CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402265
Graphitic Silicon Nitride: A Metal-Free Ferromagnet with Charge and Spin Current Rectification Sabyasachi Sen[b] and Swapan Chakrabarti*[a] As a first example, herein we show that g-Si4N3 is expected to act as a metal-free ferromagnet featuring both charge and spin current rectification simultaneously. Such rectification is crucial for envisioning devices that contain both logic and memory functionality on a single chip. The spin coherent quantum-transport calculations on g-Si4N3 reveal that the chosen system is a unique molecular spin filter, the currentvoltage characteristics of which is asymmetric in nature, which can create a perfect background for synchronous charge and spin current rectification. To shed light on this highly unusual
in-silico observation, we have meticulously inspected the biasdependent modulation of the spin-polarized eigenstates. The results indicate that, whereas only the localized 2p orbitals of the outer-ring (OR) Si atoms participate in the transmission process in the positive bias, both OR Si and N atoms contribute in the reverse bias. Furthermore, we have evaluated the spin-polarized electron-transfer rate in the tunneling regime, and the results demonstrate that the transfer rates are unequal in the positive and negative bias range, leading to the possible realization of a simultaneous logic–memory device.
1. Introduction Theoretical simulation and experimental fabrication of electronic devices at dimensions below 100 nm are now at the heart of modern material research. In this context, the emergence of spin-operated electronic devices represents a stepchange in the development of electronics that is expected to lead to the construction of devices with a wide range of possible applications. Information processing, fabrication of logic and memory devices, and magnetic sensors, are significant potential areas of application in which both electronic charge and spin act as carriers of information.[1–3] Long coherence time and less power dissipation are the two fundamental advantages of spintronic devices over their charge analogues. In conventional electronics, the asymmetry in charge current due to reversal of the applied bias is designated as the charge current rectification, and such devices have the potential to act as logic gates. An asymmetry in the net spin current due to the reversal of the applied bias is known as spin current rectification, and the corresponding devices are suitable for memory applications. In particular, long spin coherence time, leading to the survival of spin current for a relatively long time, makes spin devices suitable for memory operation.[2, 3] Hence, a spintronic device showing rectifying of both charge and spin would be ideal for the simultaneous implementation of logic and memory functionalities in a single molecular device. [a] Dr. S. Chakrabarti Department of Chemistry, University of Calcutta 92, A.P.C. Road, Kolkata 700 009 (India) E-mail: [email protected] [b] Dr. S. Sen Department of Physics, JIS College of Engineering Block A, Phase - III, Kalyani, Nadia (India) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402265.
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In general, charge current rectification in a molecular electronic device is attributed to the spatial asymmetry due to the electrodes, molecule-electrode junction or due to the molecule itself. Additionally, spin current rectification in molecular devices can be achieved by bridging the molecule between two dissimilar magnetic electrodes or by using a magnetic and nonmagnetic electrodes.[3, 4] However, to achieve the dual effect of logic and memory functions inside a single molecule, gaining magnetism and spatial asymmetry from the molecule alone is the best option. Conventionally, it is assumed that such devices could result from transition-metal-based systems with strong structural asymmetry.[5, 6] Unfortunately, such systems have the disadvantage of very short spin relaxation time arising from strong spin-orbit coupling, which ultimately influences the performance of the spintronic device.[7] Remarkably, the ferromagnetic behavior of certain metal-free systems such as graphene nanoribbon,[8] edge-modified zigzag graphene nanoribbon by B/N dopants,[9] nanotubes, nanodots, and vacancy h-BN monolayers,[10] and ferroelectric poly(vinylidene fluoride) physisorbed onto graphene[11] offer some promise in this direction. In this context, the recent work of Du and coworkers[7] deserves special note: these authors obtained a metal-free ferromagnetic state from graphitic carbon nitride (g-C4N3)[12] and demonstrated that the system showed halfmetallic behavior. Nevertheless, a metal-free ferromagnet with simultaneous charge and spin current rectification is still hard to pin down. In this article, inspired by the idea of Du and co-workers,[7] we focus on the graphitic Si4N3 system, the precursor of which, Si3N4, is commercially viable.[13, 14] Our calculations reveal that, like g-C4N3, a (2X2) super cell of g- Si4N3 will have ferromagnetic ordering in the ground state and, surprisingly, the quantum transport calculations manifestly reflect that this particular ChemPhysChem 2014, 15, 2756 – 2761
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CHEMPHYSCHEM ARTICLES system has the ability to rectify both the charge and spin current coherently even in the presence of the same nonmagnetic electrodes. The projected device density of states, combined with molecular eigenstate analyses, clearly suggest that the dissimilar participation of the 2p orbital of the outer-ring (OR) Si and N atoms in the positive and negative bias range is responsible for these unique in-silico observations.
Computational Methods Figure 1 represents the optimized geometry of a (2X2) super cell of the g-Si4N3 system [henceforth described as (2X2) g-Si4N3] and the related two-probe configuration used for quantum transport studies. The geometry of (2X2) g-Si4N3 was optimized for three different spin states, namely ferromagnetic (FM), anti-ferromagnetic (AFM), and nonmagnetic (NM) states. All the calculations related to geometry optimization were performed with the Gaussian 09 suite of programs[15] using the B3LYP[16, 17] hybrid density functional and the TZVP basis set. The results of the geometry optimization suggest that the FM state is stable by 10 and 1.48 eV with respect to the AFM and NM states, respectively. The consistency of the results for the FM and AFM states was verified by optimizing the geometry with a larger basis set, TZVPP. It is worth noting that the energy difference between the FM and AFM states is small; therefore, to establish the correct ground state of the system, we estimated the ground state energies of the FM and AFM states by using the BHandLYP[17, 18] functional in combination with the TZVPP basis and again found that the FM state was more stable (9.58 meV). The
Figure 1. a) Optimized geometry of (2X2) g-Si4N3. b) Two-probe system of (2X2) g-Si4N3 physisorbed onto Au (111) surface. c) Spin density plot of (2X2) g-Si4N3 in the ferromagnetic quintet state.
