-
铁电体中极化拓扑畴(如涡旋畴)有望带来一系列新颖物理现象、新性能和新应用前景(如存储器件应用), 从而引起了广泛兴趣. 尤其是近年来在铁电纳米结构中发现了一系列有趣的新奇极化拓扑畴态, 例如涡旋、中心畴、斯格明子、麦韧(Meron, 也有称半子)等, 引发了新一轮探索热潮. 这些发现为进一步探索其中蕴含的丰富多彩的物理现象创造了条件, 也为调控和设计高性能材料和器件提供了新的基元和序构, 从而形成拓扑电子学的概念. 过去十年, 这一领域经历了快速发展, 成长为铁电物理领域的前沿热点. 本文将回顾近年来在铁电纳米结构中奇异极化拓扑畴的研究新进展, 并简要讨论了该领域所存在的问题和潜在发展方向.Exotic ferroelectric topological states (such as vortex state) have received intensive attention in the past decade, creating a new area for exploring the emerging physical phenomena and functionalities, as well as new applications (such as memory). In recent years, a series of discoveries in novel topological states, such as vortex, central domain, skyrmion and meron states, has inspired an upsurge of research interests. Moreover, the effort to manipulate such a topological domain structure hints the possibilities for the local, deterministic control of order parameters so that the static interface conductivity can be successfully controlled at topologically protected domain walls. These encouraging discoveries create a new avenue to the fertile emerging physic phenomena, and offer new possibilities for developing potential high-performance materials and new nano-electronic devices based on these exotic states. In the past decade, this field has developed rapidly and become a hot research topic in ferroelectrics. In this paper, we review the recent progress in the field of exotic topological state in nanoferroelectrics, and discuss some existing problems and potential directions.
-
Keywords:
- topological defects /
- polarized topological states /
- ferroelectric domains /
- nanoferroelectrics
[1] Rabe K M, Ahn C H, Triscone J M 2007 Physics of Ferroelectrics, a Modern Perspective (Berlin: Springer) pp1−390
[2] Scott J F 2000 Ferroelectric Memories (Berlin: Springer) pp1−223
[3] Scott J F 1989 Science 246 1400
Google Scholar
[4] Scott J F 2007 Science 315 954
Google Scholar
[5] Dawber M, Rabe K M, Scott J F 2005 Rev. Mod. Phys. 77 1083
Google Scholar
[6] Gruverman A, Kholkin A 2006 Rep. Prog. Phys. 69 2443
Google Scholar
[7] Han H, Kim Y, Alexe M, Hesse D, Lee W 2011 Adv. Mater. 23 4599
Google Scholar
[8] Varghese J, Whatmore R W, Holmes J D 2013 J. Mater. Chem. C 1 2618
Google Scholar
[9] Bibes M 2012 Nat. Mater. 11 354
Google Scholar
[10] Gregg J M 2009 Phys. Status Solidi A 206 577
Google Scholar
[11] Mermin N D 1979 Rev. Mod. Phys. 51 591
Google Scholar
[12] Seidel J, Martin L W, He Q, et al. 2009 Nat. Mater. 8 229
Google Scholar
[13] Catalan G, Seidel J, Ramesh R, Scott J F 2012 Rev. Mod. Phys. 84 119
Google Scholar
[14] Seidel J, Fu D, Yang S Y, Alarcon-Llado E, Wu J, Ramesh R, Ager J W 2011 Phys. Rev. Lett. 107 126805
Google Scholar
[15] Bednyakov P S, Sturman B I, Sluka T, Tagantsev A K, Yudin P V 2018 NPJ Comput. Mater. 4 65
Google Scholar
[16] Jiang A Q, Zhang Y 2019 NPG ASIA Mater. 11 2
Google Scholar
[17] Huyan H X, Li L Z, Addiego C, Gao W P, Pan X Q 2019 Natl. Sci. Rev. 6 669
