Construction of novel ferroelectric topological structures and their structural characteristics at sub-angström level

Wang Yu-Jia; Geng Wan-Rong; Tang Yun-Long; Zhu Yin-Lian; Ma Xiu-Liang

doi:10.7498/aps.69.20201718

Abstract

In this paper, the recent progress of ferroelectric topologies is briefly reviewed with the emphasis on the important role of state-of-the-art aberration-corrected transmission electron microscopy in revealing the topological features in nanoscale ferroelectric materials. By identifying the ion displacement at a sub-angström level, the corresponding polarization distribution can be determined which uncovers the characteristics of topological structures. The formation mechanisms of ferroelectric topological structures and their evolutions under external fields are summarized from the perspective of strain, screening, and external fields for two prototypical ferroelectric materials, PbTiO₃ and BiFeO₃. For the PbTiO₃, its topological structures such as flux-closures, vortices, bubbles, skyrmions, and merons can be well demonstrated in a thickness-strain-screening phase diagram, which could be a guideline for better understanding the topological structures and also for the future exploration. For BiFeO₃, its topological structures reported are classified as two categories: one is the unscreened topological structure such as vortices and the other is the screened topological structure (center-type domains). Finally, we present the prospects for the future development of the ferroelectric topologies.

Keywords:

ferroelectric topological structures /
aberration-corrected transmission electron microscopy /
PbTiO₃ /
BiFeO₃

Authors and contacts

1.
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
2.
School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

Corresponding author: Ma Xiu-Liang, xlma@imr.ac.cn

Funds: Project supported by the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDJ-SSW-JSC010), the National Natural Science Foundation of China (Grant Nos. 51671194, 51971223, 51922100), and the Program of Shenyang National Laboratory for Materials Science, China (Grant Nos. L2019R06, L2019R08, L2019F01, L2019F13)

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Cited By

图 1 铁电材料中单胞尺度离子位移的STEM表征^[21]　(a) PTO单胞的示意图, 黄、红、蓝色小球分别代表Pb, Ti和O原子; (b) PTO单胞沿[100]方向的投影; (c) 沿[100]方向采集的PTO晶体的HAADF-STEM像

Figure 1. TEM characterization of the ionic displacement within the unit cells of ferroelectric materials^[21]: (a) Schematic perspective view of the unit cell PTO (yellow, Pb; red, Ti; blue, O); (b) projection of the unit cell along the [100] direction; (c) HAADF-STEM image of the PTO crystal along [100].

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图 2 通量全闭合畴结构的STEM研究^[21]　(a) GSO衬底上PTO/STO多层膜的低倍HAADF-STEM像; (b) 对图(a)进行几何相位分析(geometric phase analysis, GPA)得到的面外正应变(ε_yy)分布图, 从中可以看到周期性的通量全闭合阵列; (c), (d) 图(a)中四个方框区域的亚埃尺度的HAADF-STEM高分辨图(c)和相应的单胞离子位移矢量图(d), 从中可以清楚地看出通量全闭合畴结构的极化分布

Figure 2. STEM study of flux-closure domain structures^[21]: (a) Low-magnification high-resolution HAADF-STEM image of the PTO/STO multilayered film grown on the GSO substrate; (b) distribution of the out-of-plane normal strain (ε_yy) obtained from the geometric phase analysis (GPA) of Fig. 1(a), where the periodic array of flux-closures is presented; (c), (d) the sub-angström HAADF-STEM high-resolution images (c) and the mappings of ionic displacements (d) of the four squares in panel (a), where the polarization distributions of two flux-closures are clearly shown.