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www.chemphyschem.org spin density isosurface of the FM state is presented in Figure 1 c, which illustrates the strong accumulation of spin density over four OR Si atoms. The calculated magnetic moments on these Si atoms are 0.975956, 0.987279, 0.976018, and 1.003249 mB, respectively. All the transport calculations were performed on the FM state of this material because this state is more stable than the AFM and NM states. For quantum transport calculations, ATK 12.8.0[19] software was used; this package utilizes Keldysh nonequilibrium Green’s function (NEGF) in the framework of density functional theory (DFT). The transport parameters were computed with the PBE functional[20] along with double-z + polarization basis function for Si and N. However, for Au, single-z basis was preferred. For the core electrons, the norm-conserving Troullier–Martins pseudopotentials[21] were employed. The Brillouin zone sampling in the direction of transport was done with a Monkhost–Pack grid using 100 k-points, and 150 Ryd mesh cut-off energy was chosen as the convergence criterion. The up and down spin current was then estimated from the spin-polarized version of the Landauer and Bttiker formula.[22, 23]
2. Results and Discussion To provide a clear understanding of the chosen system, we constructed a 2D sheet of g-Si4N3 (see the Supporting Information, Figure S1) by repetition of the unit cell [(2X2) g-Si4N3, shown in ball & stick]. In the unit cell, each of the four OR Si atoms has one unpaired electron spin, resulting in four spin centers within the unit cell, thereby making the system magnetic. Reports on geometry optimization established the ferromagnetic arrangement of these four spin centers as the stable configuration and this is in good agreement with an earlier study on a similar system.[7] In the present case, we wanted to study the spin-polarized I–V relationship of such a system. In the quantum transport study we only consider the unit cell of the 2D g-Si4N3 sheet (not the entire 2D sheet), therefore, during geometry optimization and quantum transport calculations, except where contact is made with Au electrodes, all other end Si atoms of the unit cell have been passivated with H atoms, keeping the spin of the four OR Si atoms undisturbed. For quantum transport calculations, the Si atoms at the top left and bottom right of (2X2) g-Si4N3 were connected with sulfur (S) atoms to provide good contact with the Au (111) electrodes. Numerous theoretical as well as experimental studies[2] have reported that Au–S contact is stable when the central region of a two-probe system is connected with Au electrodes. The total charge current obtained from the system is expressed as IC ðVÞ ¼ I # ðVÞ þ I " ðVÞ. For the present system, the net charge current has been estimated over the applied bias range of 0.5 to + 0.5 V and is plotted in Figure 2 a. Figure 2 depicts a rectifying nature of the charge current, and this feature is predominant at a bias voltage close to 0.5 V. With a forward bias voltage of 0.5 V, the charge current is estimated as 27.548 nA, whereas in the reverse bias (0.5 V) the same is noted as 687.242 nA; thus, the (2X2) g-Si4N3 system sandwiched between two Au (111) electrodes should act a moChemPhysChem 2014, 15, 2756 – 2761
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Figure 2. a) Net charge current through (2X2) g-Si4N3 physisorbed onto Au(111) surface. b) Net spin current plotted against the applied bias.
lecular charge rectifier with rectification ratio 24.947 in this small bias range. It is worth commenting that the net charge current mostly comes from the down spin channel of the system and therefore the charge current rectification is highly spin-selective. Motivated by the tantalizing prospect of (2X2) g-Si4N3 acting as a spin-selective (down spin) charge current rectifier, we examined whether the system could also act as a resource for spin current rectification. Spin current rectification in a spatially asymmetric system can be of two types: primarily weak rectification, in which the direction of spin current reverses and the magnitude of the spin current changes due to the reversal of the applied bias, is expected to occur in asymmetric magnetic junctions. This feature is analogous to the charge current rectification. In contrast, in the strong rectification regime, the spin current direction is not altered even when the applied bias di 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org rection is reversed; such a system has no charge current analogue. As per existing theories, strong spin current rectification is attainable only at a very high bias,[4] and one such example is the spin current rectification in Au-octane thiolate (OT)/Fe junction, as reported by Dalgleish and co-workers.[4] Keeping these findings in mind, the net spin current through the system has been calculated by using the formula, h IS ðVÞ ¼ 4pe ½I # ðVÞ I " ðVÞ and is plotted in Figure 2 b. The bias dependent IS ðVÞ shows rectification in the studied bias region with rectification ratio 25; clearly this would increase if a large bias range is taken. The emergence of this dual rectification action in both the spin-polarized charge current and net spin current indicates that the (2X2) g-Si4N3 system could be suitable for simultaneous logic and memory functions. It is worth mentioning that (2X2) g-Si4N3 is an intrinsic molecular spin filter and the current through the system is contributed by only one spin channel (down spin in this case). This feature directly influences the bias dependence of both IC ðVÞ and IS ðVÞ, making them nearly identical in nature. Therefore, rectification action in a molecular spin filter would be simultaneous in IC ðVÞ and IS