Recent advances in two-dimensional ferromagnetism: materials synthesis, physical properties and device applications

Pu Huang a, Peng Zhang a, Shaogang Xu a, Huide Wang b, Xiuwen Zhang *a and Han Zhang *b
aShenzhen Key Laboratory of Flexible Memory Materials and Devices, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China. E-mail: xiuwenzhang@szu.edu.cn
bCollaborative Innovation Centre for Optoelectronic Science & Technology, and Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology of Ministry of Education, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China. E-mail: hzhang@szu.edu.cn

Received 17th October 2019 , Accepted 15th December 2019

First published on 16th December 2019


Two-dimensional (2D) ferromagnetism is critical for both scientific investigation and technological development owing to its low-dimensionality that brings in quantization of electronic states as well as free axes for device modulation. However, the scarcity of high-temperature 2D ferromagnets has been the obstacle of many research studies, such as the quantum anomalous Hall effect (QAHE) and thin-film spintronics. Indeed, in the case of the isotropic Heisenberg model with finite-range exchange interactions as an example, low-dimensionality is shown to be contraindicated with ferromagnetism. However, the advantages of low-dimensionality for micro-scale patterning could enhance the Curie temperature (TC) of 2D ferromagnets beyond the TC of bulk materials, opening the door for designing high-temperature ferromagnets in the 2D limit. In this paper, we review the recent advances in the field of 2D ferromagnets, including their material systems, physical properties, and potential device applications.


1. Introduction

Ferromagnetism represents a form of magnetic order with the parallel alignment of intrinsic magnetic dipole moments or spin of electrons in the crystal.1 Ferromagnetic phases with spontaneous magnetization even in the absence of an external magnetic field can be achieved from their high-temperature counter parts possessing no macroscopic net magnetic moments.2,3 The ferromagnetic state in three-dimensional (3D) materials, such as elemental metals (e.g., Fe, Co, Ni4) and their alloys, rare-earth metals (e.g., Gd, Tb, Dy5), and multicomponent compounds (e.g., LaMnO3[thin space (1/6-em)]6), has been found for quite a long time, triggering extensive applications from the ancient compass to the modern data-storage devices.7 In comparison with the investigation of ferromagnetism in 3D materials, the research process on low-dimensional ferromagnets is relatively slow, although the beginning of this kind of research can be traced back to 1970s.3 Actually, two-dimensional (2D) ferromagnetism was initially probed in 3D crystalline magnetic materials, where distinct interactions between spins located within the individual planes of the crystal lattice have been observed.8,9 With the discovery of graphene, the rapidly expanding family of 2D materials has been proven to have excellent application prospects in many fields such as electronics,10–12 optoelectronics,13–33 catalysis,34–36 batteries,37 supercapacitors,38,39 biomedicine,40–46 sensing,47–51 and ferromagnetism.52 Meanwhile, with the development of epitaxial synthesis and exfoliation techniques, the successful implementation of 2D materials (e.g., graphene,26,53–56 transition metal dichacolgenides (TMDs),57–60 topological insulators,61–63 black phosphorus,11,64,65 Mxene,66 antimonium,67,68 bismuth,69 tellurium,70–72etc.) has become more and more simple and reliable, making their various related applications, especially the ferromagnetic applications, develop rapidly. These 2D materials provide an exciting platform for studying the interplay between various competing electronic and magnetic phenomena at the nanoscale involving the quantum confinement effect. Benefiting from the accelerating miniaturization of magnetic units in spintronic devices, such as giant magneto-resistance, spin valve, magnetic random-access memory (MRAM) and other spin logic devices,73 the studies on nano-magnetism have been extremely vigorous in recent years.

On the basis of the Mermin–Wagner theorem,77 short-range isotropic interactions do not induce long-range ordering in low-dimensional systems with continuous symmetry at finite temperatures, as demonstrated by the 2D isotropic Heisenberg model that does not have the ferromagnetic solution. In other words, realizing ferromagnetic coupling in 2D materials requires lowering the symmetries, which is usually realized by the applied magnetic field or the inherent strong anisotropy of the crystal. Recently, Xu and Zhang et al. reported ferromagnetic behavior in atomically thin layers of chromium germanium telluride (Cr2Ge2Te6[thin space (1/6-em)]78) and chromium triiodide (CrI3[thin space (1/6-em)]74), using a polarmagneto-optical Kerr effect microscopy technique. Moreover, room-temperature ferromagnetism was achieved in monolayer VSe2.76 These inspiring results shed considerable light on seeking new 2D ferromagnetic materials, especially those with high Curie temperature (TC). More importantly, the in-depth physics about the sophisticated palate of magnetoelectric interaction raises great interest for the modern condensed matter physics.

In this review, we will focus on the recent progress on the synthesis of 2D ferromagnets, magnetism-related phenomena, including but not limited to magnetic anisotropy, anomalous Hall effect, magnetic phase transitions, Gilbert damping etc., as well as the 2D ferromagnetic devices, such as vdW heterojunctions and spin valves. We attempt to summarize the underlying magnetic mechanism and issues that have not yet been uncovered for the associated 2D magnetic nanostructures. We believe that the general insight into the 2D ferromagnetism not only provides guidelines for further engineering the magnetic properties, but also suggests promising candidates for future applications in spintronic devices.

2. Two-dimensional ferromagnetic material systems

Magnetic van der Waals (vdW) materials have emerged as promising candidates for spintronic applications with the discovery of intrinsic ferromagnetism in monolayer atomic crystals in recent years.74,77,78 The long-range magnetic ordering in 2D vdW materials opens the door for exploring the low-dimensional fundamental science and integrating the spintronic device seamlessly within the 2D limit. Although great progress has been made via various synthesis methods such as mechanical exfoliation from the epitaxially grown bulk single crystal,77 the achievement of tunable ferromagnetism, especially the control of the spin orientation, magnetic domain phase, and the magnetic long-range ordering at ambient temperature, still remains a great challenge, which is difficult to overcome.

2.1. Experimental synthesis and characterization

Xu et al.74 prepared the chromium iodide bulk crystals (CrI3) by mixing chromium powder and anhydrous iodine beads, and then exfoliated the CrI3 flakes from monolayer to few-layer structures with graphite encapsulation to prevent reaction with oxygen and moisture. The encapsulated CrI3 flakes present layer-dependent ferromagnetic phase transition from ferromagnetism in the monolayer, to antiferromagnetism in the bilayer, and back to ferromagnetism in the trilayer and bulk [Fig. 1(a)]. Zhang et al.75 fabricated bulk Fe3GeTe2 crystals via chemical vapor transport, and then exfoliated thin Fe3GeTe2 flakes (14–250 nm thick) on Si (111) substrates. To facilitate the Fe3GeTe2 exfoliation, they heated the sample to 50 °C and transferred the flakes into an ultrahigh vacuum chamber (∼10−11 Torr). The subsequent measurements show an enhancement of the perpendicular magnetic anisotropy in Fe3GeTe2 microstructures, which undergoes transition from the out-of-plane stripe domain phase to the in-plane vortex phase at 230 K and persists beyond room temperature [Fig. 1(b) and (c)]. Surprisingly, their result is opposite to that of conventional magnetic materials for which the finite-size microstructure leads to the reduction of TC.86,87 However, the in-depth mechanism is still unclear and more detailed experimental and theoretical studies are required to explore the influence of finite size on vdW magnetic properties. McGuire et al.88 mechanically exfoliated CrCl3 flakes with Scotch tape onto 90 nm SiO2 substrates and obtained their 2D structures. Furthermore, they observed a magnetic phase transition for CrCl3 flakes at lower temperature, which is attributed to the spin–lattice coupling within vdW interactions on the basis of DFT calculations. According to the previous experimental results,89–92 bulk VSe2 exhibits paramagnetic characteristics, whereas ferromagnetic transition can be induced when it is constrained into the monolayer limit.76 Batzill et al.76 grew mono- and few-layer VSe2 flakes on HOPG or MoS2 substrates by e-beam evaporation of V and simultaneous deposition of atomic Se from a hot wall Se-cracker source. After the HOPG or MoS2 substrates were transferred into the vacuum chamber and annealed under ultra-high vacuum at 300 °C for 5 h, VSe2 began to grow with a slow rate of ∼0.06 ml min−1. The following experimental measurements revealed the strong ferromagnetic ordering with Curie temperature TC above room temperature (compared with its paramagnetic bulk phase),74 as shown in Fig. 1(d) and (e). Wang et al.79 mixed raw material powders of Cr, Ge, and Te with a stoichiometric ratio of 1[thin space (1/6-em)]:[thin space (1/6-em)]4[thin space (1/6-em)]:[thin space (1/6-em)]20 for the growth of single-crystal Cr2Ge2Te6 by the Te self-flux method. They applied the Scotch tape approach to obtain few-layered Cr2Ge2Te6 from its bulk phase and demonstrate its tunable magnetization characteristics below TC.
image file: c9nr08890c-f1.tif
Fig. 1 (a) Layer-dependent magnetic ordering in an atomically-thin CrI3 from monolayer (1L) to a triple layer (3L). Adapted with permission.74 Copyright 2017, Springer Nature. (b) Magnetic domain images of patterned Fe3GeTe2 indicate that out-of-plane stripe contrast is weakened and then it evolves into the in-plane direction as the temperature increases from 220 K to 240 K. (c) Temperature dependence of the magnetic stripe contrast and the spatially averaged contrast. [(b) and (c)] Reproduced with permission.75 Copyright 2018, American Chemical Society. [(d) and (e)] The in-plane and out-of-plane M-H loops for monolayer VSe2 on HOPG and temperature dependent magnetic properties of VSe2 films on the MoS2 substrate. Adapted with permission.76 Copyright 2018, Springer Nature.

Many issues remain in the materials preparation of 2D ferromagnets, such as the controllable synthesis with high speed growth, large area realization and stability under an ambient atmosphere. Up to now, the commonly used method for preparing 2D ferromagnetic materials is mainly the mechanical exfoliation,74,75,77,88 in which it is usually difficult to effectively control the morphology, size and uniformity of layer thickness. Achieving the growth of large, high-quality single crystals of 2D components (i.e., conductors, semiconductors, and insulators) is critical for the industrial application of 2D devices in general. Therefore, exploring a large-area controllable preparation method for 2D ferromagnetic materials is a challenge for current 2Dferromagnetic materials research. In fact, Liu et al.80 have recently realized the controllable epitaxial growth of single crystal monolayer h-BN (∼100-square-centimetre) on a low-symmetry Cu (110) vicinal surface that is obtained by annealing an industrial copper foil [Fig. 2(b)]. They revealed that the epitaxial growth can be controlled by the coupling of Cu 〈211〉 step edges with h-BN zigzag edges, which breaks the equivalence of antiparallel h-BN domains, enabling a unidirectional domain alignment. This growth method is general for many other 2D material synthesis processes, e.g., it is applied in realizing the large area and high speed (60 μm s−1) growth of graphene on the Cu substrate.93 These discoveries are expected to facilitate the widespread integration of two-dimensional devices and to achieve the epitaxial growth of a wide range of 2D materials. In addition to their common layered structure that can be easily exfoliated due to their relatively low exfoliation energy, one can also turn the attention to conventional non-layered bulk materials. Although it is difficult to directly obtain their atomic layers due to the challenge of breaking the intrinsic isotropic chemical bonds and the unsaturated dangling bonds on the surface, which usually increase the system total energy significantly and make the structure unstable, it is still possible to obtain the ultra-thin monolayer 2D flake via self-limited epitaxial growth,81,94 which apparently enriches the research scope of 2D ferromagnets beyond vdW layered materials [Fig. 2(c)].


image file: c9nr08890c-f2.tif
Fig. 2 (a) Exfoliated layer ferromagnets, including CrI3, Cr2Ge2Te6 and VSe2. Adapted with permission.74,76,79 Copyright 2018, Springer Nature. (b) In situ observation of the unidirectional growth of h-BN domains and the shape evolution reproduced as a colour-coded superposition of outlines extracted from the images recorded over 760 s. Adapted with permission.80 Copyright 2019, Springer Nature. (c) OM/AFM images of self-limited grown nonlayered CdS flakes and the electron configuration of the In/Cd–S motif on the flake surfaces. Reproduced with permission.81 Copyright 2018, Wiley-VCH.

The synthesis of 2D ferromagnetic materials could benefit from the analysis of structural symmetry, atomic bonding characteristics for the individual crystal surface and vdW interface, and uncovering the atomic arrangement and magnetic domain evolution, which is critical for realizing the controllable synthesis of 2D ferromagnets. Furthermore, the cooperation of theory and experiment would greatly promote the research progress of 2D ferromagnetic materials, especially the adoption of high-throughput (HT) calculation, and HT experiment and machine learning95–98 methods could accelerate the design of new high-temperature 2D ferromagnets.

