Here, we studied the crystal structure stability of the 2D ferromagnetic Janus CrSTe bilayer in AB- and AC-stacking, and found that the AB-stacking CrSTe bilayer is more stable than AC-stacking one. The TC of AB-stacking CrSTe is close to room temperature. The MGS exchange coupling constant, and TC of the AB-stacking CrSTe bilayer can be tuned by strain. It is found that the MGSs of the AB- and AC-stacking CrSTe bilayer are ferromagnetic and interlayer antiferromagnetic within a certain small strain range, indicating that the CrSTe bilayers are expected to be used in the double spin filter. The reason for the difference of the MGS of two stacking orders is the difference of layer spacing.
The first-principles calculations based on the density functional theory (DFT) were performed to simulate the electronic and magnetic properties of all structures and the detail of the calculation method is shown in the supplementary material. Due to the unique synthetic method of the 2D Janus monolayers of transition metal dichalcogenides,34–3634. A.-Y. Lu, H. Zhu, J. Xiao, C.-P. Chuu, Y. Han, M.-H. Chiu, C.-C. Cheng, C.-W. Yang, K.-H. Wei, Y. Yang, Y. Wang, D. Sokaras, D. Nordlund, P. Yang, D. A. Muller, M.-Y. Chou, X. Zhang, and L.-J. Li, Nat. Nanotechnol. 12(8), 744–749 (2017). https://doi.org/10.1038/nnano.2017.10035. J. Zhang, S. Jia, I. Kholmanov, L. Dong, D. Er, W. Chen, H. Guo, Z. Jin, V. B. Shenoy, L. Shi, and J. Lou, ACS Nano 11(8), 8192–8198 (2017). https://doi.org/10.1021/acsnano.7b0318636. K. Zhang, Y. Guo, Q. Ji, A.-Y. Lu, C. Su, H. Wang, A. A. Puretzky, D. B. Geohegan, X. Qian, S. Fang, E. Kaxiras, J. Kong, and S. Huang, J. Am. Chem. Soc. 142(41), 17499–17507 (2020). https://doi.org/10.1021/jacs.0c07051 the Janus bilayers are expected to be constructed by stacking two Janus monolayers through the transfer method.3737. Y. Liu, X. Duan, H.-J. Shin, S. Park, Y. Huang, and X. Duan, Nature 591(7848), 43–53 (2021). https://doi.org/10.1038/s41586-021-03339-z Therefore, we first calculated the ground states of the Janus CrSTe monolayer. The optimized lattice constants of the CrSTe monolayer is a = b = 3.47 Å, which is consistent with the previous theoretical work.3333. Q. R. Cui, J. H. Liang, Z. J. Shao, P. Cui, and H. X. Yang, Phys. Rev. B 102(9), 094425 (2020). https://doi.org/10.1103/PhysRevB.102.094425 The crystal structure of the CrSTe monolayer is similar to the trigonal CdI2-type CrTe2 monolayer, but the top layer Te atoms are replaced by S atoms [Fig. S1(a)]. To confirm the stability of the crystal structure, we calculated the phonon spectrum using PHONOPY software.3838. S. Mann, P. Rani, R. Kumar, and V. K. Jindal, AIP Conf. Proc. 1675, 030035 (2015). https://doi.org/10.1063/1.4929251 The phonon spectra of CrSTe monolayer demonstrated that there is no imaginary frequency throughout the Brillouin zone [Fig. S1(b)], indicating that the CrSTe Janus structure is dynamically stable.The Janus CrSTe bilayers, which are stacked from a monolayer structure, have several stacking orders. Here, we focus on a form of antiparallel stack, so that the chalcogenide atoms (S, Te) and transition metal atoms (Cr) in the upper and lower layers can be opposite to each other. There are two stable stacking orders: One is AB stacking order where the S atoms in the lower layer are opposite to Cr atoms in the upper layer [Fig. 1(a)], and the other one is AC-stacking order where the Te atoms in the upper layer are opposite to Cr atoms in the lower layer [Fig. 1(b)]. Because of the difference in the stacks of atoms between layers, AB- and AC-stacking orders will have different energies. DFT was performed to calculate the MGS of AB- and AC-stacking CrSTe (Table S1). The DFT calculations showed that both AB- and AC-stacking CrSTe are ferromagnetic through a Cr-S/Te-Cr superexchange in which these bond angles (Table S1) approach 90°.39–4139. P. W. Anderson, Phys. Rev. 115(1), 2–13 (1959). https://doi.org/10.1103/PhysRev.115.240. J. Kanamori, J Phys. Chem. Solids. 