ðVÞ, implying that such materials should be suitable for the design of molecular devices executing dual logic and memory operations. It is also worth noting that we did not find any rectification (neither charge nor spin) in the similar system, g-C4N3, indicating that the rectification property is an intrinsic property of the studied system. Therefore, the question should arise: what makes the g-Si4N3 system so special? To address this important and unavoidable question, we need to substantiate the origin of the rectification action of (2X2) g-Si4N3. This has been done in two steps. In the first step, we examined the projected device density of states (PDDOS) of the system at both zero and finite bias. The equilibrium (zero bias) PDDOS of inner-ring Si and N atoms was compared with the PDDOS of the OR Si atoms and the results are presented in Figure 3 a. At the equilibrium state, the PDDOS analysis suggests that density of states at the Fermi level (eF ) is mainly dominated by the 2p orbitals of the OR Si atoms, which remain extremely high in the down spin channel, whereas the contribution of the PDDOS at the eF that corresponds to the 2p orbital of the inner-ring Si and N atoms are also found to be non-negligible and, therefore, all the atoms in the g-Si4N3 share a significant role in the zero bias transmission spectra of the system. However, the situation changes drastically when the two-probe setup is placed under the influence of finite bias. To get an idea of the field-induced changes of the PDDOS, two extreme biases (0.5 and 0.5 V) were investigated; the relevant results are depicted in Figure 3 b and c. In the positive bias, a comparison of these figures reveals that, within the bias window, the PDDOS of the down-spin channel has contributions from the 2p orbital of OR Si atoms alone, leaving the inner-ring Si and N atoms completely neglected. Furthermore, at 0.5 V, the 2p orbital contributions of the OR Si atoms were found to be much higher in magnitude compared with its forward bias counterpart and, more interestingly, the inner-ring N atoms again begin to contribute to a significant extent in the overall PDDOS of the system. This dissimilar biasChemPhysChem 2014, 15, 2756 – 2761
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Figure 4, we present the molecular projected self-consistent Hamiltonian states (MPSH)[24] corresponding to the singly occupied highest molecular orbital (SOHMO) of the down-spin channel. Zero bias transmission spectra presented in Figure S2 of the Supporting Information, quite clearly establishes the down-spin channel as the active spin channel. The MPSH state corresponding to the energy levels in the proximity of SOHMO are provided in the Supporting information (Figure S3). These figures illustrate that the dominant transmission channel is the SOHMO. It is evident from Figure 4 that, under the forward bias, the SOHMO of the molecule lies between the (eF ) of the left (1.23 eV) and right (0.73 eV) electrodes. Consequently, the electrons from the right electrode get transferred to the molecule through resonance tunneling and the molecular energy level becomes empty after tunneling of electrons to the left electrode. Similarly, when reverse bias is applied, the molecular SOHMO is again between the Figure 3. Spin-polarized PDDOS plot of (2X2) g-Si4N3 physisorbed onto Au(111) surface a) in equilibrium (zero (eF ) of both electrodes (0.23 eV bias), b) at + 0.5 V, and c) at 0.5 V. Dotted lines indicate bias window. In each panel, (i) denotes PDDOS related to the p orbital of the OR Si atoms, (ii) denotes PDDOS related to the p orbital of inner-ring Si atoms, and (iii) defor left and 0.73 eV for right); notes PDDOS related to the p orbital of inner-ring N atoms however, it is evident from Figure 4 b that the direction of flow would be opposite in this case, dependent PDDOS contribution of the OR Si and inner-ring Si because the electrons primarily get transferred from the left and N clearly explains the origin of the rectifier action of the electrode to the molecular energy level and thereafter move (2X2) g-Si4N3 system. The PDDOS analyses also provide an imto the right electrode. portant insight into the probable spin-selective charge rectifiTo explain the origin of the observed rectification action, we cation of (2X2) g-Si4N3. The equilibrium PDDOS depicted in Figestimated the rate of electron transfer from either of the elecure 3 a clearly shows that the density of states across the (eF ) trodes by applying the Fermi Golden rule approach (FGRA).[25] are mainly present in the down-spin channel, demonstrating Within the FGRA, the spin-polarized electron transfer rate 2p metallic features, whereas its up-spin counterpart has no subthrough the tunnel barrier is given by gðeÞ ¼ h jG j2 1ðeF Þ. stantial PDDOS at the (eF ), which results in an insulating nature Here, 1ðeF Þis the density of states of the electrons at of the up-spin channel. These results clearly provide an interthe (eF ) of the respective electrode, and the tunneling papretation of the spin selectiveness of the rectification process. rameter j G j 2 is calculated by using WKB approximation, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A schematic illustration of the conduction mechanism under ð2 mð eVb Þ jGj2 1expð2 d Þ, where Vb is the voltage drop across h finite bias and resulting rectification action is given in Figure 4 (upper panel). The system shown in Figure 4 a resembles the the tunnel junction, and f and d are the height and width of conduction mechanism of the two-probe system when + 0.5 V the tunnel barrier, respectively. During the calculation, the is applied to the left electrode, keeping the right electrode at height (f) of the tunnel barrier is estimated from the energy 0.0 V, whereas Figure 