2.2. Theoretical investigation and prediction

On the basis of DFT calculations, Lado and Fernández-Rossier99 suggested that the large magnetic anisotropy in CrI3 originates from an anisotropic exchange interaction through a super-exchange mechanism,100 which stems from the strong spin-orbital coupling (SOC) effect in the heavier iodine ions. Kan et al.82 proposed a double-orbital model and revealed that the super-exchange-driven ferromagnetism is closely related to the virtual exchange gap, i.e., the ferromagnetic coupling can be increased significantly by lowering the gap with isovalent alloying [Fig. 3(a)–(c)]. Based on the model they predicted that the ferromagnetic coupling in monolayers CrWI6 and CrWGe2Te6 can be enhanced by 3–5 times without introducing carriers. Petrovic et al.83 observed a second-stage magnetic transition in CrI3 below TC and described the low temperature thermal demagnetization by the spin-wave model with Moriya's self-consistent renormalization.101 They demonstrated that the magnetic anisotropy in CrI3 comes predominantly from the anisotropic symmetric super-exchange via Cr–I–Cr with large SOC rather than the single ion anisotropy [Fig. 3(d) and (e)], which is in contrast to the argument of Lado and Fernández-Rossier.99 Huang et al. predicted a series of 2D transition metal magnetic compounds, namely FeX2, NiX2, CoCl2 and CoBr2 monolayers (X = Cl, Br, I) that exhibit ferromagnetism, while VX2, CrX2, MnX2 and CoI2 are antiferromagnetic due to the competition between direct nearest neighbor d–d exchange and super-exchange via the halogen p state.102 Victor Pardo et al. found a periodic atomic distortion in VSe2 with a 4 × 4 × 3 supercell by the DFT calculation,103 which induces a strong reduction in the density of states at the Fermi level and the non-magnetic phase transition. However, it should be noted that a huge discrepancy exists in the saturation magnetization between a monolayer VSe2 grown on different substrates, e.g., VSe2/MoS2 (15μB per V-atom),76 and exfoliated multi-layer VSe2 (0.3 × 10−3μB per V-atom).104 Moreover, previous DFT calculations of bulk and monolayer VSe2 show that the ferromagnetic phase is the most stable structure,105,106 whereas the values of the magnetic moment are in significant disagreement with the experimental results.
image file: c9nr08890c-f3.tif
Fig. 3 [(a) to (c)] Schematic diagrams of the super-exchange interaction and ferromagnetic coupling, including ferromagnetic/antiferromagnetic alignments and exchange energy in CrI3 and CrGeTe3 monolayers. Reproduced with permission.82 Copyright 2018, American Chemical Society. [(d) and (e)] Temperature-dependent reduced magnetization of CrI3 fitted using the spin-wave model and (inset) single-particle model and the magnetic entropy change magnetization isothermals obtained by rotating from the ab plane to the c axis in various fields.83 Copyright 2018, American Physical Society.

Above all, the theoretical exploration about 2D ferromagnetism is still underway with many issues and puzzles required to be clarified. We believe further detailed investigations are needed to probe the inter/intra-layer interaction and the origin of ferromagnetism within the 2D limit. Particularly, a relative general model is needed to describe the complicated ferromagnetic interaction, which is not only the recognition of the magnetic mechanism but also crucial to predict or design new 2D ferromagnets. In addition, the influence of substrates or other external perturbations on the magnetic stability is needed to be considered, as strain is capable of destroying the magnetism.106

3. Modulation of ferromagnetism in 2D materials

3.1. Magnetic doping

Defect doping, which is the intentional introduction of impurity elements into a material, plays a significant role in functionalizing 2D systems by changing the intrinsic properties of pristine atomic layers.107,108 Magnetic dopants (e.g., Fe, Co, Ni, Mn etc.) intercalated into 2D TMDs have been promising as diluted magnetic semiconductors and some of them have been predicted to exhibit ferromagnetic behavior at room temperature. For instance, transition metal (e.g., Nb, Co, Mn) doped MoS2 nanosheets60,109,110 and Fe doped SnS2[thin space (1/6-em)]84 have been synthesized via the chemical vapor deposition method and provide the possibility of electronic control of magnetism. However, complete understanding of the in-depth micro-mechanism about the defect induced magnetic properties in 2D systems still requires further research.

Wu et al.111 investigated the magnetism of Fe-doped SnS2 in detail and demonstrated that the ferrimagnetism originates from the exchange interaction between intralayer Fe atoms, whereas interlayer Fe interaction leads to the paramagnetic state. Wei et al.84 mixed Sn, S, and FeCl3 powders in different stoichiometric ratios and obtained Fe-doped SnS2via the direct vapor transport technique [Fig. 4(a)–(d)]. Finally, they realized Fe doped SnS2 in experiments and proved that long-range ferromagnetic ordering (TC 31 K) in the Fe-doped SnS2 monolayer is energetically stable according to DFT calculations. Yamasaki et al.112 fabricated bulk crystals of Cr1/3TaS2 and Fe1/4TaS2 by chemical vapour transport, then exfoliated thin flakes of the materials from bulk crystals using adhesive tape and deposited on either SiO2/doped Si substrates or polydimethylsiloxane (PDMS) sheets. Magneto-transport in the exfoliated tens of nanometers of thick flakes revealed ferromagnetic ordering below their Curie temperature TC (∼110 K) as well as strong in-plane magnetic anisotropy. Storchak et al.85 functionalized layered silicene with rare-earth atoms (Gd and Eu) ranging from the bulk down to one monolayer and found the evolution from the antiferromagnetism of the bulk to the intrinsic 2D in-plane ferromagnetism of ultrathin layers [Fig. 4(e)–(g)]. Zeng et al.113 predicted a series of stable 2D transition metal dihydrides (MH2, M = Sc, Ti, V, Cr, Fe, Co, Ni) with ferromagnetic or antiferromagnetic characteristics. Among them, monolayer CoH2 is a ferromagnetic metal at room-temperature TC (339 K), while ScH2 can possess half-metallicity through hole doping and maintain a relatively high TC (160 K). Moreover, they proposed a synthetic approach to realize CoH2 and ScH2 monolayers in experiments. González-Herrero et al.114 demonstrated that a magnetic moment can be induced in hydrogen adsorbed graphene with a ∼20 meV spin splitting state at the Fermi energy. Based on scanning tunneling microscopy detection and DFT calculations, they found that such a spin-polarized state is essentially localized on the carbon sublattice opposite to the chemisorbed hydrogen site, forming extended spin textures and direct coupling between the magnetic moments at unusually long distances.


image file: c9nr08890c-f4.tif
Fig. 4 [(a) and (b)] AFM and Raman spectra of the Fe0.021Sn0.979S2 and SnS2 monolayer. [(c) and (d)] Magnetic hysteresis loop measurement at 2 K using a vibrating sample magnetometer and schematic of the Fe 3d electron arrangement with spin in Fe-SnS2. [(a) to [d]] Adapted with permission.84 Copyright 2018, Springer Nature. (e) Schematics of the MBE synthesized MSi2 silicene at the Si (111) substrate and the structural characterization, including RHEED and X-ray diffraction scan image of 4–5 layer GdSi2 and HAADF-STEM image of monolayer GdSi2. [(f) and (g)] Temperature dependence of the AFM/FM magnetic moment in bulk GdSi2 and 4–5 layer GdSi2. [(e) to (g)] Adapted with permission.85 Copyright 2018, Springer Nature. (h) Schematic illustration of the synthesis process for F-antimonene. [(i) and (j)] The wide range (2–800 K) MT measurements to determine TC of F-antimonene and pure antimonene. [(h) to (j)] Reproduced with permission.52 Copyright 2019, Wiley-VCH.

3.2. Non-magnetic doping induced magnetic ordering

The above-mentioned 2D ferromagnetic materials involve the elements with valence d-electrons or f-electrons, such as Cr, Fe, Co, and Eu, with magnetic ordering originating from the partially filled d-bands or f-bands. On the other hand, materials based on elements with only sp-valence electrons could also exhibit spin splitting and magnetic ordering in certain circumstances – these materials can have high magnitudes of spin-wave stiffness,115 leading to potentially higher Curie temperature. The ferromagnetism as well as anti-ferromagnetism in graphene-related materials have been studied extensively,116 induced by defects, grain boundaries, nanostructure boundaries, etc. Zhao et al.117 realized ferromagnetism in the BN nanosheet with random substitution of B and/or N atoms by C atoms, suggesting a Curie temperature higher than 400 K. Tang et al.52 studied the magnetic properties of the air-stable few-layer antimonene under fluorination, revealing a robust ferromagnetism with the Curie temperature of 717 K, induced by the low-density sp-electron spin-polarized impurity sub-bands [Fig. 4(h)–(j)]. Louie et al.118 found that tunable ferromagnetism and half-metallicity can be induced in monolayer GaSe by carrier (hole) doping. The averaged electron spin magnetic moment per carrier reaches a plateau near 1.0μB, leading to a half-metallic state of GaSe, and then descends abruptly. They demonstrated that this itinerant magnetism originates from a Stoner mechanism with an exchange-field splitting of the electronic states near the VBM, where the density of states are very high and exhibit a sharp van Hove singularity.118 These studies demonstrate that the non-magnetic dopants in non-magnetic materials could favor spontaneous spin polarization and local moment formation, as well as long-range magnetic ordering.

3.3. Strain modulation

It has been demonstrated that strain engineering can effectively tune the electronic characteristics for low-dimensional materials (e.g., using substrate lattice mismatch59,120,121). For the 2D material family, strain engineering has been used as a powerful technique to tune their physical quantities and generate novel properties, such as band gap, carrier mobility and excitonic absorption.59,122,123 Moreover, structural deformation induced by external strain also has an influence on the magnetic stability. It is known that magnetic anisotropy energy defines the stability of magnetization in a specific direction with respect to the crystal lattice and is an important parameter for spintronic applications. Hence, magnetic characteristics (e.g., anisotropy and TC) modulated by strain have become a subject of field-regulated ferromagnetism recently.

In general, 2D atomic structures possess a unique mechanical advantage and can usually sustain larger strains than their 3D bulk counterpart.124 For instance, single-layer MoS2 and FeSe can sustain external strains up to 11% and 6%, respectively.120,121,125 The softness of single layer 2D structures implies that strain engineering of their electronic and magnetic properties can be realized in these systems. Indeed, Miao et al.119 proposed a promising alternative approach to create 2D intrinsic ferromagnetism from bulk vdW antiferromagnets, as realized in the CrOX monolayers which can be easily exfoliated from their bulk counterparts. The robust long-range ferromagnetic ordering lies in the out-of-plane direction of 2D CrOX, indicating the easy magnetization axis with large spin polarization and magneto-crystalline anisotropy energy [Fig. 5(a)]. Moreover, under appropriate strains, the TC of CrOX monolayers can be further enhanced up to 204 K. Kan et al.82 have predicted the room-temperature ferromagnetic phase transition for monolayers CrWI6 and CrWGe2Te6 under a small in-plane ∼4% tensile strain [Fig. 5(b) and (c)]. Lam et al.126 demonstrated that monolayer chromium trihalides CrX3 (X = Cl, Br, I) are soft with 2D Young's moduli of 34, 29 and 24 N m−1 through DFT calculations. In particular, all three compounds exhibit ferromagnetic ordering under zero strain, whereas their antiferromagnetic phase transition occurs upon a compressive strain, which is demonstrated by Webster et al.127 They further revealed a strain dependence magnetic anisotropy in CrX3, i.e., the anisotropy is enhanced with compressive strains for CrI3, which is opposite for CrBr3 and CrCl3.126


image file: c9nr08890c-f5.tif
Fig. 5 (a) Crystal structures of transition-metal oxyhalides and the Curie temperature comparison between CrOCl under 5% biaxial tensile strain and recently discovered 2D ferromagnetic compounds. Reproduced with permission.119 Copyright 2018, American Chemical Society. [(b) and (c)] Total exchange energy, magnetic anisotropic energy and magnetic moment per site as a function of temperature for monolayer CrI3, CrWI6 and CrWGe2Te6 (under 4% tensile strain case) from Monte-Carlo simulations. Reproduced with permission.82 Copyright 2018, American Chemical Society.

3.4. Electric field modulation

Manipulating a quantum state via electrostatic gating has been of great importance for many model systems in nanoelectronics.128,129 However, the effective tuning of the electron spins or the magnetism of a system by external electric field has been challenging. Wang et al.79 prepared exfoliated few-layered Cr2Ge2Te6 from its single-crystal using the Scotch tape method, and then deposited it onto silicon oxide with h-BN encapsulation. They found that the layered Cr2Ge2Te6 devices possess tunable magnetism via gating, as characterized by micro-area Kerr measurements below TC [Fig. 6(a) and (b)]. They attributed the observed bipolar magnetism tunability to the rebalance of the spin-polarized band structure with shifting Fermi level. Xu et al.130 found the electrostatic gate control of magnetism in CrI3 bilayers using magneto-optical Kerr effect (MOKE) microscopy [Fig. 6(c) and (d)], revealing the switching between antiferromagnetic and ferromagnetic states realized by external voltage. They further demonstrated the spin-layer locking induced by a time-reversal pair of layered antiferromagnetic states, which leads to a linear dependence of their MOKE signals on gate voltage with opposite slopes. Mak et al.131 fabricated dual-gate field-effect devices of atomically thin CrI3 with h-BN as the gate dielectrics and few-layer graphene as the gate and contact electrodes, realizing the control of magnetism in bilayer antiferromagnetic CrI3via using a small gate voltage. They proposed that the external electric field creates an interlayer potential difference, which leads to a linear magnetoelectric effect and interlayer spin–flip transition [Fig. 6(e)–(g)]. Furthermore, they demonstrated that electrostatic doping can effectively modify the magnetic properties of both monolayer and bilayer CrI3 by using CrI3/graphene vertical heterostructures.132
image file: c9nr08890c-f6.tif
Fig. 6 [(a) and (b)] Electrical transport and magnetic properties of Cr2Ge2Te6 FETs and the renormalized Kerr angle measured at 20 K with fixed ionic gate voltages of 0, −2 and −4 V. Adapted with permission.79 Copyright 2018, Springer Nature. [(c) and (d)] Intensity of the polar MOKE signal of a non-encapsulated bilayer CrI3 device as a function of gate voltage and magnetic field and the gate-induced variation of the metamagnetic transition at −50 V, 0 V and 50 V. Adapted with permission.130 Copyright 2018, Springer Nature. (e) AFM bilayer CrI3 consists of two FM monolayers with an AFM interlayer coupling and zero net magnetization. [(f) and (g)] Electrical switching of the magnetic order in bilayer CrI3 and the MCD signal as a function of magnetic field under representative electric fields. [(e) to (g)] Adapted with permission.131 Copyright 2018, Springer Nature.

