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Fe3GeTe2是目前发现的少数几种二维铁磁材料之一. 基于密度泛函理论的第一性原理方法, 我们对二维Fe3GeTe2剪裁而成的纳米带NR(n)的结构稳定性和磁电子学特性进行了详细研究. 计算的结合能及分子动力学模拟表明纳米带的结构是非常稳定的. 纳米带呈现较大的磁矩及磁化能, 这说明它们具有较高的磁稳定性. 特别是在费米能级上, 纳米带具有较高的自旋极化率(SPF), 如NR(5)的SPF可达100%. 同时发现SPF随纳米带宽度变化有明显的奇偶振荡效应, 且纳米带的SPF比2维单层的情况有明显优势. 此外, 拉伸效应的计算结果表明, 应变可以灵活地调节纳米带的SPF使其在接近零值和85.6%之间变化, 这意味着可设计一个机械开关来控制低偏压下的自旋输运, 使其可逆地工作在高自旋极化与无自旋极化之间.
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关键词:
- Fe3GeTe2纳米带 /
- 磁电子学特性 /
- 自旋极化 /
- 拉伸效应
Fe3GeTe2 monolayer is one of the currently fabricated 2-dimensional (2D) ferromagnetic materials. Based on the first principle of density functional theory, we here study the structural stability and magneto-electronic properties of nanoribbons NR(n) obtained by cutting 2D Fe3GeTe2. The calculated binding energy and molecular dynamics simulation results identify that nanoribbons are rather stable. The large magnetic moment and magnetized energy prove the extremely high magnetism stability for NR(n). Moreover, with the increase of the width, the magnetic moment of the nanoribbons generally increases, and gradually tends to a stable value. In particular, the nanoribbons possess a high spin polarization efficiency at the Fermi level (SPF). For example, the SPF for NR(5) is up to 100%. With the width variation of the nanoribbons, the SPF has a significant odd-even oscillating effect, that is, the spin-polarization of the odd nanoribbons is higher than that of the adjacent even nanoribbons, especially when the width is in the range of n ≤ 12. This means that the α-spin and β-spin are quite different in the density of states at the Fermi level when the width is odd or even. This may be caused by the difference of the quantum confinement effect for the odd or even nanoribbons, respectively. Meanwhile, when the width of the nanoribbons is wide enough, the odd-even oscillation effect of the spin polarizability is stabilized in a relatively small range, and the nanoribbons finally tend to be 2D Fe3GeTe2 monolayer. The nanoribbons have an obvious advantage on SPF over the 2D Fe3GeTe2 monolayer. In addition, the calculation of the strain effect demonstrates that the strain can flexibly tune the SPF varying from approximately zero to 85.6%, and the SPF reaches a maximum of 85.6% at a stretch of 4%, which is a fairly high value; then reaches a minimum at a stretch of 8%, almost being zero, which means that a mechanical switch can be designed to control the low-bias spin transition, allowing it work between high spin polarization and spin unpolarization.[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva1 I V, Firsov A A 2004 Science 306 666
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Hashmi A, Hong J 2017 J. Phys. Chem. C 66 238501
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图 1 (a) 2D FGT单层原子结构的顶视图和边视图, 阴影部分表示所剪裁的纳米带NR(n); (b)宽度n = 9时的FGT纳米带, 黑色虚线框代表纳米带的一个单胞
Fig. 1. (a) Top and side view of atomic structure for 2D FGT monolayer, the shaded region indicates the cutting nanoribbon NR(n); (b) the FGT nanoribbon with width n = 9, and the black dashed-line box represents the unit cell of NR(9).
图 2 退火模拟前后的FGT纳米带的结构图 (a) NR(4); (b) NR(5); (c) NR(6); (d) NR(8); (e) NR(9)
Fig. 2. The ribbon structures before and after annealing simulation: (a) NR(4); (b) NR(5); (c) NR(7); (d) NR(8); (e) NR(9).
图 3 自旋极化电荷密度 (a) NR(4), (b) NR(5), (c) NR(6), (d) NR(8)和(e) NR(9), 等值面值取为0.01|e|Å–3
Fig. 3. The spin-polarized charge density: (a) NR(4), (b) NR(5), (c) NR(6), (d) NR(8), and (e) NR(9), the isosurface value is set as 0.01|e|Å–3.