4 b represents the situation when 0.5 V gap between the Fermi energy of the electrode and energy is applied to the left electrode only. In the bottom panels of corresponding to the SOHMO of the central region; and the 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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the emergence of relatively large spin-polarized current (downspin in this case) through the device only at negative bias, thereby creating an asymmetric current flow through the system, making it conducive for rectification action. A molecular-level origin of the high rate of electron transfer though the molecule at negative bias is provided by analyzing the molecular projected self-consistent Hamiltonian states (MPSH)[24] of the twoprobe system shown in Figure 4 (bottom panel). The figure includes the MPSH states of the two optimum voltages, namely 0.5 V for the active spin channel (down spin). At 0.5 V, the Figure 4. Spin-polarized conduction mechanism through (2X2) g-Si4N3 physisorbed onto Au (111) surface when MPSH states are strongly deloa) 0.5 V is applied to the left electrode keeping the right electrode at 0.0 V, and b) 0.5 V is applied to the left electrode keeping the right electrode at 0.0 V; bottom figures show the MPSH state corresponding to the SOHMO calized and dominated by the of the two-probe system. 2p-orbital contribution of both OR Si atoms and N atoms, and width (d) of the tunnel barrier is the length of the active their contribution is clearly reflected in the delocalized p region extended from the left to right electrode contact nature of the electron density. However, at + 0.5 V, electrons points. In Figure 4, gR refers to the spin-polarized electron are localized over the Si atoms in the shape of a pure p orbital transfer rate between the right electrode and the molecule and, indeed, this localization is responsible for the quenching and gL is the spin-polarized electron transfer rate between the of the electron transfer rate with respect to the net current obtained in the forward bias. It is worth noting that at + 0.5 V, left electrode and the molecule. The gL and gR, thus obtained, part of down-spin MPSH state is concentrated over the topwere plotted against the applied bias and the results are preright side OR Si atom, which is indicative of probable coupling sented in Figure 5. The figure demonstrates that, at negative with the right electrode; however, it is also evident that no bias, the gL values are much larger compared with gR and the such coupling appears at 0.5 V. Hence, it appears that during opposite trend is clear in the positive bias. The contrasting the fabrication process, any gold ad atom close to this Si atom bias dependence, and asymmetric nature of gL and gR indicates can influence the net current through the device. At the same time, a review of the literature illustrates that net current though such nanodevices depends on the extent of electron delocalization in the central region, which is more at 0.5 V, resulting in larger current at that bias.
3. Conclusions
Figure 5. Plot of spin-polarized electron-transfer rate against applied bias.
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This nonequilibrium Green’s function study establishes (2X2) gSi4N3 as a simple transition-metal-free ferromagnet that exhibits both charge and spin current rectification. To the best of our knowledge, this is the first transition-metal-free system that is structurally simple and, due to charge and spin rectification, is capable of executing both logic and memory action. The current through the system is essentially due to downspin transmission. The PDDOS analysis clearly suggests that this spin-selective rectification is mostly controlled by the 2porbital contribution of the outer ring Si atoms of the molecular system. Whereas the schematic diagram illustrates the conduction mechanism, asymmetric bias-dependence of the spin-polarized electron transfer rate explains the emergence of spinpolarized rectification action. MPSH analyses suggested the ChemPhysChem 2014, 15, 2756 – 2761
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CHEMPHYSCHEM ARTICLES molecular origin of the observed rectification action. Finally, if realized experimentally, such a system could be expected to replace the present transition-metal-based spin-selective rectifier and form the basis of a new class of designed material.
Acknowledgements S.S. acknowledges CSIR, Govt. of India [03(1256)/12/EMR-II] for the research funding. S.C. acknowledges INDNOR bilateral project for funding support and CRNN, University of Calcutta for providing computational resources. Keywords: charge transfer · density functional calculations · magnetic properties · quantum chemistry · semiconductors [1] I. Zutic, J. Fabian, S. D. Sarma, Rev. Mod. Phys. 2004, 76, 323 – 410. [2] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, D. M. Treger, Science 2001, 294, 1488 – 1495; S. Sanvito, Chem. Soc. Rev. 2011, 40, 3336 – 3355; K. Stokbro, J. Taylor, M. Brandbyge, J. L. Mozos, P. Ordejon, Comput. Mater. Sci. 2003, 27, 151 – 160. [3] S. Sen, S. Chakrabarti, J. Am. Chem. Soc. 2010, 132, 15334 – 15339. [4] H. Dalgleish, G. Kirczenow, Phys. Rev. B 2006, 73, 235436. [5] B. Dieny, V. S. Speriosu, B. A. Gurney, S. S. P. Parkin, D. R. Wilhoit, K. P. Roche, S. Metin, D. T. Peter-son, S. Nadimi, J. Magn. Magn. Mater. 1991, 93, 101 – 104. [6] B. Braunecker, D. E. Feldman, F. Li, Phys. Rev. B 2007, 76, 085119. [7] A. Du, S. Sanvito, S. C. Smith, Phys. Rev. Lett. 2012, 108, 197207. [8] Y.-W. Son, M. L. Cohen, S. G. Louie, Nature 2006, 444, 347 – 349. [9] Er. Kan, Z. Li, J. Yang, J. G. Hou, J. Am. Chem. Soc. 2008, 130, 4224 – 4225. [10] Y. L. Lee, S. Kim, C. Park, J. Ihm, Y. W. Son, ACS Nano 2010, 4, 1345 – 1350.
