Lithium doped graphene as spintronic devices

Generating spintronic devices has been a goal for the nano-science. We have used density function theory to determine magnetic phases of single layer and bilayer lithium doped graphene nanoflakes. We have introduced graphene flakes as single molecular magnets, spin on/off switches and spintronic memory devices. To aim this goal, adsorption energies, spin polarizations, electronic gaps, magnetic properties and robustness of spin-polarized states have been studied in the presence of dopants and second layers. We find that for bilayer SMMs with two layers of different sizes the highest occupied molecular orbital and the lowest unoccupied molecular orbital switch between the layers. Based on this switch of molecular orbitals in a bilayer graphene SMM, spin on/off switches and spintronic memory devices could be achievable.


Introduction
Today, parallel to the developing of technology, molectronic, i.e. molecular electronic, is an avenue for search towards finding new applications of materials on a scale where quantum mechanics dominates electron kinetic behaviour [1,2]. Meanwhile, single molecular magnets (SMMs), magnetic molecules with stable magnetization at room temperature, have a special role [3][4][5][6][7]. SMMs could be used as ferromagnetic materials (FM) which are the basis of spintronic devices, spin amplifiers, and those devices which magnetically store information at a molecular level. When a current passes through a SMM, the current will be spin polarized as do a spin amplifier. A very high spin polarized current with its magnetization parallel to the SMM magnetization flows for a time equivalent to the relaxation time (giant spin amplification) [8,9].
For large currents, this process can lead to a selective drain of spins with one orientation from the source electrode, thus transfer a large amount of the magnetic moment from one lead to the other [4].
The high coherence time, the absence of conformational changes, weak spin-orbit and hyperfine interactions of carbon (C) atoms make the development of carbon based SMMs more desirable [4,10]. Meanwhile, the hexagonal arrangement of carbon atoms in two dimensions, graphene based materials, have a special role. The low efficiency of the spin relaxation, for manipulated bilayer graphene up to a nanosecond [11][12][13], the scalability of the total spin, and its stability up to room temperature for single layer graphene render graphene as an excellent candidate for spintronic devices; such as spin memories, transistors, and qubits [14][15][16][17]. Furthermore, it has been proved that magnetic graphene nano-flakes (GNFs) hold the promise of an extremely long spin relaxation and decoherence times, with weak coupling between electron spins, and longrange magnetic order [18]. It is noteworthy that GNFs transport properties could be changed with the application of the electric [19] and magnetic fields [20], additional layers [21], and by controlling its geometry [22][23][24][25].
From the theoretical part of view, it is found that boron and nitrogen zigzag and armchair doped graphene nanoribbons could be FM [26]. Moreover, it is predicted that ZGNRs have a magnetic insulating ground state with FM ordering at each zigzag edge and antiparallel spin orientation between the two edges [27][28][29]. In addition, it has been predicted that the edge effect is of great importance for spin related properties of GNRs [30]. While, there are not many cases studied doped magnetic properties of GNF, especially for the case of bilayer ones. Consequently, the study of these SMMs is a missing part of molectronic [31]. Here, we have considered this part of theoretical study to plan a better magnet which makes better contacts with leads and wires in a circuit, or to give suggestions for isolating a material which works better at room temperature.
Furthermore, control of unidirectional logic flow, preservation of the intrinsic properties for nondestructive readout of the spin states are all open issues [31]. We have determined a reasonable correlation between the quantum interference picture and orbital interaction pictures. The orbital view provides a better understanding of the intermolecular transport phenomena and connects the analysis of the wave function to the intuitive quantum interference effects [32], what we try to study in this article.
Furthermore, different methods have been developed to create graphene components with different shapes, sizes, and edge states [33][34][35][36][37][38]. Nano cutting, electro-beam lithography [39,40] or C 60 transformation [41], heat-induced fractionalization of graphite [42], heat-induced conversion of nanodiamonds [43,44] and silicon carbide [45], unzipping of carbon nanotube [46] are some methods to produce GNFs in laboratories. Furthermore, bilayer graphene could be defined by topgates [47], and it could be produced asymmetrically by use of an epitaxial growth method [48]. Consequently, the ability to modify the electronic properties of finite-size graphene by varying their size, shape, and edge orientation or defects is an important part of graphene based molectronic researches. While, a range of experiments from charge detection in bilayer GNFs and observation of spin states in GNF [20,49] to observation of excited states in quantum dots [50,51] all indicate that the spintronic devices based on the GNF are reachable by modern nano-scale fabrication methods.