Google Scholar
[18] Kornev I, Fu H, Bellaiche L 2004 Phys. Rev. Lett. 93 196104
Google Scholar
[19] Tang Y L, Zhu Y L, Ma X L, Borisevich A Y, Morozovska A N, Eliseev E A, Wang W Y, Xu Y B, Zhang Z D, Pennycook S J 2015 Science 348 547
Google Scholar
[20] Yadav A K, Nelson C T, Hsu S L, et al. 2016 Nature 530 198
Google Scholar
[21] Ma J, Ma J, Zhang Q, Peng R, Wang J, Liu C, Wang M, Li N, Chen M, Cheng X, Gao P, Gu L, Chen L Q, Yu P, Zhang J, Nan C W 2018 Nat. Nanotechnol. 13 947
Google Scholar
[22] Kim K E, Jeong S, Chu K, Lee J H, Kim G Y, Xue F, Koo T Y, Chen L Q, Choi S Y, Ramesh R, Yang C H 2018 Nat. Commun. 9 403
Google Scholar
[23] Han M J, Wang Y J, Tang Y L, Zhu Y L, Ma J Y, Geng W R, Zou M J, Feng Y P, Zhang N B, Ma X L 2019 J. Phys. Chem. C 123 2557
Google Scholar
[24] Li Z, Wang Y, Tian G, Li P, Zhao L, Zhang F, Yao J, Fan H, Song X, Chen D, Fan Z, Qin M, Zeng M, Zhang Z, Lu X, Hu S, Lei C, Zhu Q, Li J, Gao X, Liu J M 2017 Sci. Adv. 3 e1700919
Google Scholar
[25] Das S, Tang Y L, Hong Z, et al. 2019 Nature 568 368
Google Scholar
[26] Wang Y J, Feng Y P, Zhu Y L, Tang Y L, Yang L X, Zou M J, Geng W R, Han M J, Guo X W, Wu B, Ma X L 2020 Nat. Mater. 19 881
Google Scholar
[27] Nelson C T, Winchester B, Zhang Y, Kim S J, Melville A, Adamo C, Folkman C M, Baek S H, Eom C B, Schlom D G, Chen L Q, Pan X 2011 Nano Lett. 11 828
Google Scholar
[28] Jia C L, Urban K W, Alexe M, Hesse D, Vrejoiu I 2011 Science 331 1420
Google Scholar
[29] Rodriguez B J, Gao X S, Liu L F, Lee W, Naumov, Ⅱ, Bratkovsky A M, Hesse D, Alexe M 2009 Nano Lett. 9 1127
Google Scholar
[30] Schilling A, Byrne D, Catalan G, Webber K G, Genenko Y A, Wu G S, Scott J F, Gregg J M 2009 Nano Lett. 9 3359
Google Scholar
[31] McQuaid R G, McGilly L J, Sharma P, Gruverman A, Gregg J M 2011 Nat. Commun. 2 404
Google Scholar
[32] McGilly L J, Gregg J M 2011 Nano Lett. 11 4490
Google Scholar
[33] Balke N, Winchester B, Ren W, et al. 2011 Nat. Phys. 8 81
Google Scholar
[34] Lin S Z, Wang X, Kamiya Y, Chern G W, Fan F, Fan D, Casas B, Liu Y, Kiryukhin V, Zurek W H, Batista C D, Cheong S W 2014 Nat. Phys. 10 970
Google Scholar
[35] Pang H, Zhang F, Zeng M, Gao X, Qin M, Lu X, Gao J, Dai J, Li Q 2016 NPJ Quantum Mater. 1 16015
Google Scholar
[36] Du K, Gao B, Wang Y, Xu X, Kim J, Hu R, Huang F T, Cheong S W 2018 NPJ Quantum Mater. 3 33
Google Scholar
[37] Zhang H Y, Song X J, Chen X G, Zhang Z X, You Y M, Tang Y Y, Xiong R G 2020 J. Am. Chem. Soc. 142 4925
Google Scholar
[38] Yadav A K, Nguyen K X, Hong Z, et al. 2019 Nature 565 468
Google Scholar
[39] Tian G, Yang W D, Chen D Y, Fan Z, Hou Z P, Marin A, Gao X S 2019 Natl. Sci. Rev. 6 626
Google Scholar
[40] Seidel J, Vasudevan R K, Valanoor N 2016 Adv. Electron. Mater. 2 1500292
Google Scholar
[41] Landau L, Lifshitz E 1935 Phys. Z. Sowjetunion 8 179
[42] Naumov I I, Bellaiche L, Fu H 2004 Nature 432 737
Google Scholar
[43] Peters J J P, Apachitei G, Beanland R, Alexe M, Sanchez A M 2016 Nat. Commun. 7 13484
