Spatially separated spin carriers in three-ports graphene nanoribbons

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Spatially separated spin carriers in three-ports graphene nanoribbons Mingjun Li a,1 , Bowen Zeng a,1 , Jin Xiao b , Can Cao a , Mengqiu Long a,c,∗ a

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School of Physics and Electronics, Central South University, Changsha 410083, China School of Science, Hunan University of Technology, Zhuzhou 412007, China Institute of Low-dimensional Quantum Materials and Devices, School of Physical Science and Technology, Xinjiang University, Urumqi, 830046, China

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Article history: Received 3 July 2019 Received in revised form 4 October 2019 Accepted 10 October 2019 Available online xxxx Communicated by R. Wu

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Keywords: Spin separation Graphene-based spintronic device Square-shaped carbon tetragon Asymmetric edge hydrogenation

Exporting the different spin signals to different ports is of practical importance to graphene-based spintronic devices. In this work, we have designed a three-ports graphene nanoribbon (GNR) device by inserting square-shaped carbon tetragon (CT) into GNR symmetrically, and calculated the magnetic moment distribution and transmission spectrum by using first-principles calculation and quantum transport simulation. Our results show that CT can bring non-equivalent path for two spin transport channels resulting in one spin is easier to transport than the other in each output port. Overall whole model, the spin states would be separated in real space but degenerated in energy. After correcting the device with asymmetric edge hydrogenation, we can achieve spatially separated spin carriers in real space and stable spin transporting. Our results suggest this model can serve as the most basic logic device for applying in future spintronics. © 2019 Published by Elsevier B.V.

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1. Introduction

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The electronic structure and transport properties of nanoscale carbon materials have been the subject of intensive research because of fundamental scientific interest and potential applications in future electronics [1–14]. Among the carbon nanostructures, zigzag graphene nanoribbons (ZGNR), in which the zigzag edge is terminated by hydrogen, has been studied extensively [15–25]. There are peculiar electronic states at each edge of ZGNR, which form a twofold degenerate flat band lying in the Fermi level [15, 26]. Upon inclusion of spin degree of freedom, it has been suggested that the ZGNR have an antiferromagnet insulating ground state (the total spin is zero) with opposite spin orientation across the ribbon between ferromagnetic ordering at each edge [27,28]. Until now, many efforts have been exploited to enrich the degree of freedom in ZGNRs and many intriguing phenomena were predicted, such as conductance depending on nanoribbon symmetry [18], half-metallic conduction [21,29] and valley filtering [30–32]. It should be noted that above-mentioned phenomena mainly focus on charge, spin and valley degree of freedom of electron but pay less attention to spatial degrees of freedom, which is meaningful for practical application. Wang et al. [20] designed

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Corresponding author at: School of Physics and Electronics, Central South University, Changsha 410083, China. E-mail address: [email protected] (M. Long). 1 The authors contributed equally to the work. https://doi.org/10.1016/j.physleta.2019.126058 0375-9601/© 2019 Published by Elsevier B.V.

a ferromagnetic sawtooth graphene nanoribbon, in which charge carriers are not only spin polarized in energy space but also spatially separated at different edge under electric field. However, such spin-semiconducting GNR device still only have one output port, suggesting that if we want to detect one spin signal, it would be affected inevitably by the other spin. Cui et al. [19] designed a topological spin switch in ZGNR by placing square-shaped carbon tetragons (CT) in structure, which can lift the spin degeneracy between the two spin propagation channels. A relatively simple way to understand this spin splitting is distinct difference in spatially transport trajectories for different spin channel. In this study, we have designed a three-ports graphene nanoribbon (GNR) device, where different spin states would be leaded to different ports thus to achieve totally spatially separated spin carriers. Firstly, we constructed a ZGNR superlattice by inserting CT symmetrically. The CT allow that one spin state pass through while suppress the other, and two spin signals would experience separation and meeting each other because of superlattice periodicity. Then we built a device model to study the propagating property of spin spinal. It is found that different spin states are exported to different ports while the magnetic moment spreading length only last about four-length narrowest ZGNR unit cell (ZUC). Without use any external magnetic field, stable spin transport more likely to require ferromagnetic device. At last, we corrected the model with asymmetric edge hydrogenation, and the model can perform perfect spatially separated spin carrier and stable spin propagation. Our results suggested ZGNR-based device can be regarded as a whole logic device which consists of three parts: spin injection,

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Fig. 1. (a) Optimized structure and magnetic moment on site. (b) Band structure, (c) HOMO and (d) LUMO of GNR superlattice. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

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spin processing and spin transport. Meantime, this device is not necessary to take into account contact resistance or Schottky barrier [33,34], which must be considered in the spin injection from metal to semiconductor materials and always are detrimental to device performance. 2. Result and discussion

