First principles study of magnetic transition of strain induced monolayer NbSi<sub>2</sub>N<sub>4</sub>

Jiang Nan; Li Ao-Lin; Qu Shui-Xian; Gou Si; Ouyang Fang-Ping

doi:10.7498/aps.71.20220939

Abstract

The effective control of two-dimensional material magnetism is a frontier research field. In this work, the influences of in-plane biaxial tension strain on the electronic structure, magnetic properties, and Curie temperature of monolayer NbSi₂N₄ are investigated by first-principles calculations based on density functional theory and Monte Carlo simulations in the frame of the Heisenberg model. We demonstrate that the monolayer NbSi₂N₄ has favorable dynamic and thermal stability through the phonon spectral calculations and ab initio molecular dynamics simulations. It is found that the intrinsic monolayer NbSi₂N₄ is a non-magnetic metal, which can be transformed into a ferromagnetic metal by 1.5% tensile strain. The electronic structure analysis of monolayer NbSi₂N₄ shows that the ferromagnetism induced by tensile strain is caused by traveling electrons. There is a half-full band at the monolayer NbSi₂N₄ Fermi level, which is mainly contributed by the dz² orbital of the Nb atom. When there is no additional strain, the band is spin-degenerate. Tensile strain can make this band more localized, which leads to Stoner instability, resulting in the ferromagnetic ordering of monolayer NbSi₂N₄ traveling electrons. The stability of the ferromagnetic coupling is enhanced with the increase of the strain degree. The calculation results of the magnetic anisotropy energy show that the strain can make the direction of the easy magnetization axis of the monolayer NbSi₂N₄ reverse from the vertical direction to the in-plane, and then back to the vertical direction. Furthermore, the strain can significantly increase the Curie temperature of monolayer NbSi₂N₄. The Curie temperature of monolayer NbSi₂N₄ is 18 K at 2% strain and 87.5 K at 6% strain, which is 386% higher than that at 2% strain. Strain engineering can effectively control the magnetic ground state and Curie temperature of single-layer NbSi₂N₄. The research results are expected to promote the development of MA₂Z₄ materials in the field of mechanical sensing device design and low-temperature magnetic refrigeration.

Keywords:

Authors and contacts

1.
School of Physics and Electronics, Central South University, Changsha 410012, China
2.
School of Physics and Technology, Xinjiang University, Urumqi 830046, China
3.
State Key Laboratory of Powder Metallurgy, and Powder Metallurgy Research Institute, Central South University, Changsha 410083, China

Corresponding author: Ouyang Fang-Ping, oyfp@csu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52073308, 12164046), the Distinguished Young Scholar Foundation of Hunan Province, China (Grant No. 2015JJ1020), and the Central South University Research Fund for Sheng-hua Scholars, China (Grant No. 502033019).

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References

[1]	Jansen R 2012 Nat. Mater. 11 400 Google Scholar
[2]	Lin X Y, Yang W, Wang K L, Zhao W S 2019 Nat. Electron. 2 274 Google Scholar
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Cited By

图 1 (a)单层NbSi₂N₄的俯视图(左)和侧视图(右), 自旋密度分布用黄色表示; (b)不考虑自旋极化时单层NbSi₂N₄的能带结构和态密度图; (c)单层NbSi₂N₄的声子谱图; (d)温度300 K, 时长10 ps的分子动力学模拟下, 系统总能量的变化; (e)考虑自旋极化时单层NbSi₂N₄的能带结构和态密度图

Figure 1. (a) Top view (left) and side view (right) of monolayer NbSi₂N₄, and the spin density distribution is represented in yellow; (b) energy band structure and density of states of monolayer NbSi₂N₄ without considering spin polarization; (c) phonon spectra of monolayer NbSi₂N₄; (d) the change of total energy of the system under the molecular dynamics simulation of temperature 300 K and duration 10 ps; (e) energy band structure and density of states of monolayer NbSi₂N₄ considering spin polarization.