Systems Geometry and Computational Details
In this article, properties of single layer (Fig.1) and bilayer (Fig.3), Lithium (Li)-doped hexagonal shaped GNFs have been studied. Because of the predicted important role of alkalimetal decorated graphene [52] and specially Li [53,54] we have used this element. The considered Li doped GNFs are also Hydrogen (H) terminated, in order to remove the effect of dangling bonds.
In the present work, we use whole-electron broken symmetry and first principles DFT calculations. The basis is 6-31g* and the hybrid exchange-correlation functional is B3LYP [55, 56] employing the Gaussian 03 software package [57] to verify the existence of the magnetic phases. The goal is answering some key questions about doped graphene magnetic properties.
First, the robustness of the spin-polarized states will be studied in the presence of both impurities and of a second layer. The answer to this question is not only scientifically interesting for better understanding of the physical mechanism of spin polarization in hexagonal nanoflakes, but also it has important technological implications in the reliability of doped hexagonal nanoflake as a new class of SMM for spintronic materials [31]. Second, the author will discuss how the magnetic structures of hexagonal nanoflakes change with the size of layer, how it acts compare and what are magnetic properties of bilayer hexagonal GNFs. Furthermore, band gaps, and magnetization of graphene flakes have been calculated as a function of second layer, and adsorbed Li distance from the centre of the flake. In addition, to study the graphene magnetization and its applications, molecular orbital theory will be employed. Finally, based on results of this study, some suggestions for the graphene based spintronic amplifier, the spin on/off switch, and the spin based memory device will be determined.

Single layer GNFs
In this section, we have studied 13 doped GNFs (  Orbital (HOMO-LUMO) gap of some of these flakes have been studied before [59]. However, these properties for a larger group of Li doped graphene have been studied here. Flakes 5, 6, and 9 are newly considered flakes; the new results are consistent with results in Ref. [59].
According to Ref. [59], edge states are generally more stable. Here, this result has been confirmed for a larger group of Li doped graphene. To describe it in detail, according to the table.1, flakes NO.5 and NO.6, which have a Li atom nearer to edges, have adsorption energies which are, respectively, -0.024 and -0.0234 eV; more than flakes NO.3 (-0.017) and 4 (-0.017eV). In addition, for flake NO.9, the adsorption energy (-0.025eV) is slightly red shifted relative to flakes NO. 10 to NO.12 (-0.026, -0.032 and -0.032eV), while this flake has more adsorption energy relative to flake NO.7 and NO.8 (-0.023 and -0.024eV) whose adsorbent is nearer to the edge.
Concerning spin polarization, the single electron of a Li atom breaks the symmetry between spin up and spin down states. As is clear in Fig. 2, all doped graphenes with one Li atom are FM [15] while the last one, which is a flake doped by two Li atoms, is NM. The NM flake does not have any localized spin polarized states even at the edges. While the ultimate goal of the use of graphene in the next generation electronic is to realize all-graphene circuits with functional devices built from graphene layers or graphene flakes [30,60], graphene doped Li has an additional advantage. It is possible to build a unique circuit of both FM and NM phases by use of Li-doped graphene. Because they have the same hexagonal carbon structure, excellent connections in a circuit are predictable.
For a better spin polarized current conduction, to join in a circuit, a contact group should be attached to localised orbitals [61]. As it is shown in Fig.1, in flakes with Li adsorbed on the edge, where spin polarization is localized, the middle part has less spin polarized regions, especially when the Li atom is adsorbed on a carbon ring which has two H atoms as the first neighbours.
When, the Li atom is adsorbed on a symmetry line pass through those benzene rings with two Hydrogen atoms in both sides, around this line, distribution of spin up density is stronger than spin down density (so that spin up states in the centre make a tunnel-like spin up zone). As for the gap, all of the flakes doped by one Li atom are spin polarized and the alpha gap is red shifted by increasing of the flake size; as is the beta gap. To describe it in detail, according to Fig.1, the alpha gap for flakes NO.5, 6 and 9 are 1.02, 0.97, 0.68eV, respectively. While, the beta gaps are 2.67, 2.68 and 1.97eV, respectively. Consequently, our results confirm previous results about gap change according to flake size and the distance from the edge states [59].
Because of the different spin distribution population through surface of flakes, each flake has different FM properties. It is noteworthy that the difference between the highest spin polarization and the lowest spin polarization of C atoms has been selected as a factor to evaluate the flakes spin polarization (table 1).  SMM NO.12 is the best candidate for gigantic spin amplification and SMM applications.
Consequently, SMMs and similarly giant spin amplifications are achievable by use of GNFs.
However, the possibility of having a better room temperature spin amplifier based on even larger graphene flakes is predictable.