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图 3 通量全闭合畴结构的STEM研究^[27,31]　(a), (b) GSO衬底上厚度比例为1 (a)和1/2 (b)的PTO/STO多层膜的面外正应变(ε_yy)分布图, 从中可以看到二维竖直通量全闭合阵列(a)与二维竖直/水平通量全闭合阵列(b); (c) 水平通量全闭合畴的原子尺度HAADF-STEM像; (d) 利用相场模拟得到的全闭合畴结构随厚度比例的相图^[27]; (e) DSO衬底上PTO/STO多层膜的水平晶格旋转(R_x)分布图; (f) 全闭合内部三角形a畴的ABF像, 图中的黄、红、蓝色圆点分别代表Pb, Ti, O原子柱^[31]

Figure 3. STEM study of flux-closure domain structures^[27,31]: (a), (b) ε_yy distributions of the PTO/STO multilayered films with the thickness ratios of 1 (a) and 1/2 (b) grown on GSO substrates, where the two-dimensional arrays of vertical flux-closures (a) and vertical/horizontal flux-closures (b) are presented; (c) atomic resolved HAADF-STEM image of one horizontal flux-closure; (d) phase diagram of the flux-closure domain structures as the function of the thickness ratio obtained from phase-field simulations^[27]; (e) distribution of the horizontal lattice rotation (R_x) of the PTO/STO multilayered films grown on the DSO substrates; (f) annular bright field image of the triangular a domain within the flux-closures (yellow, Pb; red, Ti; blue, O)^[31].

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图 4 极性涡旋、泡泡结构和斯格明子的实验与模拟结果　(a) DSO衬底上的PTO₁₀/STO₁₀超晶格中极性涡旋的TEM实验结果(左)和相场模拟结果(右)^[29]; (b) STO衬底上的PZT/STO/PZT多层膜中的极性泡泡结构的TEM实验结果、示意图和有效哈密顿量模拟结果^[48]; (c) STO衬底上的PTO/STO超晶格中的极性斯格明子的TEM实验结果^[52]

Figure 4. Experimental and simulation results of polar vortices, bubbles and skyrmions: (a) TEM (left) and phase-field simulation (right) results of polar vortices in the PTO₁₀/STO₁₀ superlattice grown on the DSO substrate^[29]; (b) TEM result of a polar bubble in the PZT/STO/PZT multilayered film grown on the STO substrate, the schematic of polar bubbles, and the effective Hamiltonian simulation results^[48]; (c) TEM result of polar skyrmions in the PTO/STO multilayered film grown on the STO substrate^[52].

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图 5 极性半子阵列的实验与模拟研究^[23]　(a)−(c) 相场模拟得到的汇聚型半子(a)、发散型半子(b)和反半子(c)的三维极化构型; (d) 根据TEM实验结果构造的极性半子阵列的概略图; (e) 一个极性半子的截面图, 从中可以看出汇聚向上的极化构型; (f) 半子阵列的平面图, 其中用圆圈标出了汇聚型半子的位置; (g) 一个汇聚型半子的平面图

Figure 5. Experimental and simulation studies of the polar meron lattice^[23]: (a)−(c) The three-dimensional polarization configurations of a convergent meron (a), a divergent meron (b) and an antimeron (c) obtained from phase-field simulations; (d) sketch of the polar meron lattice based on TEM images; (e) cross-sectional image of a single polar meron, which possesses the up-convergent polarization configuration; (f) plane-view image of the polar meron lattice, where the positions of convergent merons are marked by circles; (g) plane-view image of a single convergent meron.

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图 6 PTO薄膜中拓扑结构的厚度-应变-屏蔽相图(不同颜色的点代表不同的拓扑结构).

Figure 6. Thickness-strain-screen phase diagram of the topological structures in PTO films. Different topological structures are marked by dots with different colors.

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图 7 绝缘BFO薄膜系统中极性拓扑结构的TEM研究^[54,55]　(a)−(c) TSO衬底上BFO薄膜的TEM实验结果^[54], 其中(a)为截面暗场像, (b)为图(a)中虚线框的高分辨HAADF-STEM像, 可以看出界面三角形畴的极化分布, (c)为三角形畴的Fe离子位移矢量图; (d)−(f) PSO衬底上BFO薄膜的TEM实验结果^[55], 其中(d)为截面暗场像, (e)为平面暗场像, 展示BFO薄膜内规则的畴组态, (f)为109°和180°畴壁交汇处的Fe离子位移矢量图

