CrO<sub>2</sub> monolayer: a two-dimensional ferromagnet with high Curie temperature and half-metallicity

Liu Bing-Xin; Li Zong-Liang

doi:10.7498/aps.73.20240246

Abstract

Owing to the complete spin-polarization of electronic states near Fermi energy, half-metallic ferromagnets, especially two-dimensional half-metallic ferromagnets, have garnered significant attention in the field of spintronics. However, the practical applications of these materials are greatly hindered by their low Curie temperatures. Therefore, the exploration of high Curie temperature half-metallic ferromagnets poses a necessary and challenging task. In this study, we predict a two-dimensional transition metal oxide, CrO₂ monolayer, and employ first-principles calculations to investigate the crystal structure, electronic properties, magnetic ground state, and ferromagnetic phase transition. The calculations of phonon spectrum, elastic constant, and molecular dynamics simulations indicate that CrO₂ monolayer is dynamically, mechanically, and thermally stable. The convex hull diagram of Cr-O systems shows that the hull energy of the predicted CrO₂ layer is only 0.18 eV, further confirming the structural stability and large possibility for experimental fabrication. More importantly, the electronic and magnetic properties of CrO₂ monolayer demonstrate that it is a two-dimensional ferromagnetic half-metal with wide band gap. Five d suborbitals are divided into E_g and T_2g orbitals because of the crystal field of Cr atom in the center of O tetrahedron, and the spin-polarizations of E_g orbitals make a major contribution to the moment around Cr atom. The ferromagnetic coupling along Cr-O-Cr chain is dominated by the superexchange interaction bridged by O 2p orbitals, similar to the typical Mn-O-Mn superexchange model. The magnetic behavior of the Cr spin lattice in a CrO₂ monolayer is described by a two-dimensional Heisenberg model, in which the exchange coupling anisotropy is ignored and the single ion anisotropy is the main consideration. By solving the Heisenberg model through using the Monte Carlo simulation method, the Curie temperature is determined to be over 400 K. The high Curie temperature ferromagnetism is rare in two-dimensional ferromagnetic materials and even rarer in semi-metallic materials, which makes it an ideal material for fabricating spintronic devices and studying spin quantum effects.

Keywords:

transition metal oxide /
two-dimensional ferromagnetic half-metal /
Curie temperature /
first-principles theory

Authors and contacts

School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

Corresponding author: Li Zong-Liang, lizongliang@sdnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11974217).

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References

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[2]	Zhang H 2015 ACS Nano 9 9451 Google Scholar
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[39]	Kresse G, Hafner J 1993 Phys. Rev. B 47 558 Google Scholar
[40]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[41]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[42]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[43]	Sun J, Ruzsinszky A, Perdew J P 2015 Phys. Rev. Lett. 115 036402 Google Scholar
[44]	Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Phys. Rev. B 57 1505 Google Scholar
[45]	Togo A, Tanaka I 2015 Scr. Mater. 108 1 Google Scholar
[46]	Martyna G J, Klein M L, Tuckerman M 1992 J. Chem. Phys. 97 2635 Google Scholar
[47]	Born M, Huang K, Lax M 1955 Am. J. Phys. 23 474 Google Scholar
[48]	Wooster W A, Wooster N 1931 Nature 127 782 Google Scholar
[49]	Dufek V, Petrů F, Brožek V 1967 Monatsh. Chem. 98 2424 Google Scholar
[50]	Zhang Q, Xu M K, Shen Z R, Wei Q 2017 J. Mater. Sci. Mater. Electron. 28 12056 Google Scholar
[51]	Zhou S M, Zhu G Y, Wang Y Q, Lou S Y, Hao Y M 2011 Chem. Eng. J. 174 432 Google Scholar
[52]	Bärnighausen H, Brauer G, Schultz N 1965 Z. Anorg. Allg. Chem. 338 250 Google Scholar
[53]	Cococcioni M, de Gironcoli S 2005 Phys. Rev. B 71 035105 Google Scholar
[54]	Henkelman G, Arnaldsson A, Jónsson H 2006 Comput. Mater. Sci. 36 354 Google Scholar
[55]	Graf T, Felser C, Parkin S S P 2011 Prog. Solid. State Ch. 39 1 Google Scholar
[56]	Zhang Y H, Wang B, Guo Y, Li Q, Wang J L 2021 Comput. Mater. Sci. 197 110638 Google Scholar
[57]	Ma F J, Lu Z Y, Xiang T 2008 Phys. Rev. B 78 224517 Google Scholar
[58]	Xu C, Feng J, Xiang H, Bellaiche L 2018 NPJ Comput. Mater. 4 57 Google Scholar
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Cited By

