Magnetism in two-dimensional materials beyond graphene

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Magnetism in two-dimensional materials beyond graphene N. Sethulakshmi 1, Avanish Mishra 2, P.M. Ajayan 3,⇑, Yoshiyuki Kawazoe 4, Ajit K. Roy 5, Abhishek K. Singh 2,⇑, Chandra Sekhar Tiwary 1,3,6,⇑ 1

Department of Material Science and Engineering and Department of Chemistry, Indian Institute of Technology, Palaj, Gandhinagar 382355, India Materials Research Centre, Indian Institute of Science, Bangalore 560012, India 3 Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA 4 New Industry Creation Hatchery Center, Tohoku University, 4-4-6 Aramaki aza Aoba, Aoba-ku, Sendai 980-8579, Japan 5 Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright Patterson AFB, OH 45433-7718, USA 6 Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur, West Bengal, India 2

Magnetic materials enjoy an envious position in the area of data storage, electronics, and even in biomedical field. This review provides an overview of low-dimensional magnetism in graphene, h-BN, and carbon nitrides, which originates from defects like vacancy, adatom, doping, and dangling bonds. In transition metal dichalcogenides, a tunable magnetism comes from doping, strain, and vacancy/ defects, and these materials offer spintronics, as well as photoelectronic potentials, since they have an additional degree of freedom called valley state (e.g. MoS2). Strain- and layer-dependent magnetic ordering has been observed in layered compounds like CrXTe3, CrI3, and trisulfides. The magnetism in 2D oxides like MoO3, Ni(OH)2, and perovskites are also interesting as they are potential candidates for next-generation devices having faster processing and large data storage capacity. Quasi 2D magnetism in MXene and in atomically thin materials supported on 3D materials will also be discussed. Finally, some of the challenges related to the control of defects and imperfections in 2D lattice, promising approaches to overcome them will be covered. Introduction Magnetism has come a long way from the remark by Helmholtz, “Our ignorance concerning magnetism is the disgrace of the nineteenth century” [1]. In recent decades, there has been immense advancement in realizing the applications of magnetism as permanent magnets in loudspeakers, electric motors, audio and video systems for communication, in data recording as magnetic storage disks, in transformers and generators, and as digital magnetic storage in credit and debit cards. In our day to day life, we deal with magnetism in phones, doorbells, refrig⇑ Corresponding authors at: Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA (P.M. Ajayan); Materials Research Centre, Indian Institute of Science, Bangalore 560012, India (A.K. Singh); Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur, West Bengal, India (C.S. Tiwary). E-mail addresses: Ajayan, P.M. ([email protected]), Singh, A.K. ([email protected]), Tiwary, C.S. ([email protected]). 1369-7021/Ó 2019 Elsevier Ltd. All rights reserved. https://doi.org/10.1016/j.mattod.2019.03.015

erators, washing machines, blenders, vacuum cleaners, and even in children’s toys. The detectable magnetic force around a magnet or electric current is within a specific range, and such an area around a magnet or current is the magnetic field. The technological advancement of magnetism has kept abreast with the theoretical concepts and the progress of research especially in magnetic field sensing. In the current context, magnetic field sensing largely focuses on electronics and biomedical fields rather than the perturbations by earth’s magnetic field. Sensors adhering to the effects of electromagnetic/magnetic field include fluxgate sensors, position sensors, proximity sensors, magnetoelastic sensors, magneto-inductive sensors, and magneto-galvanic sensors, which have various applications in navigation, automobiles, nuclear power plants, and fiber optics. Novel technologies utilizing large magnetic field sensing in close correlation with electronic transport mechanisms include SQUID, Hall effect, 107

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spintronics, giant and anisotropic magnetoresistance, magnetoimpedance magneto diodes or transistors, magnetic tunnel junctions, and microelectromechanical system-based magnetic sensors [2–4]. Giant Magneto Resistance (GMR) and Tunnel Magneto Resistance (TMR) sensors using ferromagnetic layers will take over automotive and consumer electronics soon as they offer high accuracy and high stability, utilizing the spin nature rather than charge of electrons [5–7]. In medical research, magnetic materials especially nanoparticles have direct applications since they can directly enter body, blood, or tissues ensuring a good biocompatibility. Magnetic hyperthermia is an in vivo therapy where heat produced by magnetic materials in the presence of external alternating magnetic field is utilized for treating tumor/cancerous cells. Additional therapeutic applications of magnetic materials are in targeted drug delivery and controlled drug release. In the field of diagnostics, magnetic nanoparticles coated with biological entities function as biomarkers by measuring change in Brownian motion. This property is conveniently used to separate/detect/isolate specific cells and in immunoassays. Nanomagnetism also finds extensive applications in Magnetic Resonance Imaging (MRI), Nuclear magnetic Resonance (NMR), medical magnets for pain relief, healing fracture, gene delivery, tissue regeneration, magneto-optic screening using laser and in magnetic field detection of parasites [5,8,9]. Biosensors utilizing functional nanomaterials especially magnetic Fe3O4 nanocomposites can modify the electrode surface with an external magnetic field. Bio/geno sensors have achieved increased performance with its amplified detection signal, biological compatibility, nontoxicity, and stable biosensing interface [10]. Systematic and long-term toxicological studies are ongoing to translate potentials of biomagnetism to clinical applications. A plethora of studies have explored and designed magnetic nanomaterials with appropriate properties adaptable for in vivo and in vitro bio-applications but a synergy need to be established between the optimized properties with therapeutic/diagnostic capabilities [9]. Fig. 1 gives an overview of diverse applications of magnetism. From a theoretical perspective, materials that possess permanent magnetic properties and in which magnetization persist even on removal of magnetic field are categorized as ferro or ferrimagnetic materials. Magnetic spin ordering mechanism in such magnetic materials is interpreted in two ways. The first case deals with overlapping of orbitals of adjacent atomic moments (Fe–O or O–Cr–O) [refer Fig. 2], where 3d valence electrons are localized to atoms. Electrostatic interaction between neighboring atoms depends on spatial separation of the electrons and the relative orientation of electron spins. In parallel spin alignment, Pauli’s exclusion principle requires them to be spatially apart while in antiparallel alignment electrons align closely and their wave functions overlap. The energy difference of these two electron spin alignments is defined as exchange or interaction energy and goes well with the concepts of molecular field theory and the Heisenberg model for magnetic ordering. This exchange interaction is in many folds stronger than magnetic dipole interaction (which aligns dipoles antiparallel), which in agreement with the magnetic anisotropy aligns electron spins providing permanent and long-range magnetization. Fig. 2 shows the elec-

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FIGURE 1

Applications of magnetism in various fields.