Google Scholar
[44] Hong Z, Damodaran A R, Xue F, Hsu S L, Britson J, Yadav A K, Nelson C T, Wang J J, Scott J F, Martin L W, Ramesh R, Chen L Q 2017 Nano Lett. 17 2246
Google Scholar
[45] Tian G, Chen D, Fan H, Li P, Fan Z, Qin M, Zeng M, Dai J, Gao X, Liu J M 2017 ACS Appl. Mater. Interfaces 9 37219
Google Scholar
[46] Li L, Cheng X, Jokisaari J R, Gao P, Britson J, Adamo C, Heikes C, Schlom D G, Chen L Q, Pan X 2018 Phys. Rev. Lett. 120 137602
Google Scholar
[47] Zhang Q, Xie L, Liu G, Prokhorenko S, Nahas Y, Pan X, Bellaiche L, Gruverman A, Valanoor N 2017 Adv. Mater. 29 1702375
Google Scholar
[48] Zhang Q, Prokhorenko S, Nahas Y, Xie L, Bellaiche L, Gruverman A, Valanoor N 2019 Adv. Funct. Mater. 29 1808573
Google Scholar
[49] Balke N, Choudhury S, Jesse S, Huijben M, Chu Y H, Baddorf A P, Chen L Q, Ramesh R, Kalinin S V 2009 Nat. Nanotechnol. 4 868
Google Scholar
[50] Vasudevan R K, Chen Y C, Tai H H, Balke N, Wu P, Bhattacharya S, Chen L Q, Chu Y H, Lin I N, Kalinin S V, Nagarajan V 2011 ACS Nano 5 879
Google Scholar
[51] Li Y, Jin Y M, Lu X M, Yang J C, Chu Y H, Huang F Z, Zhu J S, Cheong S W 2017 NPJ Quantum Mater. 2 43
Google Scholar
[52] Damodaran A R, Clarkson J D, Hong Z, Liu H, Yadav A K, Nelson C T, Hsu S L, McCarter M R, Park K D, Kravtsov V, Farhan A, Dong Y, Cai Z, Zhou H, Aguado-Puente P, García-Fernández P, Íñiguez J, Junquera J, Scholl A, Raschke M B, Chen L Q, Fong D D, Ramesh R and Martin L W 2017 Nat. Mater. 16 1003
Google Scholar
[53] Kim K E, Kim Y J, Zhang Y, Xue F, Kim G Y, Song K, Choi S Y, Liu J M, Chen L Q, Yang C H 2018 Phys. Rev. Mater. 2 084412
Google Scholar
[54] Stoica V A, Laanait N, Dai C, Hong Z, Yuan Y, Zhang Z, Lei S, McCarter M R, Yadav A, Damodaran A R, Das S, Stone G A, Karapetrova J, Walko D A, Zhang X, Martin L W, Ramesh R, Chen L Q, Wen H, Gopalan V, Freeland J W 2019 Nat. Mater. 18 377
Google Scholar
[55] Chen P, Zhong X, Zorn J A, Li M, Sun Y, Abid A Y, Ren C, Li Y, Li X, Ma X, Wang J, Liu K, Xu Z, Tan C, Chen L, Gao P, Bai X 2020 Nat. Commun. 11 1840
Google Scholar
[56] Zheng Y, Chen W J 2017 Rep. Prog. Phys. 80 086501
Google Scholar
[57] Prosandeev S, Ponomareva I, Kornev I, Naumov I, Bellaiche L 2006 Phys. Rev. Lett. 96 237601
Google Scholar
[58] Lich L V, Shimada T, Wang J, Dinh V H, Bui T Q, Kitamura T 2017 Phys. Rev. B 96 134119
Google Scholar
[59] Crassous A, Sluka T, Tagantsev A K, Setter N 2015 Nat. Nanotechol. 20 614
Google Scholar
[60] He Q, Yeh C H, Yang J C, Singh-Bhalla G, Liang C W, Chiu P W, Catalan G, Martin L W, Chu Y H, Scott J F, Ramesh R 2012 Phys. Rev. Lett. 108 067203
Google Scholar
[61] Sanchez-Santolino G, Tornos J, Hernandez-Martin D, Beltran J I, Munuera C, Cabero M, Perez-Munoz A, Ricote J, Mompean F, Garcia-Hernandez M, Sefrioui Z, Leon C, Pennycook S J, Munoz M C, Varela M, Santamaria J 2017 Nat. Nanotechnol. 12 655
Google Scholar
