Spinristor: A Swiss Army Knife of Molecular Electronics

Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno, Czech Republic CEITEC – Central European Institute of Technology, Masaryk University, Kamenice 5/C4, CZ–62500 Brno, Czech Republic Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, Flemingovo nám. 2, CZ–16610, Prague, Czech Republic Faculty of Science, Charles University, Albertov 2038/6, Prague 2, 128 43, Czech Republic Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland


What is a spinristor?
The holy grail of molecular electronics [1][2][3][4][5][6] is the miniaturization of electronic circuits through replacing circuit components with single molecules with 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 starting from simple wires, 9 rectifiers, 8,10 and switches 11,12 to more complicated transistors 13 and memristors [14][15][16][17][18][19] have been proposed, fabricated, and some even commercialized. 20 So far the general trend in molecular electronics has been replicating macroscopic circuit components on a nanoscale level. However, molecular electronics can do better. Here, we use in silico multiscale modeling to devise 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 spinfilter. 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 functionality of a switch, a rectifier, and a spin-filter.

Design of molecular spinristors
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, 12,17,24 (2) transition metal complexes (TMCs) whose conductivity changes upon spin-crossover or redox processes, 14,18,19 and (3) endohedral fullerenes. 15,16 While the relevant organic systems have a closed-shell electronic structure that rules out spin filtering properties, the TMCs can, hypothetically, enable spin-filtering properties, if the transition metals in their ground electronic state 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 theoretically. 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 C70-D5h(1), that is connected to four electrodes, Fig. 1. The primary function of the proposed spinristor is spin-filtering when a low potential between source and drain electrodes, VSD, is applied, Figs. 1ab. The spin-filtering arises from the spinpolarized electronic structure of the M@C70, vide infra. When the VSD and the gate voltage, VG, increase up to a certain threshold, the enclosed metal atom relocates to a different position Fig. 1c and 1d, in an electric-field-driven switching process. This leads to a change in the overall conductivity of the system akin to a memristor, 15 but, in the spinristor, also the spinfiltering ratio changes. Overall, the proposed system will function as a switching spin-filter or a spin-filtering memristor, shortly spinristor.
The so-far experimentally reported EMF switching molecular components typically remain functional at temperatures near absolute zero because their switching barriers are rather low. 16,25,26 This stems mainly from the quasi-isotropic nature of the fullerene interior and largely ionic (i.e. non-directional) character of the metal-cage bonding. 27,28 For example, the Gd@C82 molecular electret operates with a barrier of ca 0.25 kcal/mol (11 meV) at 1.6 K, 16 and Li@C60, a multistate molecular switch in STM experiments, works at 5 K. 29 Should the switch work in realistic data storage and processing, it should ideally have an energy barrier equal to or higher than 50kT, which turns to a comparatively large switching barrier of about 35-38 kcal.mol −1 at the working temperature of the present-day computers. 30,31 If the energy barrier halves, the year-long stability reaches the day-long stability. 31  (1). Averaged values for various connections of the system to electrodes. Note that the absolute values are reported here for the current for a more clear view of the spin asymmetry of the passing current, ISD. (e) 3D representation of a spinristor. The position of the enclosed metal can be controlled through a quadrupolar field, applied via source, drain, and a pair of gate electrodes that are separated from the fullerene by two layers of an isolator material that fixes the elliptical fullerene in its position between source and drain electrodes.
To ensure a sufficiently large switching barrier in the proposed spinristor, we arrived at two model EMFs, Ti@C70-D5h(1) and Zr@C70-D5h(1), that show field-free barriers for relocation of their metal of 16.6 and 23.0 kcal.mol −1 , respectively. We utilized the fact that group 4 to 6 elements are known to form strong polar-covalent bonds to carbon atoms 32,33 and that C70-D5h(1) fullerene has an elliptical non-isotropic shape with distinct binding sites for the selected metal atoms. The proposed systems should combine reasonable switching barriers with spin-polarized electronic structures because of the enclosed metal, which brings in the spin-filtering function. However, in the case of Zr@C70, our computations predict that the external electric potential does not decrease the switching barrier to a level to be applicable in a real device. The Zr@C70 can still function as a spin filter. Therefore, we keep the discussion in the main text limited to the Ti@C70-D5h(1) system while all data regarding the Zr@C70 are collected in SI.
We note that the proposed molecules have not been synthesized so far and serve as models here. Nevertheless, a few analogous systems have been experimentally observed. In particular, Hf@C84 has been isolated 34 and Ti@Cn (n=28, 80, 90), as well as Zr@C28, have been detected in mass-spectroscopy experiments. 35,36 Proof of concept; computations predict Ti@C70-D5h(1) to function as a molecular spinristor Density functional theory (DFT) computations using B97D3 functional predict the ground-state local minimum structure (LM1/LM1´) of Ti@C70 to be a closed-shell singlet, with the lowest triplet state at just 3.5 kcal.mol -1 above it, Fig. 2a. The closed-shell singlet groundstate may seem to contradict the spin-filtering function. However, when connected to the electrodes the triplet is the ground state of the system. In LM1, the metal is connected to the interior of the fullerene cage in the electron-rich polar region. 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. To switch between the local minima, the Ti@C70 has to pass through the respective transition state (TS) that is computed to be 16.6 kcal.mol −1 higher than LM1, and LM2, (TS/TS′), is a triplet in the gas phase for Ti@C70. Therefore, an intersystem crossing occurs while the metal switches its position, Fig. 2b. For simplicity, we consider switching between LM1 and LM1′. It can be safely assumed that when the applied external electric field (EEF) is strong enough for LM1 to pass through TS, the system will not stop at LM2 as the barrier between LM2 and TS′ is notably smaller than the one between LM1 and TS on the potential energy surface (PES) of the molecule, Fig. 2a. Controlling the position of metals inside EMFs by an EEF 15,37 can be realized via scanning tunneling microscopy 25,26,29 or, as recently reported, in a circuit. 16 In principle, an increasing EEF reduces and eventually removes the energy barrier for switching by destabilizing the local minimum structures, in which the dipole moment vector of the structures are parallel to and along with the polarity of the applied field, Fig. 1c. 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 it is expected from the Hammond postulate. 37 Additionally, the application of a quadrupolar field via the gate electrodes reduces the energy barrier further by manipulating the energies of TS/TS′ or the intermediate LM2, directly; see Fig. 1d. We found that destabilizing LM2 is a more efficient way to achieve LM1′ from LM1 than stabilizing TS/TS′.
We define the switching EEF as the field(s) (dipolar or quadrupolar) that is large enough to change the nature of a local minimum structure, e.g.LM1, on the PES, to a transition state or a non-stationary point so that the Ti relocates to another minimum position, e.g. LM1′.
A strong and short pulse of an electric potential that is equal to the switching EEF switches the position of the Ti between LM1 and LM1′ within the time scale of a single molecular vibration (within the domain of terahertz) by eradicating LM1 on the PES. 15 The computed switching EEF for Ti@C70 is ca 1.75 V.Å -1 in the case of a uniform dipolar EEF in our model (see Fig. 1d. Using electrodes with sharp tips can intensify the electric field locally, and therefore the voltage needed to achieve the switching EEF can be reduced by an order of magnitude or even more. 38 Using a quadrupolar electric field (Fig. 1c) with voltage at the gate electrodes further helps the system to pass through the intrinsic barrier by affecting the energies of LM2 and TS/TS′, Fig. 1d.
The EEF-control of the position of Ti 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 VSD applied between the source and drain electrodes, Fig.   1a. The DFT-coupled non-equilibrium Green's function (DFT-NEGF) computations predict that Ti@C70 behaves as a molecular rectifier and a spin-filter at the same time when VSD is applied, as illustrated in Fig. 1b. Different connection modes, presented in  Fig. 3c, suggest that the contribution of the partially occupied d-orbitals of titanium, which are half-filled due to π-back donation from the carbon atoms to the enclosed titanium atom, is the origin of the spin-filtering properties, Table S1 and The S-functionalized system is a better conductor for the spin-down electrons, it is a more efficient rectifier for the spin-up electrons.

