Interlayer distance and interlayer number regulating interlayer magnetism

Interlayer distance and interlayer number regulating interlayer magnetism

Fig.1 Interlayer distance and interlayer number regulating interlayer magnetism. a: The interlayer electron kinetic energy term, Pauli and Coulomb repulsion competition determine the interlayer magnetic ground state. b: Total-energy differences between the interlayer AFM/FM configurations as a function of interlayer Se-Se distance. c: Evolution of energy differences between interlayer FM and AFM configurations as a function of the layer number. T d: Experimental confirmation of ferromagnetism of CrSe2 enhanced with the number of layers. e: CrSe2 remains stable after exposure to air for several months.

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Nature Materials

Van der Waals epitaxial growth of air-stable CrSe2 nanosheets with thickness-tunable magnetic order

It is found that in weakly interlayer coupled CrI3 system, the horizontal sliding change stack can regulate interlayer magnetism, and the vertical change of interlayer distance can also be another dimension to regulate two-dimensional magnetism. The researchers found that MX2 (M=V, Cr, Mn; X=S, Se, Te) in the double layer, the phenomenon of interlayer antiferromagnetic — ferromagnetic transition will occur with the change of the layer spacing, which is the result of the competition between the kinetic energy of electrons moving in the layer, the Pauli repulsion of electrons and the Coulomb repulsion of electrons[1] (FIG. 1 a-b).

This work is the first to show that interlayer distance can be used as a new degree of freedom to regulate two-dimensional magnetism, highlighting the importance of non-metallic elements and their interlayer Pauli repulsion not considered in previous models.

We found that the above magnetic coupling mechanism is also applicable to the layers. With the increase of layer thickness, the kinetic energy of electrons moving along the direction of CrSe2 layer increases, gradually represses the interlayer antiferromagnetic coupling caused by Pauli and Coulomb repulsion, and macro ferromagnetism gradually takes the upper hand. In cooperation with the experimental groups, we confirmed the above theoretical image, which is the first international confirmation that CrSe2 is a two-dimensional magnetic material with thickness-dependent magnetic coupling transition between layers and is highly stable in air[2] (FIG. 1 c-e). It has initially overcome the difficulty of insufficient air stability of two-dimensional magnetic materials that had puzzled the scientific community for a long time. As soon as this work was published, it quickly gained academic attention. Professor Andrew T.S. Wee from the National University of Singapore quoted and positively appraised this work for a long time, and Ki Kang Kim from Sungkyunkwan University in Korea wrote a review article affirming this work.

REFERENCES

1. Wang, C. et al. Bethe-Slater-curve-like behavior and interlayer spin-exchange coupling mechanisms in two-dimensional magnetic bilayers. Phys. Rev. B 102, 020402 (2020).

2. Li, B. et al. Van der Waals epitaxial growth of air-stable CrSe2 nanosheets with thickness-tunable magnetic order. Nature Materials 20, 818-825 (2021).

High Tc two-dimensional ferromagnetic semiconductors

High Tc two-dimensional ferromagnetic semiconductors

Fig.1 Theoretical prediction of new magnetic materials. a: The Tc of twelve magnetic single-layer materials is predicted to reach 100K to 500K. b: Strong anisotropy with spin-, dichroism- and mobility-anisotropy locking. c: CrOCl bulk phase magnetic ground state. d-e: The computational simulation is highly consistent with the experimentally measured anisotropic Raman diagrams.

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Science Bulletin

A family of high-temperature ferromagnetic monolayers with locked spin-dichroism-mobility anisotropy: MnNX and CrCX (X = Cl, Br, I; C = S, Se, Te)

The search for room temperature ferromagnetic semiconductors is one of 125 important questions posed in Science. In previous studies, researchers found that strong electron doping (1 e/Cr) of CrS2 can lead to its transformation from AFM metal to FM semiconductor, and replacing S with Cl atoms to form CrSCl monolayer is one of the feasible ideas to realize such doping.

Based on the above thought, 12 kinds of single-layer ferromagnetic materials with high Tc are predicted: MnNX and CrCX (where X=Cl,Br,I; C=S,Se,Te)[1]. Based on the anisotropic Heisenberg model and renormalized spin wave theory, Tc of this series of materials is predicted to range from 100K to 500K (Figure 1a). Eight members among them show semiconducting bandgaps varying from roughly 0.23 to 1.85 eV. These semiconducting monolayers also show extremely large anisotropy along the two in-plane lattice directions of these layers. Additional orbital anisotropy leads to a spin-locked linear dichroism, in different from previously known circular and linear dichroisms in layered materials. Together with the mobility anisotropy, it offers a spin-, dichroism- and mobility-anisotropy locking. These results manifest the potential of this 2D family for both fundamental research and high performance spin-dependent electronic and optoelectronic devices (Figure 1b).

