Abstract
1. Introduction
Magnetism, which is the macroscopic spin ordering in spatial space, has attracted many studies in the recently flourishing research of two-dimensional (2D) materials[
Pioneering efforts have been made in exfoliation of monolayer and few-layers of magnetic layered bulk materials, such as NiPS3[
2. Methods
In this paper, we investigate both electronic structures and magnetic orderings of bulk and monolayer forms of chromium diiodides, based on the state-of-the-art first-principles calculations[
3. Results and discussion
3.1. Bulk CrI2
The bulk CrI2 crystallizes in the P63mc space group and is consisting of two CrI2 monolayers in AB stacking. The crystal structure of bulk CrI2 is shown in Fig. 1(a), the chromium and iodine atoms are displayed with blue and purple spheres, respectively. The spin-polarized band structures of bulk CrI2 is shown in Fig. 1(b) (antiferromagnetic) and Fig. 1(c) (ferromagnetic), to compare the total energy difference between ferromagnetic and antiferromagnetic orderings, a 2 × 1 × 1 supercell is used, and the band dispersions of spin majority and spin minority is indicated by red and green lines. The corresponding spin spatial distribution is illustrated in inserts of Figs. 1(b) and 1(c)) with the same color-coding. Since the total energy difference between ferromagnetic and antiferromagentic states is 20 meV/unit cell, one can find out that, bulk CrI2 take a ferromagnetic ground state.
Figure 1.(Color online) (a) Crystal structure of bulk CrI2, and spin-polarized band structure and spin spatial distribution of (b) ferromagnetic and (c) antiferromagnetic orderings.
3.2. CrI2 monolayer
CrI2 monolayer is cleaved from a fully relaxed bulk crystal. Each chromium atom is bonded to six iodine atoms in the monolayer, and all the atoms are arranged in the 1T phase. Noticing the similarity of CrI2 monolayer to the famous transitional metal dichalcogenide monolayers, it is necessary to consider the 2H phase. The 1T and 2H phases of CrI2 monolayers are illustrated in Fig. 2.
Figure 2.(Color online) (a) 1T and (b) 2H phases of CrI2 monolayers. The chromium and iodine atoms are illustrated with blue and purple spheres, respectively.
In Fig. 3, the spin-resolved band structures, the total spin density of states (DOS) and spin spatial distributions of 1T and 2H CrI2 monolayers are shown. 2 × 1 × 1 supercells are also employed, to determine the magnetic ground states, by performing constrained spin-polarized first-principles calculations. The numerical results for 1T-FM, 1T-AFM, 2H-FM, 2H-AFM are displayed in panels Figs. 3(a)–3(d) accordingly, and the total energies for each configuration are listed in Table 1. One can find from Table 1 the most energy-favored configuration is 1T-AFM, which implies the ground state of monolayer CrI2 is antiferromagnetic.
Figure 3.(Color online) The spin-resolved band structures, total spin density of states (DOS) and spin spatial distributions of (a) 1T-FM, (b) 1T-AFM, (c) 2H-FM, and (d) 2H-AFM.
Table 1 shows the total energies of the FM state and the AFM state of the 1T phase, where the energy differences between the FM and the AFM states are obtained by performing DFT+U calculations within Dudarev’s approach. The Ueff (U–J) varies from 1 to 4 eV, and the corresponding total energy differences are of 30 meV, which indicates the AFM state is more energetic favorable.
3.3. CrI2 bilayer
To investigate the magnetic effect of the interlayer interaction, we construct a CrI2 bilayer from 1T CrI2 monolayers, and to clarify the influence of stacking patterns, both AB stacking and AA stacking models are constructed. As shown in Fig. 4, we denote these models, for convenience, as AA-FM, AA-AFM-a, AA-AFM-f, AB-FM, AB-AFM-a and AB-AFM-f, where the appendix a (f) indicates that the intra-layer initial magnetic moment is set antiferromagnetic (ferromagnetic). The interlayer distance between the adjacent chromium layers in equilibrium is obtained by relaxation and reads XX for the AA stacking and XX for the AB stacking, respectively.
Figure 4.(Color online) Configurations of the model (a) AA-FM, (b) AA-AFM-a, (c) AA-AFM-f, (d) AB-FM, (e) AB-AFM-a, and (f) AB-AFM-f. The up and down arrows indicate the signs of initial magnetic moments in constrained DFT calculations.
The spin-resolved band structures, total spin density of states and spin spatial distributions of each CrI2 bilayers are shown in Fig. 5. The total energies for each configuration are listed in Table 2. From Table 3, one can find the ground states of CrI2 bilayers are always antiferromagnetic independent of the stacking patterns, which implies the interlayer interaction is still antiferromagnetic in CrI2 up to few layers.
Figure 5.(Color online) (The spin-resolved band structures, total spin density of states (DOS) and spin spatial distributions of model (a) AA-FM, (b) AA-AFM-a, (c) AA-AFM-f, (d) AB-FM, (e) AB-AFM-a, and (f) AB-AFM-f.