10(2), 87–98 (1959). https://doi.org/10.1016/0022-3697(59)90061-741. Q. Cui, L. Wang, Y. Zhu, J. Liang, and H. Yang, Front. Phys. 18(1), 13602 (2023). https://doi.org/10.1007/s11467-022-1217-7 However, the ferromagnetic energy of the AB-stacking CrSTe unit cell is −34.4 eV, lower than that of the AC-stacking of −34.38 eV, indicating that the AB-stacking order is more stable. The reason is that the atomic radii of Te are larger than those of S, and the layer spacing of the AB-stacking CrSTe is smaller than that of the AC-stacking one (Table S1), so the interlayer coupling of the AB-stacking is stronger, resulting in lower energies. Meanwhile, the magnetic moment of Cr atoms is 3.13 μB, and induced magnetic moments of S atoms and Te atoms are −0.2 and −0.15 μB for the CrSTe bilayer (Table S1), respectively.We also calculated the energy barrier required to drive from AB- to AC-stacking order in CrSTe. There are two pathways, namely, one is the form that starting from AB-stacking, passing through AA-stacking [Fig. 1(c)] and arriving at AC-stacking, namely, AB–AA–AC, and the other one is the form that starting from AB-stacking to the transition state [TS, Fig. 1(c)] and arriving AC-stacking, namely, AB–TS–AC. The barrier energy from AB-stacking to TS is ΔE1 [Fig. 1(d)], from TS to AC-stacking is ΔE2, from AB-stacking to AA-stacking is ΔE3, and from AA-stacking to AC-stacking is ΔE4. For the CrSTe bilayer, both barrier energies of the transition pathway AB–AA–AC are much larger than AB–TS–AC, so AB–TS–AC is probably the optimal transition pathway. Because the AB-stacking is more stable and has lower energy, the barrier energies for ΔE1 of the CrSTe bilayer are much larger than that of ΔE2 in the AB–TS–AC pathway (Table I).TABLE I. Barrier energies for the CrSTe bilayer unit cell.
ΔE1ΔE2ΔE3ΔE4Energy (meV/unit cell)23.324.8178.5260.01As the AB-stacking is the most stable state for CrSTe bilayer, we calculated its band [Fig. S2(a)] and TDOS [Fig. S2(b)] and the result demonstrated that it is a metallic magnetic material. The phonon spectra were calculated using PHONOPY and showed that only ZA mode has a tiny imaginary frequency around the Γ point [Fig. S2(c)], all branches are positive, which confirms that AB-stacking CrSTe is dynamically stable. Meanwhile, we calculated the magnetic crystal anisotropy energy (MAE) with the consideration of SOC and found that the easy magnetic axis is parallel to the b axis. The MAE is defined as Ec–Eb, where Ec and Eb are the total energy of c and b axes. Previous theories suggested that the 5p orbital of Te atoms in the CrTe2 bilayer contributes significantly to the magnetic crystal anisotropy.4242. Q. Q. Li, S. Li, D. Wu, Z. K. Ding, X. H. Cao, L. Huang, H. Pan, B. Li, K. Q. Chen, and X. D. Duan, Appl. Phys. Lett. 119(16), 162402 (2021). https://doi.org/10.1063/5.0068018 The Janus CrSTe bilayer contains several chalcogenide elements, so we analyzed the combined effects of the 5p orbitals of these chalcogenide atoms. The 5p orbital projected density of states (PDOS) of Te + S atoms for AB-stacking CrSTe [Fig. S3(a)] show that near the Fermi level, the py orbital plays a dominant role, so the easy axis is all along the b director. In addition, in order to obtain the intralayer nearest exchange constant J1, intralayer second-neighbor exchange constant J2, interlayer