The work was published in Sci.Bull. 2019, making it one of the 10 most downloaded articles of that year. The material predictions has been verified and cited by several different experimental groups in Nat. Mat (1 paper), Nat. Nanotech. (2 papers), Adv. Mater. (2 papers) and Nano Letters (1 paper). The magnetic properties and anisotropic electronic structure were confirmed to be consistent with our theoretical prediction.

On this basis, the researchers, in collaboration with experimental collaborators, determined the bulk phase magnetic ground state and magnetic field evolution of CrOCl[2] (FIG. 1c-e). Combined with the magnetic transport measurements of experimental collaborators, the layered dependent magnetic field evolution behavior of the CrSBr system was investigated[3].

REFERENCES

1. Wang, C. et al. A family of high-temperature ferromagnetic monolayers with locked spin-dichroism-mobility anisotropy: MnNX and CrCX (X = Cl, Br, I; C = S, Se, Te). Science Bulletin 64, 293-300 (2019)

2. Gu, P. et al. Magnetic Phase Transitions and Magnetoelastic Coupling in a Two-Dimensional Stripy Antiferromagnet. Nano Letters 22, 1233-1241 (2022)

3. Ye, C. et al. Layer-Dependent Interlayer Antiferromagnetic Spin Reorientation in Air-Stable Semiconductor CrSBr. ACS Nano 16, 11876-11883 (2022)

Layer number regulated intra-layer magnetism

Layer number regulated intra-layer magnetism

Fig.1 Layer number regulated intra-layer magnetism. a-b: differential charge density between layers. Red represents the accumulation of charge in the interlayer region after the two layers are stacked on top of each other. c-d: Single layer CrTe2 zigzag antiferromagnetic ground state and easy magnetization axis direction. e-g: Spin reorientation transformation of CrTe2 monolayer.

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Nature Communications

Spin mapping of intralayer antiferromagnetism and field-induced spin reorientation in monolayer CrTe2

Charge redistribution induced by interlayer interaction is relatively small at the vdW gap of a CrI3 bilayer in comparison with other bilayers like BP, Te, PtSe2, PtS2, and CrS2, suggesting a limited overlap of interlayer wave functions in the CrI3 bilayer. It is exceptional that such a small overlap could even appreciably affect the interlayer magnetism through direct exchange between two interlayer I atoms separated by 4.20 Å2

A question then arises of how do strongly overlapped interlayer wave functions affect interlayer magnetism and whether there are any generalized spin-exchange coupling mechanisms solely for such a noncovalent interaction. The interlayer differential charge density shows that the interlayer electron coupling of of CrX2(X = S, Se, Te) systems is significantly stronger than that of CrI3. It is expected that different interlayer magnetic coupling mechanisms exist in CrX2. The bulk phase of this kind of material shows ferromagnetism, and many studies speculate that the single layer should also be the ferromagnetic ground state. However, the theoretical prediction of the researchers found that the single layer of this kind of material is striped antiferromagnetic ground state. The in-plane magnetic orders of CrX2 mono and few layers are tunable between striped antiferromagnetic (sAFM) and ferromagnetic (FM) orders by manipulating charge transfer between Cr t2g and eg orbitals. Such charge transfer is realizable through interlayer coupling, direct charge doping, or substituting S with Cl atoms[1,2].

However, due to the fact that antiferromagnetic orders usually do not exhibit macroscopic magnetic moments, experimental detection is very difficult, and the antiferromagnetic ground state of CrX2(X=S,Se,Te) materials mentioned in the above theoretical prediction are still lacking of experimental evidence in the two-dimensional limit. By combining spin polarised scanning tunnelling microscopy and first-principles calculations, we investigate the magnetism of vdW ML CrTe2, which has been successfully grown through molecular-beam epitaxy. We observe a stable antiferromagnetic (AFM) order at the atomic scale in the ML crystal, whose bulk is ferromagnetic, and correlate its imaged zigzag spin texture with the atomic lattice structure. confirming the theoretical prediction of the researchers (FIG. 1 c). Previous studies of two-dimensional magnetic materials usually assumed that the material’s easy magnetization axis was along the conventional lattice base vector or out of plane direction. The researchers calculated that the magnetic moment direction of the CrTe2 single layer was in the y-z plane at an Angle of 70 degrees from the z direction (FIG. 1 d), resulting in a novel spin reorientation transition mode under magnetic field (FIG. 1 e-g). The real space intrinsic antiferromagnetic order discovered and confirmed in this study, the magnetic order transformation in the single-layer limit, and the spin reorientation under external magnetic fields have not been previously reported before[3].