tron spin ordering in most common magnetic oxides like CrO2, FeO, and Fe3O4, leading to ferromagnetism or antiferromagnetism. The second case assumes the lattice has itinerant or delocalized conduction electrons (mainly in metals) and utilizes band theory to explain the non-integral values of magnetic moments. Band theory explains the macroscopic phenomena like Pauli paramagnetic susceptibility following the interaction of magnetic field with delocalized spins [11,12]. Apart from transition metal compounds, magnetic ordering can be found in a variety of other systems. Over the years, various exchange interactions, such as double exchange, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, and superexchange mechanisms, have been proposed to explain spin ordering in half-metallic compounds, where one-type spin state dominate over the other at Fermilevel. Such materials have high tunable magnetic order concerning the crystallographic structure, substrate/material strain, and external electric field, making them potential candidates for multifunctional applications. Rare earth compounds, such as manganites (Eg. GdMnO3, SrMnO3), are perfect examples for those half-metallics, and magnetic ordering is in coherence with other translational, electrical, or thermal properties like magnetoresistance, magnetostriction, and thermoelectricity[11–14]. Application of spin of the electron for devices, storage, transport, etc., referred to as spintronics, has stimulated immense interest in the scientific community. Realizing similar spin-based phenomena at nanoscale mainly guides the search for lowdimensional (LD) magnetic materials. Upon reducing dimensionality, a radical change occurs in the material characteristics (such as electrical, magnetic, and structural) with exciting prospects for future technological applications. In general, commonly known LD materials like graphene, carbon nanotubes are candidature materials as fuel cell electrode catalysts, in

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FIGURE 2

Ferro-/Antiferro-magnetic ordering in CrO2, FeO, and Fe3O4 systems.

molecular electronics and in clinical biology. Similarly, highly porous nanofiber finds applications in tissue engineering and commercial applications in garments and sport apparels. Stacked structures of one-dimensional (1D) nanowires can form complex integrated circuits in semiconductor technologies, such as diodes, logic gates, or transistors. Zero-dimensional (0D) metal nanoparticles and their nanocomposites are utilized in sensors, coating devices, fuel cells, and optical devices and in biomedical field [15,16]. In addition to large surface to volume ratio of LD materials, their high carrier mobility and density as in twodimensional (2D) graphene provide increased electrical sensitivity. Increased sensitivity makes graphene utilized as an enhancement sensor along with chemical, humidity, or bio sensors for detecting one single biomolecule or individual chemical bond. Field effect Transistors using 2D materials like MoS2 have less noise due to high bandgap, and sensors utilizing such materials offer high sensitivity necessary for protein detection. Inducing magnetism in Quasi 2D materials like Transition Metal Dichalcogenides (TMDs) through defects, intercalation of magnetic ions, or by strain is being carried out with a view toward their futuristic application in thin-channeled transistors and spinelectronic devices. Van der Waals materials like manganese selenides (MnSe) can also be developed as 2D magnetic materials with higher transition temperatures for immediate technological applications in magnetic sensors, probes, and spin devices with contributions to theoretical concepts like quantum phases, 2D superconductivity, and exotic magnetic ground states [17,18].

Magnetism in low dimensions On reducing dimensionality, magnetic moment per atom increases due to less quenching of orbital magnetic moments

with a tunable semiconductor gap. Moreover, materials having antiferromagnetic ordering in bulk phase can be ferromagnetic in lower dimension due to ordering of spin domains. Further, interplay of magnetic and electric properties in two dimensions is elementary for next-generation super slim electronics and optical and quantum information devices. Novel concepts like quantum Hall effect, carrier doped field effect transistor and straindependent magnetism have activated research in the area of LD compounds to explore spin transport mechanisms and magneto elastic coupling mechanisms (or lattice – spin coupling). The concept of LD magnetism can be traced back to 1925, when Ising proposed a 1D lattice model to provide a microscopic view of the alignment of neighboring magnetic moments along a favored direction in coherence with the Weiss molecular field theory. Later in 1931, Hans Bethe described a method for solving quantum mechanical ground state of the antiferromagnetic 1D Heisenberg model. LD magnetism remained only a theoretical concept for about 40 years before realizing that such magnetism could be found in real materials as such or synthesized by ingenious crystal growth techniques. Presently, magnetism in LD is an active area of research in theoretical and experimental low energy physics as it would lead to understanding of ground/ excited states, the interplay of quantum and thermal fluctuations, and spin–orbit interaction, further leading to the understanding of exotic magnetic phases at lower dimensions [19,20]. 2D magnetic materials, where spin dominates over charge is believed to be the fundamental pointer enabling studies on topology, superconductors, and spintronics, thus strengthening their theoretical and experimental credibilities [21,22]. In 2D magnetism, it is perceived that single-ion anisotropy and small magnetic field affect the transition temperature in comparison with its bulk counterpart. The flexibility of these materials could reveal 109

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theoretical aspects of coupling between lattice and spin magnetic moments, evolution of magneto-elastic coupling with thickness, and strain-dependent magnetic ordering giving prominence to the spin ordering mechanisms. Theoretical backbone of 2D materials is the Mermin–Wagner theorem, which states that “In 1D and 2D, continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions” [23]. Magnetic analog of this theorem says that at any nonzero temperature, one- or two-dimensional isotropic Heisenberg models with exchange interactions of finite range cannot be ferromagnetic or antiferromagnetic. This can be explained by the following relation of magnetization at finite temperature and can be written as follows: M ðT Þ ¼ M ðT ¼ 0Þ  DMðTÞ;

where, DM(T) is the reduction due to thermal excitation of spinwaves. DM diverges in case of isotropic spins and breakdown of magnetic ordering happens (evident excitation of spinwaves). However, with an easy axis of magnetization (anisotropy), DM does not diverge due to the formation of gapped spin wave dispersion. It modifies the dispersion relation with an additive constant; for ferromagnets, it becomes E = A + Bk2, which shifts the lower integration limit from 0 to A for calculating the reduction in magnetization due to finite temperature. Therefore, the magnetic ordering can be stabilized. Hence, long-range magnetic ordering of ferro/antiferro type is sustained in 2D systems only if thermal fluctuations are suppressed and a possible opponent for thermal fluctuations could be magnetic anisotropy. In the case of 2Dmaterials, thermal fluctuation and magnetic anisotropy are order of few meV (0.1 meV). It is proposed that external magnetic field in LD systems could enhance effective anisotropy from the near-zero magnetocrystalline anisotropy, leading to magnetic ordering in lower dimensions [20].

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The technological advancement in the fields of spintronics, magnetoresistance, magnetic refrigeration, and biomagnetism is closely knit with the progress of magnetic materials. Interplay of spin–orbit interactions and quantum and thermal fluctuations becomes more prominent at lower dimensions, thus rendering interesting spin ordering mechanisms. It is expected that future electronics would be mostly based on spin control and spin transport properties rather than utilizing the electronic charge since spin state of electron persists for nanoseconds, while electron momentum drops within few femtoseconds, thereby lending immense significance to the magnetism in LD materials. Table 1 provides a comparison of bulk and low-dimensional magnetism. Discovery of graphene, a truly atomicthin 2D form of carbon, spearheaded an area of electronics based on carbon materials. Even though graphene is nonmagnetic, magnetic moments can be induced into their lattice, and even magnetic sensors using graphene working on the principle of hall effect have been devised. Magnetism in graphene is perceived as an additional adornment to their multifunctionality with future implications in electronic industry by rendering greater data processing speed, higher storage, and low power consumption by effective control and manipulation of spin polarization [24–26]. Aromatic hydrocarbons like graphene on interaction with metal ions offer strong interaction with the polymer and finds applications in biosensing or as corrosion resistive mesh electrodes in electroplating [27,28]. Biomedical applications of graphene are in biosensing, cancer therapy, gene delivery, cell imaging, and scaffold for tissue engineering [29]. Theoretical background for graphene magnetism suggests that removal of a single pz orbital will leave graphene with single p state at Fermilevel. Nevertheless, electrostatic Coulomb repulsion forbids occupation of two electrons of same spins in such a p