图 4 投影能带结构 (a) NR(4), (b) NR(5), (c) NR(6), (d) NR(8)和(e) NR(9); (f)不同宽度NR(n)的磁性原子的平均磁矩, 其中n为FGT纳米带的宽度
Fig. 4. The projected band structure for (a) NR(4), (b) NR(5), (c) NR(6), (d) NR(8), and (e) NR(9), respectively; (f) magnetic moment per magnetic atom for NR(n) versus ribbon widths, where n represents the width of the FGT nanoribbons.
图 5 不同FGT纳米带的总态密度(DOS)、投影态密度(PDOS)以及费米能级上的自旋极化率 (a) NR(4), (b) NR(5), (c) NR(6), (d) NR(8) 和 (e) NR(9); (f) 不同宽度纳米带NR(n)的在费米能级上自旋极化率SPF, 其中n为FGT纳米带的宽度
Fig. 5. The DOS and PDOS for (a) NR(4), (b) NR(5), (c) NR(6), (d) NR(8), and (e) NR(9); (f) the spin polarity efficiency at the Fermi level (SPF) for ribbons with various different widths NR(n), where n represents the width of the FGT nanoribbons.
图 6 应变效应 (a) 对NR(9)施加拉伸应力的模型图, 仅铁磁基态下被考虑; (b)施加不同应变时的态密度(DOS)变化情况; (c)费米能级上的自旋极化率SPF 随应变的变化; (d)磁矩(M)和磁化能(EM)随应变的变化
Fig. 6. Strain effects: (a) The schematic for NR(9) applied by stretching strain, only the FM ground state is taken into account; (b) the DOS versus strains; (c) the spin polarity efficiency at the Fermi level SPF versus strains; (d) the magnetic moment (M) and magnetize energy (EM) versus strains.
表 1 FGT纳米带的结合Eb(单位: eV/atom), 磁化能EM (单位: meV/atom)和费米能级上的自旋极化率SPF(%), MM 和HM分别表示磁金属和半金属
Table 1. The binding energy Eb (in eV/atom), magnetic energy EM (in meV /atom), and spin polarized efficiency SPF(%) for FGT nanoribbons, MM and HM represent the magnetic metal and half-metal, respectively.
Structure NR(4) NR(5) NR(6) NR(8) NR(9) Eb –4.472 –4.545 –4.590 –4.648 –4.665 EM 132.958 135.814 186.930 130.815 129.212 SPF 29.570 100 55.918 11.573 66.823 Magnetic phase MM HM MM MM MM 
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva1 I V, Firsov A A 2004 Science 306 666
Google Scholar
[2] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451
Google Scholar
[3] Zhang M, Wang X X, Cao W Q, Yuan J, Cao M S 2019 Adv. Opt. Mater. 7 1900689
Google Scholar
[4] Zeng Y, Wu D, Cao X, Zhou W, Tang L, Chen K 2019 Adv. Funct. Mater. 531 1800390
Google Scholar
[5] Cao M S, Wang X X, Zhang M, Shu J C, Cao W Q, Yang H J, Fang X Y, Yuan J 2019 Adv. Funct. Mater. 29 1807398
Google Scholar
[6] Cahangirov S, Topsakal M, Aktürk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804
Google Scholar
[7] Tang P, Chen P, Cao W, Huang H, Cahangirov S, Xian L, Rubio A 2014 Phys. Rev. B 90 121408
Google Scholar
[8] Latzke D W, Zhang W, Suslu A, Chang T R, Lin H, Jeng H T, Lanzara A 2015 Phys. Rev. B 91 235202
Google Scholar
[9] Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802
Google Scholar
[10] Kuang W, Hu R, Fan Z, Zhang Z 2019 Nanotechnology 30 145201
Google Scholar
[11] Blase X, Rubio A, Louie S G, Cohen M L 1995 Phys. Rev. B 51 6868
[12] Zhang S, Yan Z, Li Y, Chen Z, Zeng H 2015 Angew. Chem. Int. Ed. 54 3112
Google Scholar
[13] Zhang S, Xie M, Li F, Yan Z, Li Y, Kan E, Zeng H 2016 Angew. Chem. Int. Ed. 55 1666
Google Scholar
