we are not aware of any studies in this direction.

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