TABLE 1

Comparison of bulk and low-dimensional magnetism. Properties

Bulk magnetism

Low-dimensional magnetism

Structure sensitive property Domain Superparamagnetic

Less effect of structure modification

Magnetic properties depend on structure changes majorly, such as coercivity Becomes single domain due to reduction in dimension Single domain: Decreasing size decreases the coercivity

Ferro/Antiferromagnetism

Magnetic moment

Spin Orbital magnetic moment

Multidomain structure Multidomain: Decreasing the size increases the coercivity Ferromagnetic particles in bulk phase Antiferromagnetic in bulk Small magnetic moment/atom, such as Ni and Fe, has 0.56 and 2.27 mB/atom, respectively Spin of the bulk phase Highly quenched especially d-orbital magnets

Hysteresis loop area

Large hysteresis loop area

Directional anisotropy or easy axis of magnetization Magnetic transition temperature Magnetoresistance

Small directional anisotropy

110

Above room temperature Small Magnetoresistance

Small ferromagnetic particle showing superparamagnetism In lower dimension, it may behave as ferromagnets due to single domain formation Huge increase in magnetic moment going from 3D to 0D, such as for Fe in 2D, 1D, and 0D values are 2.96, 3.3, and 4.0 mB/atom, respectively Surface spin contributes more Less quenching of orbital magnetic moment, such as for Fe in 0D magnetic moment is 4 mB/atom, close maximum possible number of 6 mB/ atom Decrease in hysteresis loop area because of reduction in neighboring spins Large directional anisotropy due to chopping of dimensions

Magnetic transition temperature decreases severely on reducing dimension Layered structure to form hybrid structures hence, Giant Magnetoresistance

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state leading to only single occupancy and thus resulting in a net magnetic moment [30]. In the case of infinite graphene structures, crystallographic directions (like armchair and zigzag) and the edges of graphene structure becomes relevant metallic or semiconducting. It is predicted that armchair nanoribbons have no magnetic moment, while a large density of low-energy states (seen as flat-band) accounts for magnetic ordering in the zigzag graphene nanoribbons [31]. It has been shown that magnetic moments at the edges couple by electron/ hole doping even though on high doping these flat bands shift away from Fermilevel suppressing magnetization [32,33]. Thus, it could be learned that edge states at zigzag face of graphene have flat energy dispersion bands with considerable density states, which can contribute to magnetic spin polarization at edges. As a result, tunable magnetic behavior in graphene nanoribbons was discovered by means of applying electric field across zigzag-shaped edge. Different spin domination at opposite edges gets converted to similar spin with application of external electric field [31,34]. Band structure of graphene has claimed that a single p state by the removal of pz orbital could generate spin polarization, but the experimental challenge lies in achieving this theoretical concept by a controlled creation of vacancies or adatoms in the graphene lattice [30,37–39]. On irradiating graphene with high-energy particles like protons and (a) if the transferred energy is larger than

(a)

(c)

the displacement threshold, a pair of point defects – a vacancy and an interstitial – is formed when the C atom leaves the equilibrium position [40–42], (b) while incident protons of low speed are able to bind with the individual carbon atoms of graphene lattice resulting in rehybridized sp3states leading to hydrogen chemisorption. Fig. 3 summarizes the contribution of carbon atoms toward graphene magnetism and the effect of H chemisorption on graphene bipartite structure. There are numerous works based on density functional theory speculating possible magnetic moment formation by vacancyor adsorbing adatom in graphene/multilayers favoring ferro/antiferro magnetism depending on defect in hexagonal sublattices [35,43–47]. Attempts to induce magnetic ordering in graphitic compounds via point defects using fluorine adatoms or by irradiation showed paramagnetic behavior close to 2 K, while the system is diamagnetic above 50 K [48]. A dilute fluorinated graphene can exhibit colossal anisotropic negative magnetoresistance, which is a result of strongly interacting defects influencing electronic structure. A first principal study on fluorine-doped graphene nanoribbons revealed that fluorination strength determines adatom height and the C–C bond length of GNRs. Also, influence of tensile strain and adatoms like tungsten on magnetic properties of fluorinated graphene has been investigated using density functional theory [39,49,50].

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FIGURE 3

(a) Schematic of induced spin-polarized electronic state by adsorption of H atom, green atom represents the A site and blue is B site of graphene’s bipartite nature, with conductance map along the line, the arrows indicate relative magnetic moment contribution of each carbon atom. (b) DFT-simulated STM and density of state (DOS) of H chemisorbed on graphene, having state above and below Fermi level of opposite spins [30]. (c) Spin density due to adsorption H atom twice at A site and once at B [35]. (d) Representation of the honeycomb lattice of graphene with its two high-symmetry directions armchair and zigzag along with unit cell. Each unit cell comprises two equivalent sub-lattices of carbon atoms, joined together by s bonds [36]. (e) Schematics of density of state and bottom spin distribution of valence band without and with the presence of transverse external field [31]. (a) and (b) Reprinted from Ref. [30] with permission from AAAS. (c) Reprinted with permission from Ref. [35], copyright (2007) by the American Physical Society. (d) Reproduced from Ref. [36] with permission of the Royal Society of Chemistry. (e) Reprinted with permission from Ref. [31], Springer Nature copyright (2006). 111

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The grain boundaries are an integral structural part and are 1D, which cannot lead to magnetic moment. There is a possibility that grain boundaries with dangling bonds can initiate grain boundary dislocation and defect called 5-8-7 defect (pentagon, octagon, and heptagon), which is magnetic and its magnetic property survives hydrogenation. Theory recommends that translational grain boundary lying along zigzag direction is closely confined to the core of the defect than tilt grain boundaries and hence can contribute to magnetic states [51,52]. Chemical/molecular doping in graphene laminates by gases/ liquids can also yield magnetic moments. Molecular doping on graphene laminates alters the carrier concentration in already irradiated graphene laminates, where the magnetic moment alignment can be switched off or on, and offers a control on the spin transport of graphene by external bias [53,54]. Magnetic origin by the introduction of transition metals in single and double vacancies of graphene sheet provided interesting theoretical results. Magnetic moments evolved from carbon sp2 hybrids and metal -s-p-d orbital are appreciable, and the bonding is found to be strong for most of the metal complexes with magnetization, even predicted for Au and Cu atoms at single vacancies of graphene sheet [55].