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图 2 (a)单层NbSi₂N₄铁磁态与无磁态间的能量差随电子温度的变化关系; (b)单层NbSi₂N₄在2%应变下的声子谱; (c) 单层NbSi₂N₄ 6%应变下的声子谱

Figure 2. (a) Variation of energy difference between ferromagnetic and nonmagnetic states of monolayer NbSi₂N₄ with electron temperature; (b) the phonon spectrum of monolayer NbSi₂N₄ at 2% strain; (c) the phonon spectrum of monolayer NbSi₂N₄ at 6% strain.

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图 3 (a) 单层NbSi₂N₄反铁磁态和铁磁态与无磁态间能量差随应变变化; (b)单层NbSi₂N₄磁矩随应变变化; (c) MAE随应变变化; (d)不同应变下, Nb原子轨道磁矩与自旋磁矩对MAE的贡献

Figure 3. (a) Energy difference between antiferromagnetic state, ferromagnetic state and non-magnetic state of monolayer NbSi₂N₄ with strain; (b) magnetic moment of monolayer NbSi₂N₄ with strain; (c) MAE with strain; (d) contribution of orbital magnetic moment and spin magnetic moment of Nb atom to MAE under different strains.

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图 4 (a) 单层NbSi₂N₄分波态密度; (b)—(e) 单层NbSi₂N₄在不同应变下的态密度; (f)铁磁态与无磁态间的能量差随磁矩变化的DFT计算曲线, 将无磁态的能量设为0 meV

Figure 4. (a) Fractional density of states of monolayer NbSi₂N₄. (b)–(e) The density of state of monolayer NbSi₂N₄ under different strains. (f) DFT calculation curve of the energy difference between the FM state and the NM state change with the magnetic moment, the energy of the NM state is set to 0 meV.

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图 5 (a)不同应变下居里温度的变化; (b), (c)在2%和6%应变下磁矩与磁化率随居里温度的变化

Figure 5. (a) Variation of Curie temperature under different strains; (b), (c) variation of magnetic moment and susceptibility with Curie temperature under 2% and 6% strain.

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表 1 在不同应变下的交换常数J和各向异性参数D

Table 1. Exchange constant J and anisotropy parameter D under different strains.