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www.chemphyschem.org [11] Y. L. Lee, S. Kim, C. Park, J. Ihm, Y. W. Son, ACS Nano 2010, 4, 1345 – 1350. [12] J. S. Lee, X. Q. Wang, H. M. Luo, S. Dai, Adv. Mater. 2010, 22, 1004 – 1007. [13] L. Weiss, T. Engelhardt, Z. Anorg. Allg. Chem. 1910, 65, 38 – 104.ok [14] L. F. Riley, J. Am. Ceram. Soc. 2004, 83, 245 – 265. [15] Gaussian 09, Revision A.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, . Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc., Wallingford CT, 2009.. [16] A. D. Becke, J. Chem. Phys. 1993, 98, 1372 – 1377. [17] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785 – 789. [18] A. D. Becke, Phys. Rev. A 1988, 38, 3098 – 3100. [19] http://www.quantumwise.com. [20] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865 – 3868. [21] N. Troullier, J. L. Martins, Phys. Rev. B 1991, 43, 1993 – 2006. [22] S. Datta, Electronic Transport in Mesoscopic Systems, Oxford University Press, New York, 1995. [23] Z. G. Zhu, G. Su, Q. R. Zheng, B. Jin, Phys. Rev. B 2004, 70, 174403. [24] S. Sen, S. Chakrabarti, J. Phys. Chem. C 2008, 112, 1685 – 1693. [25] C. Kergueris, J.-P. Bourgoin, S. Palacin, D. Esteve, C. Urbina, M. Magoga, C. Joachim, Phys. Rev. B 1999, 59, 12505 – 12513.
Received: April 21, 2014 Published online on July 8, 2014
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Graphitic Silicon Nitride: A Metal-Free Ferromagnet with Charge and Spin Current Rectification Sabyasachi Sen[b] and Swapan Chakrabarti*[a] As a first example, herein we show that g-Si4N3 is expected to act as a metal-free ferromagnet featuring both charge and spin current rectification simultaneously. Such rectification is crucial for envisioning devices that contain both logic and memory functionality on a single chip. The spin coherent quantum-transport calculations on g-Si4N3 reveal that the chosen system is a unique molecular spin filter, the currentvoltage characteristics of which is asymmetric in nature, which can create a perfect background for synchronous charge and spin current rectification. To shed light on this highly unusual
in-silico observation, we have meticulously inspected the biasdependent modulation of the spin-polarized eigenstates. The results indicate that, whereas only the localized 2p orbitals of the outer-ring (OR) Si atoms participate in the transmission process in the positive bias, both OR Si and N atoms contribute in the reverse bias. Furthermore, we have evaluated the spin-polarized electron-transfer rate in the tunneling regime, and the results demonstrate that the transfer rates are unequal in the positive and negative bias range, leading to the possible realization of a simultaneous logic–memory device.
1. Introduction Theoretical simulation and experimental fabrication of electronic devices at dimensions below 100 nm are now at the heart of modern material research. In this context, the emergence of spin-operated electronic devices represents a stepchange in the development of electronics that is expected to lead to the construction of devices with a wide range of possible applications. Information processing, fabrication of logic and memory devices, and magnetic sensors, are significant potential areas of application in which both electronic charge and spin act as carriers of information.[1–3] Long coherence time and less power dissipation are the two fundamental advantages of spintronic devices over their charge analogues. In conventional electronics, the asymmetry in charge current due to reversal of the applied bias is designated as the charge current rectification, and such devices have the potential to act as logic gates. An asymmetry in the net spin current due to the reversal of the applied bias is known as spin current rectification, and the corresponding devices are suitable for memory applications. In particular, long spin coherence time, leading to the survival of spin current for a relatively long time, makes spin devices suitable for memory operation.[2, 3] Hence, a spintronic device showing rectifying of both charge and spin would be ideal for the simultaneous implementation of logic and memory functionalities in a single molecular device. [a] Dr. S. Chakrabarti Department of Chemistry, University of Calcutta 92, A.P.C. Road, Kolkata 700 009 (India) E-mail: [email protected] [b] Dr. S. Sen Department of Physics, JIS College of Engineering Block A, Phase - III, Kalyani, Nadia (India) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402265.
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
In general, charge current rectification in a molecular electronic device is attributed to the spatial asymmetry due to the electrodes, molecule-electrode junction or due to the molecule itself. Additionally, spin current rectification in molecular devices can be achieved by bridging the molecule between two dissimilar magnetic electrodes or by using a magnetic and nonmagnetic electrodes.[3, 4] However, to achieve the dual effect of logic and memory functions inside a single molecule, gaining magnetism and spatial asymmetry from the molecule alone is the best option. Conventionally, it is assumed that such devices could result from transition-metal-based systems with strong structural asymmetry.[5, 6] Unfortunately, such systems have the disadvantage of very short spin relaxation time arising from strong spin-orbit coupling, which ultimately influences the performance of the spintronic device.[7] Remarkably, the ferromagnetic behavior of certain metal-free systems such as graphene nanoribbon,[8] edge-modified zigzag graphene nanoribbon by B/N dopants,[9] nanotubes, nanodots, and vacancy h-BN monolayers,[10] and ferroelectric poly(vinylidene fluoride) physisorbed onto graphene[11] offer some promise in this direction. In this context, the recent work of Du and coworkers[7] deserves special note: these authors obtained a metal-free ferromagnetic state from graphitic carbon nitride (g-C4N3)[12] and demonstrated that the system showed halfmetallic behavior. Nevertheless, a metal-free ferromagnet with simultaneous charge and spin current rectification is still hard to pin down. In this article, inspired by the idea of Du and co-workers,[7] we focus on the graphitic Si4N3 system, the precursor of which, Si3N4, is commercially viable.[13, 14] Our calculations reveal that, like g-C4N3, a (2X2) super cell of g- Si4N3 will have ferromagnetic ordering in the ground state and, surprisingly, the quantum transport calculations manifestly reflect that this particular ChemPhysChem 2014, 15, 2756 – 2761
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CHEMPHYSCHEM ARTICLES system has the ability to rectify both the charge and spin current coherently even in the presence of the same nonmagnetic electrodes. The projected device density of states, combined with molecular eigenstate analyses, clearly suggest that the dissimilar participation of the 2p orbital of the outer-ring (OR) Si and N atoms in the positive and negative bias range is responsible for these unique in-silico observations.