Nitrides, carbides, and hexagonal boron nitrides Nitrides and carbides of light (p block) are other potential candidates for 2D magnetic behavior since the introduction of holes in the graphitic-carbon nitride and the contracted behavior of 2p states in N and C favor magnetic moment formation. The phenomenon of electron spinpolarization of p-conjugated systems like graphene could be found in carbon nitrides, which possess porous frameworks with well-ordered vacancies. Graphene-like material, carbon nitride, is proposed to exhibit ferromagnetic ground state, and it has been proved by spin-polarized density functional theory calculations that graphene-like C2N (g-C2N), g-C4N3 has tunable magnetic coupling properties with respect to hole doping. The localized p nitrogen atoms or biaxial compressive strain plays a decisive role in magnetic moment formation unlike p magnetism of graphene. A variation from C4N3, g-C3N4 with introduction of extra hole has gained more prominence with respect to magnetic properties, where electron spinpolarization and ferromagnetism can be practically achieved. Theoretically, it has been proposed that in heptazinebased g-C3N4, the electronic structures can be tuned by doping with carbon atoms with an induced moment of 1.0 mB per carbon atom. The prediction of metal-free magnetism and ferromagnetic ground state crafts these materials for metal-free spintronics application [56–60]. Boron nitrides are another promising member for light element magnetism involving s-p electrons. Magnetic origin in nitrides is attributed to two mechanisms: through-bond spin polarization leading to ferromagnetic ordering mediated by an atom, while p–p interaction favors antiferromagnetic ordering [61]. Edge passivation of B or N atoms in zigzag boron nitride nano-ribbons can tune the magnetic ordering via half metallicity. Fluorination in hexagonal boron nitride (h-BN) could lead to weak ferromagnetism at room temperature, where the electrophilic nature of fluorine influences charge distribution around 112

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nitrogen atoms [refer Fig. 4(a)] [62,63]. Fluorinated BN (F-BN) sheet with variation in fluorination shows the coexistence of both ferromagnetic and antiferromagnetic ordering, hence leading to frustrated magnetization [refer Fig. 4 (b) to (d)]. First report of spin glass texture in 2D materials was found in case of F-BN [64]. Increased concentration of fluorine stabilizes the spinpolarized phase and induces magnetism at higher doping concentration. In half fluorinated single layers of BN, ferromagnetic and antiferromagnetic ordering can be modulated by isotropic strain. Apart from fluorination, density functional calculations proposed that doping by 5d transition metal atoms in h-BN sheets can also generate magnetic moments. In the case of hybrid BN nanoribbons, tailoring of line defect and the applied tensile strain work favorably toward tuning the bandgap and in stabilizing the ground-state ferromagnetic ordering [65]. There are reports suggesting that vacancy of B or N atoms, changing B/N atom ratio or replacement by C atoms can lead to spontaneous magnetization in 2D boron nitride sheets. Recently, it has been observed that metal-free ternary 2D carbon nanosheets (BCN) have tunable band gap and prefer ferromagnetic ordering to antiferromagnetic ordering. On substituting C atoms in a BN nanotube/nanosheet, an effective magnetic moment of 1 mB is generated, independent of the substitutional site (B or N). The observed magnetism in BCN structure is of ferromagnetic nature and originates from carbon doping, ruling out the possibility of extrinsic magnetic impurities. On removal of carbon dopants from the BN lattice, induced ferromagnetic response disappears as it is evidenced from the gradual decrease of saturation magnetization and coercive field [refer Fig. 4(e)]. This establishes carbon doping on honeycomb BN lattice as the most efficient method for obtaining spontaneous spin polarization and long-range magnetic ordering. Edge-based magnetism has also been theoretically proposed in armchair BCNhybrid nanoribbons and the magnetic moment formation is due to unpaired B or N atoms. Tailoring the edges of these BCN nanoribbons, such as by oxygen adsorption, is of great relevance for a clear understanding of the intriguing spin-polarized states, magnetic metallicity, and half metallicity in these LD magnetic hybrids [64–66]. Hydrogenation of graphene called graphane is believed to be an electronic insulator, while magnetic moment formation is observed in semi hydrogenated graphene or graphone with Curie temperature close to room temperature. A semi hydrogenated SiC (H–SiC) sheet is a ferromagnetic semiconductor and ordering changes to antiferromagnetic with H–CSi structure, indicating that magnetic ordering can be controlled by adsorption site of H atom [67]. Fig. 5(a) depicts structures of H–SiC and H–CSi. Chemically exfoliated nanosheets of FeC2 from bulk ThFeC2 (paramagnetic) is found to exhibit half metallicity, as well as ferromagnetism, with a Tc of 245 K. The magnetic origin is mainly attributed to small crystal field splitting and the high spin states of Fe atoms in FeC2 nanosheets due to the weak ligand effect of C2 dimers. Dual presence of ferromagnetism and half metallicity in metal-carbide sheets makes them ideal for spintronic applications [refer Fig. 5(b)] [68]. Development of next-generation spintronic devices demands for 2D materials with large values of spinpolarization ratio, magnetic anisotropic energy, and Curie temperature. Theoretically proposed 2D nanosheet of Fe2Si,

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FIGURE 4

(a) The spin-resolved charge density of half-fluorinated BN sheet. Yellow (cyan) denotes positive (negative) values [61]. (b) XRD and Raman spectra for h-BN and F-BN sheet, showing broadening and red shift of the peaks, respectively, and low-magnification bright-field TEM image of the thin F-BN sheets. (c) Magnetic hysteresis curve at room temperature for 8.1% fluorine doped F-BN, and (d) susceptibility vs. temperature with zero filed cooling (ZFC) and field cooling (FC) [62]. (e) The structure of BCN and seven possible site for doping of second carbon atom in BN sheet, hysteresis loop for BN and BCN sheet at 300 K, effect of c elimination on ferromagnetic effect in BCN sheets burned (in presence of O2) [64]. (a) Reproduced from Ref. [61] with permission of the Royal Society of Chemistry. (b) to (d) Reprinted from Ref. [62] with permission from AAAS. (e) Reproduced from Ref. [64] with permission of John Wiley and sons.

one of the distinct counterparts of Fe2Si alloy, is identified to be very promising material. Fe2Si has a ferromagnetic ground-state phase with 100% spinpolarization, and magnetic anisotropy energy comparable to Fe and Co. Curie temperature of 760 K was found using Ising model [refer Fig. 5(c)] [69]. Experimental capabilities of Fe2Si need to be performed to assess spin polarization behavior for device realization.

Transition metal dichalcogenides Transition metal dichalcogenides (TMDs) with structure MX2 [e.g. MoS2, WS2, MoSe2, WSe2, SnS2, SnSe2, ReS2, ReSe2, MnSe2, and their alloys] are another set of promising 2D materials due to their distinct structural and electronic properties tunable to doping, strain, and chemical composition. TMDs are interesting 2D materials like graphene with regard to their layered structure, tunability of band gap with the number of layers, metal-ligand bonding, and the presence of dislocations of finite thickness. TMDs find applications in spintronics, energy storage devices, catalysts, and optoelectronics [70,71].

