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WIREs Comput Mol Sci
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# Prospects of spintronics based on 2D materials

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Spintronics holds the promise for future information technologies. Devices based on manipulation of spin are most likely to replace the current silicon complementary metal‐oxide semiconductor devices that are based on manipulation of charge. The challenge is to identify or design materials that can be used to generate, detect, and manipulate spin. Since the successful isolation of graphene and other two‐dimensional (2D) materials, there has been a strong focus on spintronics based on 2D materials due to their attractive properties, and much progress has been made, both theoretically and experimentally. Here, we summarize recent developments in spintronics based on 2D materials. We focus mainly on materials of truly 2D nature, that is, atomic crystal layers such as graphene, phosphorene, monolayer transition metal dichalcogenides, and others, but also highlight current research foci in heterostructures or interfaces. In particular, we emphasize roles played by computation based on first‐principles methods which has contributed significantly in the designs of spintronic materials and devices. We also highlight challenges and suggest possible directions for further studies. WIREs Comput Mol Sci 2017, 7:e1313. doi: 10.1002/wcms.1313

• Structure and Mechanism > Computational Materials Science
• Electronic Structure Theory > Ab Initio Electronic Structure Methods
• Electronic Structure Theory > Density Functional Theory
Spin‐dependent electron transport properties of 8‐ZGNR obtained by Zeng et al. (a) I–V curves for (M L , M R ) = (1, 0) and (−1,0). (b) I–V curves for (M L , M R ) = (1, 1) and (1, − 1), respectively. See Ref for more details. Reprinted with permission from Ref . Copyright 2011 American Institute of Physics.
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Schematic diagram of ZGNR‐based bipolar spin diodes proposed by Zeng et al. Either or both GNR leads can be magnetized by an external magnetic field. The magnetization direction is represented by M L (or M R ) = 1 or −1, corresponding to upward and downward magnetization respectively, while M L (or M R ) = 0 indicates that the corresponding lead is nonmagnetic. Figure (a) shows that under the magnetic configuration of (M L , M R ) = (1,0) and a positive bias, only spin‐down electrons are transported through the device, while figure (b) shows that only spin‐up electrons are allowed transport from left to right leads under a negative bias and the same magnetic configuration of the electrodes. The device behaves as a bias‐controlled bipolar spin diode device. Reprinted with permission from Ref . Copyright 2011 American Physical Society.
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Edge‐specific electronic and magnetic properties of zigzag graphene nanoribbons. The bandgaps (eV) measured by tunneling spectroscopy and calculated using the mean‐field Hubbard model are shown as a function of ribbon width (nm). A sharp semiconductor (antiferromagnetic) to metal (ferromagnetic) transition occurs at ~7 nm which is caused by temperature and doping effects. See Ref for more details. Reprinted with permission from Ref . Copyright 2014 Macmillan Publishers Limited. All rights reserved.
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(a) Design of the reprogrammable magnetologic gate, performing boolean expression OR(XOR(A,X),XOR(B,Y)). The inputs are the magnetization directions of the contacts labelled by A, B, X, and Y. Steady‐state currents, driven by V dd , flow between A(B) and X(Y). The output is given by a transient current response, I M (t), caused by an in‐plane single rotation of M. (b) A similar structure but with a pinned middle contact. The transient current, I M (t), is triggered by a voltage signal, clk2, applied to a (nonmagnetic) back‐contact beneath the midsection. Semiconductor regions beneath the contacts are heavily doped. Different logic operations can be performed using the magnetization alignments of A and B. Reprinted with permission from Ref . Copyright 2007 Nature Publishing Group.
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(a) Device structure and measurement setup used by Wen et al. to demonstrate XOR operation in graphene magnetologic gates at room temperature.. A, B, and M are MgO/Co electrodes. The spin channel is a single‐layer graphene. R is Ti/Au nonmagnetic reference electrode used as ground point. I OUT and V OUT are the measured current and voltage signal, respectively. R sen is a variable resistor. V OFFS is an ac voltage source. External magnetic field H is applied to the easy axis of the electrodes. See Ref for further details of the device. (b) I OUT measured as a function of H. Top left inset: truth table of XOR logic operation. Reprinted with permission from Ref . Copyright 2016 American Physical Society.
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Schematics of the three‐terminal device proposed by Dery et al. The channel indicates the current flow region of n‐doped semiconductor grown on top of an insulating substrate.
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(a) Nonlocal and (b) local spin transport measurement geometries. (c) Nonlocal magnetoresistance measured on a typical graphene nonlocal spin valve with tunneling contacts. Figures (a) and (b) are reprinted with permission from Ref . Copyright 2014 Macmillan Publishers Limited. Figure (c) is reprinted with permission from Ref . Copyright 2010 The American Physical Society.