图 1 CrO₂单层的原子结构图　(a)俯视图; (b)侧视图; (c)立体图, 黑色虚线框表示原胞; (d) CrO₂单层的声子谱; (e) CrO₂单层在1000 K下总势能随时间的演化曲线, 时间范围为5 ps, 插图为经过5 ps分子动力学模拟后CrO₂最终构型的俯视图和侧视图

Figure 1. Atomic structure of CrO₂ monolayer: (a) Top view; (b) side view; (c) oblique view, the unit cell is marked by the black dashed line square; (d) phonon spectra of CrO₂ monolayer; (e) total energy evolution with time at 1000 K. The illustration shows a top and side view of the final configuration of CrO₂ after 5 ps molecular dynamics simulation.

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图 2 (a) Cr-O系统的凸包图, 五角星表示本工作中的CrO₂单层结构; (b) Cr原子的d轨道电子数对Hubbard U的响应关系, 红线和蓝线表示自洽计算和非自洽计算的结果

Figure 2. (a) Convex hull of formation energy of the Cr-O systems, the star is the CrO₂ monolayer in this work; (b) the response of d electron number to the small U perturbation, red and blue symbols correspond to the results from the self-consistent and non-self-consistent calculations.

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图 3 CrO₂投影到Cr原子3d轨道和O原子2p轨道上的分轨道态密度, 费米能级用垂直虚线表示, 费米能级设置为0 eV

Figure 3. Projected density of states on the Cr 3d and O 2p suborbitals, the Fermi energy represented by vertical dashed lines, the Fermi energy is set to zero.

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图 4 不同方法计算CrO₂的能带结构, 费米能级设置为0 eV　(a) GGA+U; (b) SCAN

Figure 4. Band structure of CrO₂ monolayer by different calculations, and Fermi energy is zero: (a) GGA + U; (b) SCAN.

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图 5 (a) CrO₂单层结构的俯视图, J₁和J₂分别表示最近邻和次近邻Cr原子间的交换耦合系数; (b) FM序; (c) AFM-I序; (d) AFM-II序, 不同磁序下的原胞用黑色虚线框表示, 红色箭头和蓝色箭头表示相反的磁矩指向

Figure 5. (a) Nearest and next-nearest neighbor exchange couplings, J₁ and J₂, represented by the double arrows; (b) ferromagnetic order; (c) antiferromagnetic order I (AFM-I); (d) antiferromagnetic order II (AFM-II), the magnetic unit cells are marked with the dashed line, red and blue arrows indicate the opposite directions of Cr magnetic moments.

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图 6 CrO₂单层的磁化强度M和磁化率$\chi $随温度的变化关系, 其中所用的磁耦合参数和磁各向异性能的计算采用了不同的方法　(a) GGA+U; (b) SCAN

Figure 6. Variation of average moment and susceptibility with temperature, the exchange couplings and anisotropic energy are derived from different calculations: (a) GGA+U; (b) SCAN.

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表 1 CrO₂在FM, AFM-Ⅰ和AFM-Ⅱ磁序的能量, 单个Cr原子的局域磁矩, 交换耦合系数J₁和J₂, 单离子磁各向异性能A和居里温度T_C. FM能量设置为零

Table 1. Energies in the FM, AFM-I, and AFM-II orders, the nearest and next-nearest neighbor exchange couplings J₁ and J₂, the anisotropic energy, the Curie temperature. The FM energy is set to zero.

Method	E_FM/meV	E_AFM-Ⅰ/meV	E_AFM-Ⅱ/meV	Moment/μ_B	J₁/(meV·S^–2)	J₂/(meV·S^–2)	A/(meV·S^–2)	T_C/K
GGA + U	0	120.23	167.96	2.4	–41.99	–9.06	–0.195	461
SCAN	0	109.71	191.43	2.2	–47.86	–3.50	–0.103	422