[14] Efetov D K, Wang L, Handschin C, Efetov K B, Shuang J, Cava R, Kim P 2016 Nature Phys. 12 328
Google Scholar
[15] Yokoya T, Kiss T, Chainani A, Shin S, Nohara M, Takagi H 2001 Science 294 2518
Google Scholar
[16] Hsu F C, Luo J Y, Yeh K W, Chen T K, Huang T W, Wu P M, Wu M K 2008 Proc. Natl. Acad. Sci. USA 105 14262
Google Scholar
[17] Peng R, Xu H C, Tan S Y, Cao H Y, Xia M, Shen X P, Xie B P 2014 Nat. Commun. 5 5044
Google Scholar
[18] Wang Q Y, Li Z, Zhang W H, Zhang Z C, Zhang J S, Ding H, Ou Y B, Deng B, Chang K 2012 Chin. Phys. Lett. 29 037402
Google Scholar
[19] Deiseroth H J, Aleksandrov K, Reiner C, Kienle L, Kremer R K 2006 Eur. J. Inorg. Chem. 2006 1561
Google Scholar
[20] Liu S, Yuan X, Zou Y, Sheng Y, Huang C, Zhang E, Zou J 2017 npj 2D Mater. Appl. 1 30
Google Scholar
[21] Zhuang H L, Xie Y, Kent P R C, Ganesh P, 2015 Phys. Rev. B 92 035407
Google Scholar
[22] Siberchicot B, Jobic S, Carteaux V, Gressier P, Ouvrard G 1996 J. Phys. Chem. 100 5863
Google Scholar
[23] Gong C 2017 Nature 546 265
Google Scholar
[24] Deiseroth H J, Aleksandrov K, Reiner C, Kienle L, Kremer R K 2006 Chem. Inform. 37 1561
[25] Zhuang H L, Kent P R C, Hennig R G 2016 Phys. Rev. B 93 134407
Google Scholar
[26] Deng Y, Yu Y, Song Y, Zhang J, Wang N Z, Sun Z, Wang J 2018 Nature 563 94
Google Scholar
[27] Chen B, Yang J H, Wang H D, Imai M, Ohta H, Michiola C, Fang M 2013 J. Phys. Soc. Jpn. 82 124711
Google Scholar
[28] Fei Z, Huang B, Malinowski P, Wang W, Song T, Sanchez J, Wu W 2018 Nature Mater. 17 778
Google Scholar
[29] Wang Y, Xian C, Wang J, Liu B, Ling L, Zhang L, Xiong Y 2017 Phys. Rev. B 96 134428
Google Scholar
[30] Zhang Y, Lu H, Zhu X, Tan S, Feng W, Liu Q, Xie D 2018 Sci. Adv. 4 6791
Google Scholar
[31] Gan Y, Sun L, Banhart F 2008 Small 4 587
Google Scholar
[32] Son Y W, Cohen M L, Louie S G 2006 Phys Rev. Lett 97 216803
Google Scholar
[33] Botello-Méndez A R, López-Urías F, Terrones M, Terrones H 2008 Nano Lett. 8 1562
Google Scholar
[34] Zhang R Y, Zheng J M, Jiang Z Y 2018 Chin. Phys. Lett. 35 017302
Google Scholar
[35] Han X, Morgan Stewart H, Shevlin S A, Catlow C R A Guo Z X 2014 Nano Lett. 14 4607
Google Scholar
[36] Brandbyge M, Mozos J L, Ordejón P, Taylor J, Stokbro K 2002 Phys. Rev. B 65 165401
Google Scholar
[37] Zhu Z, Zhang Z H, Wang D, Deng X Q, Fan Z Q, Tang G P 2015 J. Mater. Chem. C 3 9657
Google Scholar
[38] Wu D, Cao X, Chen S, Tang L, Feng Y, Chen K, Zhou W 2019 J. Mater. Chem. A 7 19037
Google Scholar
[39] Zhang H L, Sun L, Han J N 2017 Acta Phys. Sin. 66 246101
[40] Liu J, Hu R, Fan Z Q, Zhang Z H 2017 66 246101
Google Scholar
Liu J, Hu R, Fan Z Q, Zhang Z H 2017 Acta Phys. Sin. 66 246101
Google Scholar
[41] Hashmi A, Hong J 2017 66 238501
Google Scholar
Hashmi A, Hong J 2017 J. Phys. Chem. C 66 238501
Google Scholar
[42] Hu R, Li Y H, Zhang Z H, Fan Z Q, Sun L 2019 J. Mater. Chem. C 7 7745
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