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The model of the ZGNR superlattice consists of triple five-length ZUC connected by four CT symmetrically, as shown in Fig. 1. The superlattice is periodic along the extending direction. For convenience of description, all models (superlattice and device) in this article are divided into left part (LP) and right part (RP). Note that the RP have two branches, which are right top part (RTP) and right bottom part (RBP), corresponding to the right top and right bottom ZUC chains, respectively. The initial spin state of LP is set as three spin configurations including PM (without spin polarization), FM (ferromagnetic ordering at each edge and parallel spin orientation between both edges) and AFM (ferromagnetic ordering at each edge and antiparallel spin orientation between both edges). After convergenced self-consistent calculation, we can get the total energy and magnetic moment distribution of the ZGNR superlattice. For the ZGNR superlattice, we found that the total energy of PM is 142 MeV higher than FM, which is further stabled by 76 MeV in the AFM. This energy difference between FM and AFM comes from the magnetic tail interaction [28]. In this superlattice, it should be attributed to interaction of the 14 carbon atoms including 10 edge carbon atoms in LP and 4 carbon atoms in CT in the RP. Average per pair edge atoms contribute 11 MeV to the energy loss from FM to AFM. The magnetic moment of each atom has been calculated and added on the superlattice with its spin direction, as shown in Fig. 1(a), where the spin up (down) state is denoted as red (blue) dot or line or region. We can see that the magnetic moment is mainly located on the outer edge of LP and inner edge of RP, and the different spin states are located on opposite edges symmetrically. It is worth noting that the superlattice can create two equivalent spatially trajectories for each spin channel, therefore the total spin is zero and the band structure hold two-folded degeneracy as shown in Fig. 1(b). Nevertheless, Cui et al.’s research [19] has demonstrated that the CT can bring two non-equivalent spatially trajectories resulting in lifting spin degeneracy, and herein,

for the single RTP or RBP, the spin propagation path is not identical for different states, which could lead to one spin state is easier to transport than the other. To better understand the spatially separated spin carriers, we turn to analyze the band-decomposed charge density of the state of the band edge, which is equivalent to the frontier molecule orbitals, i.e., the highest occupied molecular orbital (HOMO) for hole and the lowest unoccupied molecular orbit (LUMO) for electron, as shown in Fig. 1(c, d). The HOMO is spatially confined along an almost straight line, and the distributions of the two spin states are perfect separated, which is consistent with the magnetic moment configuration. Opposite result is found in LUMO, which just swap the location of the spin distribution. And such spin-separated behavior confirms that the CT do well at spin filtering in real space. Furthermore, we built a three electrodes model (TEM) as shown in Fig. 2(a), where the electrode regions are shaded in cyan, the electrode is semi-infinite and the edge carbon atom are terminated by a hydrogen atom. Upon inclusion of the spin, our result shows the AFM configuration is also the ground state with the lowest energy. The AFM spin configuration of central region are shown in Fig. 2(a). Symmetry of spin path guarantee no difference in transmission spectrum as shown in Fig. 2(b). Fig. 2(c, d) shown real-space distribution of local device density of states (LDOS) for the states with the transmission peaks near the fermi level marked by the black circle in Fig. 2(b). We found that the LDOS for the spin up and spin down, regardless of the energy above fermi level or below it, have almost symmetric distribution at both edges. These properties are very similar to that of ZGNR [21]. The benefit of this structure is that the RP have two isolated ports, both of which only support path for only one spin propagation. Around the CT, the spin distribution and the LDOS shows obvious polarized, which is felt by electron. This significant difference directly reflects the spin signals of the two right ports are different. The magnetic moment rapidly decreases when the ZUC is away from CT. This makes sense since the ground state of ZUC is AFM state, the spin splitting caused by CT will decay in diffusion direction. From Fig. 2, it can be estimated visually that the magnetic moment spreading length is about four width of ZUC (almost 1 nm). Furthermore, we built the following three similar models, which gradually increase the width of the right electrode on the TEM. The spin distributions of these models are shown in Fig. 3. It is obvious that the charge density present spin polarization around the CT, even after the width is widened.

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Fig. 2. (a) Optimized structure, (b) transmission spectrum and LDOS of transmission peak at (c) −0.2 eV and (d) 0.24 eV of TEM.

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Fig. 3. (a-c) Spin distribution of three widened TEM.