[62] Tian G, Yang W D, Song X, Zheng D F, Zhang L Y, Chen C, Li P L, Fan H, Yao J X, Chen D Y, Fan Z, Hou Z P, Zhang Z, Wu S J, Zeng M, Gao X S, Liu J M 2019 Adv. Funct. Mater. 29 1807276
Google Scholar
[63] Yang W D, Tian G, Zhang Y, Xue F, Zheng D F, Zhang L Y, Wang Y D, Chen C, Fan Z, Hou Z P, Chen D Y, Gao J W, Zeng M, Qin M H, Chen L Q, Gao X S, Liu J M 2020 https://arxiv.org/abs/2006.02011
-
图 1 铁电材料中的极化拓扑结构示意图 (a) 涡旋畴; (b) 反涡旋畴; (c) 通量闭合畴; (d) 六重对称结构的涡旋畴; (e) 中心发散型拓扑畴; (f) 中心汇聚型拓扑畴; (g) 斯格明子; (h) 半子或麦韧(Meron)
Fig. 1. Polar topological states in ferroelectric materials: (a) Vortex; (b) anti-vortex; (c) flux-closure; (d) six-fold vortex; (e) center-divergent; (f) convergent states; (g) skyrmion; (h) Meron.
图 2 (SrTiO3)n/(PbTiO3)n多层膜和超晶格中观测到的涡旋畴结构 (a) 左边为多层膜中利用透射电镜数据计算的应力分布图, 右边为基于透射电子显微图像计算出的极化分布局部放大图[19]; (b) 左边为更薄的超晶格中透射电子显微镜的暗场像, 右边为基于透射电子显微图像计算出的单个涡旋极化分布放大图[20]; (c) (SrTiO3)n/(PbTiO3)n 超晶格结构中不同拓扑畴结构变化与原子层数n关系的相图[44]
Fig. 2. Vortex domain states in (SrTiO3)n/(PbTiO3)n multilayers and superlattices: (a) The left panel presents the geometric phase analysis (GPA) image, the right panel is a local polarization distribution map for a single closure domain[19]; (b) the left panel is a cross-section dark-field TEM image of (SrTiO3)n/(PbTiO3)n superlattices, and the right panel is the local magnification of polarization distribution of a single vortex structure[20]; (c) a calculated phase diagram for (SrTiO3)n/(PbTiO3)n illustrating the length scales within which different topological states can be stabilized[44].
图 3 BiFeO3纳米岛中的中心型拓扑畴结构 (a) 在SrTiO3衬底上的BiFeO3纳米岛阵列中四种典型中心型拓扑畴结构的矢量PFM图像[24], 其中A图为中心汇聚型拓扑畴, B图为中心发散型拓扑畴, C图为双中心畴, D图为反双中心畴, E图为相场模拟获得的两种中心畴的极化分布图; (b) 在Nb-SrTiO3衬底上的BiFeO3纳米点中的中心型拓扑畴[23], 其中A图为在单个BiFeO3的面内TEM像, B图为对应区域的原子级分辨率的HAADF-STEM图像, C图为基于TEM图像计算出的极化分布局部放大图, 对应于B图中白色方框区域, D图为中心型拓扑畴的极化矢量分布; E图为BiFeO3纳米点中的中心型拓扑畴结构分布示意图
Fig. 3. Topological center-domain structures in BiFeO3 nanoislands: (a) Four types of center-domain states in BiFeO3 nanodots on SrTiO3 substrate observed by vector PFM analysis[24], where panel A illustrates the center-convergent, panel B illustrates the center-divergent, panel C illustrates the double-center domain with convergent, panel D illustrates the divergent center states, and panel E illustrates the cylinder model for phase-field simulation and two type of polar vector contour maps derived from the simulation; (b) topological center-domain states in BiFeO3 nanodots on Nb-SrTiO3 substrate[23], where panel A and B illustrate the plan-view TEM image for a single nanodot and atomically resolved HAADF-STEM images corresponding to the red square area in panel A, panel C is local magnified view of polarization distribution calculated by TEM corresponding to the white square area in panel B, panel D is the polarization vector distributions of the nanoisland, panel E is the schematic of domain configuration in these BFO nanoislands based on the analysis of both PFM and TEM characterization.