As to monolayer CrI3, hole/electron doping significantly strengthens/weakens the magnetic order by modulating the saturation magnetization, coercive force, and TC.132 Remarkably, the moderate electron doping (above ∼2.5 × 1013 cm−2) can induce a ferromagnetic transition for bilayer CrI3 [Fig. 7(a)–(d)]. They emphasize the strongly doping-dependent interlayer exchange coupling, which can be used to realize the switching of magnetization in bilayer CrI3. Zhang et al.133 demonstrated that the ferromagnetic transition temperature of layered Fe3GeTe2 is suppressed compared with its bulk (205 K) [Fig. 7(e)–(g)], and the ionic gate can significantly raise TC to room temperature.133 San-Jose et al.55 found that two types of magnetic order in bilayer graphene, i.e., lattice antiferromagnetism and spiral ferromagnetism, are both concentrated at AA-stacked regions and can be switched by a vertical electrical field. Ferromagnetic polarized AA regions evolved into spiral magnetic ordering, keeping a relative 120° misalignment between neighboring regions due to a frustrated antiferromagnetic exchange. They suggested that the precise thresholds for such electric switching of magnetic order depend on the specific twist angle (≤2°).55 However, other crucial details such as longer-range interactions, spontaneous deformations, interlayer screening etc., have not been considered and needed to be further studied.


image file: c9nr08890c-f7.tif
Fig. 7 [(a) to (d)] Schematic side view of a dual-gate bilayer CrI3 field-effect device (left upper panel), doping density-magnetic field phase diagram (right upper panel), interlayer exchange constant J and spin-flip transition field Hsf as a function of gate voltage and gate induced doping density (lower panels). The gate-voltage controlled MCD is obtained from monolayer CrI3 at 4 K. Adapted with permission.132 Copyright 2018, Springer Nature. (e) Atomic structure and optical image of few-layer Fe3GeTe2 flakes exfoliated on top of the Al2O3 thin film. (f) Phase diagram and coercive field as the gate voltage. (g) Hall resistance Rxy of few-layer Fe3GeTe2 as a function of magnetic field with different gate voltages obtained at T = 10 K and 240 K. [(e) to (g)] Adapted with permission.133 Copyright 2018, Springer Nature.

4. Physical properties of 2D ferromagnetic materials

4.1. Magnetic anisotropy: the condition needed for 2D ferromagnetism

In the realm of 2D ferromagnetism, magnetic anisotropy is the critical factor because it prevents the random spin reorientation induced by thermal fluctuation.77 The anisotropy mainly comes from the lattice structure of the material itself, so that the Heisenberg model with SOC possesses single-ion anisotropy, which destroys the isotropy of the Hamiltonian and induces 2D ferromagnetism. Extensive theoretical and experimental efforts74,82,119 have been made to enhance the magnetic anisotropy of the magnetic nanostructures to promote the stability of magnetization, for potential applications at high temperature. Generally speaking, magnetic anisotropy depends on two factors: the spin–orbit coupling which contributes to magneto-crystalline anisotropy and the magneto-static dipole–dipole interaction. The magneto-crystalline anisotropy usually occurs at a surface or interface134,135 owing to the lack of neighbors and the lowered symmetry, which is evaluated by the magnetic anisotropy energy (EMAE). The reliable determination of EMAE for a given material requires highly accurate electronic structures and proper treatment of the weak SOC Hamiltonian. Thus, non-collinear non-self-consistent calculations are necessary to evaluate the total energies after the self-consistent ground states were achieved. According to the magnetic anisotropy theorem, EMAE can be determined by the formula EMAE = E(→) − E(↑), where the arrow indicates the direction of magnetization. Usually for the 2D system, the formula can be rewritten as EMAE = E(0°) − E(90°), where E(θ) is the computed total energies from the Kohn–Sham equations as a function of the angle θ between the magnetic moment and the atomic plane. EMAE < 0 (>0) describes in/out-of plane easy-axis situations (parallel or perpendicular to the 2D system), respectively.

4.2. Magnetic proximity effect

Benefitting from the fabrication of 2D atomic heterostructures, the proximity effect becomes prominent and can be used to tune the characteristics of the pristine layer.136 The proximity effect can drive a given material forming superconducting,137–139 magnetic,140,141 or topological states,142,143 through the adjacent regions. In bulk materials, the sample size could dwarf the characteristic lengths of proximity effects which usually can be ignored. However, in the monolayer vdW limit such as graphene or TMDs, the situation is different; even short-range magnetic proximity effects exceed their thickness. Taking advantage of the magnetic proximity effect, Leutenantsmeyer et al.144 presented the direct measurement of room temperature ferromagnetism in graphene by spin transport. Wang et al.140 placed graphene on an atomically flat yttrium iron garnet (YIG) ferromagnetic thin film and demonstrated that the anomalous Hall conductance can be kept up to ∼300 K. Katmis et al.145 demonstrated the topologically enhanced interface magnetism by coupling a ferromagnetic insulator (EuS) to a topological insulator (Bi2Se3) in a bilayer system by using the spin-polarized neutron reflectivity experiments, which persists up to room temperature. Scharf et al.146 provided the description of Coulomb interaction in magnetic proximity effects and elucidated how they transformed the neutral excitons X0 in TMDs on magnetic substrates (from dark to bright states). Yang et al.147 reported that a strong spin polarization of π orbitals in graphene can be induced through the interaction with the EuO magnetic insulator due to the magnetic proximity effect, which results in 24% spin polarization of the orbitals and a large exchange-splitting band gap (36 meV). They further revealed the possible engineering of graphene spin-gating by a proximity of a few magnetic insulators, including EuO, EuS, YIG and cobalt ferrite (CFO).148 Usually the adjacent magnetic insulator could induce a magnetic exchange field and enable efficient control of local spin generation and modulation without compromising the material structures. Using the graphene/EuS heterostructure, Wei et al.149 demonstrated that the coupling between graphene and magnetic insulator produces a substantial magnetic exchange field (>14 T), which leads to a significant enhancement of the spin signal originating from the Zeeman spin Hall effect. Lazić et al.150 showed the tunable magnetic proximity effect in 2D heterostructures due to the vdW bonding interaction, which both modulates the magnitude of spin polarization and enables its sign change in physisorbed graphene, e.g., Co/bilayer graphene, Co/BN/graphene, and Co/BN/benzene. Eremeev et al.151 found that the charge redistribution and orbital mixing between the topological insulator and magnetic insulator at the interface cause drastic modifications of the electronic structure due to the magnetic proximity effect. Wu et al.152 fabricated graphene–BiFeO3 heterostructures and found that the magnetic proximity effect results in a strong Zeeman splitting in graphene with the exchange field up to hundreds of tesla, which leads to the transformation from a quantum Hall state into a ferromagnetic state or a canted antiferromagnetic state. Inyang et al.153 determined the scaling between the proximity-induced magnetization in Pt and the temperature dependent interface magnetization for the adjacent ferromagnet, which is induced by the effective magnetic susceptibilities of heavy metal and is in contrast to the generally expected linear scaling for ferromagnetic interface magnetization. Karpiak et al.154 evidenced the existence of an out-of-plane proximity-induced ferromagnetic exchange interaction between graphene and magnetic insulator Cr2Ge2Te6, as the lifetime of perpendicular spins is much longer than that of the in-plane counterpart, which indicates the proximity-induced anisotropic spin texture in graphene. A general theory has recently been established to extract the exchange coupling fields induced by proximity through the Hanle spin precession analysis.155 Most recently, Tong et al.156 found that the magnetic proximity effect in the vdW moiré superlattice depends sensitively on the interlayer atomic registry due to the spin-dependent interlayer orbital coupling. The spatial variation of the atomic distribution leads to a lateral modulation of a magnetic proximity field and generates a miniband spin splitting, which strongly depends on the moiré periodicity and can be tuned mechanically by a relative twisting and/or strain between the vdW layers. They further showed the effective modulation of miniband spin splitting via a perpendicular electric field because of the modulation on the interlayer distance.

4.3. Quantum anomalous Hall effect

The theoretical discovery of topological phases157,158 substantially advanced the condensed matter physics, leading to a deeper understanding of materials for technological applications. The intriguing quantum anomalous Hall state was predicted by Haldane in 1988,159 and was realized in experiment in 2013 by introducing magnetic dopants in the 2D form of 3D topological insulators with a small energy gap opened between the topological surface states at 30 mK.160 Significant efforts have been made to raise the critical temperature of the QAHE state.161 Qiao et al.162 found from theoretical calculations that graphene on the (111) surface of room-temperature multiferroic BiFeO3 can host the QAHE state due to the magnetic proximity effect plus the topological band structure of graphene. Similarly, Zhang et al.163 predicted robust QAHE in the vdW heterostructure formed by graphene and 2D Cr2Ge2Te6 with a relatively high Curie temperature of 61 K. The experimental attempts on this type of graphene-based heterostructure demonstrate anomalous Hall conductance approaching the QAHE conductance.164 Chen et al.165 predicted the QAHE state in the intrinsically ferromagnetic CoBr2 monolayer with a Curie temperature of 27 K. Combining experiments with theoretical calculations, Tian et al.166 revealed the strong topological character of MnBi6Te10 possessing Dirac surface states, which can evolve into the antiferromagnetic topological insulator phase at T < 10.8 K. Moreover, the ferromagnetic axion insulator phase emerges at small field (0.1 T) and leads to a saturated anomalous Hall resistivity up to 10 K, which can also be preserved even when external field decreases to zero at 2 K. Hao et al.167 revealed a gapless surface Dirac cone in single crystal MnBi2Te4 using high-resolution angle-resolved photoemission spectroscopy (ARPES) characterization and first principles calculation, which is quasi-2D and stable under massive surface absorbents. Through magneto-transport, bulk magnetization and neutron scattering measurement, Wang et al.168 investigated the magnetic and transport properties for trigonal Cr5Te8 single crystals and demonstrated the appearance of the topological Hall effect with current along the c axis and field in the ab plane, which stems from the noncoplanar spin configurations with scalar spin chirality during the spin flop process. Chen et al.169 reported the ferromagnetic vdW compound MnSb1.8Bi0.2Te4 (TC = 26 K) with excess anomalous Hall signal which is beyond the conventional AHE. Recently, numerous topological materials have been predicted from high-throughput calculations170–172 – the combination of strong SOC with spatial anisotropicity in their 2D structures could render them candidate base materials for QAHE phases, opening the arena for the design of high-temperature QAHE materials.

4.4. Giant magnetoresistance

Giant magnetoresistance is a quantum mechanical magnetoresistance phenomenon discovered by Albert Fert and Peter Grünberg,173,174 which presents a significant change in the electrical resistance when the magnetization of the adjacent ferromagnetic layers transfer between parallel and antiparallel alignments. The giant magnetoresistance effect is based on the dependence of electron scattering on the spin orientation and offers a new knob to control the overall resistance via manipulating the magnetization direction, which lays the foundation of modern data storage technology, such as hard disk drives,175,176 biosensors,177 microelectromechanical systems (MEMS) and other devices.178 This effect has also been extended to 2D ferromagnets, and exhibit more novel features. Xu et al.179 fabricated multiple spin filter magnetic tunnel junctions composed of graphene/CrI3/graphene vdW heterostructures, revealing a drastic enhancement (19[thin space (1/6-em)]000%) of tunneling magnetoresistance for the four-layer device at low temperatures, which is significantly larger than conventional barrier-based ferromagnetic tunnel junctions (e.g., MgO180,181). They attributed these effects to the intrinsic interlayer antiferromagnetic ordering of the atomically thin CrI3. Wang et al.182 found that tunneling conduction in the direction perpendicular to the exfoliated CrI3 crystalline planes exhibits a ten times magnetoresistance enhancement, which originates from multiple transitions between different magnetic states as characterized by the evolution of magnetoresistance with magnetic field and temperature. On the basis of tight-binding models and DFT calculations, Zhong et al.183 demonstrated a giant magneto band structure effect dominated significantly by the magnetization direction. Through the analysis while rotating the magnetic moment of CrI3 from out-of-plane to in-plane, they observed a direct-to-indirect band structure transition, which indicates the magnetic field controlled photoluminescence.