A recent research by Li et al. showed that Fe-doped SnS2 monolayers exhibited ferromagnetic ordering with Tc around 31 K and perpendicular anisotropy (easy axis) at 2 K even though SnS2 is diamagnetic [refer Fig. 6(a)] [72]. Similar control of magnetic ordering via transition metal dopants/hydrogenation was observed in the case of MoS2 [70,71,73]. MoS2 nanosheets adsorbed with fluorine atoms were experimentally found to generate a magnetic moment of 0.06 emu/g [75]. Superexchangemediated ferromagnetism has also been theoretically proposed in 2H single-layer VS2 [76]. A unique phenomenon called Valley Hall effect, where electrons are excited to a specific valley detected in monolayer MoS2 systems, is a testament to the existence of the extra degree of freedom called valley state of electrons apart from charge and spin [refer Fig. 6(c)] [77]. This third degree of freedom envisages photoelectronic potentials of 2D materials apart from spintronics. The influence of transition metal, alkali metals, and alkaline-earth (like Ca) dopants on the electronic and magnetic properties of ZrS2 monolayer points toward spintronic applications [76,77]. Fig. 6(b) depicts spin density distribution on doping in ZrS2. 113

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(a) Structures of the SiC with partial H adsorption, H–SiC and H–CSi structures [67]. (b) Spin density for the top left ferromagnetic, two different antiferromagnetic top right and bottom left, and ferrimagnetic configurations of the FeC2, the energy difference with respect to minimum energy phase and two different possible spin (J1, J2) [68]. (c) Spin density distribution at surface, spin-resolved band structure, and magnetization (inset: specific capacity) variation with temperature for Fe2Si sheet [69]. (a) Reprinted from Ref. [67] with the permission of AIP publishing. (b) Reprinted with permission from Ref. [68], copyright (2016) American Chemical Society. (c) Reprinted with permission from Ref. [69], copyright (2017) American Chemical Society.

(a)

(b)

(c)

(d)

FIGURE 6

(a) SnS2 showing diamagnetic behavior, ferromagnetic behavior of Fe-doped SnS2, with an easy axis for magnetization (perpendicular to surface) of sheet, and magnetization as a function of temperature for Fe-SnS2 from 2 K to 100 K. The applied magnetic field was 1000 Oe, Curie temperature is 31 K [72]. (b) Spin densities after doping of one of the transition metal in chronological order V, Cr, Mn, Fe, Co, and Cu and it’s around S atoms in 1T-ZrS2, different spin densities are shown by yellow and aqua color [78]. (c) Schematics for the optical selection rule in case of valley dependence, schematic of anomalous Hall effect driven by a net valley polarization in MoS2 [77]. (d) The strain-induced magnetism in case of NbS/Se2 two-dimensional material [80]. (b) Reprinted from Ref. [78] with permission from Elsevier copyright (2017). (c) Reprinted from Ref. [77] with permission from AAAS. (d) Reprinted with permission from Ref. [80], copyright (2012) American Chemical Society. 114

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The ferromagnetic ordering observed in bulk MoS2 due to zigzag edges within the grain boundaries can be extended to explain magnetic behavior in monolayer and nanosheets of MoS2 [81]. Influence of substrate strain and doping results in tunable ferromagnetic ordering as investigated in WS2 monolayers. Straindependent spin polarization observed in VX2 (X = S and Se) is attributed to ionic – covalent bonding between the V and X atoms. The ferromagnetic ordering originates through-bond and space interactions [79,82]. Ferromagnetic ordering observed for grain boundaries consisting of 5–7 defects provides a new approach to get magnetic semiconductors in 2D through grain boundary concept. In addition to general methods for inducing magnetic moment, such as substitution/adsorption, by foreign atoms (Fe, Co, Ni, and Mn), vacancies or cutting to finite systems composed of zigzag edges, magnetism in NbX2 (X = S, Se) can be introduced by applying tensile strain [refer Fig. 6(d)]. As per density functional calculations, 4d orbital of Nb atom changes spin orientation through self-exchanging their population densities, favorably for ferromagnetic ordering [80,83]. Substitutional doping in TMDs with groups V–VII [like Cr, Mn, and Fe] elements rather than dopants at interstitial or defect sites has been investigated and it has a profound influence on the structure and material properties. First-principles calculations established that electron donors, such as Re and Mn, lead to n-type doped

MoS2, and experimental result proved that structure and magnetism can be tailored by substitutional doping [74,84,85]. Computational theory revealed that long-range magnetic ordering can be realized in transition metal (Mn and Fe)-doped WSe2 with respect to delocalized p states of Se atoms, a strong correlation of exchange interaction/coupling mechanism with spatial positions, distances, and concentrations of dopants. On alloying semiconducting WSe2 with half-metallic VSe2 ferromagnet, mixed diselenides with many atomic configurations of W1xVxSe2 could be generated with special quasirandom approach. On inducing V atoms in W1xVxSe2 monolayers, transition occurs from nonmagnetic to ferromagnetic half-metallic with a magnetic moment of 1.0 lB per V atom arising due to shift of Fermi level to valence band upon p doping. Increasing doping concentration of V increases the half-metallic character and magnetic moment per atom [86]. Fig. 7(a), (b) shows quasi random atomic configuration of W1xVxSe2 and their density of states. Metal vacancies and chalcogen-metal antisites in MoSe2 and MoTe2 also induce magnetic moment in the range of 0.9–2.8 mB, which is highly dependent on hydrostatic pressure [refer Fig. 7(e)] [87]. There have also been reports on ferromagnetic ordering arising from zigzag edges in MoSe2 nanoflakes [88]. The TMD material NbX2 (X = S and Se) (discussed earlier) has stimulated the research interest in the past few years as magnetic moment of Nb ions are

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(a) Special Quasirandom atomic configurations of mixed dichalcogenide W1xVxSe2 at different concentrations of V atom, 0.25%, 0.50%, and 0.75%; (b) density of state for all three cases [86]. (c) Excess of charges carried by the sheets (negatively charged) after exfoliation using Li-intercalated NbSe2, and the ferromagnetic spin in NbSe2. (d) Magnetic hysteresis loop, for NbSe2 at 30 and 2 K, respectively [83]. (e) Spin-polarized density of states, DOS (states/eV), of Mo defects in the antiferromagnetic (AFM) phase of MoTe2, spin up and spin down states shown by blue and orange colors, and differential conductance spectra in scanning tunneling spectroscopy shows the two types of defect and far from any defect [87]. (a) and (b) Reprinted with permission from Ref. [86], copyright (2016) IOP Publishing Ltd. 115

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quenched by covalent Nb–Se interaction and hence ferromagnetism can be induced by means of surface molecular adsorption [refer Fig. 7(c),(d)]. Other correlated effects like superconductivity, the Kondo effect (scattering of conduction electrons by magnetic ions) and intrinsic negative magnetoresistance arise from the coupling of conduction electrons with induced moments [83]. In addition to TMDs, transition metal trichlorides like TiCl3 and VCl3 sheets also showed evidence for half metallicity without external influence and also favored ferromagnetic ordering. Such materials can also be used for spintronic devices [89]. Van der Waals crystals and TMDs have developed into a large area enriched with rich theory regarding role of vacancies/adatoms/ dopants or strain in influencing structural, electrical, mechanical, and spin ordering properties to have future directions in realizing slim electronics.

