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借助第一性原理计算, 对VOBr2单层的结构、磁性以及铁电性进行了系统研究. 计算结果表明低温下VOBr2会产生自发铁电极化, 从高对称顺电相转变为铁电相结构. 与同族姊妹材料VOI2不同的是, V的二聚化现象不仅无法在VOBr2中稳定存在, 还会导致局域磁矩淬灭. 此外, VOBr2易磁化轴在面内a轴方向, 面内a, b轴上近邻磁矩均为反铁磁耦合. VOBr2中的铁电极化主要由V在a轴方向V—O—V链上的铁电位移产生, 大小约为40 μC/cm2. 与铁电同步翻转相比, 通过分步翻转不同链上的铁电极化, 可以有效降低铁电翻转能垒, 从而有望通过低能外场实现部分或个别链上的铁电翻转, 为低能耗高密度铁电存储器件设计提供新的思路和方向.On the basis of first-principles calculations, the structure, magnetism and ferroelectricity of VOBr2 monolayer are studied systematically in the present work. The calculation results indicate that a spontaneous ferroelectric distortion takes place at low temperature, causing the structure of VOBr2 to transform from a centrosymmetric paraelectric phase to a ferroelectric one. In contrast with its sister compound VOI2, the dimerization of V is unstable in VOBr2 and may quench the local magnetic moment on V ions. Additionally, the easy magnetization axis of VOBr2 monolayer is in-plane along the a-axis, and the magnetic coupling between adjacent local moments is antiferromagnetic both along the a-axis and along the b-axis. Moreover, the ferroelectric displacement of V ions occurs in the a-axis, along the V—O—V chains direction, resulting in a polarization of about 40 μC/cm2. Comparing with the ferro-to-paraelectric reversal pathway, the energy barrier can be effectively reduced for ferroelectric switching on partial or individual V—O—V chains. It is reasonable to believe that the dipole moment flipping on specific chain can be achieved through a moderate external field, thereby providing new direction for designing the low-energy-consumption and high-density ferroelectric memory device.
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Keywords:
- first-principles calculation /
- two-dimensional material /
- oxyhalide /
- magnetic and ferroelectric properties
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图 1 Br2单层高对称结构示意图(a)、轨道投影能带图(b)、态密度分布(c)
Fig. 1. (a) Structure diagram, (b) orbital-projected band, and (c) projected DOS of VOBr2 monolayer with high symmetry.
图 2 (a)单层VOBr2高对称相下2 × 2 × 1超胞的声子谱; (b), (c)声子谱虚频对应的两种二聚化畸变模式Dim1和Dim2; (d), (e)声子谱虚频对应的两种铁电畸变模式FE和AFE
Fig. 2. (a) Calculated phonon spectrum of high symmetry VOBr2 2 × 2 × 1 supercell; (b), (c) two dimerization distortion modes Dim1 and Dim2; (d), (e) FE and AFE distortion modes, corresponding to the imaginary frequencies in the phonon spectrum.
图 3 4种畸变结构的声子谱 (a) FE相; (b) AFE相; (c) Dim1相; (d) Dim2相
Fig. 3. Calculated phonon spectrum of the four structural phases: (a) FE; (b) AFE; (c) Dim1; (d) Dim2.
图 4 (a)单层VOBr2 2 × 2 × 1超胞的畸变模式分析; (b) FE1和AFE1畸变结构的声子谱
Fig. 4. (a) Distortion mode analysis of 2 × 2 × 1 super cell of VOBr2 monolayer; (b) calculated phonon spectra of VOBr2 monolayer in FE1 and AFE1 distortion modes.
图 5 (a)含磁优化计算考虑的4种常见磁序: FM表示近邻V离子自旋平行排列, 即铁磁序; aAbF表示近邻V离子自旋沿a轴反平行排列, 沿b轴平行排列; aFbA表示V离子自旋沿a轴平行排列, 沿b轴反平行排列; GAFM表示近邻V离子间自旋均反平行排列; (b) FE相GAFM磁基态下的投影态密度分布
Fig. 5. (a) Four magnetic orders considered in the magnetic ground state calculations. FM denotes the spin parallel arrangement, aAbF denotes the antiferromagnetic (ferromagnetic) coupling between neighbouring V ions along a (b)-axis, aFbA represents the ferromagnetic (antiferromagnetic) coupling along a (b)-axis, and GAFM denotes the antiferromagnetic coupling between neighbouring V ions along both directions. (b) Projected DOS of the GAFM ground state within the FE structural phase.