Sulfur linkers strongly affect the spin-filtering function
Sulfur functionalization is a routine approach to fabricate stable molecule-electrode connections via the formation of strong Au-S bonds with the electrodes. Therefore, we further probed the effect of the sulfur functionalization of Ti@C70 on its transmission properties.
Twenty-five possible isomers of dithiol derivate Ti@C70(SH)2 with sulfur atoms attached to the α carbons of the cage were optimized and the transmission properties of the two lowest energy isomers were computed; see Table S2 for the relative energies of the isomers. The S-functionalization does not change the spin-filtering performance of the Ti@C70 system, Fig.   4b. Finally, the spin-and orbital-resolved partial density of states suggest that in the Ti@C70S2 system the spin conductivity is the result of the contribution of the d-orbitals of the titanium atom, Fig. 4c, akin to the parent compound. To perform non-equilibrium Green′s function (NEGF) computations we dissected our systems into three regions, that consist of a scattering region and two semi-infinite electrodes. 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 consists of 5 and 4 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 α-carbon atoms of the fullerene. Five possible connection modes were considered, see Fig. S2. We fixed the distance between the tip and the α-C to 2.33 Å that is the optimized bond length of α-C-Au at PBE 47 /DZP 48 computational level as described elsewhere. 15 DFT-NEGF computations using generalized gradient approximation (GGA) functional developed by Perdew, Burke, and Ernzerhof (PBE) 47 as implemented in the TranSiesta package 48 combined with double-ζ polarized basis set as implemented in Siesta suite of programs were used for all electron transport computations. 49 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 1×1×100 Monkhorst-Pack k-point grid for the nanowire electrodes. 50,51 All the transport properties were carried out for the applied voltage in the range of ±1 V. The electron distribution through the main eigenchannels, that is the expectation value of the eigenchannels greater than 10 -5 , were analyzed using Tomáš Belloň for providing the TOC graphics.

Author Contributions
EFB and AJ contributed equally to this work. EFB, ZB, and LT performed NEGF calculations. AJ and LT performed electric field calculations. EFB and CFN provided the initial idea. CFN and MS have coordinated the project and participated in writing.

Table of contents graphics
A metallofullerene can act as a molecular electronic component that enables switching between two distinctly different spin-filtering functions.