Nanoscale periodic domain patterns in tetragonal ferroelectrics: A phase-field study
Nanoscale periodic domain patterns in tetragonal ferroelectrics: A phase-field study
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DOI：
10.1103/physrevb.93.174120
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发表时间：
2016-05
影响因子：
3.7
通讯作者：
A. R. Balakrishna;J. Huber;Ingo Munch
中科院分区：
文献类型：
--
作者：
A. R. Balakrishna;J. Huber;Ingo Munch
铁电体形成磁区图案，在施加的边界条件下使其能量最小化。在忽略磁区壁能的线性约束理论中，多阶层合体形式的周期性磁区图案可以被识别为最小能量态。然而，当这些叠层(在宏观晶体中形成)包括几个纳米大小的域时，域壁能量变得显著，并且这种尺度上的叠层图案的行为是未知的。本文采用考虑梯度能和应变能贡献的相场模型来研究纳米多阶层合板的稳定性和演化过程。计算了层合板中的应力、电场和磁化壁能。文中还讨论了尺度效应。在没有外加载荷的情况下，与更复杂的多阶层合板相比，条纹域图案的能态更低，后者大多坍塌成更简单的图案。然而，复杂层合板可以通过施加电场、平均应变和极化等外部载荷来稳定。这项研究提供了对宏观单晶上可能形成的但由纳米级周期图案组成的磁区图案的洞察，以及外部载荷对这些图案的影响。
Ferroelectrics form domain patterns that minimize their energy subject to imposed boundary conditions. In a linear, constrained theory, that neglects domain wall energy, periodic domain patterns in the form of multi-rank laminates can be identified as minimum-energy states. However, when these laminates (formed in a macroscopic crystal) comprise domains that are a few nanometers in size, the domain-wall energy becomes significant, and the behaviour of laminate patterns at this scale is not known. Here, a phase-field model, which accounts for gradient energy and strain energy contributions, is employed to explore the stability and evolution of the nanoscale multi-rank laminates. The stress, electric field, and domain wall energies in the laminates are computed. The effect of scaling is also discussed. In the absence of external loading, stripe domain patterns are found to be lower energy states than the more complex, multi-rank laminates, which mostly collapse into simpler patterns. However, complex laminates can be stabilized by imposing external loads such as electric field, average strain and polarization. The study provides insight into the domain patterns that may form on a macroscopic single crystal but comprising of nanoscale periodic patterns, and on the effect of external loads on these patterns.