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(a) Schematic illustration of spin diode proposed by Wang et al. The spin diode consists of ferromagnetic/strained/normal graphene junction. (b) The band diagram for conducting electrons through the graphene junction. H ex is the exchange field in graphene due to the proximity effect, V 0 is the offset of conduction bands of the ferromagnetic and strained graphene. W is the width of the strained graphene. An external bias (V b ) is required to overcome the band offset and inject spin down electrons through the strained tunnel barrier. It gives rise to the spin rectification effect for the spin diode. Reprinted with permission from Ref . Copyright 2014 AIP Publishing LLC.
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(a) Schematic illustration of the sFET proposed by Semenov et al. The device consists of a graphene channel (shown by circles with bonds) and a ferromagnetic gate dielectric. The ferromagnetic source (S) and drain (D) have collinear magnetic moments along the y axis (large arrows), while the ferromagnetic dielectric directs its magnetization along the x axis (filled circle with a dot). The figure illustrates the condition, where the electron spin (small arrow) reverses its direction due to the exchange interaction with the ferromagnetic gate dielectric, leading to a suppressed conductance of the device. When an applied bias V g (along the z axis) alters the exchange interaction and, subsequently, the degree of spin rotation, the electron has a finite probability to be collected by the drain. A similar scenario can be realized when the magnetic orientations of the source and drain are antiparallel to each other. (b) Schematic of the model proposed by Yokoyama et al. consisting of a normal/ferromagnetic/normal graphene junction. (c) Model proposed by Michetti et al. consisting of a double‐gated graphene bilayer structure in which the central part (c) is characterized by the use of a ferromagnetic oxide as spacer between the upper layer and the top gate. The oxide thickness t ox and the interlayer distance d 0 are indicated. The potential of the top gate V GT and the one of the back gate V GB are externally fixed, inducing potential values V U and V L on the upper and lower graphene layer, respectively, via nonlinear Poisson equation. Figures (a), (b) and (c) are reprinted with permission from Ref . Copyright 2007 American Institute of Physics, Ref . Copyright 2008 The American Physical Society, and Ref . Copyright 2010 American Chemical Society, respectively.
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Illustration of unpolarized current, spin polarized current, fully spin polarized current, and pure spin current.
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(a) Model for Ni(111)/(h‐BN)3/graphene device. (b) The calculated I–V curve of the Ni(111)/(h‐BN)3/graphene device. (c) Schematic diagram showing the effect of a tunnel barrier on the spin polarization of the current injected from the Ni(111) electrode to graphene. The subscript 3 indicates three atomic layers of h‐BN between graphene and Ni electrode. Reprinted with permission from Ref . Copyright 2014 American Physical Society.
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Diffusion path of a single Co atom adsorbed on graphene with 5‐5‐8 line defect. Labeled 1, 2, 3, ⋯ and I, II, III, ⋯, indicate the local minima and transition states, respectively. The top right inset presents the corresponding geometric path. The lower left insets shows the spin density and charge density of configuration 3, with iso‐surface of 0.005 and 0.01 e3, respectively. A 1D Co nanowire is predicted to grow along the topological line defect. Reprinted with permission from Ref . Copyright Springer.
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Vacancy structure and formation energies in black phosphorus. (a) Unreconstructured structure of a single vacancy in monolayer phosphorene. (b) SV‐(5|9) and SV‐(55|66) structures and their formation energies in monolayer (1 L), bilayer (2 L), and bulk black phosphorus. Note that for monolayer black phosphorus, the positively charged vacancy state is stable if the Fermi energy is ≤0.24 eV above the valence band maximum and the negatively charged state is more stable if the Fermi energy is higher. Reprinted from Ref . Copyright 2015 Nature Publishing Group.
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(a) Schematic illustration of monolayer MoS2 with two S vacancies symmetrically located on two sides of MoS2, subject to in‐plane tensile strain. (b) Variations of calculated magnetocrystalline anisotropy energy and magnetic moment with applied tensile strain. The symmetric two S vacancy defect shows the largest magnetic moment among various vacancy types investigated and a transition from out‐of‐plane to in‐plane magnetization occurs at ~13% of tensile strain. Reprinted with permission from Ref . Copyright 2015 American Chemical Society.