REFERENCES

1. C. Wang, X. Zhou, Y. Pan, J. Qiao, X. Kong, C.-C. Kaun, and W. Ji, Layer and Doping Tunable Ferromagnetic Order in Two-Dimensional CrS2 Layers, Phys. Rev. B 97, 245409 (2018).

2. Wang, C. et al. Bethe-Slater-curve-like behavior and interlayer spin-exchange coupling mechanisms in two-dimensional magnetic bilayers. Phys. Rev. B 102, 020402 (2020).

3. Xian, J.-J. et al. Spin mapping of intralayer antiferromagnetism and field-induced spin reorientation in monolayer CrTe2. Nature Communications 13, 257 (2022)

Stacking tunable interlayer magnetism in bilayer CrI3

Stacking tunable interlayer magnetism in bilayer CrI3

Fig.1 Transition pathways between the two phases in FM and AFM configurations.

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Physical review B

Stacking tunable interlayer magnetism in bilayer CrI3

In early 2017, the first observations of long-range magnetic order in pristine 2D crystals were reported in Cr2Ge2Te6 and CrI3, leading the research upsurge of two-dimensional intrinsic magnetism and its regulation. The interlayer antiferromagnetic (AFM) groundstate of bilayer CrI3 has been reported in several papers [Nature 546, 270 (2017); Science 360, 1214 (2018); Science 360, 1218 (2018)]. However, the density functional theory calculations of the low-temperature phase structure found that the low-temperature bilayer CrI3 has a stable interlayer ferromagnetic groundsate, which is not consistent with experiments. Therefore, one of the focuses of the study of magnetic correlation of bilayer CrI3 is to determine its true material structure and interlayer coupling mechanism.

Bulk CrI3 exhibits a vdW structure and possesses a rhombohedral structure with the R3 space group symmetry at low temperature (the LT phase). When temperature increases to 210–220 K, it undergoes a structural phase transition to a monoclinic lattice with the C2/m space group symmetry (the HT phase) It is generally believed that the experimental low temperature measurement is a low temperature stable structure. However, the CrI3 bilayer prepared at room temperature may not undergo structural transformation during the rapid cooling process and maintain the high-temperature phase structure. The researchers speculate that different stacking in the CrI3 system may correspond to different interlayer magnetic ground states. Based on the above prediction, we found that the interlayer AFM coupling results from a different stacking order with the C2/m space group symmetry, rather than the graphene-like one with R3 as previously believed[2].

This work solves the problem of the source of the AFM coupling between the two layers of CrI3 in a series of recent experiments and proposes a magnetic coupling mechanism in the weak non-covalent coupling limit. In the past, it was generally assumed that the van der Waals (vdW) interaction dominated the interlayer interaction of two-dimensional materials, and the effect of interlayer coupling on magnetic regulation was significantly underestimated. This work realizes from a new perspective that after the p orbitals of I are polarized by Cr into pxy and pz orbitals with opposite magnetization directions, different interlayer stacking orders leads to different direct exchange between p orbitals of interlayer I atoms, which ultimately determines the magnetic coupling between layers.

This work has been cited positively by Professor Cheung Xiang and Professor Novoselov. The theoretical predictions of this work have been verified and cited by many different experimental groups published in Nature, Science, Nature sub-journals and PRL. Further, in collaboration with experimental collaborators, the theoretical image of orbital splitting of I-pxy and pz was verified by combining scanning tunneling microscopy (STM) and density functional theory (DFT) calculations[3].