Computational Methods Figure 1 represents the optimized geometry of a (2X2) super cell of the g-Si4N3 system [henceforth described as (2X2) g-Si4N3] and the related two-probe configuration used for quantum transport studies. The geometry of (2X2) g-Si4N3 was optimized for three different spin states, namely ferromagnetic (FM), anti-ferromagnetic (AFM), and nonmagnetic (NM) states. All the calculations related to geometry optimization were performed with the Gaussian 09 suite of programs[15] using the B3LYP[16, 17] hybrid density functional and the TZVP basis set. The results of the geometry optimization suggest that the FM state is stable by 10 and 1.48 eV with respect to the AFM and NM states, respectively. The consistency of the results for the FM and AFM states was verified by optimizing the geometry with a larger basis set, TZVPP. It is worth noting that the energy difference between the FM and AFM states is small; therefore, to establish the correct ground state of the system, we estimated the ground state energies of the FM and AFM states by using the BHandLYP[17, 18] functional in combination with the TZVPP basis and again found that the FM state was more stable (9.58 meV). The
Figure 1. a) Optimized geometry of (2X2) g-Si4N3. b) Two-probe system of (2X2) g-Si4N3 physisorbed onto Au (111) surface. c) Spin density plot of (2X2) g-Si4N3 in the ferromagnetic quintet state.
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www.chemphyschem.org spin density isosurface of the FM state is presented in Figure 1 c, which illustrates the strong accumulation of spin density over four OR Si atoms. The calculated magnetic moments on these Si atoms are 0.975956, 0.987279, 0.976018, and 1.003249 mB, respectively. All the transport calculations were performed on the FM state of this material because this state is more stable than the AFM and NM states. For quantum transport calculations, ATK 12.8.0[19] software was used; this package utilizes Keldysh nonequilibrium Green’s function (NEGF) in the framework of density functional theory (DFT). The transport parameters were computed with the PBE functional[20] along with double-z + polarization basis function for Si and N. However, for Au, single-z basis was preferred. For the core electrons, the norm-conserving Troullier–Martins pseudopotentials[21] were employed. The Brillouin zone sampling in the direction of transport was done with a Monkhost–Pack grid using 100 k-points, and 150 Ryd mesh cut-off energy was chosen as the convergence criterion. The up and down spin current was then estimated from the spin-polarized version of the Landauer and Bttiker formula.[22, 23]
2. Results and Discussion To provide a clear understanding of the chosen system, we constructed a 2D sheet of g-Si4N3 (see the Supporting Information, Figure S1) by repetition of the unit cell [(2X2) g-Si4N3, shown in ball & stick]. In the unit cell, each of the four OR Si atoms has one unpaired electron spin, resulting in four spin centers within the unit cell, thereby making the system magnetic. Reports on geometry optimization established the ferromagnetic arrangement of these four spin centers as the stable configuration and this is in good agreement with an earlier study on a similar system.[7] In the present case, we wanted to study the spin-polarized I–V relationship of such a system. In the quantum transport study we only consider the unit cell of the 2D g-Si4N3 sheet (not the entire 2D sheet), therefore, during geometry optimization and quantum transport calculations, except where contact is made with Au electrodes, all other end Si atoms of the unit cell have been passivated with H atoms, keeping the spin of the four OR Si atoms undisturbed. For quantum transport calculations, the Si atoms at the top left and bottom right of (2X2) g-Si4N3 were connected with sulfur (S) atoms to provide good contact with the Au (111) electrodes. Numerous theoretical as well as experimental studies[2] have reported that Au–S contact is stable when the central region of a two-probe system is connected with Au electrodes. The total charge current obtained from the system is expressed as IC ðVÞ ¼ I # ðVÞ þ I " ðVÞ. For the present system, the net charge current has been estimated over the applied bias range of 0.5 to + 0.5 V and is plotted in Figure 2 a. Figure 2 depicts a rectifying nature of the charge current, and this feature is predominant at a bias voltage close to 0.5 V. With a forward bias voltage of 0.5 V, the charge current is estimated as 27.548 nA, whereas in the reverse bias (0.5 V) the same is noted as 687.242 nA; thus, the (2X2) g-Si4N3 system sandwiched between two Au (111) electrodes should act a moChemPhysChem 2014, 15, 2756 – 2761
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Figure 2. a) Net charge current through (2X2) g-Si4N3 physisorbed onto Au(111) surface. b) Net spin current plotted against the applied bias.