Metal monochalcogenides A new class of materials called metal monochalcogenides (GaS, GaSe, GaTe, and InSe) is another candidate for layered 2D materials, in which covalently bonded metal and chalcogenide atoms are connected by weak interlayer van der Waals forces. These materials possess a unique band structure favoring spin polarization by removing degeneracies between orbital states. It is theoretically established that their distinct feature of higher density of states (DOS) at or near Fermi level (EF) lead to different transitions or distortion phases, such as magnetic ordering [refer Fig. 8 (a)] [90]. Spin polarization in metal monochalcogenides can be enhanced by doping, vacancy defects, leading to ferromagnetism and half-metallicity. Density functional theory (DFT) calculations provided a possibility of ferromagnetic phase by hole doping in monolayers of GaSe and SrX (X = S, Se) semiconductors [Fig. 8(b)] [91]. A recent study on Fe adsorbed GaSe monolayer explained the strong orbit coupling between Fe and adjacent Ga /Se atoms leading to hybridization of Fe-3d, Se-4p, and Ga4p orbitals further resulting in conduction interface states of ntype near the Fermi level.. Half-metallicity with full-spin polarization at Fermi level is probable in such systems along with longrange ferromagnetic ordering [92]. Fig. 8(c), (d) shows total density of states and spin charge distribution of Fe/GaSe.

Transition-metal nitrides Transition-metal nitrides (TMNs) are believed to be prospective materials since the coexistence of half metallicity along with magnetic ordering is a requirement preferably for magnetoresistance. TMNs exhibit intriguing properties like half-metallicity, piezoelectricity, and photocatalyticity. Of late, VN (vanadium nitride) lattices with stable 2D configuration having two polymorphs, honeycomb and tetragonal,have been proved to exhibit higher spin polarization rate near Fermilevel with p2d2 and sd2 hybridization [refer Fig. 8(e), (f)]. The half metallicity of these VN structures are preserved even on contact with 2D MoS2 [93]. Also, magnetocrystalline anisotropy energy (MAE), which is fundamental to magnetic behavior (easy axis for magnetization) is one order larger than Fe and Ni. Thus, TMNs meet the requirements needed for spin polarization mechanism-based devices.

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Layered compounds and oxides Layered compounds: Layered magnetic composites like sulfides and oxides are another class of prime candidates for LD magnetism. Transition metal phosphorous trisulfide (Thiophosphate: TMPS3; TM = Mn, Fe, Co, Ni, Zn and Cd) is one among them. It has been theoretically proposed that carrier doping could lead to transition of antiferromagnetic ground state to ferromagnetic in MnPS3 and also could possess ferrotoroidicity [94,95]. On Exfoliation, FePS3 exhibits an Ising-type antiferromagnetic behavior arising from spin–phonon interaction with a slight variation of transition temperature in the bulk to monolayer range. It has been shown that exfoliated CrXTe3 nanosheets have ferromagnetic ordering, further enhanced by strain [96,97]. These are the frontrunners as ferromagnetic semiconductors since they possess unidirectional spin-polarized valence and conduction band charge carriers easily feasible for carrier injection and detection [98,99]. Density functional based theoretical calculations focused on the zigzag spin texture in monolayer CrSiTe3 and the probability of strain tunable 2D magnetism in ABX3 compounds [Fig. 9(b)] [100]. Fig. 9(b) shows magnetic behavior of CrSiTe3. It was found that antiferromagnetic CrSiTe3 can be converted into ferromagnetic by application of 3% in-plane tensile strain. Bilayer of van der Waals crystal Cr2Ge2Te6 showed ferromagnetic ordering under external magnetic field (less than 0.3 Tesla) with a decrease in temperature. Gong et al. has shown that Cr2Ge2Te6 atomic layers can be mechanically exfoliated using adhesive tapes and deposited on Si/SiO2 substrate. Transition temperature observed close to liquid helium is believed to be a characteristic of 2D magnetism, since the chances of substrate magnetism (as SiO2 is nonmagnetic) and ambient effects (air exposure time is less) can be ruled out [Fig. 9(d)] [101]. In a similar chromium compound, Cr2Si2Te6, magnetic anisotropy and ferromagnetic phase have been experimentally proven, while in Cr2Sn2Te6, theoretical statements suggest a higher transition temperature [102,103]. Recently, layer-dependent magnetization is also observed in CrI3 samples, where a strong coupling between magnetism and crystal structure has been established [Fig. 9(g)] [104,105]. It is a perfect Ising ferromagnet with spin orientation (out-of-plane) and TC at 45 K and the magnetization reaches bulk limit on going from bilayer to trilayer. Another feature observed in bilayers is negligible anisotropy arising from intrinsic magnetocrystalline anisotropy, and out-of-plane spin orientation is nearly compensated by shape preferring in-plane spin orientation [106]. Electric control of magnetism in bilayer CrI3 has been discovered as a linear magnetoelectric effect produced by applied electric field, which depends on interlayer antiferromagnetic order. It is also proved that bilayer and monolayer magnetic properties of CrI3 can be tuned by electrostatic doping [107,108]. These van der Waal materials are viewed as magnetic insulators, where magnetic ground state on applying electric field and field-induced metamagnetic transition has been observed. They are perceived to be key candidates for understanding tunneling magnetoresistance, magnons and spin-based tunneling junctions advantageous for next-generation spinbased technology [109–111].

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(a) GaSe monolayer band structure in the out-of-plane spin-polarized ferromagnetic state. Colors show different spin states; the band structures are at the carrier density of 0 and 7  013/cm2 [90]. (b) Polarization energy and magnetic moment in the out-of-plane state as the function of carrier concentration in case of SrS and SrSe [91]. (c) Total density of state of GaSe and Fe-adsorbed GaSe. (d) Spin charge of Fe/GaSe in the various range of energy. The yellow and blue colours represent charge densities of majority and minority spin channels respectively [92]. (e) Top and side view of t-VN and h-BN, and (f) band structure and density of state of both type of spin for t-VN (top) and h-BN (bottom) [93]. (a): Reprinted with permission from Ref. [90], copyright (2015) by the American Physical Society. (e) and (f) Reprinted with permission from Ref. [93], copyright (2018) American Chemical Society.

Isolated monolayers of metallic Ge-Te-based compounds like Fe3GeTe2 exhibited an itinerant ferromagnetism on cross over from 3D to 2D. Recently, layered metallic Fe3GeTe2 is being utilized for magnetotransport and gate tunable magnetic studies [112,113]. Magnetocrystalline anisotropy in Fe3GeTe2 originates from the asymmetric crystallographic environments of iron (Fe) and the concentration Fe decides the Curie temperature and Coercive field is a metallic ferromagnet [114,115]. Other layered compounds like Mn2Bi2Te4, categorized theoretically as an Atype antiferromagnetic topological insulator, could be ideal for magnetoelectric phenomena and quantum anomalous Hall effect, correlating spin and charge effects of electrons [116]. Heavy TMDs like PtS2, PtSe2 on hydrogenation shift to ferromagnetic metals from their semiconducting state due to the spin ordering of Pt 5d electrons [Fig. 9(c)] [117]. Moreover, layered composites VI2 and Co(OH)2 with structure similar to dichalcogenides have fully spin-polarized bands around the Fermi level

and are perceived to be magnetic semiconductor with spintronic potentials.