图 4 铁电斯格明子和麦韧拓扑态 (a) SrTiO3衬底上的(SrTiO3)n/(PbTiO3)n超晶格中的极化斯格明子阵列[25], 其中上图为暗场下的截面TEM图像, 中图为暗场下的面内STEM图像, 下图为计算得出的极化斯格明子的结构图像; (b) SmScO3衬底上的PbTiO3薄膜中的麦韧态[26], 其中上图为截面HAADF-STEM图像, 中图为计算出的对应区域应力分布图, 下图为计算得出的极化麦韧的结构
Fig. 4. The polar skymion bubble and polar meron states: (a) Polar skyrmion bubbles in a (SrTiO3)n/(PbTiO3)n superlattice on SrTiO3 substrate[25], where the upper panel is a cross-section dark-field TEM image, the middle panel is a planar-view dark-field STEM image, and the bottom panel is chematic skyrmion bubble configuration from calculations; (b) polar merons in a untrathin PbTiO3 film on SmScO3 substrate[26], where the upper panel is the cross-section HAADF-STEM image, the middle panel is the corresponding geometric phase analysis (GPA) image, and the bottom panel is a meron configuration from calculations.
图 5 外场调控极化拓扑畴 (a) 通过导电针尖施加扫描偏压在BFO薄膜上写出通量闭合畴结构; 沿直线排列的几个通量闭合涡旋畴结构(上), 通过极化翻转获得的几个通量闭合涡旋畴结构的面内PFM图像(下)[33]; (b) 通过导电针尖施加扫描偏压在BFO薄膜上写出的涡旋畴结构的面内PFM图像[49]; (c) 通过导电针尖施加脉冲电压在BFO薄膜上写出的中心型结构的面内PFM图像[50]; (d) 通过导电针尖施加电压调控BFO纳米点中的中心型拓扑畴的可逆翻转[24]; (e) 在(SrTiO3)n/(PbTiO3)n超晶格中利用亚皮秒激光诱导a1/a2畴和极化涡旋畴混合结构转化为单一的三维拓扑畴超晶相(3D supercrysal phase), 并且可通过退火实现可逆转换[54]; (f) 在(SrTiO3)n/(PbTiO3)n超晶格中利用机械应力诱导涡旋畴消失和恢复; 在机械应力作用下涡漩态阵列的消失和恢复的演化TEM图像(上), 根据HRTEM图像计算得到的快速反傅里叶变换图像(下)[55]
Fig. 5. External field control of polar topological domains: (a) Creation of closure in-plane domains in BFO film by using scan bias. Domain configuration for several closure domain states arranged along a line (upper panel), in-plane PFM image after switching several closure domains (bottom panel)[33]; (b) in-plane PFM image of a vortex domain structure which was created by using scan bias[49]; (c) in-plane PFM image of a created center-type domain structure[50]; (d) PFM images showing the electric switching of BiFeO3 center domains by scanning electric bias[24]; (e) phase transition from a mixed phase of in-plane a1/a2 domains and polar vortex to a single 3D supercrystal phase triggered by sub-picosecond optical pulses in a (SrTiO3)n/(PbTiO3)n superlattice[54]; (f) Mechanical manipulation of vortices in a (SrTiO3)n/(PbTiO3)n superlattice. A chronological high resolution TEM image series acquired under mechanical loads (upper panel) and the corresponding inverse fast Fourier transform maps (bottom panel)[55].
