论文标题

多轴铁电的混合型域壁的介观结构

Mesoscopic structure of mixed type domain walls in multiaxial ferroelectrics

论文作者

Morozovska, Anna N., Eliseev, Eugene A., Fomichov, Yevhen M., Kalinin, Sergei V.

论文摘要

在分析Landau-Ginzburg-Devonshire(LGD)方法的框架内研究了多轴铁电膜中180度未充电旋转域壁的结构。有限元建模(FEM)用于以数值方式求解耦合的非线性Euler-lagrange(EL)微分方程的第二个阶数值,用于两个偏振组成部分。我们表明,膜壁的结构和膜的相应(元)稳定相位由单个主参数,无量纲的铁电各向异性μ控制。我们拟合了由FEM计算的单生域壁的静态轮廓,具有极化组件的双曲功能,并从拟合到FEM曲线中提取了五个依赖性参数。拟合结果的高精度使我们得出结论,分析函数可以视为具有立方非线性的静态EL方程的高临界性变化解。我们进一步得出了多轴铁电膜中多域180度结构结构的静态EL方程的两组分析解。对膜厚度和其表面边界条件的自由能依赖性的分析允许选择与最小能量相对应的域状态。单域状态是在表面上零极化衍生物的基础,而多域状态最小化了在表面上零极化的系统能量。违反直觉,对于在表面上为零极化的多域状态的能量分为两个水平0和1,而每个水平都是近距离亚级的无限集,形态的特征是两种组分极化节点的不同结构。

The structure of 180-degree uncharged rotational domain wall in a multiaxial ferroelectric film is studied within the framework of analytical Landau-Ginzburg-Devonshire (LGD) approach. The Finite Element Modelling (FEM) is used to solve numerically the system of the coupled nonlinear Euler-Lagrange (EL) differential equations of the second order for two components of polarization. We show that the structure of the domain wall and corresponding (meta)stable phase of the film are controlled by a single master parameter, dimensionless ferroelectric anisotropy μ. We fitted the static profile of a solitary domain wall, calculated by FEM, with hyperbolic functions for polarization components, and extracted the five μ-dependent parameters from the fitting to FEM curves. The high accuracy of the fitting results allows us to conclude that the analytical functions can be treated as the high-accuracy variational solution of the static EL equations with cubic nonlinearity. We further derive the two-component analytical solutions of the static EL equations for a polydomain 180-degree domain structure in a multiaxial ferroelectric film. The analysis of the free energy dependence on the film thickness and boundary conditions at its surfaces allows to select the domain states corresponding to the minimal energy. The single-domain state is ground for zero polarization derivative at the surfaces, while the poly-domain states minimize the system energy for zero polarization at the surfaces. Counterintuitively, the energy of the polydomain states split into two levels 0 and 1 for zero polarization at the surfaces, and each of the levels is the infinite set of the close-energy sub-levels, which morphology is characterized by different structure of the two-component polarization nodes.

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