lecular charge rectifier with rectification ratio 24.947 in this small bias range. It is worth commenting that the net charge current mostly comes from the down spin channel of the system and therefore the charge current rectification is highly spin-selective. Motivated by the tantalizing prospect of (2X2) g-Si4N3 acting as a spin-selective (down spin) charge current rectifier, we examined whether the system could also act as a resource for spin current rectification. Spin current rectification in a spatially asymmetric system can be of two types: primarily weak rectification, in which the direction of spin current reverses and the magnitude of the spin current changes due to the reversal of the applied bias, is expected to occur in asymmetric magnetic junctions. This feature is analogous to the charge current rectification. In contrast, in the strong rectification regime, the spin current direction is not altered even when the applied bias di 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org rection is reversed; such a system has no charge current analogue. As per existing theories, strong spin current rectification is attainable only at a very high bias,[4] and one such example is the spin current rectification in Au-octane thiolate (OT)/Fe junction, as reported by Dalgleish and co-workers.[4] Keeping these findings in mind, the net spin current through the system has been calculated by using the formula, h IS ðVÞ ¼ 4pe ½I # ðVÞ I " ðVÞ and is plotted in Figure 2 b. The bias dependent IS ðVÞ shows rectification in the studied bias region with rectification ratio 25; clearly this would increase if a large bias range is taken. The emergence of this dual rectification action in both the spin-polarized charge current and net spin current indicates that the (2X2) g-Si4N3 system could be suitable for simultaneous logic and memory functions. It is worth mentioning that (2X2) g-Si4N3 is an intrinsic molecular spin filter and the current through the system is contributed by only one spin channel (down spin in this case). This feature directly influences the bias dependence of both IC ðVÞ and IS ðVÞ, making them nearly identical in nature. Therefore, rectification action in a molecular spin filter would be simultaneous in IC ðVÞ and IS ðVÞ, implying that such materials should be suitable for the design of molecular devices executing dual logic and memory operations. It is also worth noting that we did not find any rectification (neither charge nor spin) in the similar system, g-C4N3, indicating that the rectification property is an intrinsic property of the studied system. Therefore, the question should arise: what makes the g-Si4N3 system so special? To address this important and unavoidable question, we need to substantiate the origin of the rectification action of (2X2) g-Si4N3. This has been done in two steps. In the first step, we examined the projected device density of states (PDDOS) of the system at both zero and finite bias. The equilibrium (zero bias) PDDOS of inner-ring Si and N atoms was compared with the PDDOS of the OR Si atoms and the results are presented in Figure 3 a. At the equilibrium state, the PDDOS analysis suggests that density of states at the Fermi level (eF ) is mainly dominated by the 2p orbitals of the OR Si atoms, which remain extremely high in the down spin channel, whereas the contribution of the PDDOS at the eF that corresponds to the 2p orbital of the inner-ring Si and N atoms are also found to be non-negligible and, therefore, all the atoms in the g-Si4N3 share a significant role in the zero bias transmission spectra of the system. However, the situation changes drastically when the two-probe setup is placed under the influence of finite bias. To get an idea of the field-induced changes of the PDDOS, two extreme biases (0.5 and 0.5 V) were investigated; the relevant results are depicted in Figure 3 b and c. In the positive bias, a comparison of these figures reveals that, within the bias window, the PDDOS of the down-spin channel has contributions from the 2p orbital of OR Si atoms alone, leaving the inner-ring Si and N atoms completely neglected. Furthermore, at 0.5 V, the 2p orbital contributions of the OR Si atoms were found to be much higher in magnitude compared with its forward bias counterpart and, more interestingly, the inner-ring N atoms again begin to contribute to a significant extent in the overall PDDOS of the system. This dissimilar biasChemPhysChem 2014, 15, 2756 – 2761
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Figure 4, we present the molecular projected self-consistent Hamiltonian states (MPSH)[24] corresponding to the singly occupied highest molecular orbital (SOHMO) of the down-spin channel. Zero bias transmission spectra presented in Figure S2 of the Supporting Information, quite clearly establishes the down-spin channel as the active spin channel. The MPSH state corresponding to the energy levels in the proximity of SOHMO are provided in the Supporting information (Figure S3). These figures illustrate that the dominant transmission channel is the SOHMO. It is evident from Figure 4 that, under the forward bias, the SOHMO of the molecule lies between the (eF ) of the left (1.23 eV) and right (0.73 eV) electrodes. Consequently, the electrons from the right electrode get transferred to the molecule through resonance tunneling and the molecular energy level becomes empty after tunneling of electrons to the left electrode. Similarly, when reverse bias is applied, the molecular SOHMO is again between the Figure 3. Spin-polarized PDDOS plot of (2X2) g-Si4N3 physisorbed onto Au(111) surface a) in equilibrium (zero (eF ) of both electrodes (0.23 eV bias), b) at + 0.5 V, and c) at 0.5 V. Dotted lines indicate bias window. In each panel, (i) denotes PDDOS related to the p orbital of the OR Si atoms, (ii) denotes PDDOS related to the p orbital of inner-ring Si atoms, and (iii) defor left and 0.73 eV for right); notes PDDOS related to the p orbital of inner-ring N atoms however, it is evident from Figure 4 b that the direction of flow would be opposite in this case, dependent PDDOS contribution of the OR Si and inner-ring Si because the electrons primarily get transferred from the left and N clearly explains the origin of the rectifier action of the electrode to the molecular energy level and thereafter move (2X2) g-Si4N3 system. The PDDOS analyses also provide an imto the right electrode. portant insight into the probable spin-selective charge rectifiTo explain the origin of the observed rectification action, we cation of (2X2) g-Si4N3. The equilibrium PDDOS depicted in Figestimated the rate of electron transfer from either of the elecure 3 a clearly shows that the density of states across the (eF ) trodes by applying the Fermi Golden rule approach (FGRA).