图 6 (a)单层VOBr2的铁电极化; (b)两种铁电翻转路径下的能垒, 红色表示途径PE的路径, 蓝色对应途径AFE的翻转路径
Fig. 6. (a) Polarization of VOBr2 monolayer. (b) Energy barriers of two ferroelectric flipping paths: FE-PE-FE (red) and FE-AFE-FE (blue).
表 1 含磁优化结果对比汇总表
Table 1. Summary of the main results of structural and magnetic optimization.
a, b/Å Ground state Local moment/μB Gap/eV Energy difference
/(eV·f.u.–1)FE 7.59, 7.15 GAFM 0.96 0.87 0.0 AFE 7.59, 7.16 aFbA 0.98 0.74 5.9 FE1 7.54, 6.83 — 0.00 0.46 71.7 AFE1 7.57, 6.82 — 0.00 0.44 84.8 
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[1] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 P. Natl. Acad. Sci. USA 102 10451
Google Scholar
[2] Tang Q, Zhou Z 2013 Progr. Mat. Sci. 58 1244
Google Scholar
[3] Gupta A, Sakthivel T, Seal S 2015 Progr. Mat. Sci. 73 44
Google Scholar
[4] Duong D L, Yun S J, Lee Y H 2017 ACS Nano 11 11803
Google Scholar
[5] An M, Dong S 2020 APL Mater. 8 110704
Google Scholar
[6] Li P, Cai T Y 2020 J. Phys. Chem. C 124 12705
Google Scholar
[7] Li P, Cai T Y 2020 Phys. Chem. Chem. Phys. 22 549
Google Scholar
[8] Chang K, Liu J W, Lin H C, Wang N, Zhao K, Zhang A M, Jin F, Zhong Y, Hu X P, Duan W H, Zhang Q M, Fu L, Xue Q K, Chen X, Ji S H 2016 Science 353 274
Google Scholar
[9] 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
[10] 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 D 2017 Nature 546 270
Google Scholar
[11] Hill N A 2000 J. Phys. Chem. B 104 6694
Google Scholar
[12] Liu X G, Pyatakov A P, Ren W 2020 Phys. Rev. Lett. 125 247601
Google Scholar
[13] Ju H, Lee Y, Kim K T, Choi I H, Roh C J, Son S, Park P, Kim J H, Jung T S, Kim J H, Kim K H, Park J G, Lee J S 2021 Nano Lett. 21 5126
Google Scholar
[14] Tan H X, Li M L, Liu H T, Liu Z R, Li Y C, Duan W H 2019 Phys. Rev. B 99 195434
Google Scholar
[15] Ding N, Chen J, Dong S, Stroppa A 2020 Phys. Rev. B 102 165129
Google Scholar
[16] Zhang Y, Lin L F, Moreo A, Alvarez G, Dagotto E 2021 Phys. Rev. B 103 L121114
Google Scholar
[17] You H P, Ding N, Chen J, Dong S 2020 Phys. Chem. Chem. Phys. 22 24109
Google Scholar
[18] Kresse G, Hafner J 1993 Phys. Rev. B 47 558
Google Scholar
[19] Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169
Google Scholar
[20] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[21] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[22] Gonze X, Lee C 1997 Phys. Rev. B 55 10355
Google Scholar
[23] Togo A, Tanaka I 2015 Scr. Mater. 108 1
Google Scholar
[24] King-Smith R D, Vanderbilt D 1993 Phys. Rev. B 47 1651
Google Scholar
[25] Resta R 1994 Rev. Mod. Phys. 66 899
Google Scholar
[26] Orobengoa D, Capillas C, Aroyo M I, Perez-Mato J M 2009 J. Appl. Crystallogr. 42 820
Google Scholar
[27] Perez-Mato J M, Orobengoa D, Aroyo M I 2010 Acta Crystallogr. A 66 558
Google Scholar
[28] Goodenough J B 1958 J. Phys. Chem. Solids 6 287
Google Scholar
[29] Kanamori J 1959 J. Phys. Chem. Solids 10 87
Google Scholar
[30] Ogawa S 1960 J. Phys. Soc. Japan 15 1901
Google Scholar
[31] Poineau F, Johnstone E V, Czerwinski K R, Sattelberger A P 2014 Acc. Chem. Res. 47 624
Google Scholar
[32] McGuire M 2017 Crystals 7 121
Google Scholar
[33] Wieder H H 1955 Phys. Rev. 99 1161
Google Scholar
[34] Lin L F, Zhang Y, Moreo A, Dagotto E, Dong S 2019 Phys. Rev. Mater. 3 111401(R
Google Scholar
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