应变/% 2 3 4 5 6

J/meV –2.430 –5.625 –8.767 –12.109 –16.753
D/meV 1.224 –0.248 0.388 0.596 0.468

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[1]	Jansen R 2012 Nat. Mater. 11 400 Google Scholar
[2]	Lin X Y, Yang W, Wang K L, Zhao W S 2019 Nat. Electron. 2 274 Google Scholar
[3]	Choudhuri I, Bhauriyal P, Pathak B 2019 Chem. Mater. 31 8260 Google Scholar
[4]	Sun Y J, Zhuo Z W, Wu X J, Yang J L 2017 Nano Lett. 17 2771 Google Scholar
[5]	Miao Y P, Huang Y H, Fang Q L, Yang Z, Xu K W, Ma F, Chu P K 2016 J. Mater. Sci. 51 9514 Google Scholar
[6]	Kaloni T P 2014 J. Phys. Chem. C 118 25200 Google Scholar
[7]	Mao Y L, Guo G, Yuan J M, Zhong J X 2019 Appl. Surf. Sci. 464 236 Google Scholar
[8]	Eean F, Arkin H, Aktürk E 2017 RSC Adv. 7 37815 Google Scholar
[9]	Huang B, Clark G, Navarro-Moratalla E, Klein D, Cheng R, Seyler K, Zhong D, Schmidgall E, McGuire M, Cobden D, Yao W, Xiao D, Jarillo-Herrero P, Xu X D 2017 Nature 546 270 Google Scholar
[10]	Gong C, Li L, Li Z L, Ji H W, Stern A, Xia Y, Cao T, Bao W, Wang C Z, Wang Y, Qiu Z Q, Cava R J, Louie S G, Xia J, Zhang X 2017 Nature 546 265 Google Scholar
[11]	Wang L, Shi Y P, Liu M F, et al. 2021 Nat. Commun. 12 2361
[12]	Hong Y L, Liu Z, Wang L, Zhou T, Ma W, Xu C, Feng S, Chen L, Chen M L, Sun D M, Chen X Q, Cheng H M, Ren W 2020 Science 369 670 Google Scholar
[13]	Novoselov K S 2020 Natl. Sci. Rev. 7 1842 Google Scholar
[14]	Yang C, Song Z, Sun X, Lu J 2021 Phys. Rev. B 103 035308 Google Scholar
[15]	Yang J S, Zhao L N, Li S Q, Liu H S, Wang L, Chen M D, Gao J F, Zhao J J 2021 Nanoscale 13 5479 Google Scholar
[16]	Chen J, Tang Q 2021 Chem. Eur. J. 27 9925 Google Scholar
[17]	Guo S D, Mu W Q, Zhu Y T, Chen X Q 2020 Phys. Chem. Chem. Phys. 22 28359 Google Scholar
[18]	Li F, Ren Y L, Wan W H, Liu Y, Ge Y F 2021 AIP Advances 11 115220 Google Scholar
[19]	Zheng F W, Zhao J Z, Liu Z, Li M L, Zhou M, Zhang S B, Zhang P 2018 Nanoscale 10 14298 Google Scholar
[20]	Wu Z W, Yu J, Yuan S J 2019 Phys. Chem. Chem. Phys. 21 7750 Google Scholar
[21]	Chen T, Liu G G, Dong X S, Li H L, Zhou G H 2022 J. Electron. Mater. 51 2212 Google Scholar
[22]	Wu Z B, Shen Z, Xue Y F, Song C S 2022 Phys. Rev. Mater. 6 014011 Google Scholar
[23]	Qin H F, Chen J, Sun B, Tang Y L, Ni Y X, Chen Z F, Wang H Y, Chen Y Z 2021 Phys. Chem. Chem. Phys. 23 22078 Google Scholar
[24]	Liu L F, Hu X H, Wang Y F, Krasheninnikov A V, Chen Z F, Sun L T 2021 Nanotechnology 32 485408 Google Scholar
[25]	Xie W Q, Lu Z W, He C C, Yang X B, Zhao Y J 2021 J. Phys. Condens. Matter 33 215803 Google Scholar
[26]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[27]	Kresse G, Furthmüller J, Hafner J 1994 Phys. Rev. B 50 13181 Google Scholar
[28]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[29]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[30]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[31]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106 Google Scholar
[32]	Joyce G 1967 Phys. Rev. 155 478 Google Scholar
[33]	Liu L, Chen S S, Lin Z Z, Zhang X 2020 J. Phys. Chem. Lett. 11 7893 Google Scholar
[34]	Duong D L, Burghard M, Schön J C 2015 Phys. Rev. B 92 245131 Google Scholar
[35]	Van Vleck J H 1937 Phys. Rev. 52 1178 Google Scholar
[36]	Sieberer M, Khmelevskyi S, Mohn P 2006 Phys. Rev. B 74 014416 Google Scholar
[37]	Zhuang H L L, Kent P R C, Hennig R G 2016 Phys. Rev. B 93 134407 Google Scholar
[38]	Kulish V V, Huang W 2017 J. Mater. Chem. C 5 8734 Google Scholar
[39]	Zhao Y, Liu Q X, Xing J P, Jiang X, Zhao J J 2022 Nanoscale Adv. 4 600 Google Scholar
[40]	Sun X Y, Yang K, Li Z Y 2022 Phys. Status Solidi RRL 16 2100611 Google Scholar

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First principles study of magnetic transition of strain induced monolayer NbSi₂N₄

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Corresponding author: Ouyang Fang-Ping, oyfp@csu.edu.cn

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应变/%	2	3	4	5	6
J/meV	–2.430	–5.625	–8.767	–12.109	–16.753
D/meV	1.224	–0.248	0.388	0.596	0.468

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First principles study of magnetic transition of strain induced monolayer NbSi2N4

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Corresponding author: Ouyang Fang-Ping, oyfp@csu.edu.cn

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First principles study of magnetic transition of strain induced monolayer NbSi₂N₄