4. Conclusion
In summary, we investigate both electronic structures and magnetic orderings of bulk and monolayer forms of chromium diiodides by first-principles calculations and demonstrate that the ground state of a free-standing monolayer of chromium diiodides is antiferromagnetic, even though the bulk possesses macroscopic ferromagnetic ordering. The stable CrI2 monolayer takes a 1T-phase configuration and the interlayer interaction remains antiferromagnetic up to few-layer scenarios. The robust antiferromagnetic feature makes monolayer or few layers CrI2 possible blocks to build flexible 2D antiferromagnetic spintronic devices. The questions of why the magnetic structures of monolayer and bulk CrI2 are opposite and how dependent antiferromagnetic interlayer interaction depend on the layer numbers are still to be answered.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 11404043) and Graduate Research Innovation Project of Chongqing (No. CYS18253).
References
[1] A M Tokmachev, D V Averyanov, O E Parfenov et al. Emerging two-dimensional ferromagnetism in silicene materials. Nat Commun, 9, 1672(2018).
[2] X Y Shi, Z J Huang, M Huttula et al. Introducing magnetism into 2D nonmagnetic inorganic layered crystals: A brief review from first-principles aspects. Crystals, 8, 24(2018).
[3] P Tao, H H Guo, T Yang et al. Strain-induced magnetism in MoS2 monolayer with defects. J Appl Phys, 115, 054305(2014).
[4] V Kochat, A Apte, J A Hachtel et al. Re doping in 2D transition metal dichalcogenides as a new route to tailor structural phases and induced magnetism. Adv Mater, 29, 1703754(2017).
[5] A Hallal, F Ibrahim, H X Yang et al. Tailoring magnetic insulator proximity effects in graphene: First-principles calculations. 2D Mater, 4, 025074(2017).
[6] N D Mermin, H Wagner. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys Rev Lett, 17, 1133(1966).
[7] N H Miao, B Xu, L G Zhu et al. 2D intrinsic ferromagnets from van der Waals antiferromagnets. J Am Chem Soc, 140, 2417(2018).
[8] X Lin, W Yang, K L Wang et al. Two-dimensional spintronics for low-power electronics. Nat Electron, 2, 274(2019).
[9] B Huang, G Clark, E Navarro-Moratalla et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature, 546, 270(2017).
[10] C Gong, L Li, Z L Li et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature, 546, 265(2017).
[11] X L Sheng, B K Nikolić. Monolayer of the 5d transition metal trichloride OsCl3: A playground for two-dimensional magnetism, room-temperature quantum anomalous Hall effect, and topological phase transitions. Phys Rev B, 95, 201402(2017).
[12] C T Kuo, M Neumann, K Balamurugan et al. Exfoliation and Raman spectroscopic fingerprint of few-layer NiPS3 van der waals crystals. Sci Rep, 6, 20904(2016).
[13] W Zhu, W Gan, Z Muhammad et al. Exfoliation of ultrathin FePS3 layers as a promising electrocatalyst for the oxygen evolution reaction. Chem Commun, 54, 4481(2018).
[14] X X Li, J L Yang. CrXTe3(X = Si, Ge) nanosheets: Two dimensional intrinsic ferromagnetic semiconductors. J Mater Chem C, 2, 7071(2014).
[15] H L Zhuang, P R C Kent, R G Hennig. Strong anisotropy and magnetostriction in the two-dimensional Stoner ferromagnet Fe3GeTe2. Phys Rev B, 93, 134407(2016).
[16] C S Yadav, A K Rastogi. Transport and magnetic properties of Fe
[17] J J Sun, C Li, D Chen et al. Controlled synthesis of ferromagnetic MnSe
[18] J L Lado, J Fernández-Rossier. On the origin of magnetic anisotropy in two dimensional CrI3. 2D Mater, 4, 035002(2017).
[19] M Abramchuk, S Jaszewski, K R Metz et al. Controlling magnetic and optical properties of the van der waals crystal CrCl3−
[20] M Gibertini, M Koperski, A F Morpurgo et al. Magnetic 2D materials and heterostructures. Nat Nanotechnol, 14, 408(2019).
[21] S J Gong, C Gong, Y Y Sun et al. Electrically induced 2D half-metallic antiferromagnets and spin field effect transistors. PNAS, 115, 8511(2018).
[22] P Hohenberg, W Kohn. Inhomogeneous electron gas. Phys Rev, 136, b864(1964).
[23] W Kohn, L J Sham. Self-consistent equations including exchange and correlation effects. Phys Rev, 140, a1133(1965).
[24] G Kresse, J Hafner. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Phys Rev B, 49, 14251(1994).
[25] G Kresse, J Furthmüller. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci, 6, 15(1996).
[26] G Kresse, J Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B, 54, 11169(1996).
[27] P E Blöchl. Projector augmented-wave method. Phys Rev B, 50, 17953(1994).
[28] G Kresse, D Joubert. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B, 59, 1758(1999).
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