Figure 7. TEM studies of polar topological structures in BFO films under the insulating boundary condition^[54,55]. (a)−(c) TEM results of BFO films grown on the TSO substrate^[54]: (a) Cross sectional dark field TEM image; (b) high resolution HAADF-STEM image of the dashed box in (a), which shows the polarization distribution of the interfacial triangular nano-domain; (c) Fe ionic displacement vector map of a single triangular nano-domain. (d)−(f) TEM results of BFO films grown on the PSO substrate^[55]: (d) Cross sectional dark field TEM image; (e) planar view dark field TEM image showing the regular domain structures in BFO thin films; (f) Fe ionic displacement vector map of the junction of 109° and 180° domain walls.

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图 8 TSO (010)_O/BFO/GSO/BFO多层膜内的涡旋^[56]　(a) 多层膜的高分辨HAADF-STEM像, 插图为第一层BFO的快速傅里叶变换中的(110)反射; (b) 对应(a)的面外晶格旋转图; (c) 图(b)中黄色矩形的HAADF-STEM像与Fe离子的反向位移矢量的叠加图; (d)为(c)中“3”, “4”标注的顺时针涡旋和逆时针涡旋, 表现为BFO中连续的极化旋转; (e)−(g) 分别为109°畴壁末端两相共存涡旋的R_X (e), 沿[001] (f)和[110] (g)方向的B位离子相对于A位子晶格的伪色等高线图; (h) 正交BFO在局部内建电场下被极化的示意图

Figure 8. Vortices in TSO (010)_O/BFO/GSO/BFO multilayers^[56]: (a) High resolution HAADF-STEM image of the multilayers. Inset is the (110) reflection for the fast Fourier transform corresponding to the first BFO layer; (b) GPA analysis of the out-of-plane lattice rotation corresponding to (a); (c) HAADF-STEM image of the yellow rectangle in (b) with an overlay of the reversed Fe ionic displacement vectors; (d) details of the clockwise and anticlockwise vortex labeled as “3” and ”4” in (c), both showing a continuous polarization rotation of BFO; (e)−(g) color contour plot of the R_X (e), B-site ionic displacement vectors with respect to the A-site sublattice along [001] (f) and [110] (g) directions, respectively; (h) schematic illustration of the orthorhombic-BFO polarized under local built-in electric fields.

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图 9 BFO纳米岛和薄膜中电荷屏蔽诱导的拓扑结构^[62,63]　(a), (b) Nb:STO衬底上生长的纳米岛的TEM平面(a)和截面(b)实验结果, 可以看出发散向上的极化构型^[62]; (c) TSO衬底上BFO薄膜中带电缺陷诱导的奇异拓扑结构^[63]

Figure 9. Topological structures induced by charge screening in BFO nanoislands and films^[62,63]: (a), (b) The planar-view (a) and cross-sectional (b) TEM results of the BFO nanoislands grown on the Nb:STO substrate, where the divergent-up polarization configuration is shown^[62]; (c) the exotic polarization states induced by charged defects in BFO films grown on the TSO substrate^[63].

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表 1 用实验手段首次观察到磁/电拓扑结构的手段和时间

Table 1. The methods and time of the first experimental observation for each magnetic/electric topological structure.

拓扑结构	铁磁		铁电
拓扑结构	手段	时间/年	手段	时间/年	材料体系
通量全闭合畴	光学显微镜	1949 ^[24]	像差校正TEM	2015^[21]	PTO/STO
涡旋	磁力显微镜	2000^[6]	像差校正TEM	2016^[29]	PTO/STO
泡泡	光学显微镜	1960^[7]	像差校正TEM	2017^[48]	PZT/STO
斯格明子	中子衍射	2009^[8]	像差校正TEM	2019^[52]	PTO/STO
半子	洛伦兹TEM	2012^[10]	像差校正TEM	2020^[23]	PTO
中心畴结构	—	—	PFM	2017^[57]	BFO
刺猬结构	—	—	像差校正TEM	2018^[63]	BFO

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