near-neighbor coupling constant J′ [Fig. 1(a)], and TC of AB-stacking CrSTe, a 23×2 supercell [Figs. S4(a) and S4(b)] was used for considering five magnetic orders, i.e., ferromagnetic order (FM), interlayer antiferromagnetism order [AFM-1, Fig. S4(c)], intralayer antiferromagnetism order [AFM-2, Fig. S4(d)], striped antiferromagnetism order [AFM-3, Fig. S4(e)], and zigzag antiferromagnetism order [AFM-4, Fig. S4(f)]. The obtained J1 value is 11.62 meV (Table S2), and the TC which is close to room temperature is 275 K [Fig. S3(b)] for AB-stacking CrSTe. We used energy mapping method43,4443. Y. Nomura, T. Nomoto, M. Hirayama, and R. Arita, Phys. Rev. Res. 2(4), 043144 (2020). https://doi.org/10.1103/PhysRevResearch.2.04314444. N. Sivadas, M. W. Daniels, R. H. Swendsen, S. Okamoto, and D. Xiao, Phys. Rev. B 91(23), 235425 (2015). https://doi.org/10.1103/PhysRevB.91.235425 to calculate the exchange constant and used the Monte Carlo method with VAMPIRE simulation package4545. R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A. Ellis, and R. W. Chantrell, J. Phys.: Condens. Matter. 26(10), 103202 (2014). https://doi.org/10.1088/0953-8984/26/10/103202 to calculate the TC. The details of these calculations are given in the supplementary material.The magnetic properties of 2D van der Waals magnetic materials are very sensitive to the strain. The strain of 2D materials can be applied by the flexible substrate.46,4746. Z. Li, Y. Lv, L. Ren, J. Li, L. Kong, Y. Zeng, Q. Tao, R. Wu, H. Ma, B. Zhao, D. Wang, W. Dang, K. Chen, L. Liao, X. Duan, X. Duan, and Y. Liu, Nat. Commun. 11(1), 1151 (2020). https://doi.org/10.1038/s41467-020-15023-347. J. Cenker, S. Sivakumar, K. Xie, A. Miller, P. Thijssen, Z. Liu, A. Dismukes, J. Fonseca, E. Anderson, X. Zhu, X. Roy, D. Xiao, J.-H. Chu, T. Cao, and X. Xu, Nat. Nanotechnol. 17(3), 256–261 (2022). https://doi.org/10.1038/s41565-021-01052-6 The effect of strain on the magnetic properties of the AB-stacking CrSTe is further investigated. The strain is in-plane biaxial and defined as ε = (a − a0)/a0, where a/a0 are lattice constants of strained/unstrained AB-stacking CrSTe, and a0 = 3.47 Å for CrSTe. The MGS of AB-stacking CrSTe can be tuned by strain (Fig. S5). For AB-stacking CrSTe, when the strain is below 4%, their MGS is FM. While when the strain exceeds 4%, their MGS is AFM-1 [Fig. 2(a)]. The reason for the magnetic transition from FM to AFM-1 should be the reduction in layer spacing [Fig. 2(b)], which enhances the interaction between the atoms of the upper and lower layers and further makes magnetism of the two layers into opposite, which is similar to the magnetic properties of the CrI348,4948. P. H. Jiang, C. Wang, D. C. Chen, Z. C. Zhong, Z. Yuan, Z. Y. Lu, and W. Ji, Phys. Rev. B 99(14), 144401 (2019). https://doi.org/10.1103/PhysRevB.99.14440149. 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 546(7657), 270–273 (2017). https://doi.org/10.1038/nature22391 and CrTe242,5042. Q. Q. Li, S. Li, D. Wu, Z. K. Ding, X. H. Cao, L. Huang, H. Pan, B. Li, K. Q. Chen, and X. D. Duan, Appl. Phys. Lett. 119(16), 162402 (2021). https://doi.org/10.1063/5.006801850. L. Wu, L. Zhou, X. Zhou, C. Wang, and W. Ji, Phys. Rev. B 106(8), L081401 (2022). https://doi.org/10.1103/PhysRevB.106.L081401 bilayers. With the increase in of the strain, the Cr–Te bonding distances hardly change and the Cr–S bonding distances increase slightly, whereas the Cr–Cr distance obviously increases (Fig. S6), so the indirect superexchange FM coupling of the intralayer increases more strongly, which results in the enhancement of the J1 [Fig. 2(b)] in FM region.33,5133. Q. R. Cui, J. H. Liang, Z. J. Shao, P. Cui, and