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If we consider the whole simulation device as a spin logic element, then the LP can be considered as spin input or injection, the CT as spin processing, the RP as spin output. The AFM configuration of the ZGNR is appropriate to be a spin input but not spin output, which require spin transmission reliability. Therefore, the RP is preferably a ferromagnet which is helpful to the transport of only one spin signal. An effective tool to tune magnetism of GNR is that the edge are terminated by different functional groups [35–39], and the ZGNR with asymmetric edge hydrogenation has been reported as a ferromagnetic semiconductor [35,40]. Therefore, we then modulated the TEM with asymmetric edge hydrogenation (ATEM), where one sublattice (corresponding to the two sublattice in graphene) with single hydrogen-saturated edges and the other sublattice with double hydrogen-saturated edges, as shown in Fig. 4. Herein the inner edge of RP and adjacent outer edge of LP belonging to same sublattice are passivated by single hydrogen, and the outer edges of RP are passivated by double hydrogen.

As shown in Fig. 4(a), we can see that the LP remains AFM configuration and the RTP becomes spin up polarization while the RBP spin down polarization, and thus the spin carriers are spatially separated in the RP. Taking one branches of edge (the top edge of LP and RTP) as an example, the transmission spectrum, projected density of state (PDOS) of CT at zero bias are shown in Fig. 4(b). Fig. 4(c) shows the transmission spectrum has four peaks without spin difference in the transmission energy range from −2.0 eV to 2.0 eV. We can find that the valence band of the top edge of LP is dominated by spin up, while its conduction band is dominated by spin down. The RTP has the same spin subband as the LP, and the PDOS of CT follow the spin character of two electrodes, therefore the transmission spectrum exhibit spin difference with spin down (spin up) passing through above (below) the Fermi level. Furthermore, we analysis two transmission peak (black circle in Fig. 4(c) near the Fermi level. The LDOS and corresponding transmission pathway (TMP) are shown in Fig. 5, where the radius of each arrow indicates that the magnitude of electron transmission and the

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Fig. 4. (a) Optimized structure. (b) The band structure of up edge of LP (left panel), transmission and PDOS of CT (middle panel) and the band structure of RTP (right panel). (c) Transmission spectrum.

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arrow itself display the direction of electron flow in real space. The LDOS of each transmission peak shows good spin-separation with the one spin signal locating one side of RP while the other spin signal staying at the other side symmetrically. The TMP at −0.4 eV energy shows that the spin up (spin down) electron transport along the RTP (RBP) but no spin down (spin up) can across it. The opposite result appears when TMP at 0.36 eV, where spin up electron across the RBP and spin down across the RTP. This device exhibits good spin input, procession and output, which could be useful in spin electronic. Experimentally, Liu et al. [41] have embedded four- and eightmembered ring in carbon-based nanostructures. Carlos et al. [42] bring four-membered ring to connect tetracene species forming linear dimer. These studies also mean that the device we predicted is likely to be prepared experimentally.

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In summary, we have designed a new spin separation device by introducing the CT symmetrically to connect ZUC chain. The CT provide two nonequivalent paths for different spin resulting in different spin are exported to different ports in superlattice or device. Especially for the ATEM device, where the edge carbon atoms of one sublattice are passivated with double hydrogen, it achieves spin polarized in real space but spin degeneracy in energy and

stable spin transporting successfully. This model can serve as the most basic logic device and can be useful for potential spintronics applications.

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4. Computational methods Our calculations in superlattice are performed with density functional theory (DFT) as implemented in Vienna ab inition simulation package (VASP) [43]. We adopt the generalized gradient approximation (GGA) [44] for the exchange correlation potential. The ion–electron interaction is treated with the projected-augmented wave (PAW) [45], and the planewave cutoff energy for the wave function is set to 400 eV. The criterion of convergence for structure relaxation is the change of total energy < 10−7 eV and the residual force on atom < 0.01 eV/Å. The vacuum space between two neighboring nanostructure is set as > 10 Å to avoid spurious interaction between periodic images. The three electrode model is used to simulate the transport properties which is calculated by a developed first-principles soft package Atomistlx Tool (ATK) [46,47], which is based on the spinpolarized density functional theory combined with nonequilibrium Green’s function (NEGF). In our calculations, the local spin density approximation (LSDA) [48,49] is used as the exchange-correlation potential, the energy cutoff is set as 75 Ry. The k-point sampling

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Fig. 5. Transmission spectrum, and LDOS, spin up transmission pathway and spin down transmission pathway of transmission peak at (a, c, d) −0.4 eV and (b, e, f) 0.36 eV.

is set as 100 in the electron transport direction. A vacuum layer of > 10 Å is added to decrease the interactive effect. The geometrical structures are fully optimized until the residual force on each atom is smaller than 0.05 eV/Å. Doublzetapolarized basis set is used and the temperature of the electrodes is set to be 300 K. The transmission spectrum

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Acknowledgements

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This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 21673296 and 11804395), and the Natural Science Foundation of Hunan Province (Grant Nos. 2017JJ3410 and 2018JJ2481).

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