-
半金属铁磁体在费米能级附近具有特殊的能带结构, 电子极化率可高达100%, 在自旋电子学领域备受关注. 但是大部分铁磁半金属材料的居里温度远低于室温, 这大大限制了二维铁磁半金属材料的实际应用. 因此寻找具有高居里温度的半金属铁磁体是一项具有挑战性的工作. 本文基于密度泛函理论框架下的第一性原理方法, 研究了过渡金属氧化物CrO2单层的晶体结构、电子特性、基态磁性和铁磁相变. 形成能计算、声子谱计算和分子动力学模拟表明CrO2具有动力学稳定性和热稳定性, 弹性常数计算表明CrO2具有力学稳定性. 基于GGA + U和SCAN方法的自旋极化计算表明CrO2单层的磁基态是铁磁态. 采用GGA + U方法计算了CrO2的电子态密度和能带结构, CrO2被确认为一种宽带隙的二维铁磁半金属. 运用蒙特卡罗模拟方法求解Heisenberg模型, 得到CrO2单层是一种居里温度超过400 K的二维本征半金属铁磁体. CrO2单层的高居里温度在二维铁磁材料中并不多见, 在半金属材料中更为稀少, 这将使它成为制备自旋电子器件和研究自旋量子效应的理想材料.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 Eg and T2g orbitals because of the crystal field of Cr atom in the center of O tetrahedron, and the spin-polarizations of Eg 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
[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 物理学报 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 物理学报 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 物理学报 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
-
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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
Fig. 4. Band structure of CrO2 monolayer by different calculations, and Fermi energy is zero: (a) GGA + U; (b) SCAN.
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
Fig. 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.
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
Fig. 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.
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TC. 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 EFM/meV EAFM-Ⅰ/meV EAFM-Ⅱ/meV Moment/μB J1/(meV·S–2) J2/(meV·S–2) A/(meV·S–2) TC/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 
下载: 导出CSV
-
[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 物理学报 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 物理学报 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 物理学报 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
下载:
计量
- 文章访问数: 2992
- PDF下载量: 122
- 被引次数: 0