H. X. Yang, Phys. Rev. B 102(9), 094425 (2020). https://doi.org/10.1103/PhysRevB.102.09442551. H. Y. Lv, W. J. Lu, D. F. Shao, Y. Liu, and Y. P. Sun, Phys. Rev. B 92(21), 214419 (2015). https://doi.org/10.1103/PhysRevB.92.214419 At the same time, the J2 has no obvious change, and the J′ increases slowly and then decreases below zero [Fig. 2(c)]. In the magnetic phase transition region, as the layer spacing decreases, the coupling of the interlayer becomes stronger, and the ferromagnetism coupling of the intralayer becomes weaker, thus J1 gradually decreases and J′ is less than 0, resulting in the MGS of AFM-1. In addition, we also calculated TC of AB-stacking CrSTe under strains of −2%, 0%, and 2%, the corresponding value are 240, 275, and 310 K, respectively [Fig. 2(d)], which are close to the room temperature, and show an increasing trend with the increase in the strain.The above-mentioned result showed that the MGS of AB-stacking CrSTe can be tuned by the strain. As the barrier energies between AB- and AC-stacking is small [Fig. 1(d)], the external electric field or magnetic field is expected to drive the transition of MGS between these two stackings. If the two MGS are different within a certain strain range, the CrSTe are expected to be used in the double spin filter [Fig. 3(a)]. Here, we calculated the MGS of AB- and AC-stacking simultaneously under the strains of magnetic phase transition region. For the CrSTe bilayer, in the strain range of 4.2%–5.8%, the MGS of AB-stacking is AFM-1 while the MGS of AC-stacking is FM [Fig. 3(b)]. Therefore, CrSTe can be used as the double spin filter in a certain strain range. At the same time, we also calculated the magnetic crystal anisotropy energy in the magnetic transition region [Fig. 3(c)]. The easy axis of magnetization of CrSTe is in-plane magnetic axis (M//b) under different strains and stacking orders.In order to understand the magnetic transition properties of AB- and AC-stacking, we calculated differential charge density distribution between layers for CrSTe under 5% strain [Fig. 4(a)]. Under the same strain or lattice constant, the interlayer coupling of AB-stacking is much stronger than that of AC-stacking due to its smaller layer spacing. The layer spacing of AB-stacking CrSTe is 3.01 Å, while that of the AC-stacking is 3.08 Å. Due to the smaller layer spacing of AB-stacking, the interlayer charge redistribution is stronger and it has considerable effect on the charge distribution of intralayer,4242. Q. Q. Li, S. Li, D. Wu, Z. K. Ding, X. H. Cao, L. Huang, H. Pan, B. Li, K. Q. Chen, and X. D. Duan, Appl. Phys. Lett. 119(16), 162402 (2021). https://doi.org/10.1063/5.0068018 resulting in the opposite spin of Cr atoms between the upper and lower layers, so their MGS turn to AFM-1 from FM. At the same time, the sliding energy barrier of 5%-CrSTe [Fig. 4(b)] in FM and AFM-1 states shows that the ground state energy slowly changes from the AFM-1 state of AB-stacking to the FM state of AC-stacking. The super-superexchange mechanism can also be used to explain changes in interlayer magnetic coupling.52,5352. C. Wang, X. Zhou, L. Zhou, Y. Pan, Z.-Y. Lu, X. Wan, X. Wang, and W. Ji, Phys. Rev. B 102(2), 020402 (2020). https://doi.org/10.1103/PhysRevB.102.02040253. J. Klein, T. Pham, J. D. Thomsen, J. B. Curtis, T. Denneulin, M. Lorke, M. Florian, A. Steinhoff, R. A. Wiscons, J. Luxa, Z. Sofer, F. Jahnke, P. Narang, and F. M. Ross, Nat. Commun. 