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Spin moment of the substitutional transition and noble metals in graphene as a function of the number of valence electrons. Black symbols correspond to the most stable configurations using GGA. Three main regimes are found: (i) filling of the metal–carbon bonding states gives rise to the non‐magnetic behavior of Ti and Sc; (ii) non‐bonding d states are filled for V, Cr, and Mn giving rise to high spin moments; (iii) for Fe all non‐bonding levels are occupied and metal–carbon antibonding states start to be filled, giving rise to the observed oscillatory behavior for Co, Ni, Cu, and Zn. Open and gray (red) symbols correspond, respectively, to calculations of Fe using GGA + U and artificially increasing the height of the metal atom over the graphene layer. The symbol marked as Zn $C 3 v$ corresponds to a Zn impurity in a high‐spin symmetric C 3v configuration. Reprinted with permission from Ref . Copyright 2010 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
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Atomic structures and doping sites of (a) graphene, (b) black and blue phosphorus, and (c) transition metal dichalcogenides (MoS2 is shown). Figures (b) and (c) are reprinted with permission from Ref . Copyright 2015 American Chemical Society, and Ref . Copyright 2015 American Chemical Society, respectively.
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Schematic spin field effect transistor.
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(a) Four states of FMTJ corresponding to different directions of polarization and magnetization. (b) Resistance versus magnetic field curves measured at 50 K in the as‐grown state of a junction (black squares) and after polarization switching with a +3 V applied electrical bias (red circles). The polarization state of the barrier as well as magnetization directions in each magnetic layer are schematically shown for each nonvolatile state. Figure (b) is reprinted with permission from Ref . Copyright 2012 Macmillan Publishers Limited.
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(a) Principle of spin transfer torque switching: A magnetic layer with fixed magnetization direction serves as polarizer for the spin of electrons flowing from one side to the other. When the soft layer magnetization is in the same direction as hard layer, the switching occurs mainly by minority electrons through scattering and when the two magnetizations are antiparallel, the switching occurs by majority electrons. (b) Schematic representation of STT‐MRAM. Reprinted with permission from Ref . Copyright 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim.
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(a) and (b) Topological‐protected spin configurations of skyrmions and domain walls. (c) Schematic diagram of a DMI at the interface between a ferromagnetic and heavy‐element metal layers. The DMI vector D12 is perpendicular to the plane of the triangle (two magnetic sites and a heavy metal atom). Because a large SOC exists only in the bottom heavy metal layer and DMI dominates only in the first atomic layer of the ferromagnetic metal (d) and (e), this DMI is, thus, not compensated by a DMI coming from a symmetric triangle. However, this interfacial DMI can be enhanced by different chiral DMI (anti‐clockwise (f), and clockwise (g)) when they are put together head‐to‐head (h) due to the additive effect. Figure (c) is reprinted with permission from Ref . Copyright 2013 Macmillan Publishers Limited. Figures (d) are (e) are reprinted with permission from Ref . Copyright 2015 American Physical Society. Figures (f), (g) and (h) are reprinted with permission from Ref . Copyright 2016 arXiv.org.
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Edelstein and inverse Edelstein effect. (a), (b) Top: Energy dispersion surfaces of the 2D states at a Rashba interface (a) and Dirac dispersion cone of the surface or interface states of a topological insulator (b). Bottom: Fermi contours of Rashba states (a) with two contours with helical spin configurations of opposite chirality and TI surface or interface states (b). (c), (d) Edelstein effect: A flow of electrons along x ($j C 2 D x <0$ in the figure) in Rashba (c) or TI (d) 2DEGs is associated with shifts δk of the Fermi contours generating an extra population of spin along the y direction (for Rashba there is a partial compensation of the contributions of the two contours). (e), (f) Inverse Edelstein effect: Injection of a spin current density spin polarized along y ($j S y 3 D <0$ in the figure) into Rashba (e) or TI (f) 2DEGs induce an extra population on one side of the Fermi contour (along the x direction), a depletion on the other side, and therefore a charge current density $j C 2 D x <0$. $j S y 3 D$ and $j C 2 D x$ of this figure can be seen as carried by the electrons of the wave vector (wavy arrow) and spin (straight arrow) in the schematic at the bottom of (a) and (b). For a circular Fermi contour, the expressions of the IEE length λ IEE are given in the bottom right of the figure as a function of the relaxation time of the topological states and Rashba coefficient α R or Fermi velocity v F of the DC. All the figures are drawn for electron‐type conduction in the 2D states. See Ref for more details. Reprinted with permission from Ref . Copyright 2016 American Physical Society.
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Schematic illustration of the (a) spin Hall effect (SHE) and (b) inverse spin Hall effect (ISHE). Here $M →$ indicates the relative orientation of the associated magnetization, $E →$ the electric field, jC the charge current, and jS the spin current. The SHE converts an incident charge current into a transverse spin current, while the ISHE converts an incident spin current into a transverse electric field. Reprinted with permission from Ref . Copyright 2014 The Royal Society of Chemistry.
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