Oxides and sulfides There have been many theoretical predictions that oxides like MoO3 can be tuned to have induced magnetic ordering by hydrogenation or external strain, apart from it, there are reports of intrinsic ferromagnetism in monolayer MnO2 [Fig. 9(e)] [121]. Hexagonal monolayer of zinc oxide (ZnO) is considered as a metal-oxide analog of BN and graphene. ZnO nanoribbons show ferromagnetic ordering, which arises from the available electronic states at the zigzag edges due to the edge passivation by hydrogen or by external electric field [Fig. 9(h)]. In hydroxides like Ni(OH)2, which has antiferromagnetic ordering in pristine state, a biaxial compressive strain of 4% leads to ferromagnetic ordering and also influences the band gap. Spin polarization and magnetic coupling in monolayer Ni(OH)2 is attributed to 117

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(a) In ABX3, transition-metal A atoms form a honeycomb structure with B2X6 ligand, occupying the interior of the honeycomb. Top view of the different spin configurations the FM, AF-Neel, AF-zigzag AF-stripy ordered, up (down) spins are represented by black filled-in (open) circles [100]. (b) Magnetic susceptibility in blue and spin magnetic moment in red with respect to temperature for monolayer of CrSiTe3 [98]. (c) The band structure of PtS2-1H, PtSe2-1H, and PtTe21H in same order, color showing different spin states [117]. (d) Crystal structure (side and top views) of Cr2Ge2Te and magnetization curve [101]. (e) Spin density of FM and AFM states of MnO2 [118]. (f) Charge density difference of the different Ni(OH)2-TMD heterostructures. The gray, red, pink, yellow, brown, and violet balls represent Ni, O, H, S, Mo, and W atoms, respectively. The green and blue isosurfaces correspond to the accumulation and depletion of electronic densities [119]. (g) Magnetic moment versus temperature measured for CrI3 in parallel and perpendicular field [105]. (h) Band structure of ZnO nanoribbon with spin up and down charge distribution. a – spin down state and b – spin up state [120]. (a) Reprinted with permission from Ref. [100], copyright (2015) by the American Physical Society. (b) Reproduced from Ref. [98] with permission of the Royal Society of Chemistry. (c) Reprinted with permission from Ref. [117], copyright (2016) by the American Physical Society. (d) Reprinted with permission from Ref. [101], Springer Nature copyright (2017). (e) Reprinted with permission from Ref. [118], copyright (2013) American Chemical Society. (f) Reprinted with permission from Ref. [119], copyright (2015) IOP Publishing Ltd. (g) Reprinted with permission from Ref. [105], copyright (2015) American Chemical Society. (h) Reprinted with permission from Ref. [120], copyright (2010) American Chemical Society.

partially filled 3d orbitals of nickel (Ni) atom. Charge density distribution of different Ni(OH)2-TMD structures is shown in Fig. 9 (f). Adjustable magnetism of these hydroxides with respect to strain is crucial for developing new spintronic devices [119,120]. Ferromagnetic (FM) order has been discovered in the 2D analog of hematite called hematene, while hematite prefers 118

antiferromagnetic (AF) order. The discovery also highlights the role of natural ores in developing highly ordered atomic layers [122]. Perovskites and mixed honeycomb oxides (A2M2TeO6 and A3M2XO6, where A = alkali metal, M = 3d transition metal, and X = Sb or Bi) are highly tunable materials with a variety of

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electrical, structural, magnetic, and thermal properties. Main features of perovskites, which draw their attention toward LD magnetism, are frustrated antiferromagnetic spin behavior, absence of static magnetism even at low temperature, and spin-gapped ground state [123]. The perovskite K2CuF4 is a promising 2D material as it forms a free-standing membrane in 2D alongwith an accessible transition temperature. The magnetic origin in K2CuF4 is quite intriguing and complex and is mainly attributed to hybridized Cu-dxy and F-p states. K2CuF4 possesses both insulating and ferromagnetic properties, which is useful for a variety of applications like a magnetic spacer in 2D heterostructures and as interface material with graphene for obtaining electric field tunable magnetic phenomena [124]. A robust ferromagnetic behavior has been claimed in 2D dFeOOH ultrathin nanosheets obtained from intermediate nanosheets of Fe(OH)2, thus extending the regime of 2D magnetism to inorganic structures [125]. Recently, the possibility of developing magnetic ordering in sulfides was also carried out. Dynamically and thermodynamically stable nanosheets of Co2S2 nanosheet could be a ferromagnetic metal with Curie temperature around 404 K [126]. Yu et al. showed that two-dimensional hexagonal beryllium sulfide nanoribbons (BeSNRs) could be promising for spintronic applications as their armchair-edged ribbons exhibit stark effect, while zigzag-edged ribbons favor spin glass magnetic state [127]. It could be believed that sulfides and oxides can pave way for designing 2D materials with excellent control over transition temperature and electro-magnetic coupling parameters.

Future directions Merging 2D and 3D Major challenges for 2D magnetism could be, optimizing thickness of monolayers, avoiding substrate effects like strain. Experi-

mental challenges that 2D magnetism encounter is how to control the effect of (1) defects or boundary in prepared samples, (2) scattering of spin-polarized moments of conduction electrons with imperfections induced in the lattice. Also, research on bicomponents like BNN (Boron nitride nanotubes) is mostly limited to theoretical concepts and efforts are ongoing to try doping of these nanostructures with light radii elements (containing only s and p electrons) perceived to be one of the most futuristic methods to obtain magnetism [61]. Theoretical studies using tight-binding method in Cadmium selenide (CdSe) nanostructures has revealed that they could give good magneto-optic response, but experimentation is still a challenging task [128]. It has been discussed earlier that zigzag-edge-based magnetism in graphene is temperature dependent and cannot extend over large dimensions even though the spin stiffness in them is appreciable than d block elements. A possible direction for developing spintronic systems based on edge-based magnetism is through an effective control over the anisotropy energy, which can possibly increase the spin correlation length and dimensions. Other possible approaches could be tuning of edges with functional groups of heavyelements or developing heterostructures with graphene coupled onto a substrate, where substrate effects could manipulate the edge characteristics favorably toward magnetization [129,130]. The edge-contact geometry is proposed as a possible approach for developing heterostructures of complimentary 2D materials, such as graphene and hexagonal boron nitride. Fig. 10(a) shows graphene-h-BN heterostructure [131]. Fig. 10 (b) shows schematic of magnetic tunnel junctions from h-BN layers grown on Fe substrate and their I-V characteristics. A complete analysis of graphene/h-BN heterostructure is given in the review by Wang et al. [132]. Artificial p-n junction can also be developed using heterostructures consisting of pristine graphene nanoribbons (p-GNRs) and nitrogen-doped graphene

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(a) Optical micrograph image of graphene/h-BN heterostructure and raw image of graphene/h-BN with the moiré pattern [132]. (b) one/two layers of h-BN grown on Fe substrate for magnetic tunnel junction, exponential dependence of the resistance normalized against the average resistance of annealed Fe as a function of the number of h-BN layers. (c) Schematic of magnetic tunnel junction with I–V characteristics of Fe/h-BN/Co [131]. (a) Reprinted from Ref. [132] with permission from Elsevier copyright (2017). 119

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nanoribbons(N-GNRs), where nitrogen incorporation provides an exquisite control of energy levels as energy bands shift by nearly 0.13 eV for each nitrogen atom [133]. Improving the magnetization and tuning the magnetic transition close to room temperature for device applications is a challenging task for 2D materials/heterostructures [134].