Bilayer Graphene Flakes
In the next step, to consider effects of an additional layer on magnetic properties of GNFs, a second layer has been added to single layer flakes. These bilayer structures have been arranged according to the number of C atoms and the Li distance from the centre (Fig.3). According to for these flakes have been gathered in Fig.3 and table2. It is worthy to mention that, because DFT is based on whole electron calculations, the radius of the largest-considered monolayer GNF is larger than that of the studied bilayer GNFs.    In addition, according to Fig.3, similar to monolayer cases, if a Li atom is adsorbed in a ring which has two H atoms or Li is on a symmetry line passing through such a ring, a tunnel of spin polarized density is visible in the SMM. Consequently, those benzene rings with two H atoms at the edge are the best sections to make contacts, because those states have a strong concentration of spin up. In addition, a tunnel of spin polarized regions happens in that vicinity.

Application Suggestions for spin amplifiers
As mentioned earlier, Li-doped single layers are generally better FM than bilayer graphenes and consequently those are better amplifiers. However, bilayer GNFs, the second layer could be managed for appropriate ferromagnetism and spin polarization. Between all bilayer, GNFs those which have a higher amount of adsorption energy and larger spin polarization are preferable for use as spintronic amplifiers. Consequently, the author suggests flakes 22 and 24 as spin amplifiers, because these flakes have both high spin density and high relative stability. The spin polarization of these bilayer GNFs is near to similar single layer GNFs.
The effect of temperature on adsorbed Li, at room temperature (270 < T < 400 K), is that Li atoms fall in the boundary condition [62]. GNFs are SMMs and room temperature spin amplifiers. In addition, if we consider bilayer GNF as an amplifier, this type of amplifier will act even better at higher temperature. In fact, because of the migration of Li and benzene ring to the edge, the spin polarization and the stability of GNFs increase generally. However, the study of managing edge states, of adsorbent type to increase spin density and whether more odd numbers of Li atoms increases spin polarization needs more research.

Spintronic on/off switch based on Li doped bilayer
Molecular orbitals (MOs) are conduction channels for electrons. These channels could be obstructed (localized) or not (delocalized); and simultaneously, those could be occupied by electrons or not. Any factor which changes this occupation allows us to tailor the electrical behaviour of the molecule [61]. MOs for GNFs are conducting channels; conversely, a nonconducting channel is a localized MO, which cannot connect both ends of the molecule attached to metallic contacts. Furthermore, shapes of frontier molecular orbitals explain qualitatively the conduction of electrons through molecules attached to macroscopic contacts [61]. Based on this analysis, the author suggests a structure similar to Fig.5 for applications in the field of a single electron on/off switch. According to Fig.5, bilayer GNFs which have layers of different sizes and a Li atom at the centre or an edge could act as a single electron on/off switch. In such a SMM, HOMO concentration is on the larger flake, while the LUMO concentration is on the smaller one. Such a switch of molecular orbitals between layers happens because of the repulsive effect of H atoms. It is worthy to mention that this structure stability and spin polarization in comparison with all other GNFs is high as discussed before. In addition, to have a single electron on/off switch for spintronic purposes, contacts should be added to the larger surface which has stronger magnetic properties and it is a stronger spin amplifier. Furthermore, based on table 2 and Fig.5, it is predictable that this type of switch will have a high on/off ratio because of the low covering effects of two doped layers with different size. However, this ratio will be decreased by the movement of Li atom to the edge of a SMM at higher temperatures (Fig.3).

Memory devices based on Li doped bilayer
According to Fig.5, when an electron transfers to the LUMO state of the depicted SMMs, there is no MO on the larger surface. This could be defined a "0" state for memory. On the other hand, when there are no electrons in the HOMO level, the probability of existence of electron in smaller surface is zero. This effect could be defined as a "1" digit for a relative memory device.
According to Fig.5, for HOMO-2, HOMO-1, HOMO, LUMO, LUMO+1 and LUMO+2 such a switch of states is the same as for HOMO-LUMO states. Consequently, it is predictable that in such a bilayer SMM one layer will be responsible for conduction. Consequently, conduction channels switch between two layers and this up and down states could be used to define a memory device. Consequently, the author suggests the usage of bilayer graphene SMM as a memory device, as well. predictable to act better as spin amplifiers. In addition, graphene SMMs which have different size could act as an on/off switch and better amplifiers. In such flakes, spin polarized MO switches between layers. Accordingly, the switch of molecular orbitals between layers could be defined as "0" and "1" states for molecular memory devices. Based on this point, the usage of bilayer SMMs as a memory device has been suggested.
immensely grateful to Dr. Edward McCann for his precious comments on an earlier version of the manuscript.