[25] are mainly present in the down-spin channel, demonstrating Within the FGRA, the spin-polarized electron transfer rate 2p metallic features, whereas its up-spin counterpart has no subthrough the tunnel barrier is given by gðeÞ ¼ h jG j2 1ðeF Þ. stantial PDDOS at the (eF ), which results in an insulating nature Here, 1ðeF Þis the density of states of the electrons at of the up-spin channel. These results clearly provide an interthe (eF ) of the respective electrode, and the tunneling papretation of the spin selectiveness of the rectification process. rameter j G j 2 is calculated by using WKB approximation, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A schematic illustration of the conduction mechanism under ð2 mð eVb Þ jGj2 1expð2 d Þ, where Vb is the voltage drop across h finite bias and resulting rectification action is given in Figure 4 (upper panel). The system shown in Figure 4 a resembles the the tunnel junction, and f and d are the height and width of conduction mechanism of the two-probe system when + 0.5 V the tunnel barrier, respectively. During the calculation, the is applied to the left electrode, keeping the right electrode at height (f) of the tunnel barrier is estimated from the energy 0.0 V, whereas Figure 4 b represents the situation when 0.5 V gap between the Fermi energy of the electrode and energy is applied to the left electrode only. In the bottom panels of corresponding to the SOHMO of the central region; and the 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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the emergence of relatively large spin-polarized current (downspin in this case) through the device only at negative bias, thereby creating an asymmetric current flow through the system, making it conducive for rectification action. A molecular-level origin of the high rate of electron transfer though the molecule at negative bias is provided by analyzing the molecular projected self-consistent Hamiltonian states (MPSH)[24] of the twoprobe system shown in Figure 4 (bottom panel). The figure includes the MPSH states of the two optimum voltages, namely 0.5 V for the active spin channel (down spin). At 0.5 V, the Figure 4. Spin-polarized conduction mechanism through (2X2) g-Si4N3 physisorbed onto Au (111) surface when MPSH states are strongly deloa) 0.5 V is applied to the left electrode keeping the right electrode at 0.0 V, and b) 0.5 V is applied to the left electrode keeping the right electrode at 0.0 V; bottom figures show the MPSH state corresponding to the SOHMO calized and dominated by the of the two-probe system. 2p-orbital contribution of both OR Si atoms and N atoms, and width (d) of the tunnel barrier is the length of the active their contribution is clearly reflected in the delocalized p region extended from the left to right electrode contact nature of the electron density. However, at + 0.5 V, electrons points. In Figure 4, gR refers to the spin-polarized electron are localized over the Si atoms in the shape of a pure p orbital transfer rate between the right electrode and the molecule and, indeed, this localization is responsible for the quenching and gL is the spin-polarized electron transfer rate between the of the electron transfer rate with respect to the net current obtained in the forward bias. It is worth noting that at + 0.5 V, left electrode and the molecule. The gL and gR, thus obtained, part of down-spin MPSH state is concentrated over the topwere plotted against the applied bias and the results are preright side OR Si atom, which is indicative of probable coupling sented in Figure 5. The figure demonstrates that, at negative with the right electrode; however, it is also evident that no bias, the gL values are much larger compared with gR and the such coupling appears at 0.5 V. Hence, it appears that during opposite trend is clear in the positive bias. The contrasting the fabrication process, any gold ad atom close to this Si atom bias dependence, and asymmetric nature of gL and gR indicates can influence the net current through the device. At the same time, a review of the literature illustrates that net current though such nanodevices depends on the extent of electron delocalization in the central region, which is more at 0.5 V, resulting in larger current at that bias.
3. Conclusions
Figure 5. Plot of spin-polarized electron-transfer rate against applied bias.
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This nonequilibrium Green’s function study establishes (2X2) gSi4N3 as a simple transition-metal-free ferromagnet that exhibits both charge and spin current rectification. To the best of our knowledge, this is the first transition-metal-free system that is structurally simple and, due to charge and spin rectification, is capable of executing both logic and memory action. The current through the system is essentially due to downspin transmission. The PDDOS analysis clearly suggests that this spin-selective rectification is mostly controlled by the 2porbital contribution of the outer ring Si atoms of the molecular system. Whereas the schematic diagram illustrates the conduction mechanism, asymmetric bias-dependence of the spin-polarized electron transfer rate explains the emergence of spinpolarized rectification action. MPSH analyses suggested the ChemPhysChem 2014, 15, 2756 – 2761
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Acknowledgements S.S. acknowledges CSIR, Govt. of India [03(1256)/12/EMR-II] for the research funding. S.C. acknowledges INDNOR bilateral project for funding support and CRNN, University of Calcutta for providing computational resources. Keywords: charge transfer · density functional calculations · magnetic properties · quantum chemistry · semiconductors [1] I. Zutic, J. Fabian, S. D. Sarma, Rev. Mod. Phys. 2004, 76, 323 – 410. [2] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, D. M. Treger, Science 2001, 294, 1488 – 1495; S. Sanvito, Chem. Soc. Rev. 2011, 40, 3336 – 3355; K. Stokbro, J. Taylor, M. Brandbyge, J. L. Mozos, P. Ordejon, Comput. Mater. Sci. 2003, 27, 151 – 160. [3] S. Sen, S. Chakrabarti, J. Am. Chem. Soc. 2010, 132, 15334 – 15339. [4] H. Dalgleish, G. Kirczenow, Phys. Rev. B 2006, 73, 235436. [5] B. Dieny, V. S. Speriosu, B. A. Gurney, S. S. P. Parkin, D. R. Wilhoit, K. P. Roche, S. Metin, D. T. Peter-son, S. Nadimi, J. Magn. Magn. Mater. 1991, 93, 101 – 104. [6] B. Braunecker, D. E. Feldman, F. Li, Phys. Rev. B 2007, 76, 085119. [7] A. Du, S. Sanvito, S. C. Smith, Phys. Rev. Lett. 2012, 108, 197207. [8] Y.-W. Son, M. L. Cohen, S. G. Louie, Nature 2006, 444, 347 – 349. [9] Er. Kan, Z. Li, J. Yang, J. G. Hou, J. Am. Chem. Soc. 2008, 130, 4224 – 4225. [10] Y. L. Lee, S. Kim, C. Park, J. Ihm, Y. W. Son, ACS Nano 2010, 4, 1345 – 1350.
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Received: April 21, 2014 Published online on July 8, 2014
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