REFERENCES

1. Liu, N. S., Cong, W. & Wei, J. Recent research advances in two-dimensional magnetic materials. ACTA PHYSICA SINICA 71 (2022). https://doi.org:10.7498/aps.71.20220301

2. Jiang, P. H. et al. Stacking tunable interlayer magnetism in bilayer CrI3. Phys. Rev. B 99, 9 (2019). https://doi.org:10.1103/PhysRevB.99.144401

3. Li, P. et al. Single-layer CrI3 grown by molecular beam epitaxy. Science Bulletin (2020).

NbSe2

NbSe2

Arxiv

Layer sliding and twisting induced electronic transitions in correlated magnetic 1T-NbSe2 bilayers

Mott and CT insulators are representative materials, like 1T-phases of TaS2, TaSe2 and NbSe2. In the strong-correlation limit of electron correlated systems, on-site Coulomb interactions split a half-filled band into two sub-bands, namely the lower (LHB) and upper Hubbard bands (UHB), forming a Mott or a CT insulator[13]. The governing coupling mechanism lies in the interlayer electronic hybridization of interfacial Se pz orbitals within a localized region of the David star, rather than previously supposed metal atoms dz2 orbitals. Subtle differences in interlayer hybridization vary the energy levels of the four Hubbard bands in the 1T-NbSe2 bilayer. Three electronic and two magnetic transitions among four insulating states were observed upon interlayer sliding or twisting, while three of the four insulating states are correlated ones. All these striking results highlight the importance of interlayer coupling in tunning correlated electronic states in NbSe2 bilayers.

Mirror twin boundaries (MTBs)[14,15] was demonstrate to be another strategy to introduce additional exotic electronic states in chalcogen-deficient 1H-MoS2[16], -MoSe2[14], and – MoTe2[17]monolayers. In some lattices with specific symmetries, such as kagome lattice, the intrinsic flat band leads to a high density of electron states. A TMD layer consisting of ordered and uniformly sized MTB triangles, namely an MTB-triangle lattice, could be a TMD phase exhibiting a well-defined lattice symmetry. Coloring-triangular (CT) lattice[18] in a MoTe2 (CT-MoTe2) monolayer comprise of uniform-sized and orderly arranged MTB triangles and normal MoTe2 domains embedded among MTBs. Dirac-like and flat electronic bands inherently existing in the CT lattice are identified by two broad and two prominent peaks. Further more, the CT-MoTe2 monolayer shows energy-dependent electronic Janus lattices, including the original atomic-lattice and an electronic Te pseudo-sublattice.

REFERENCES

1. Zhang H, et al. Tailored Ising superconductivity in intercalated bulk NbSe2. Nature Physics 18, 1425-1430 (2022).

2. Cao Y, et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43-50 (2018)

3. Klanjšek M, et al. A high-temperature quantum spin liquid with polaron spins. Nature Physics 13, 1130-1134 (2017)

4. Law KT, Lee PA. 1T-TaS2 as a quantum spin liquid. Proceedings of the National Academy of Sciences 114, 6996-7000 (2017)

5. Chen Y, et al. Strong correlations and orbital texture in single-layer 1T-TaSe2. Nature Physics 16, 218-224 (2020)

6. Liu M, et al. Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator. Science Advances 7, eabi6339 (2021)

7. Wang YD, et al. Band insulator to Mott insulator transition in 1T-TaS2. Nature Communications 11, 4215 (2020)

8. Grasset R, et al. Pressure-induced collapse of the charge density wave and Higgs mode visibility in 2H− TaS2. Physical Review Letters 122, 127001 (2019)

9. Lian C-S, Si C, Duan W. Unveiling Charge-Density Wave, Superconductivity, and Their Competitive Nature in Two-Dimensional NbSe2. Nano Letters 18, 2924-2929 (2018)

10. Li H, et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650-654 (2021)

11. Regan EC, et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359-363 (2020)

12. Zhou Y, et al. Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Nature 595, 48-52 (2021)

13. Zaanen J, Sawatzky GA, Allen JW. Band gaps and electronic structure of transition-metal compounds. Physical Review Letters 55, 418-421 (1985)

14. Liu H, et al. Dense Network of One-Dimensional Midgap Metallic Modes in Monolayer MoSe2 and Their Spatial Undulations. Physical Review Letters 113, 066105 (2014)

15. Hong J, et al. Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe2. Nano Letters 17, 6653-6660 (2017)

16. Zhou W, et al. Intrinsic Structural Defects in Monolayer Molybdenum Disulfide. Nano Letters 13, 2615-2622 (2013)

17. Diaz HC, Ma Y, Chaghi R, Batzill M. High density of (pseudo) periodic twin-grain boundaries in molecular beam epitaxy-grown van der Waals heterostructure: MoTe2/MoS2. Applied Physics Letters 108, 191606 (2016)

18. Zhang S, et al. Kagome bands disguised in a coloring-triangle lattice. Physical Review B 99, 100404 (2019)