4.5. Magnon

Magnon represents a collective behavior of magnetic moments in a specific system, which can generally be treated as one complete precession distributed over a chain of spins (a quantized spin wave) and obeys the Bose–Einstein statistics.184 The control of magnon-mediated spin current is useful for information logic devices and computing applications.185 Magnon was firstly detected in experiments by Brockhouse et al.,186 using the inelastic neutron scattering method. The Bose–Einstein condensation of magnons has been proved in an antiferromagnetic TlCuCl3 compound at low temperatures by Nikuni et al.187 Furthermore, room temperature magnons in YIG films were reported by Demokritov et al.188 Uchida et al. observed the generation of spin currents in the Pt/BiY2Fe5O12 interface with Au nanoparticles embedded in the BiY2Fe5O12 layer.189 They suggested that the spin-current generation originates from non-equilibrium magnons excited by surface plasmon induced evanescent electromagnetic fields in BiY2Fe5O12. Balatsky et al.190 found that Coulomb interactions between fermions in honeycomb layered chromium trihalides induce strong temperature and momentum-dependent renormalization of the magnon bands near a Dirac cone, thus clarifying the long debated puzzle of spin-wave anomalies in CrBr3.191,192 Ghazaryan et al.193 studied the tunneling effect in graphene/CrBr3/graphene vdW heterostructures and demonstrated that the inelastic tunneling through thin ferromagnetic CrBr3 barriers is mainly associated with magnon emission at low temperature, i.e., the spin state (up or down) of a tunneling electron will be flipped between the initial and final states during the magnon process. Very recently, Xing et al.194 reported the experimental observation of long-distance magnon propagation over several micrometers in quasi-two-dimensional vdW antiferromagnet MnPS3, which is comparable to the bulk ferromagnetic insulator YIG. They demonstrated that the magnon diffusion length is sensitive to temperature and layer thickness, which could be attributed to the surface impurity-induced magnon scattering.

4.6. Anisotropic Gilbert damping

Gilbert damping is a fundamental parameter in magnets and describes the relaxation of magnetization to the equilibrium constant value, which determines the performance of many spintronic devices.195–197 Based on the SOC band structure with regard to the orientation of the magnetization direction, theoretical studies suggested that damping should be anisotropic in single-crystalline ferromagnetic metals (e.g., Fe, Co, Ni).4 However, electron scattering will dramatically reduce the anisotropic characteristics with the smearing of energy bands, leading to the challenge for direct observation of anisotropic damping in 3D bulk. Only a few experiments attempted to prove this phenomenon, whereas convincing evidence is still lacking. Until most recently, Back et al. reported the emergence of anisotropic magnetic damping in the 2D ferromagnetic metal/semiconductor interface of the Fe/GaAs(001) heterojunction.198 They demonstrated that the fourfold symmetry exists in the Fe/GaAs(001) heterojunction, thus no in-plane distortions occur, which is different from Fe/InAs(001) where there is structural anisotropy originating from crystal growth.199,200 Through DFT calculations, they further attributed the anisotropic Gilbert damping to interfacial symmetry-breaking of Fe atoms in light of the rapid reduction of anisotropy with increasing Fe film thickness.

4.7. Circular optical polarization

Ferromagnets give rise to time reversal symmetry breaking due to the inherent spontaneous magnetization. The observation of net circular polarized emission provides a convenient probe for the appearance of spontaneous magnetic ordering. In fact, investigation about the interaction between a ferromagnet and circular polarized response was initialized in the 3D heterojunction and has been extensively studied for many years.205,206 Jonker et al.207 injected the spin-polarized electrons into Si (001) from an iron film through an Al2O3 tunnel barrier. They found that the circular polarization of the electroluminescence resulting from radiative recombination traces the Fe magnetization, thus confirming that these spin-polarized electrons originate from the Fe contact. Also the circular polarized electroluminescence was determined in III–V heterostructures with a p-type ferromagnetic semiconductor as the spin polarizer.208 With the rapid development of low dimensional materials, the research scope is extended to magneto-optical interactions within the 2D limit. Most recently, Xu et al.209 reported the intimate connection between the magnetization direction and circularly polarized photoluminescence in CrI3. The circular polarization exists in the monolayer ferromagnetic form, whereas vanishes in the bilayer antiferromagnetic structure. They suggested that this phenomenon originates from the parity-forbidden d–d transition of Cr3+ complexes, which displays a broad linewidth due to strong vibronic coupling. Furthermore, they fabricated heterostructures formed by monolayer WSe2 and 2D magnetic CrI3 and demonstrated the wide continuous tuning of the valley polarization via the optical control of the CrI3 magnetization and valley Zeeman splitting.209 The WSe2 photoluminescence intensity is dominated by the relative alignment between photoexcited spins in WSe2 with the CrI3 magnetization due to the ultrafast spin-dependent charge hopping across the heterostructure interface.

4.8. Current-induced spin–orbit torques

Current-induced spin–orbit torques (SOTs) in an inversion-asymmetric system have attracted scientific and technological interest in recent years.210 The manipulation of magnetic characteristics by SOTs evidences the microscopic interactions between charge and spin in a variety of materials and enables the designing of spintronics with potential applications in data storage and low-power memory and logic devices. Garello et al.211 provided a general scheme to measure the amplitude and direction of SOTs and demonstrated that heavy-metal/ferromagnetic layers present different SOTs with odd and even behaviour considering their magnetization reversal. They found that such torques possess strongly anisotropic field-like and spin transfer-like components, which are determined by the type of heavy-metal layer and annealing treatment. Akyol et al.212 studied the effect of the oxide layer on the current-induced SOTs in perpendicularly magnetized MgO-capped Hf/CoFeB and TaOx-capped Hf/CoFeB and found significantly stronger torques for the former than the latter, which may be attributed to the different Rashba like Hamiltonian arising from the difference in the electric potential profiles across the oxide/ferromagnet interfaces, as well as possible structural and oxidation differences in the underlying CoFeB and Hf layers. Liu et al.213 investigated the effects of electrostatic gating on the current-induced phenomena in ultrathin ferromagnet/heavy-metal heterostructures and demonstrated that the spin current produced by the spin Hall effect plays a dominant role in current-induced phenomena, while the interfacial Rashba effect also provides a considerable contribution to the current-induced torque. Ando et al.214 reported that incorporating oxygen into Pt turns the heavy metal into an electrically insulating generator of the SOTs, which leads to the electrical switching of perpendicular magnetization in a ferrimagnet and can be controlled through voltage-driven oxygen migration. Wang et al.215 realized the switchable magnetization of few-layered Fe3GeTe2/Pt through the SOTs originating from the current in the Pt layer, which is quantitatively characterized by their harmonic measurements. Alghamdi et al.216 exfoliated Fe3GeTe2 flakes (∼15–23 nm) and sputtered 5 nm Pt onto the atomically flat surface forming Fe3GeTe3/Pt heterostructures. They further found that the spin current generated in Pt presents damping-like SOTs on Fe3GeTe2 magnetization with high switching efficiency, which is comparable to that of the heterostructures containing conventional 3D ferromagnetic metals and much larger than that of heterostructures containing 3D ferrimagnetic insulators.

4.9. Skyrmions in 2D magnets

Magnetic skyrmions are one special kind of topological spin textures that can be stabilized by Dzyaloshinskii–Moriya interactions (DMIs).217 Skyrmions have attracted intense interest during the past decades for their promising potential in spintronics technology, such as energy-efficient logic and memory devices. Early research studies about skyrmions are focusing on the bulk materials (e.g., MnSi, FeCoSi, MnGe, FeGe etc.),218–220 and investigations on atomic-scale skyrmions within the 2D limit have emerged in the recent years. Heinze et al.221 observed magnetic skyrmions in 2D ultrathin Fe/Ir(111) bilayers at low temperature (T = 11 ± 2 K), which was attributed to the significant interfacial DMIs. Yang et al.222 verified the physical mechanisms of DMIs in bilayers Co/Pt using first principles calculations. Soumyanarayanan et al.223 realized the tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers by varying the Fe/Co composition that influences the magnetic interactions thus governing skyrmion formation. Boulle et al.224 also reported the observation of stable skyrmions in sputtered ultrathin Pt/Co/MgO nanostructures at room temperature without magnetic field. Most recently, the successful synthesis of a variety of 2D intrinsic vdW magnets stimulates the research for finding 2D hosts with intrinsic DMIs and skyrmions. Park et al.225 reported the experimental observation of magnetic skyrmions in Fe3GeTe2 vdW ferromagnet flakes and demonstrated that the skyrmion crystal state is homochiral and can be generated by both dynamically using current pulses and statically using the magnetic field-cooling process. On the basis of first principles calculations, they further unveiled the possible origin of DMIs. Wu et al.226 demonstrated that large interfacial DMIs at the 1T′-WTe2/Fe3GeTe2 interface could be induced due to the strong SOC in 1T′-WTe2, which breaks the inversion symmetry and stabilizes Néel-type skyrmions in the vdW heterostructures. Wang et al.227 reported the Néel-type, zero-field-stabilized skyrmions in Fe3GeTe3 nanoflakes (20 nm thick) at cryogenic temperature using advanced magnetic electron microscopy. Their further first principles calculations revealed finite interfacial DMIs in the Te/Fe3Ge/Te slabs that determines the spin chirality in Fe3GeTe2. Using cryo-Lorentz transmission electron microscopy, Han et al.228 found the topologically nontrivial skyrmionic bubbles with homochirality in exfoliated insulating 2D vdW Cr2Ge2Te6, which originates from the competition between dipolar interactions and uniaxial magnetic anisotropy. Yuan et al.229 investigated the intrinsic magnetic skyrmions in the monolayer Janus TMDs, i.e., MnSTe, MnSeTe, VSeTe, and MnSSe. Due to the out-of-plane geometric asymmetry and strong SOC, monolayer MnSTe and MnSeTe can stabilize sub-50 nm intrinsic skyrmions without magnetic field, while monolayer VSeTe with an in-plane easy axis forms magnetic domains rather than skyrmions. Combining the ferromagnetic monolayer (CrX3, X = Cl, Br, and I) with the antiferromagnetic substrate (MnPX3, X = S, Se, Te), Tong et al. realized the moiré skyrmions in 2D magnets originating from the moiré pattern vdW heterostructures.230 They found that skyrmion vorticity and location in the moiré pattern can be switched by magnetic field in the strong interlayer coupling situation, while the metastable skyrmion excitations can be moved between the ordered moiré trapping sites by current pulses for the weak interlayer coupling case.

5. Ferromagnetic 2D devices

Manipulating exchange interactions in magnetic heterostructures has been proven to be an effective method to engineer functional materials.231 Thus the incorporation of magnetism with a semiconductor is particularly enticing for spintronics. The use of 2D materials to form magnetic heterostructures has the advantage that the proximity-induced exchange interaction, which is usually considered as a perturbation for bulk materials, can fundamentally alter the electronic structure of the 2D systems due to their atomic thickness. Compared to the approach of interfacing 2D materials with 3D magnets, a vdW heterostructure has the following advantages: (i) no need to consider lattice mismatch, thus almost maintaining the pristine layered structure without chemical modification and interfacial damage, which is necessary to study the optimal interactions between different layers. (ii) The interlayer twisting angle and stacking order can be treated as new knobs to study and engineer the magnetic characteristics (e.g., spin textures). (iii) The flexibility of the layered structure enables controlling the stacking process and facilitating the formation of vdW heterostructures with a diversity of 2D ferromagnets. Therefore, ferromagnetic 2D heterostructures provide a convenient platform to explore the magnetism related condensed matter physics and make it possible for realizing the application of spintronics.