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map

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Zhang H 2015 ACS Nano 9 9451 Google Scholar
[3]	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
[4]	Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H, Yao W, Xiao D, Jarillo-Herrero P, Xu X 2017 Nature 546 270 Google Scholar
[5]	Gong C, Zhang X 2019 Science 363 eaav4450 Google Scholar
[6]	Balan A P, Radhakrishnan S, Woellner C F, Sinha S K, Deng L, de los Reyes C, Rao B M, Paulose M, Neupane R, Apte A, Kochat V, Vajtai R, Harutyunyan A R, Chu C W, Costin G, Galvao D S, Martí A A, van Aken P A, Varghese O K, Tiwary C S, Iyer A M M R, Ajayan P M 2018 Nat. Nanotechnol. 13 602 Google Scholar
[7]	Balan A P, Radhakrishnan S, Kumar R, Neupane R, Sinha S K, Deng L Z, de los Reyes C A, Apte A, Rao B M, Paulose M, Vajtai R, Chu C W, Costin G, Martí A A, Varghese O K, Singh A K, Tiwary C S, Anantharaman M R, Ajayan P M 2018 Chem. Mater. 30 5923 Google Scholar
[8]	Zhang Y, Chu J W, Yin L, Shifa T A, Cheng Z Z, Cheng R Q, Wang F, Wen Y, Zhan X Y, Wang Z X, He J 2019 Adv. Mater. 31 1900056 Google Scholar
[9]	Wang H D, Lei P H, Mao X Y, Kong X, Ye X Y, Wang P F, Wang Y, Qin X, Meijer J, Zeng H L, Shi F Z, Du J F 2022 Chin. Phys. Lett. 39 047601 Google Scholar
[10]	Feng P J, Zhang X H, Zhang S, Liu D P, Gao M, Ma F J, Yan X W, Xie Z Y 2022 ACS Omega 7 43316 Google Scholar
[11]	Liu D P, Zhang S, Gao M, Yan X W, Xie Z Y 2021 Appl. Phys. Lett. 118 223104 Google Scholar
[12]	Feng P J, Zhang S, Liu D P, Gao M, Ma F J, Yan X W, Xie Z Y 2022 J. Phys. Chem. C 126 10139 Google Scholar
[13]	Liu D P, Feng P J, Gao M, Yan X W 2021 Phys. Rev. B 103 155411 Google Scholar
[14]	Zhang S, Feng P J, Liu D P, Wu H F, Gao M, Xu T S, Xie Z Y, Yan X W 2022 Phys. Rev. B 106 235402 Google Scholar
[15]	Wang Y, Guo Y, Wang Z K, Fu L, Zhang Y, Xu Y J, Yuan S J, Pan H Z, Du Y W, Wang J L, Tang N J 2021 ACS Nano 15 12069 Google Scholar
[16]	Wang Y, Xu W, Fu L, Zhang Y, Wu Y Z, Wu L T, Yang D Y, Peng S Z, Ning J, Zhang C, Cui X, Zhong W, Liu Y, Xiong Q H, Han G Q, Hao Y 2023 ACS Appl. Mater. Interfaces 15 54797 Google Scholar
[17]	Wang Y, Xu W, Yang D Y, Zhang Y, Xu Y J, Cheng Z X, Mi X K, Wu Y Z, Liu Y, Hao Y, Han G Q 2023 ACS Nano 17 24320 Google Scholar
[18]	Zha H M, Li W, Zhang G J, Liu W J, Deng L W, Jiang Q, Ye M, Wu H, Chang H X, Qiao S 2023 Chin. Phys. Lett. 40 087501 Google Scholar
[19]	Huang P, Zhang P, Xu S G, Wang H D, Zhang X W, Zhang H 2020 Nanoscale 12 2309 Google Scholar
[20]	Lin Z C, Peng Y X, Wu B C, Wang C S, Luo Z C, Yang J B 2022 Chin. Phys. B 31 087506 Google Scholar
[21]	Cava R J 2000 J. Am. Ceram. Soc. 83 5 Google Scholar
[22]	Wilson R M 2019 Phys. Today 72 19 Google Scholar
[23]	Chen H H, Yang Y F, Zhang G M, Liu H Q 2023 Nat. Commun. 14 5477 Google Scholar
[24]	Rasmussen F A, Thygesen K S 2015 J. Phys. Chem. C 119 13169 Google Scholar
[25]	Topsakal M, Cahangirov S, Bekaroglu E, Ciraci S 2009 Phys. Rev. B 80 235119 Google Scholar
[26]	Yang J, Jiang Y L, Li L J, Muhire E, Gao M Z 2016 Nanoscale 8 8170 Google Scholar
[27]	Zhang F, Zhu J J, Zhang D L, Schwingenschlögl U, Alshareef H N 2017 Nano Lett. 17 1302 Google Scholar
[28]	de Groot R A, Mueller F M, van Engen P G, Buschow K H J 1983 Phys. Rev. Lett. 50 2024 Google Scholar
[29]	Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, von Molnár S, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488 Google Scholar
[30]	Schwarz K 1986 J. Phys. F: Met. Phys. 16 L211 Google Scholar
[31]	Dedkov Yu S, Rüdiger U, Güntherodt G 2002 Phys. Rev. B 65 064417 Google Scholar