13(1), 5420 (2022). https://doi.org/10.1038/s41467-022-32737-8 For AB-stacking, the MGS is AFM-1, the spacing between the two layers is relatively small, and there are overlap densities of interfacial Te1 and S2 atoms p orbitals from the spin density map [Fig. 4(c)]. These overlap spin densities will affect the spin directions of interlayer Te1 and S2 atoms and then affect the spin distribution of Cr atoms t2g orbitals, so that the spin directions of Cr1 and Cr2 atoms in the upper and lower layers turn opposite to each other, showing interlayer antiferromagnetic coupling. For AC-stacking, due to the larger layer spacing, there is no or less overlap of the interfacial Te1 and S2 atoms p orbitals spin densities [Fig. 4(d)], i.e., quite weak exchange effect between the layers. Therefore, Te1 and S2 atoms of p orbital spin directions remain spin down. Finally, AC-stacking CrSTe maintain the ferromagnetic coupling in the interlayer. The 5p orbital PDOS of Te + S atoms for the AB-stacking CrSTe [Fig. 4(e)] and AC-stacking CrSTe [Fig. 4(f)] under 5% strain were performed. For AB-stacking CrSTe and AC-stacking CrSTe, the py orbital plays a dominant role, so their easy axis is along the b director (M//b). Thus, the magnetic anisotropy of the Janus bilayer is mainly dominated by the 5p orbital distribution of the chalcogens atoms.We have investigated the crystal structure and magnetic property of the 2D ferromagnetic Janus CrSTe bilayer in AB-stacking and AC-stacking and found that the AB-stacking CrSTe bilayer with smaller layer spacing is more stable than AC-stacking one. The TC of AB-stacking CrSTe is close to room temperature. The MGS, exchange coupling constant, and TC of the AB-stacking CrSTe bilayer can be tuned by strain. It is found that the MGSs of the AB- and AC-stacking CrSTe bilayer are ferromagnetic and interlayer antiferromagnetic within a certain strain range, indicating that the CrSTe is expected to be used in the double spin filter. The reason for the difference of the MGS of two stacking orders is the difference of layer spacing. Our result demonstrated that the 2D Janus CrSTe bilayers are good candidates for spintronic nanodevices with stable performance and low-power consumption at room temperature.
See the supplementary material for theoretical calculation method; calculation of the exchange coupling constant; phonon spectra for Janus monolayer CrSTe; band and phonon spectra of AB-stacking CrSTe, TDOS, and PDOS of AB-stacking CrSTe; magnetic property and bond length of the AB-stacking CrSTe under various strains; and the 5p orbitals PDOS of AB-stacking and AC-stacking CrSTe.This work was supported by the National Natural Science Foundation of China (Grant Nos. 11974106, 51872086, 62174051, 51991340, and 51991343), the Natural Science Foundation of Hunan Province (Grant Nos. 2020JJ1001 and 2022JJ10022), the Hunan Province “Huxiang Talents” Project (Grant No. 2021RC3038), the Shenzhen Basic Research Project (Grant No. JCYJ20210324142012035), and the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX0126).
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Qiu Qiu Li: Data curation (lead); Methodology (lead); Writing – original draft (lead); Writing – review & editing (lead). Bo Li: Writing – original draft (lead); Writing – review & editing (lead). Ke-Qiu Chen: Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead). Xi Dong Duan: Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead). Wen-Wen Liu: Data curation (lead). Zhong-Ke Ding: Software (lead). Hui Pan: Validation (equal). Xuan-Hao Cao: Resources (equal). Wei-Hua Xiao: Software (equal). Nan-Nan Luo: Data curation (equal). Jiang Zeng: Software (equal). Li-Ming Tang: Resources (equal).
The data that support the findings of this study are available within the article and its supplementary material.REFERENCES
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