图 6 拓扑畴的畴壁电流与涡心导电增强 (a) LaAlO3衬底上BFO纳米岛中心拓扑畴壁导电模式示意图(左), 中心收敛型(右前)和中心发散型(右后)畴壁的CAFM成像图[21]; (b)外电场下畴壁电流切换耐久性测试(左), 具有畴壁电流读取的拓扑畴存储器交叉结构器件原型示意图(右)[21]; (c) 涡旋畴的PFM成像图(左)及对应的CAFM成像图(右), 显示出明显的涡心导电增强效应[33]
Fig. 6. Enhanced electric conductivity at domain walls and vortex cores: (a) CAFM images of quadrant center domains in an array of square-shape BiFeO3 nanoislands on LaAlO3 substrate (left panel), different conductive domain wall states for respective convergent (right front panel) and divergent domains (right rear panel) [21]; (b) endurance performance of resistive switching in domain wall conduction (left panel), and a crossbar device architecture of conceptual memory prototype based on domain wall current (right panel)[21]; (c) the PFM image of vortex domains (left panel) and corresponding CAFM image of vortex core (right panel), shows enhanced electric conductivity[33].
-
[1] Rabe K M, Ahn C H, Triscone J M 2007 Physics of Ferroelectrics, a Modern Perspective (Berlin: Springer) pp1−390
[2] Scott J F 2000 Ferroelectric Memories (Berlin: Springer) pp1−223
[3] Scott J F 1989 Science 246 1400
Google Scholar
[4] Scott J F 2007 Science 315 954
Google Scholar
[5] Dawber M, Rabe K M, Scott J F 2005 Rev. Mod. Phys. 77 1083
Google Scholar
[6] Gruverman A, Kholkin A 2006 Rep. Prog. Phys. 69 2443
Google Scholar
[7] Han H, Kim Y, Alexe M, Hesse D, Lee W 2011 Adv. Mater. 23 4599
Google Scholar
[8] Varghese J, Whatmore R W, Holmes J D 2013 J. Mater. Chem. C 1 2618
Google Scholar
[9] Bibes M 2012 Nat. Mater. 11 354
Google Scholar
[10] Gregg J M 2009 Phys. Status Solidi A 206 577
Google Scholar
[11] Mermin N D 1979 Rev. Mod. Phys. 51 591
Google Scholar
[12] Seidel J, Martin L W, He Q, et al. 2009 Nat. Mater. 8 229
Google Scholar
[13] Catalan G, Seidel J, Ramesh R, Scott J F 2012 Rev. Mod. Phys. 84 119
Google Scholar
[14] Seidel J, Fu D, Yang S Y, Alarcon-Llado E, Wu J, Ramesh R, Ager J W 2011 Phys. Rev. Lett. 107 126805
Google Scholar
[15] Bednyakov P S, Sturman B I, Sluka T, Tagantsev A K, Yudin P V 2018 NPJ Comput. Mater. 4 65
Google Scholar
[16] Jiang A Q, Zhang Y 2019 NPG ASIA Mater. 11 2
Google Scholar
[17] Huyan H X, Li L Z, Addiego C, Gao W P, Pan X Q 2019 Natl. Sci. Rev. 6 669
Google Scholar
[18] Kornev I, Fu H, Bellaiche L 2004 Phys. Rev. Lett. 93 196104
Google Scholar
[19] Tang Y L, Zhu Y L, Ma X L, Borisevich A Y, Morozovska A N, Eliseev E A, Wang W Y, Xu Y B, Zhang Z D, Pennycook S J 2015 Science 348 547
Google Scholar
[20] Yadav A K, Nelson C T, Hsu S L, et al. 2016 Nature 530 198
Google Scholar
[21] Ma J, Ma J, Zhang Q, Peng R, Wang J, Liu C, Wang M, Li N, Chen M, Cheng X, Gao P, Gu L, Chen L Q, Yu P, Zhang J, Nan C W 2018 Nat. Nanotechnol. 13 947
Google Scholar
[22] Kim K E, Jeong S, Chu K, Lee J H, Kim G Y, Xue F, Koo T Y, Chen L Q, Choi S Y, Ramesh R, Yang C H 2018 Nat. Commun. 9 403