Xu et al.179 realized multiple-spin-filter magnetic tunnel junctions by using CrI3 as a spin-filter tunnel barrier and reached a record of enhanced magnetoresistance for four-layer junction structures [Fig. 8(a)]. Furthermore, they realized effective control of the spin and valley pseudo-spin in the CrI3/WSe2 ferromagnetic heterostructure via flipping the magnetization of CrI3.141,231 Ultrafast spin-dependent charge hopping across the heterostructure interface indicates the strong dependence of the relative alignment between photoexcited spin and magnetization. Wu et al.232 demonstrated that the topological surface states of Bi2Se3 can be persisted and magnetized via forming the CrI3/Bi2Se3/CrI3 heterostructure. Mak et al.131 fabricated dual-gate graphene/BN/CrI3 field-effect devices and realized the effective control of magnetism in bilayer antiferromagnetic CrI3 by tuning gate voltage. Zhang et al.133 developed a device fabrication technique using isolated Fe3GeTe2 monolayers from the layered bulk material, realizing the ferromagnetic transition at room temperature. Controlled fabrication methods enable the tailoring of layered structures with specific spin-dependent transport characteristics, which usually combine a variety of 2D structures ranging from conductor and superconductor to insulator in respect of the conductivity. The rise of ferromagnetic and antiferromagnetic insulators with magnetic ordering (e.g., CrI3) enriches the family of 2D functional materials. Recently, incorporating atomic thin layered CrI3 into vdW devices has been realized.141 Benefitting from these findings, the 2D spin-dependent transport device–spin valve with adjustable conductivity via manipulating the relative orientation of two ferromagnetic electrodes emerges. Tombros et al. reported the lateral graphene spin valve with a relative long spin relaxation length over micrometre-scale distances (1.5–2 μm) at room temperature.233 Jarillo-Herrero et al. demonstrated a double spinfilter in graphite/CrI3/graphite junctions where the CrI3 tunnel barrier and the decoupled magnetic layers can be treated as a magnetic memory bit for data storage [Fig. 8(b)].201 Furthermore, they realized the collective magnetic behavior (i.e., magnons) in CrI3. Taking advantage of the spin–orbit torques determined by crystal symmetries, MacNeill et al.202 determined the device selectivity of out-of-plane antidamping between the low- and high-symmetry axes of WTe2/permalloy bilayers [Fig. 8(c)]. Gong et al.203 predicted electric spin field effect transistors in bilayer A-type antiferromagnetic (i.e., intralayer ferromagnetism and interlayer antiferromagnetism) vdW crystals, in which the energy levels of the constituent layers are lifted in opposite directions [Fig. 8(d)]. Fernández-Rossier et al. took advantage of the spin proximity effect and proposed a new type of vdW spin valve composed of CrI3/bilayer graphene/CrI3.204 The phase transition between ferromagnetic and antiferromagnetic states for the up/down layer can be used as a knob to manipulate the in-plane conductance of the intercalated graphene conductor,204 as shown in Fig. 8(e).


image file: c9nr08890c-f8.tif
Fig. 8 (a) Schematic of magnetic states in bilayer CrI3, the 2D spin-filter magnetic tunnel junction and its tunneling current at selected magnetic fields.179 Copyright 2018, American Association for the Advancement of Science. (b) Optical micrograph of a tetralayer CrI3 tunnel junction and conductance through a bilayer and tetralayer CrI3 tunnel barrier as a function of an out-of-plane applied magnetic field.201 Copyright 2018, American Association for the Advancement of Science. (c) Bilayer WTe3/permalloy sample geometry and schematic of the spin–orbit torque measurement system. Adapted with permission.202 Copyright 2018, Springer Nature. (d) Schematics of a spin field-effect transistor based on 2D antiferromagnetic half metals and its predicted spin-polarized current.203 Copyright 2018, National Academy of Sciences. (e) vdW spin valve structure, where the 2D conductor is sandwiched between two ferromagnets. The magnetization of the bottom ferromagnetic layer is pinned, whereas the top layer can switch, resulting in parallel and antiparallel states with distinct in-plane conductance.204 Copyright 2018, American Physical Society.

6. Summary and outlook

We have reviewed the recent progress on 2D ferromagnetic materials, encompassing their synthesis, magnetic-related physical phenomena and device applications. Searching for better 2D ferromagnets is still underway, accompanied by a lot of challenges and opportunities, such as intriguing quantum states and novel informatics devices based on 2D FM materials. Stacking ferromagnets as building blocks in hybrid multilayers enable the creation of new spin textures and exotic Berry phases.234,235 The potential incorporation of these 2D ferromagnets into spintronic, optoelectronic, and quantum devices stimulates many pioneering research studies.179,201–204 However, achieving this goal still requires overcoming many scientific and technical challenges, such as manipulating the robust magnetic ordering at ambient temperatures, understanding the origin of 2D ferromagnetism thoroughly, introducing quantum band topology into high-temperature 2D ferromagnets, and integrating the 2D FM-based device into modern electronic processes. The recent high-throughput prediction of novel 2D materials236,236 and topological materials237–239 offers a new arena for designing new 2D ferromagnetic materials to overcome the challenges in the practical application of 2D FM's for information technologies.

Conflicts of interest

The authors have no existing conflicts to declare.

Acknowledgements

The research was supported by the National Natural Science Foundation of China (Grant No. 11804230, 11774239, 61827815, 61805147, 61435010, and 61675135), the Science and Technology Innovation Commission of Shenzhen (Grant No. KQTD2015032416270385, KQTD20170810105439418, KQTD20180412181422399, JCYJ20170818093035338, JCYJ20170412110137562, ZDSYS201707271554071, GJHZ20180413181813768), the Science and Technology Development Fund (Grant No. 007/2017/A1 and 132/2017/A3), Macao SAR, China, and the National Key R&D Program of China (Grant No. 2016YFB0700700).