[32]	Ji Y, Strijkers G J, Yang F Y, Chien C L, Byers J M, Anguelouch A, Xiao G, Gupta A 2001 Phys. Rev. Lett. 86 5585 Google Scholar
[33]	Xie W H, Liu B G, Pettifor D G 2003 Phys. Rev. B 68 134407 Google Scholar
[34]	程志梅, 王新强, 王风, 鲁丽娅, 刘高斌, 段壮芬, 聂招秀 2011 60 096301 Google Scholar Cheng Z M, Wang X Q, Wang F, Lu L Y, Liu G B, Duan Z F, Nie Z X 2011 Acta Phys. Sin. 60 096301 Google Scholar
[35]	Kobayashi K I, Kimura T, Sawada H, Terakura K, Tokura Y 1998 Nature 395 677 Google Scholar
[36]	Alijani V, Winterlik J, Fecher G H, Naghavi S S, Felser C 2011 Phys. Rev. B 83 184428 Google Scholar
[37]	许佳玲, 贾利云, 靳晓庆, 郝兴楠, 马丽, 侯登录 2019 68 157501 Google Scholar Xu J L, Jia L Y, Jin X Q, Hao X N, Ma L, Hou D L 2019 Acta Phys. Sin. 68 157501 Google Scholar
[38]	Zhao J T, Zhao K, Wang J J, Yu X Q, Yu J, Wu S X 2012 Acta Phys. Sin. 61 213102 (in Chinses) [赵建涛, 赵昆, 王家佳, 余新泉, 于金, 吴三械 2012 61 213102]Google Scholar Zhao J T, Zhao K, Wang J J, Yu X Q, Yu J, Wu S X 2012 Acta Phys. Sin. 61 213102 (in Chinses)Google Scholar
[39]	Kresse G, Hafner J 1993 Phys. Rev. B 47 558 Google Scholar
[40]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[41]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[42]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[43]	Sun J, Ruzsinszky A, Perdew J P 2015 Phys. Rev. Lett. 115 036402 Google Scholar
[44]	Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Phys. Rev. B 57 1505 Google Scholar
[45]	Togo A, Tanaka I 2015 Scr. Mater. 108 1 Google Scholar
[46]	Martyna G J, Klein M L, Tuckerman M 1992 J. Chem. Phys. 97 2635 Google Scholar
[47]	Born M, Huang K, Lax M 1955 Am. J. Phys. 23 474 Google Scholar
[48]	Wooster W A, Wooster N 1931 Nature 127 782 Google Scholar
[49]	Dufek V, Petrů F, Brožek V 1967 Monatsh. Chem. 98 2424 Google Scholar
[50]	Zhang Q, Xu M K, Shen Z R, Wei Q 2017 J. Mater. Sci. Mater. Electron. 28 12056 Google Scholar
[51]	Zhou S M, Zhu G Y, Wang Y Q, Lou S Y, Hao Y M 2011 Chem. Eng. J. 174 432 Google Scholar
[52]	Bärnighausen H, Brauer G, Schultz N 1965 Z. Anorg. Allg. Chem. 338 250 Google Scholar
[53]	Cococcioni M, de Gironcoli S 2005 Phys. Rev. B 71 035105 Google Scholar
[54]	Henkelman G, Arnaldsson A, Jónsson H 2006 Comput. Mater. Sci. 36 354 Google Scholar
[55]	Graf T, Felser C, Parkin S S P 2011 Prog. Solid. State Ch. 39 1 Google Scholar
[56]	Zhang Y H, Wang B, Guo Y, Li Q, Wang J L 2021 Comput. Mater. Sci. 197 110638 Google Scholar
[57]	Ma F J, Lu Z Y, Xiang T 2008 Phys. Rev. B 78 224517 Google Scholar
[58]	Xu C, Feng J, Xiang H, Bellaiche L 2018 NPJ Comput. Mater. 4 57 Google Scholar
[59]	Šabani D, Bacaksiz C, Milošević M V 2020 Phys. Rev. B 102 014457 Google Scholar
[60]	张杰 2023 博士学位论文 (北京: 中国科学院物理研究所) Zhang J 2023 Ph. D. Dissertation (Beijing: Institute of Physics, Chinese Academy of Sciences

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Vol. 73, Issue 10 - 2024-05-20

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CrO₂ monolayer: a two-dimensional ferromagnet with high Curie temperature and half-metallicity

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Corresponding author: Li Zong-Liang, lizongliang@sdnu.edu.cn

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CrO2 monolayer: a two-dimensional ferromagnet with high Curie temperature and half-metallicity

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Corresponding author: Li Zong-Liang, lizongliang@sdnu.edu.cn

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CrO₂ monolayer: a two-dimensional ferromagnet with high Curie temperature and half-metallicity