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A single-layer graphene exchange coupled with Yttrium iron magnet ferromagnetic thin film showed anomalous Hall effect, and the observed magnetic ordering is a proximity effect, which could lead to spin transport in next-generation spintronics based on proximity effects [135,136]. Similarly, signature for substrate induced magnetism has been observed in case of MoSe2 monolayer deposited on Ni (111) substrate, since hexagonal symmetry of transition metals like Ni and Cu tune the electronic configuration of TMDs. Such a metal-TMDs structure is viewed as a promising candidate for LD magnetism with applications in electronic devices [137]. The flexibility of TMD materials with weak interlayer bonding, easy tuning of crystallographic orientation, and sharp atomic interfaces offers secure coupling of layers within a heterostructure as observed in the case of MoS2/WS2, MoSe2/WSe2, and bilayer structures consisting of undoped and Cr-doped Bi2Se3 [138,139]. Stacking monolayer of semiconductors to form heterostructures like Ni(OH)2–XN with X = B, Al, and Ga theoretically shows that monolayer XN significantly changes the magnetic coupling in Ni(OH)2. The major explanation for such tunable magnetic property in heterostructure is the appreciable change in magnetic moment of single Ni due to lattice mismatch. In correlation to spintronics, data storage application is also at the center of attention and an important aspect regarding it is tunnel magnetoresistance (TMR) or magnetic tunnel junction (MTJ). Currently, tunnel or insulating layer sandwiched between both ferrimagnets are metal oxides (Al2O3, MnO2, etc.) and the major issue involved with these oxides is non-uniformity while reducing the thickness. Single layer of BN grown on Fe and covered by Co shows TMR value of 6 %; the value of resistance increases with number of layers. The value of TMR is less and BN is an insulating layer only; nonetheless, realization of MTJ with 2D magnetic materials apart from Fe/ Co will improve the performance with simultaneous huge reduction in device size as well [131]. With regard to other magnetic concepts like frustrated magnetism and spin liquids, there exist a fundamental thought that a superconducting phase is seen in the environment of magnetically ordered states of layered cuprates and ironpnictides, hence

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quasi 2D magnetism is an area that is being increasingly explored and experimented. A prominent candidate for quasi magnetism is MXenes, which are obtained by etching out A layers from bulk MAX phase at room temperature [140,141]. MAX phase is represented as Mn+1AXn, where M is early transition metal, A is group II or III elements, X is C or/and N, and n can have values from 1 to 3. The surface of MXene gets terminated by different functional group, depending upon the chemical environment, due to unsaturated charges during the exfoliation. MXene monolayer possesses strong metallicity, large density of states near the Fermi level, and tunable magnetism by in-plane strain, which make these materials interesting to explore specially to achieve strain influence in heterostructures [142–144]. There have been reports of competitive ferromagnetic and antiferromagnetic exchange interactions in MAX phases and hetero-epitaxial films of magnetic MXenes like Mn2GaC or its doped compounds are favored for magnetoresistive and magnetostrictive applications [145,146]. MXenes like Cr2C, Cr2N are ferromagnetic, while Ti3C2 and Ti3N2 are antiferromagnetic [147–149]. Experimental investigations on heterostructures based on 2D Sc2CF2 and MoS2 showed extreme sensitivity to in plane biaxial strain. Shift of Hf (5d) bands due to tensile strain leading to ferromagnetic ordering in the MXene, Hf2C, confirms the sensitivity of magnetic moments to strain even though metallicity is uninfluenced by strain [150]. Table 2 gives an overview of the 2D magnetic materials included in the present review. Spin polarization can be established by incorporating 2D electronic materials on magnetic insulators (as in graphene on YIG) [151] and a similar placing of vdW magnets on other materials lends magnetism in them. Such material systems are model schemes of interfacial engineering where the vital properties like electron concentration, crystal field, and spin states can be tailored. For a successful technological or device implementation of 2D magnetism, there are certain prerequisites like tuning to room temperature, effective injection and tunneling of spins, and controlling spin diffusion. Hence, 2D magnet synthesis should grow beyond exfoliation to other features like interfacial/ integrated mechanisms like monolithic structure of 2D with vdW or other functional materials. Low-power spintronic devices and magnetoresistive randomaccess memory (MRAM) based on spin transfer torque effect are other exciting arenas for bilayer structures of 2D and magnetic materials. In 2D materials having strong spin orbit coupling, a longitudinal current could deflect electrons toward the interface resulting in spin injection to the magnetic material. Such polarized spin current tune the magnetic moment direction of

TABLE 2

2D magnetic materials. Light p block graphene/graphene like

Graphene/fluorinated graphene molecular/chemical doped graphene

Nitrides, carbides, boron nitrides hBN, F-BN, and BCN

Hydrogenated graphene H-SiC

2D chalcogenides

Mixed W1xVxSe2 Nitrides VN

Trichlorides TiCl3, VCl3

Layered composites

MoX2, WX2, VX2, SnX2, ReX2, NbX2 (X = S, Se, Te) Monochalcogenides GaS, GaSe, GaTe, InSe Fe adsorbed GaSe TMPS3 (TM = Mn, Fe) CrSiTe3 CrI3

Cr2Ge2Te6 Fe3GeTe2

Oxides/Sulfides MXenes

MnO2, ZnO, MoO3Co2S2 Mn2GaC Cr2C, Cr2N

Perovskites K2CuF4 A2M2XO6 Sc2CF2-MoS2

VI2, CoOH2 Ni(OH)2-XN (X = B, Al, Ga) d-FeOOH Ti3C2, Ti3N2

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magnetic materials, thus exerting spin orbit torque. Reverse of spin orbit torque mechanism called spin pumping where the excited magnons in magnetic materials travel in the reverse direction (from magnetic material to 2D material) where it is converted to charge current. The mechanism governing the interchange of charge and spin current is decided by some key spintronic phenomena like intrinsic spin–orbit interaction, inverse Rashba-Edelstein effect, inverse Hall effect, and spin mixing conductance [152,153]. In summary, this review discusses magnetism in 2D materials like graphene, nitrides, carbides, TMDs, and monochalcogenides. In contrast to 3D magnetism, strongly enhanced spin fluctuations, exotic ground states, surface spin contributions, large magnetic moments, and less orbital moment quenching are the highlights of 2D magnetic materials. Tunability and perfect control of magnetic states in LD materials is crucial for developing flexible electronics, as well as for optimizing functional devices. As future prospects of 2D magnetism, spin coupling to external perturbations like strain, proximity, light, or pressure could be deciding factors for exchange interactions or magnetic anisotropy. Investigations of 2D materials can be broadened to include multifunctional applications in optics as opto-electronic, magneto-resistance, magneto-optical or in photo-acoustic arenas and in thermodynamics as spin-Seebeck effects [154], spin calorimetry favorably for developing thermospin devices.

Acknowledgements NS acknowledges Department of Science and Technology, Government of India for granting project under DST Women in Science (WoS-A) program [No.SR/WOS-A/PM-35/2017(G)]. Y. K. is thankful for the support by AOARD. A.M. and A.K.S. acknowledge the computation facilities at the Materials Research Centre, the Thematic Unit of Excellence, and the Supercomputer Education and Research, Indian Institute of Science, Bangalore, India. A.K.S. and A.M. are thankful for support from DST Nano Mission, and A.M. acknowledges UGC India for a Senior Research Fellowship. CST acknowledges Ramanujan fellowship. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]

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