Google Scholar
[23] Han M J, Wang Y J, Tang Y L, Zhu Y L, Ma J Y, Geng W R, Zou M J, Feng Y P, Zhang N B, Ma X L 2019 J. Phys. Chem. C 123 2557
Google Scholar
[24] Li Z, Wang Y, Tian G, Li P, Zhao L, Zhang F, Yao J, Fan H, Song X, Chen D, Fan Z, Qin M, Zeng M, Zhang Z, Lu X, Hu S, Lei C, Zhu Q, Li J, Gao X, Liu J M 2017 Sci. Adv. 3 e1700919
Google Scholar
[25] Das S, Tang Y L, Hong Z, et al. 2019 Nature 568 368
Google Scholar
[26] Wang Y J, Feng Y P, Zhu Y L, Tang Y L, Yang L X, Zou M J, Geng W R, Han M J, Guo X W, Wu B, Ma X L 2020 Nat. Mater. 19 881
Google Scholar
[27] Nelson C T, Winchester B, Zhang Y, Kim S J, Melville A, Adamo C, Folkman C M, Baek S H, Eom C B, Schlom D G, Chen L Q, Pan X 2011 Nano Lett. 11 828
Google Scholar
[28] Jia C L, Urban K W, Alexe M, Hesse D, Vrejoiu I 2011 Science 331 1420
Google Scholar
[29] Rodriguez B J, Gao X S, Liu L F, Lee W, Naumov, Ⅱ, Bratkovsky A M, Hesse D, Alexe M 2009 Nano Lett. 9 1127
Google Scholar
[30] Schilling A, Byrne D, Catalan G, Webber K G, Genenko Y A, Wu G S, Scott J F, Gregg J M 2009 Nano Lett. 9 3359
Google Scholar
[31] McQuaid R G, McGilly L J, Sharma P, Gruverman A, Gregg J M 2011 Nat. Commun. 2 404
Google Scholar
[32] McGilly L J, Gregg J M 2011 Nano Lett. 11 4490
Google Scholar
[33] Balke N, Winchester B, Ren W, et al. 2011 Nat. Phys. 8 81
Google Scholar
[34] Lin S Z, Wang X, Kamiya Y, Chern G W, Fan F, Fan D, Casas B, Liu Y, Kiryukhin V, Zurek W H, Batista C D, Cheong S W 2014 Nat. Phys. 10 970
Google Scholar
[35] Pang H, Zhang F, Zeng M, Gao X, Qin M, Lu X, Gao J, Dai J, Li Q 2016 NPJ Quantum Mater. 1 16015
Google Scholar
[36] Du K, Gao B, Wang Y, Xu X, Kim J, Hu R, Huang F T, Cheong S W 2018 NPJ Quantum Mater. 3 33
Google Scholar
[37] Zhang H Y, Song X J, Chen X G, Zhang Z X, You Y M, Tang Y Y, Xiong R G 2020 J. Am. Chem. Soc. 142 4925
Google Scholar
[38] Yadav A K, Nguyen K X, Hong Z, et al. 2019 Nature 565 468
Google Scholar
[39] Tian G, Yang W D, Chen D Y, Fan Z, Hou Z P, Marin A, Gao X S 2019 Natl. Sci. Rev. 6 626
Google Scholar
[40] Seidel J, Vasudevan R K, Valanoor N 2016 Adv. Electron. Mater. 2 1500292
Google Scholar
[41] Landau L, Lifshitz E 1935 Phys. Z. Sowjetunion 8 179
[42] Naumov I I, Bellaiche L, Fu H 2004 Nature 432 737
Google Scholar
[43] Peters J J P, Apachitei G, Beanland R, Alexe M, Sanchez A M 2016 Nat. Commun. 7 13484
Google Scholar
[44] Hong Z, Damodaran A R, Xue F, Hsu S L, Britson J, Yadav A K, Nelson C T, Wang J J, Scott J F, Martin L W, Ramesh R, Chen L Q 2017 Nano Lett. 17 2246
Google Scholar
[45] Tian G, Chen D, Fan H, Li P, Fan Z, Qin M, Zeng M, Dai J, Gao X, Liu J M 2017 ACS Appl. Mater. Interfaces 9 37219
Google Scholar
[46] Li L, Cheng X, Jokisaari J R, Gao P, Britson J, Adamo C, Heikes C, Schlom D G, Chen L Q, Pan X 2018 Phys. Rev. Lett. 120 137602
Google Scholar