References

  1. S. Chikazumi, Physics of Ferromagnetism 2e, Oxford Univ. Press, 2009 Search PubMed.
  2. A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford Univ. Press, 2001 Search PubMed.
  3. B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, John Wiley & Sons, 2011 Search PubMed.
  4. C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1996 Search PubMed.
  5. M. Jackson, IRM Quarterly, Institute for Rock Magnetism, 2000, vol. 10, p. 6 Search PubMed.
  6. G. H. Jonker and J. H. Van Santen, Physica, 1950, 16, 337–349 CrossRef CAS.
  7. J. F. Scott, Nat. Mater., 2007, 6, 256 CrossRef CAS PubMed.
  8. A. Ron, E. Zoghlin, L. Balents, S. D. Wilson and D. Hsieh, Nat. Commun., 2019, 10, 1654 CrossRef CAS PubMed.
  9. L. D. Casto, A. J. Clune, M. O. Yokosuk, J. L. Musfeldt, T. J. Williams, H. L. Zhuang, M.-W. Lin, K. Xiao, R. G. Hennig, B. C. Sales, J.-Q. Yan and D. Mandrus, APL Mater., 2015, 3, 041515 CrossRef.
  10. Z. Guo, S. Chen, Z. Wang, Z. Yang, F. Liu, Y. Xu, J. Wang, Y. Yi, H. Zhang and L. Liao, Adv. Mater., 2017, 29, 1703811 CrossRef PubMed.
  11. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen and Y. Zhang, Nat. Nanotechnol., 2017, 9, 372–377 CrossRef PubMed.
  12. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti and A. Kis, Nat. Nanotechnol., 2011, 6, 147–150 CrossRef CAS PubMed.
  13. L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan and L. Qian, Laser Phys. Lett., 2016, 13, 045801 CrossRef.
  14. J. Li, H. Luo, B. Zhai, R. Lu, Z. Guo, H. Zhang and Y. Liu, Sci. Rep., 2016, 6, 30361–30361 CrossRef CAS PubMed.
  15. H. Mu, Z. Wang, J. Yuan, S. Xiao, C. Chen, Y. Chen, Y. Chen, J. Song, Y. Wang, Y. Xue, H. Zhang and Q. Bao, ACS Photonics, 2015, 2, 832–841 CrossRef CAS.
  16. X. Ren, Z. Li, Z. Huang, D. Sang, H. Qiao, X. Qi, J. Li, J. Zhong and H. Zhang, Adv. Funct. Mater., 2017, 27, 1606834 CrossRef.
  17. X. Jiang, S. Liu, W. Liang, S. Luo, Z. He, Y. Ge, H. Wang, R. Cao, F. Zhang, Q. Wen, J. Li, Q. Bao, D. Fan and H. Zhang, Laser Photonics Rev., 2018, 12, 1700229 CrossRef.
  18. P. Yan, R. Lin, H. Chen, H. Zhang, A. Liu, H. Yang and S. Ruan, IEEE Photonics Technol. Lett., 2014, 27, 264–267 Search PubMed.
  19. L. Lu, X. Tang, R. Cao, L. Wu, Z. Li, G. Jing, B. Dong, S. Lu, Y. Li, Y. Xiang, J. Li, D. Fan and H. Zhang, Adv. Opt. Mater., 2017, 5, 1700301 CrossRef.
  20. Y. Jiang, L. Miao, G. Jiang, Y. Chen, X. Qi, X. Jiang, H. Zhang and S. Wen, Sci. Rep., 2015, 5, 16372 CrossRef CAS PubMed.
  21. Q. Wang, Y. Chen, L. Miao, G. Jiang, S. Chen, J. Liu, X. Fu, C. Zhao and H. Zhang, Opt. Express, 2015, 23, 7681–7693 CrossRef CAS PubMed.
  22. M. Liu, Z. Cai, S. Hu, A. Luo, C. Zhao, H. Zhang, W. Xu and Z. Luo, Opt. Lett., 2015, 40, 4767–4770 CrossRef CAS PubMed.
  23. Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li and H. Zhang, Laser Photonics Rev., 2018, 12, 1800016 CrossRef.
  24. R. Cao, H. Wang, Z. Guo, D. K. Sang, L. Zhang, Q. Xiao, Y. Zhang, D. Fan, J. Li and H. Zhang, Adv. Opt. Mater., 2019, 7, 1900020 CrossRef.
  25. Y. Ge, Z. Zhu, Y. Xu, Y. Chen, S. Chen, Z. Liang, Y. Song, Y. Zou, H. Zeng, S. Xu, H. Zhang and D. Fan, Adv. Opt. Mater., 2018, 6, 1701166 CrossRef.
  26. H.-J. Li, L.-L. Wang, H. Zhang, Z.-R. Huang, B. Sun, X. Zhai and S.-C. Wen, Appl. Phys. Express, 2014, 7, 024301 CrossRef.
  27. Y. Song, X. Shi, C. Wu, D. Tang and H. Zhang, Appl. Phys. Rev., 2019, 6, 021313 Search PubMed.
  28. Y. Song, K. You, Y. Chen, J. Zhao, X. Jiang, Y. Ge, Y. Wang, J. Zheng, C. Xing and H. Zhang, Nanoscale, 2019, 11, 12595–12602 RSC.
  29. B. Wang, S. P. Zhong, Z. B. Zhang, Z. Q. Zheng, Y. P. Zhang and H. Zhang, Appl. Mater. Today, 2019, 15, 115–138 CrossRef.
  30. L. Wu, Y. Dong, J. Zhao, D. Ma, W. Huang, Y. Zhang, Y. Wang, X. Jiang, Y. Xiang, J. Li, Y. Feng, J. Xu and H. Zhang, Adv. Mater., 2019, 31, 1807981 CrossRef PubMed.
  31. Y. Zhang, C.-K. Lim, Z. Dai, G. Yu, J. W. Haus, H. Zhang and P. N. Prasad, Phys. Rep., 2019, 795, 1–51 CrossRef CAS.
  32. Q. Guo, A. Pospischil, M. Bhuiyan, H. Jiang, H. Tian, D. Farmer, B. Deng, C. Li, S.-J. Han, H. Wang, Q. Xia, T.-P. Ma, T. Mueller and F. Xia, Nano Lett., 2019, 16, 4648–4655 CrossRef PubMed.
  33. M. Huang, M. Wang, C. Chen, Z. Ma, X. Li, J. Han and Y. Wu, Adv. Mater., 2019, 28, 3481–3485 CrossRef PubMed.
  34. X. Ren, J. Zhou, X. Qi, Y. Liu, Z. Huang, Z. Li, Y. Ge, S. C. Dhanabalan, J. S. Ponraj, S. Wang, J. Zhong and H. Zhang, Adv. Energy Mater., 2017, 7, 1700396 CrossRef.
  35. Z. Zhang, Y. Liu, L. Ren, H. Zhang, Z. Huang, X. Qi, X. Wei and J. Zhong, Electrochim. Acta, 2016, 200, 142–151 CrossRef CAS.
  36. Y. Xu, M. Gao, G. Zhang, X. Wang, J. Li, S. Wang and Y. Sang, Chin. J. Catal., 2015, 36, 1936–1942 CrossRef CAS.
  37. R. Wang, X. Li, Z. Wang and H. Zhang, Nano Energy, 2017, 34, 131–140 CrossRef CAS.
  38. Z. Huang, Z. Zhang, X. Qi, X. Ren, G. Xu, P. Wan, X. Sun and H. Zhang, Nanoscale, 2016, 8, 13273–13279 RSC.
  39. M. A. Bissett, S. D. Worrall, I. A. Kinloch and R. A. W. Dryfe, Electrochim. Acta, 2016, 201, 30–37 CrossRef CAS.
  40. W. Tao, X. Ji, X. Xu, M. A. Islam, Z. Li, S. Chen, P. E. Saw, H. Zhang, Z. Bharwani, Z. Guo, J. Shi and O. C. Farokhzad, Angew. Chem., Int. Ed., 2017, 56, 11896–11900 CrossRef CAS PubMed.
  41. H. Xie, Z. Li, Z. Sun, J. Shao, X. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Wang, H. Zhang and P. K. Chu, Small, 2016, 12, 4136–4145 CrossRef CAS PubMed.
  42. Z. Sun, Y. Zhao, Z. Li, H. Cui, Y. Zhou, W. Li, W. Tao, H. Zhang, H. Wang, P. K. Chu and X.-F. Yu, Small, 2017, 13, 1602896 CrossRef PubMed.
  43. M. Qiu, D. Wang, W. Liang, L. Liu, Y. Zhang, X. Chen, D. K. Sang, C. Xing, Z. Li, B. Dong, F. Xing, D. Fan, S. Bao, H. Zhang and Y. Cao, Proc. Natl. Acad. Sci. U. S. A., 2018, 115, 501–506 CrossRef CAS PubMed.
  44. C. Xing, G. Jing, X. Liang, M. Qiu, Z. Li, R. Cao, X. Li, D. Fan and H. Zhang, Nanoscale, 2017, 9, 8096–8101 RSC.
  45. Z. Li, H. Xu, J. Shao, C. Jiang, F. Zhang, J. Lin, H. Zhang, J. Li and P. Huang, Appl. Mater. Today, 2019, 15, 297–304 CrossRef.
  46. T. Xue, W. Liang, Y. Li, Y. Sun, Y. Xiang, Y. Zhang, Z. Dai, Y. Duo, L. Wu, K. Qi, B. N. Shivananju, L. Zhang, X. Cui, H. Zhang and Q. Bao, Nat. Commun., 2019, 10, 28 CrossRef CAS PubMed.
  47. P. Wan, X. Wen, C. Sun, B. K. Chandran, H. Zhang, X. Sun and X. Chen, Small, 2015, 11, 5409–5415 CrossRef CAS PubMed.
  48. H. Wang, D. K. Sang, Z. Guo, R. Cao, J. Zhao, M. N. U. Shah, T. Fan, D. Fan and H. Zhang, Chin. Phys. B, 2018, 27, 087308 CrossRef.
  49. S. Bai, C. Sun, H. Yan, X. Sun, H. Zhang, L. Luo, X. Lei, P. Wan and X. Chen, Small, 2015, 11, 5807–5813 CrossRef CAS PubMed.
  50. T. Wang, Y. Guo, P. Wan, H. Zhang, X. Chen and X. Sun, Small, 2016, 12, 3748–3756 CrossRef CAS PubMed.
  51. S. Yang, Y. Liu, W. Chen, W. Jin, J. Zhou, H. Zhang and G. S. Zakharova, Sens. Actuators, B, 2016, 226, 478–485 CrossRef CAS.
  52. X. Tang, L. Hu, T. Fan, L. Zhang, L. Zhu, H. Li, H. Liu, J. Liang, K. Wang, Z. Li, S. Ruan, Y. Zhang, D. Fan, W. Chen, Y.-J. Zeng and H. Zhang, Adv. Funct. Mater., 2019, 29, 1808746 CrossRef.
  53. A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 6, 183–191 CrossRef CAS PubMed.
  54. Z. Sun, Z. Liu, J. Li, G.-A. Tai, S.-P. Lau and F. Yan, Adv. Mater., 2012, 24, 5878–5883 CrossRef CAS PubMed.
  55. L. A. Gonzalez-Arraga, J. L. Lado, F. Guinea and P. San-Jose, Phys. Rev. Lett., 2017, 119, 107201 CrossRef PubMed.
  56. A. Hallal, F. Ibrahim, H. Yang, S. Roche and M. Chshiev, 2D Mater., 2017, 4, 025074 CrossRef.
  57. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli and F. Wang, Nano Lett., 2010, 10, 1271–1275 CrossRef CAS PubMed.
  58. B. Wen, Y. Zhu, D. Yudistira, A. Boes, L. Zhang, T. Yidirim, B. Liu, H. Yan, X. Sun, Y. Zhou, Y. Xue, Y. Zhang, L. Fu, A. Mitchell, H. Zhang and Y. Lu, arXiv preprint arXiv, 2019, 1902.05661.
  59. H. J. Conley, B. Wang, J. I. Ziegler, R. F. Haglund Jr., S. T. Pantelides and K. I. Bolotin, Nano Lett., 2013, 13, 3626–3630 CrossRef CAS PubMed.
  60. J. Suh, T. E. Park, D. Y. Lin, D. Fu, J. Park, H. J. Jung, Y. Chen, C. Ko, C. Jang, Y. Sun, R. Sinclair, J. Chang, S. Tongay and J. Wu, Nano Lett., 2014, 14, 6976–6982 CrossRef CAS PubMed.
  61. Y. Chen, M. Wu, P. Tang, S. Chen, J. Du, G. Jiang, Y. Li, C. Zhao, H. Zhang and S. Wen, Laser Phys. Lett., 2014, 11, 055101 CrossRef.
  62. M. Liu, N. Zhao, H. Liu, X.-W. Zheng, A.-P. Luo, Z.-C. Luo, W.-C. Xu, C.-J. Zhao, H. Zhang and S.-C. Wen, IEEE Photonics Technol. Lett., 2014, 26, 983–986 Search PubMed.
  63. H. Liu, D. Li, C. Ma, X. Zhang, X. Sun, C. Zhu, B. Zheng, Z. Zou, Z. Luo, X. Zhu, X. Wang and A. Pan, Nano Energy, 2019, 59, 66–74 CrossRef CAS.
  64. Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang and X. Yu, Adv. Funct. Mater., 2015, 25, 6996–7002 CrossRef CAS.
  65. Y. Saito and Y. Iwasa, ACS Nano, 2015, 9, 3192–3198 CrossRef CAS PubMed.
  66. Y. Song, Y. Chen, X. Jiang, Y. Ge, Y. Wang, K. You, K. Wang, J. Zheng, J. Ji and Y. Zhang, Adv. Opt. Mater., 2019, 1801777 CrossRef.
  67. Y. Song, Z. Liang, X. Jiang, Y. Chen, Z. Li, L. Lu, Y. Ge, K. Wang, J. Zheng and S. Lu, 2D Mater., 2017, 4, 045010 CrossRef.
  68. Y. Wang, P. Huang, M. Ye, R. Quhe, Y. Pan, H. Zhang, H. Zhong, J. Shi and J. Lu, Chem. Mater., 2017, 29, 2191–2201 CrossRef CAS.
  69. L. Lu, Z. Liang, L. Wu, Y. Chen, Y. Song, S. C. Dhanabalan, J. S. Ponraj, B. Dong, Y. Xiang, F. Xing, D. Fan and H. Zhang, Laser Photonics Rev., 2018, 12, 1700221 CrossRef.
  70. Z. Xie, C. Xing, W. Huang, T. Fan, Z. Li, J. Zhao, Y. Xiang, Z. Guo, J. Li, Z. Yang, B. Dong, J. Qu, D. Fan and H. Zhang, Adv. Funct. Mater., 2018, 18, 1705833 CrossRef.
  71. W. Huang, Y. Zhang, Q. You, P. Huang, Y. Wang, Z. N. Huang, Y. Ge, L. Wu, Z. Dong, X. Dai, Y. Xiang, J. Li, X. Zhang and H. Zhang, Small, 2019, 15, 1900902 CrossRef PubMed.
  72. Y. Wang, G. Qiu, R. Wang, S. Huang, Q. Wang, Y. Liu, Y. Du, W. A. Goddard, M. J. Kim, X. Xu, P. D. Ye and W. Wu, Nat. Electron., 2018, 1, 228–236 CrossRef.
  73. D. Sander, S. Valenzuela, D. Makarov, C. Marrows, E. Fullerton, P. Fischer, J. McCord, P. Vavassori, S. Mangin, P. Pirro, B. Hillebrands, A. D. Kent, T. Jungwirth, O. Gutfleisch, C. G. Kim and A. Berger, J. Phys. D: Appl. Phys., 2017, 50, 363001 CrossRef.
  74. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero and X. Xu, Nature, 2017, 546, 270–273 CrossRef CAS PubMed.
  75. Q. Li, M. Yang, C. Gong, R. V. Chopdekar, A. T. N′diaye, J. Turner, G. Chen, A. Scholl, P. Shafer, E. Arenholz, A. K. Schmid, S. Wang, K. Liu, N. Gao, A. S. Admasu, S.-W. Cheong, C. Hwang, J. Li, F. Wang, X. Zhang and Z. Qiu, Nano Lett., 2018, 18, 5974–5980 CrossRef CAS PubMed.
  76. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M. H. Phan and M. Batzill, Nat. Nanotechnol., 2018, 13, 289–293 CrossRef CAS PubMed.
  77. N. D. Mermin and H. Wagner, Phys. Rev. Lett., 1966, 17, 1133 CrossRef CAS.
  78. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia and X. Zhang, Nature, 2017, 546, 265–269 CrossRef CAS PubMed.
  79. Z. Wang, T. Zhang, M. Ding, B. Dong, Y. Li, M. Chen, X. Li, J. Huang, H. Wang, X. Zhao, Y. Li, D. Li, C. Jia, L. Sun, H. Guo, Y. Ye, D. Sun, Y. Chen, T. Yang, J. Zhang, S. Ono, Z. Han and Z. Zhang, Nat. Nanotechnol., 2018, 13, 554–559 CrossRef CAS PubMed.
  80. L. Wang, X. Xu, L. Zhang, R. Qiao, M. Wu, Z. Wang, S. Zhang, J. Liang, Z. Zhang, Z. Zhang, W. Chen, X. Xie, J. Zong, Y. Shan, Y. Guo, M. Willinger, H. Wu, Q. Li, W. Wang, P. Gao, S. Wu, Y. Zhang, Y. Jiang, D. Yu, E. Wang, X. Bai, Z.-J. Wang, F. Ding and K. Liu, Nature, 2019, 570, 91–95 CrossRef CAS PubMed.
  81. B. Jin, P. Huang, Q. Zhang, X. Zhou, X. Zhang, L. Li, J. Su, H. Li and T. Zhai, Adv. Funct. Mater., 2018, 28, 1800181 CrossRef.
  82. C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xiang, K. Deng and E. Kan, J. Am. Chem. Soc., 2018, 140, 11519–11525 CrossRef CAS PubMed.
  83. Y. Liu and C. Petrovic, Phys. Rev. B, 2018, 97, 174418 CrossRef CAS.
  84. B. Li, T. Xing, M. Zhong, L. Huang, N. Lei, J. Zhang, J. Li and Z. Wei, Nat. Commun., 2017, 8, 1958 CrossRef PubMed.
  85. A. M. Tokmachev, D. V. Averyanov, O. E. Parfenov, A. N. Taldenkov, I. A. Karateev, I. S. Sokolov, O. A. Kondratev and V. G. Storchak, Nat. Commun., 2018, 9, 1672 CrossRef PubMed.
  86. O. Iglesias and A. Labarta, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 184416 CrossRef.
  87. L. Sun, P. C. Searson and C. L. Chien, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 61, R6463 CrossRef CAS.
  88. M. A. McGuire, G. Clark, K. C. Santosh, W. M. Chance, G. E. Jellison, V. R. Cooper, X. Xu and B. C. Sales, Phys. Rev. Mater., 2017, 1, 014001 CrossRef.
  89. C. Van Bruggen and C. Haas, Solid State Commun., 1976, 20, 251–254 CrossRef CAS.
  90. M. Bayard and M. J. Sienko, J. Solid State Chem., 1976, 19, 325–329 CrossRef CAS.
  91. S. Barua, M. C. Hatnean, M. R. Lees and G. Balakrishnan, Sci. Rep., 2017, 7, 10964 CrossRef PubMed.
  92. Q. Cao, F. F. Yun, L. Sang, F. Xiang, G. Liu and X. Wang, Nanotechnology, 2017, 28, 475703 CrossRef PubMed.
  93. X. Xu, Z. Zhang, L. Qiu, J. Zhuang, L. Zhang, H. Wang, C. Liao, H. Song, R. Qiao, P. Gao, Z. Hu, L. Liao, Z. Liao, D. Yu, E. Wang, F. Ding, H. Peng and K. Liu, Nat. Nanotechnol., 2016, 11, 930–935 CrossRef CAS PubMed.
  94. X. Hu, P. Huang, B. Jin, X. Zhang, H. Li, X. Zhou and T. Zhai, J. Am. Chem. Soc., 2018, 140, 12909–12914 CrossRef CAS PubMed.
  95. Q. Yan, J. Yu, S. K. Suram, L. Zhou, A. Shinde, P. F. Newhouse, W. Chen, G. Li, K. A. Persson and J. M. Gregoire, Proc. Natl. Acad. Sci. U. S. A., 2017, 114, 3040–3043 CrossRef CAS PubMed.
  96. J. R. Hughes, N. Roberts, S. McGowan, D. Hay, E. Giannoulatou, M. Lynch, M. D. Gobbi, S. Taylor, R. Gibbons and D. R. Higgs, Nat. Genet., 2014, 46, 205–212 CrossRef CAS PubMed.
  97. X. Xing, C. Xu, B. Chen, C. Li, S. C. Virgil and R. H. Grubbs, J. Am. Chem. Soc., 2018, 140, 17782–17789 CrossRef CAS PubMed.
  98. S. Lu, Q. Zhou, Y. Ouyang, Y. Guo, Q. Li and J. Wang, Nat. Commun., 2018, 9, 3405 CrossRef PubMed.
  99. J. L. Lado and J. Fernández-Rossier, 2D Mater., 2017, 4, 035002 CrossRef.
  100. P. Anderson, Phys. Rev., 1950, 79, 350 CrossRef.
  101. T. Moriya, Phys. Rev., 1960, 120, 91 CrossRef CAS.
  102. V. V. Kulish and W. Huang, J. Mater. Chem. C, 2017, 5, 8734–8741 RSC.
  103. A. O. Fumega and V. Pardo, arXiv preprint arXiv, 2018, 1907.02034.
  104. K. Xu, P. Chen, X. Li, C. Wu, Y. Guo, J. Zhao, X. Wu and Y. Xie, Angew. Chem., Int. Ed., 2013, 52, 10477–10481 CrossRef CAS PubMed.
  105. F. Li, K. Tu and Z. Chen, J. Phys. Chem. C, 2017, 118, 21264–21274 CrossRef.
  106. Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu and B. Huang, ACS Nano, 2012, 6, 1695–1701 CrossRef CAS PubMed.
  107. W. Zhou, X. Zou, S. Najmaei, Z. Liu, Y. Shi, J. Kong, J. Lou, P. M. Ajayan, B. I. Yakobson and J.-C. Idrobo, Nano Lett., 2013, 13, 2615–2622 CrossRef CAS PubMed.
  108. S. McDonnell, R. Addou, C. Buie, R. M. Wallace and C. L. Hinkle, ACS Nano, 2014, 8, 2880–2888 CrossRef CAS PubMed.
  109. B. Li, L. Huang, M. Zhong, N. Huo, Y. Li, S. Yang, C. Fan, J. Yang, W. Hu, Z. Wei and J. Li, ACS Nano, 2015, 9, 1257–1262 CrossRef CAS PubMed.
  110. K. Zhang, S. Feng, J. Wang, A. Azcatl, N. Lu, R. Addou, N. Wang, C. Zhou, J. Lerach, V. Bojan, M. J. Kim, L.-Q. Chen, R. M. Wallace, M. Terrones, J. Zhu and J. A. Robinson, Nano Lett., 2015, 15, 6586–6591 CrossRef CAS PubMed.
  111. L. Sun, W. Zhou, Y. Liang, L. Liu and P. Wu, Comput. Mater. Sci., 2016, 117, 489–495 CrossRef CAS.
  112. Y. Yamasaki, R. Moriya, M. Arai, S. Masubuchi, S. Pyon, T. Tamegai, K. Ueno and T. Machida, 2D Mater., 2017, 4, 041007 CrossRef.
  113. Q. Wu, Y. Zhang, Q. Zhou, J. Wang and X. C. Zeng, J. Phys. Chem. Lett., 2018, 9, 4260–4266 CrossRef CAS PubMed.
  114. H. González-Herrero, J. M. Gómez-Rodrlguez, P. Mallet, M. Moaied, J. J. Palacios, C. Salgado, M. M. Ugeda, J. Veuillen, F. Yndurain and I. Brihuega, Science, 2016, 352, 437–441 CrossRef PubMed.
  115. D. M. Edwards and M. I. Katsnelson, J. Phys.: Condens. Matter, 2006, 18, 7209 CrossRef CAS.
  116. O. V. Yazyev, Rep. Prog. Phys., 2010, 73, 056501 CrossRef.
  117. C. Zhao, Z. Xu, H. Wang, J. Wei, W. Wang, X. Bai and E. Wang, Adv. Funct. Mater., 2014, 24, 5985–5992 CrossRef CAS.
  118. T. Cao, Z. Li and S. G. Louie, Phys. Rev. Lett., 2015, 114, 236602 CrossRef PubMed.
  119. N. Miao, B. Xu, L. Zhu, J. Zhou and Z. Sun, J. Am. Chem. Soc., 2018, 140, 2417–2420 CrossRef CAS PubMed.
  120. P. Zhang, X.-L. Peng, T. Qian, P. Richard, X. Shi, J.-Z. Ma, B. B. Fu, Y.-L. Guo, Z. Q. Han, S. C. Wang, L. L. Wang, Q.-K. Xue, J. P. Hu, Y.-J. Sun and H. Ding, Phys. Rev. B, 2016, 94, 104510 CrossRef.
  121. R. Peng, H. C. Xu, S. Y. Tan, H. Y. Cao, M. Xia, X. P. Shen, Z. C. Huang, C. H. P. Wen, Q. Song, T. Zhang, B. P. Xie, X. G. Gong and D. L. Feng, Nat. Commun., 2014, 5, 5044 CrossRef CAS PubMed.
  122. N. S. Bennett, N. E. B. Cowern and B. J. Sealy, Appl. Phys. Lett., 2009, 94, 252109 CrossRef.
  123. O. B. Aslan, M. Deng and T. F. Heinz, Phys. Rev. B, 2018, 98, 115308 CrossRef CAS.
  124. K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi and B. H. Hong, Nature, 2009, 457, 706–710 CrossRef CAS PubMed.
  125. S. Bertolazzi, J. Brivio and A. Kis, ACS Nano, 2011, 5, 9703–9709 CrossRef CAS PubMed.
  126. W. B. Zhang, Q. Qu, P. Zhu and C. H. Lam, J. Mater. Chem. C, 2015, 3, 12457–12468 RSC.
  127. L. Webster and J. Yan, Phys. Rev. B, 2018, 98, 144411 CrossRef CAS.
  128. N. Papior, T. Gunst, D. Stradi and M. Brandbyge, Phys. Chem. Chem. Phys., 2016, 18, 1025–1031 RSC.
  129. E. A. Osorio, K. Moth-Poulsen, H. S. van der Zant, J. Paaske, P. Hedegård, K. Flensberg, J. Bendix and T. Bjørnholm, Nano Lett., 2009, 10, 105–110 CrossRef PubMed.
  130. B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, P. Jarillo-Herrero and X. Xu, Nat. Nanotechnol., 2018, 13, 544–548 CrossRef CAS PubMed.
  131. S. Jiang, J. Shan and K. F. Mak, Nat. Mater., 2018, 17, 406–410 CrossRef CAS PubMed.
  132. S. Jiang, L. Li, Z. Wang, K. F. Mak and J. Shan, Nat. Nanotechnol., 2018, 13, 549–553 CrossRef CAS PubMed.
  133. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen and Y. Zhang, Nature, 2018, 563, 94–99 CrossRef CAS PubMed.
  134. V. E. Campbell, M. Tonelli, I. Cimatti, J.-B. Moussy, L. Tortech, Y. J. Dappe, E. Rivière, R. Guillot, S. Delprat, R. Mattana, S. Pierre, O. Philippe, C. Fadi, O. Edwige, K. Florian, C. Vijay Gopal, S. Nicolas, G. Nathalie, G. Anouk, M. Frederic, A. Marie-Anne, S. Philippe and M. Talal, Nat. Commun., 2016, 7, 13646 CrossRef CAS PubMed.
  135. D. S. Chuang, C. A. Ballentine and R. C. O'Handley, J. Appl. Phys., 1994, 75, 6427–6427 CrossRef.
  136. L. Wang, Q. Feng, Y. Kim, R. Kim, K. H. Lee, S. D. Pollard, Y. J. Shin, H. Zhou, W. Peng, D. Lee, M. Wenjie, Y. Hyunsoo, J. H. Han, K. Miyoung, L. Qingyou and T. W. Noh, Nat. Mater., 2018, 17, 1087 CrossRef CAS PubMed.
  137. P. G. D. Gennes, Rev. Mod. Phys., 1964, 36, 225–237 CrossRef.
  138. D. K. Efetov, L. Wang, C. Handschin, K. B. Efetov, J. Shuang, R. Cava, T. Taniguchi, K. Watanabe, J. Hone, C. R. Dean and P. Kim, Nat. Phys., 2016, 12, 328–332 Search PubMed.
  139. A. I. Buzdin, Rev. Mod. Phys., 2005, 77, 935–976 CrossRef CAS.
  140. Z. Wang, C. Tang, R. Sachs, Y. Barlas and J. Shi, Phys. Rev. Lett., 2015, 114, 016603 CrossRef PubMed.
  141. K. L. Seyler, D. Zhong, B. Huang, X. Linpeng, N. P. Wilson, T. Taniguchi, K. Watanabe, W. Yao, D. Xiao, M. A. McGuire, K.-M. C. Fu and X. Xu, Nano Lett., 2018, 18, 3823–3828 CrossRef CAS PubMed.
  142. M. Gmitra, D. Kochan, P. Högl and J. Fabiank, Phys. Rev. B, 2016, 93, 155104 CrossRef.
  143. L. Fu and C. L. Kane, Phys. Rev. Lett., 2008, 100, 096407 CrossRef PubMed.
  144. J. C. Leutenantsmeyer, A. A. Kaverzin, M. Wojtaszek and B. J. van Wees, 2D Mater., 2016, 4, 014001 CrossRef.
  145. F. Katmis, V. Lauter, F. S. Nogueira, B. A. Assaf, M. E. Jamer, P. Wei, B. Satpati, J. W. Freeland, I. Eremin, D. Heiman, P. Jarillo-Herrero and J. S. Moodera, Nature, 2016, 533, 513–516 CrossRef CAS PubMed.
  146. B. Scharf, G. Xu, A. Matos-Abiague and I. Žutić, Phys. Rev. Lett., 2017, 119, 127403 CrossRef PubMed.
  147. H.-X. Yang, A. Hallal, D. Terrade, X. Waintal, S. Roche and M. Chshiev, Phys. Rev. Lett., 2013, 110, 046603 CrossRef CAS PubMed.
  148. A. Hallal, F. Ibrahim, H. Yang, S. Roche and M. Chshiev, 2D Mater., 2017, 4, 025074 CrossRef.
  149. P. Wei, S. Lee, F. Lemaitre, L. Pinel, D. Cutaia, W. Cha, F. Katmis, Y. Zhu, D. Heiman, J. Hone, J. S. Moodera and C.-T. Chen, Nat. Mater., 2016, 15, 711–716 CrossRef CAS PubMed.
  150. P. Lazić, K. Belashchenko and I. Žutić, Phys. Rev. B, 2016, 93, 241401 CrossRef.
  151. S. V. Eremeev, V. N. Men'Shov, V. V. Tugushev, P. M. Echenique and E. V. Chulkov, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 144430 CrossRef.
  152. Y.-F. Wu, H.-D. Song, L. Zhang, X. Yang, Z. Ren, D. Liu, H.-C. Wu, J. Wu, J.-G. Li, Z. Jia, B. Yan, X. Wu, C.-G. Duan, G. Han, Z.-M. Liao and D. Yu, Phys. Rev. B, 2017, 95, 195426 CrossRef.
  153. O. Inyang, L. Bouchenoire, B. Nicholson, M. Tokaç, R. M. Rowan-Robinson, C. J. Kinane and A. T. Hindmarch, Phys. Rev. B, 2019, 100, 174418 CrossRef.
  154. B. Karpiak, A. W. Cummings, K. Zollner, M. Vila, D. Khokhriakov, A. M. Hoque, A. Dankert, P. Svedlindh, J. Fabian, S. Roche and S. P. Dash, 2D Mater., 2020, 7, 015026 CrossRef.
  155. A. W. Cummings, J. Phys.: Mater., 2019, 2, 045007 Search PubMed.
  156. Q. Tong, M. Chen and W. Yao, Phys. Rev. Appl., 2019, 12, 024031 CrossRef CAS.
  157. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys., 2010, 82, 3045 CrossRef CAS.
  158. X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys., 2011, 83, 1057 CrossRef CAS.
  159. F. D. M. Haldane, Phys. Rev. Lett., 1988, 61, 2015 CrossRef CAS PubMed.
  160. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma and Q.-K. Xue, Science, 2013, 340, 167–170 CrossRef CAS PubMed.
  161. C.-X. Liu, S.-C. Zhang and X.-L. Qi, arXiv preprint arXiv, 2015, 1508.07106.
  162. Z. Qiao, W. Ren, H. Chen, L. Bellaiche, Z. Zhang, A. H. MacDonald and Q. Niu, Phys. Rev. Lett., 2014, 112, 116404 CrossRef PubMed.