[47] Zhang Q, Xie L, Liu G, Prokhorenko S, Nahas Y, Pan X, Bellaiche L, Gruverman A, Valanoor N 2017 Adv. Mater. 29 1702375
Google Scholar
[48] Zhang Q, Prokhorenko S, Nahas Y, Xie L, Bellaiche L, Gruverman A, Valanoor N 2019 Adv. Funct. Mater. 29 1808573
Google Scholar
[49] Balke N, Choudhury S, Jesse S, Huijben M, Chu Y H, Baddorf A P, Chen L Q, Ramesh R, Kalinin S V 2009 Nat. Nanotechnol. 4 868
Google Scholar
[50] Vasudevan R K, Chen Y C, Tai H H, Balke N, Wu P, Bhattacharya S, Chen L Q, Chu Y H, Lin I N, Kalinin S V, Nagarajan V 2011 ACS Nano 5 879
Google Scholar
[51] Li Y, Jin Y M, Lu X M, Yang J C, Chu Y H, Huang F Z, Zhu J S, Cheong S W 2017 NPJ Quantum Mater. 2 43
Google Scholar
[52] Damodaran A R, Clarkson J D, Hong Z, Liu H, Yadav A K, Nelson C T, Hsu S L, McCarter M R, Park K D, Kravtsov V, Farhan A, Dong Y, Cai Z, Zhou H, Aguado-Puente P, García-Fernández P, Íñiguez J, Junquera J, Scholl A, Raschke M B, Chen L Q, Fong D D, Ramesh R and Martin L W 2017 Nat. Mater. 16 1003
Google Scholar
[53] Kim K E, Kim Y J, Zhang Y, Xue F, Kim G Y, Song K, Choi S Y, Liu J M, Chen L Q, Yang C H 2018 Phys. Rev. Mater. 2 084412
Google Scholar
[54] Stoica V A, Laanait N, Dai C, Hong Z, Yuan Y, Zhang Z, Lei S, McCarter M R, Yadav A, Damodaran A R, Das S, Stone G A, Karapetrova J, Walko D A, Zhang X, Martin L W, Ramesh R, Chen L Q, Wen H, Gopalan V, Freeland J W 2019 Nat. Mater. 18 377
Google Scholar
[55] Chen P, Zhong X, Zorn J A, Li M, Sun Y, Abid A Y, Ren C, Li Y, Li X, Ma X, Wang J, Liu K, Xu Z, Tan C, Chen L, Gao P, Bai X 2020 Nat. Commun. 11 1840
Google Scholar
[56] Zheng Y, Chen W J 2017 Rep. Prog. Phys. 80 086501
Google Scholar
[57] Prosandeev S, Ponomareva I, Kornev I, Naumov I, Bellaiche L 2006 Phys. Rev. Lett. 96 237601
Google Scholar
[58] Lich L V, Shimada T, Wang J, Dinh V H, Bui T Q, Kitamura T 2017 Phys. Rev. B 96 134119
Google Scholar
[59] Crassous A, Sluka T, Tagantsev A K, Setter N 2015 Nat. Nanotechol. 20 614
Google Scholar
[60] He Q, Yeh C H, Yang J C, Singh-Bhalla G, Liang C W, Chiu P W, Catalan G, Martin L W, Chu Y H, Scott J F, Ramesh R 2012 Phys. Rev. Lett. 108 067203
Google Scholar
[61] Sanchez-Santolino G, Tornos J, Hernandez-Martin D, Beltran J I, Munuera C, Cabero M, Perez-Munoz A, Ricote J, Mompean F, Garcia-Hernandez M, Sefrioui Z, Leon C, Pennycook S J, Munoz M C, Varela M, Santamaria J 2017 Nat. Nanotechnol. 12 655
Google Scholar
[62] Tian G, Yang W D, Song X, Zheng D F, Zhang L Y, Chen C, Li P L, Fan H, Yao J X, Chen D Y, Fan Z, Hou Z P, Zhang Z, Wu S J, Zeng M, Gao X S, Liu J M 2019 Adv. Funct. Mater. 29 1807276
Google Scholar
[63] Yang W D, Tian G, Zhang Y, Xue F, Zheng D F, Zhang L Y, Wang Y D, Chen C, Fan Z, Hou Z P, Chen D Y, Gao J W, Zeng M, Qin M H, Chen L Q, Gao X S, Liu J M 2020 https://arxiv.org/abs/2006.02011
下载:
计量
- 文章访问数: 11225
- PDF下载量: 790
- 被引次数: 0