  163. J. Zhang, B. Zhao, Y. Yao and Z. Yang, Phys. Rev. B: Condens. Matter Mater. Phys., 2015, 92, 165418 CrossRef.
  164. C. Tang, B. Cheng, M. Aldosary, Z. Wang, Z. Jiang, K. Watanabe, T. Taniguchi, M. Bockrath and J. Shi, APL Mater., 2018, 6, 026401 CrossRef.
  165. P. Chen, J.-Y. Zou and B.-G. Liu, Phys. Chem. Chem. Phys., 2017, 19, 13432–13437 RSC.
  166. S. Tian, S. Gao, S. Nie, Y. Qian, C. Gong, Y. Fu, H. Li, W. Fan, P. Zhang, T. Kondo, S. Shin, J. Adell, H. Fedderwitz, H. Ding, Z. Wang, T. Qian and H. Lei, arXiv preprint arXiv, 2019, 1910.10101.
  167. Y.-J. Hao, P. Liu, Y. Feng, X.-M. Ma, E. F. Schwier, M. Arita, S. Kumar, C. Hu, M. Zeng, Y. Wang, Z. Hao, H.-Y. Sun, K. Zhang, J. Mei, N. Ni, L. Wu, K. Shimada, C. Chen, Q. Liu and C. Liu, Phys. Rev. X, 2019, 9, 041038 Search PubMed.
  168. Y. Wang, J. Yan, J. Li, S. Wang, M. Song, J. Song, Z. Li, K. Chen, Y. Qin, L. Ling, H. Du, L. Cao, X. Luo, Y. Xiong and S. Yuping, Phys. Rev. B, 2019, 100, 024434 CrossRef CAS.
  169. Y. Chen, Y.-W. Chuang, S. H. Lee, Y. Zhu, K. Honz, Y. Guan, Y. Wang, K. Wang, Z. Mao, C. Heikes, P. Quarterman, P. Zajdel, J. A. Borchers, W. Ratcliff II and J. Zhu, arXiv preprint arXiv, 2019, 1910.13057.
  170. T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang, H. Weng and C. Fang, Nature, 2019, 566, 475–479 CrossRef CAS PubMed.
  171. M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig and Z. Wang, Nature, 2019, 566, 480–485 CrossRef CAS PubMed.
  172. F. Tang, H. C. Po, A. Vishwanath and X. Wan, Nature, 2019, 566, 486–489 CrossRef CAS PubMed.
  173. G. Binasch, P. Grünberg, F. Saurenbach and W. Zinn, Phys. Rev. B: Condens. Matter Mater. Phys., 1989, 39, 4828 CrossRef CAS PubMed.
  174. M. N. Baibich, J. M. Broto, A. Fert, F. N. V. Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich and J. Chazelas, Phys. Rev. Lett., 1988, 61, 2472 CrossRef CAS PubMed.
  175. J.-G. Zhu, Y. Zheng and G. A. Prinz, J. Appl. Phys., 2000, 87, 6668–6673 CrossRef CAS.
  176. K. Tsunekawa, D. D. Djayaprawira, M. Nagai, H. Maehara, S. Yamagata, N. Watanabe, S. Yuasa, Y. Suzuki and K. Ando, Appl. Phys. Lett., 2005, 87, 072503 CrossRef.
  177. M. M. Miller, G. A. Prinz, S.-F. Cheng and S. Bounnak, Appl. Phys. Lett., 2002, 81, 2211–2213 CrossRef CAS.
  178. M. R. J. Gibbs, E. W. Hill and P. J. Wright, J. Phys. D: Appl. Phys., 2004, 37, R237 CrossRef CAS.
  179. T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao and X. Xu, Science, 2018, 360, 1214–1218 CrossRef CAS PubMed.
  180. S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki and K. Ando, Nat. Mater., 2004, 3, 868 CrossRef CAS PubMed.
  181. S. S. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant and S.-H. Yang, Nat. Mater., 2004, 3, 862 CrossRef CAS PubMed.
  182. Z. Wang, I. Gutierrezlezama, N. Ubrig, M. Kroner, M. Gibertini, T. Taniguchi, K. Watanabe, A. Imamoglu, E. Giannini and A. F. Morpurgo, Nat. Commun., 2018, 9, 2516 CrossRef PubMed.
  183. P. Jiang, L. Li, Z. Liao, Y. X. Zhao and Z. Zhong, Nano Lett., 2018, 18, 3844–3849 CrossRef CAS PubMed.
  184. S. A. Bender, R. A. Duine and Y. Tserkovnyak, Phys. Rev. Lett., 2012, 108, 246601 CrossRef PubMed.
  185. A. V. Chumak, V. I. Vasyuchka, A. A. Serga and B. Hillebrands, Nat. Phys., 2015, 11, 453–461 Search PubMed.
  186. B. N. Brockhouse, Phys. Rev., 1957, 106, 859–864 CrossRef CAS.
  187. T. Nikuni, M. Oshikawa, A. Oosawa and H. Tanaka, Phys. Rev. Lett., 2000, 84, 5868–5871 CrossRef CAS PubMed.
  188. S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands and A. N. Slavin, Nature, 2006, 443, 430–433 CrossRef CAS PubMed.
  189. K. Uchida, H. Adachi, D. Kikuchi, S. Ito, Z. Qiu, S. Maekawa and E. Saitoh, Nat. Commun., 2015, 6, 5910–5910 CrossRef CAS PubMed.
  190. S. S. Pershoguba, S. Banerjee, J. C. Lashley, J. Park, H. Ȧgren, G. Aeppli and A. V. Balatsky, Phys. Rev. X, 2018, 8, 011010 Search PubMed.
  191. W. B. Yelon and R. Silberglitt, Phys. Rev. B: Solid State, 1971, 4, 2280–2286 CrossRef.
  192. E. J. Samuelsen, R. Silberglitt, G. Shirane and J. P. Remeika, Phys. Rev. B: Solid State, 1971, 3, 157 CrossRef.
  193. D. Ghazaryan, M. T. Greenaway, Z. Wang, V. H. Guarochico-Moreira, I. J. Vera-Marun, J. Yin, Y. Liao, S. V. Morozov, O. Kristanovski, A. I. Lichtenstein, M. I. Katsnelson, F. Withers, A. Mishchenko, L. Eaves, A. K. Geim, K. S. Novoselov and A. Misra, Nat. Electron., 2018, 1, 344–349 CrossRef CAS.
  194. W. Xing, L. Qiu, X. Wang, Y. Yao, Y. Ma, R. Cai, S. Jia, X. C. Xie and W. Han, Phys. Rev. X, 2019, 9, 011026 CAS.
  195. A. Brataas, A. D. Kent and H. Ohno, Nat. Mater., 2012, 11, 372 CrossRef CAS PubMed.
  196. D. E. Nikonov and I. A. Young, J. Mater. Res., 2014, 29, 2109–2115 CrossRef CAS.
  197. L. Frangou, S. Oyarzun, S. Auffret, L. Vila, S. Gambarelli and V. Baltz, Phys. Rev. Lett., 2016, 116, 077203 CrossRef CAS PubMed.
  198. L. Chen, S. Mankovsky, S. Wimmer, M. A. W. Schoen, H. S. Körner, M. Kronseder, D. Schuh, D. Bougeard, H. Ebert, D. Weiss and C. H. Back, Nat. Phys., 2018, 14, 490–494 Search PubMed.
  199. R. Meckenstock, D. Spoddig, Z. Frait, V. Kambersky and J. Pelzl, J. Magn. Magn. Mater., 2004, 272, 1203–1204 CrossRef.
  200. G. Wastlbauer and J. A. C. Bland, Adv. Phys., 2005, 54, 137–219 CrossRef CAS.
  201. D. R. Klein, D. Macneill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier and P. Jarillo-Herrero, Science, 2018, 360, 1218–1222 CrossRef CAS PubMed.
  202. D. MacNeill, G. M. Stiehl, M. H. D. Guimaraes, R. A. Buhrman, J. Park and D. C. Ralph, Nat. Phys., 2017, 13, 300–305 Search PubMed.
  203. S.-J. Gong, C. Gong, Y.-Y. Sun, W.-Y. Tong, C.-G. Duan, J.-H. Chu and X. Zhang, Proc. Natl. Acad. Sci. U. S. A., 2018, 115, 8511–8516 CrossRef CAS PubMed.
  204. C. Cardoso, D. Soriano, N. A. García-Martínez and J. Fernández-Rossier, Phys. Rev. Lett., 2018, 121, 067701 CrossRef CAS PubMed.
  205. G.-M. Choi, A. Schleife and D. G. Cahill, Nat. Commun., 2017, 8, 15085 CrossRef CAS PubMed.
  206. M. Wu, Z. Li, T. Cao and S. G. Louie, Nat. Commun., 2019, 10, 2371 CrossRef PubMed.
  207. B. T. Jonker, G. Kioseoglou, A. T. Hanbicki, C. H. Li and P. E. Thompson, Nat. Phys., 2007, 3, 542–546 Search PubMed.
  208. Y. Ohno, D. K. Young, B. Beschoten, F. Matsukura, H. Ohno and D. D. Awschalom, Nature, 1999, 402, 790–792 CrossRef CAS.
  209. K. L. Seyler, D. Zhong, D. R. Klein, S. Gao, X. Zhang, B. Huang, E. Navarro-Moratalla, L. Yang, D. H. Cobden, M. A. McGuire, W. Yao, D. Xiao, P. Jarillo-Herrero and X. Xu, Nat. Phys., 2018, 14, 277–281 Search PubMed.
  210. A. Manchon, J. Železný, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello and P. Gambardella, Rev. Mod. Phys., 2019, 91, 035004 CrossRef CAS.
  211. K. Garello, I. M. Miron, C. O. Avci, F. Freimuth, Y. Mokrousov, S. Blügel, S. Auffret, O. Boulle, G. Gaudin and P. Gambardella, Nat. Nanotechnol., 2013, 8, 587–593 CrossRef CAS PubMed.
  212. M. Akyol, J. G. Alzate, G. Yu, P. Upadhyaya, K. L. Wong, A. Ekicibil, P. K. Amiri and K. L. Wang, Appl. Phys. Lett., 2015, 106, 032406 CrossRef.
  213. R. H. Liu, W. L. Lim and S. Urazhdin, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 220409 CrossRef.
  214. H. An, T. Ohno, Y. Kanno, Y. Kageyama, Y. Monnai, H. Maki, J. Shi and K. Ando, Sci. Adv., 2018, 4, eaar2250 CrossRef PubMed.
  215. X. Wang, J. Tang, X. Xia, C. He, J. Zhang, Y. Liu, C. Wan, C. Fang, C. Guo, W. Yang, Y. Guang, X. Zhang, H. Xu, J. Wei, M. Liao, X. Lu, J. Feng, X. Li, Y. Peng, H. Wei, R. Yang, D. Shi, X. Zhang, Z. Han, Z. Zhang, G. Zhang, G. Yu and X. Han, Sci. Adv., 2019, 5, eaaw8904 CrossRef PubMed.
  216. M. Alghamdi, M. Lohmann, J. Li, P. R. Jothi, Q. Shao, M. Aldosary, T. Su, B. P. T. Fokwa and J. Shi, Nano Lett., 2019, 19, 4400–4405 CrossRef CAS PubMed.
  217. U. K. Roessler, A. N. Bogdanov and C. Pfleiderer, Nature, 2006, 442, 797–801 CrossRef CAS PubMed.
  218. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii and P. Böni, Science, 2009, 323, 915–919 CrossRef PubMed.
  219. X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa and Y. Tokura, Nature, 2010, 465, 901–904 CrossRef CAS PubMed.
  220. X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui and Y. Tokura, Nat. Mater., 2011, 10, 106–109 CrossRef CAS PubMed.
  221. S. Heinze, K. Von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer and S. Blügel, Nat. Phys., 2011, 7, 713–718 Search PubMed.
  222. H. Yang, A. Thiaville, S. Rohart, A. Fert and M. Chshiev, Phys. Rev. Lett., 2015, 115, 267210 CrossRef PubMed.
  223. A. Soumyanarayanan, M. Raju, A. L. G. Oyarce, A. K. C. Tan, M.-Y. Im, A. P. Petrović, P. Ho, K. H. Khoo, M. Tran, C. K. Gan, F. Ernult and C. Panagopoulos, Nat. Mater., 2017, 16, 898–904 CrossRef CAS PubMed.
  224. O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T. O. Mentes, A. Sala, L. D. Buda-Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigné, A. Stashkevich, S. M. Chérif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I. M. Miron and G. Gaudin, Nat. Nanotechnol., 2016, 11, 449–454 CrossRef CAS PubMed.
  225. T.-E. Park, L. Peng, X. Zhang, S. J. Kim, K. M. Song, K. Kim, M. Weigand, G. Schütz, S. Finizio, J. Raabe, J. Xia, Y. Zhou, M. Ezawa, X. Liu, J. Chang, H. C. Koo, Y. D. Kim, M. Chshiev, A. Fert, H. Yang, X. Yu and S. Woo, arXiv preprint arXiv, 2019, 1907.01425.
  226. Y. Wu, S. Zhang, J. Zhang, W. Wang, Y. L. Zhu, J. Hu, K. Wong, C. Fang, C. Wan, X. Han, Q. Shao, T. Taniguchi, K. Watanabe, Z. Mao, X. Zhang and K. L. Wang, arXiv preprint arXiv, 2019, 1907.11349.
  227. H. Wang, C. Wang, Y. Zhu, Z.-A. Li, H. Zhang, H. Tian, Y. Shi, H. Yang and J. Li, arXiv preprint arXiv, 2019, 1907.08382.
  228. M.-G. Han, J. A. Garlow, Y. Liu, H. Zhang, J. Li, D. DiMarzio, M. W. Knight, C. Petrovic, D. Jariwala and Y. Zhu, Nano Lett., 2019, 19, 7859–7865 CrossRef CAS PubMed.
  229. J. Yuan, Y. Yang, Y. Wu, Y. P. Feng, Y. Chen, X. Yan, G. Xu and L. Shen, arXiv preprint arXiv, 2019, 1906.10836.
  230. Q. Tong, F. Liu, J. Xiao and W. Yao, Nano Lett., 2018, 18, 7194–7199 CrossRef CAS PubMed.
  231. D. Zhong, K. L. Seyler, X. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K.-M. C. Fu and X. Xu, Sci. Adv., 2017, 3, e1603113 CrossRef PubMed.
  232. Y. Hou and R. Wu, arXiv preprint arXiv, 2018, 1802.07358.
  233. N. Tombros, C. Jozsa, M. Popinciuc, H. T. Jonkman and B. J. V. Wees, Nature, 2007, 448, 571–574 CrossRef CAS PubMed.
  234. C. Day, Phys. Today, 2009, 62, 12 CAS.
  235. D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava and M. Z. Hasan, Science, 2009, 323, 919–922 CrossRef CAS PubMed.
  236. N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi and N. Marzari, Nat. Nanotechnol., 2018, 13, 246–252 CrossRef CAS PubMed.
  237. M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig and Z. Wang, Nature, 2019, 566, 480–485 CrossRef CAS PubMed.
  238. F. Tang, H. C. Po, A. Vishwanath and X. Wan, Nature, 2019, 566, 486–489 CrossRef CAS PubMed.
  239. T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang, H. Weng and C. Fang, Nature, 2019, 566, 475–479 CrossRef CAS PubMed.

This journal is © The Royal Society of Chemistry 2020