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Size-dependent and distinguishing degenerated vortex states in ferroelectric nanodots under controllable surface charge conditions

机译：在可控表面电荷条件下，尺寸依赖性和将退化的涡旋状态区分解在铁电纳米棒中

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Here we propose a method to detect the degenerated tetragonal vortex states ( i.e. , the toroidal axis is along the x -, y - or z -axis) in ferroelectric nanodots by applying a controllable surface charge (CSC) condition. Electrodes are placed at two parallel surfaces of the nanodot to form a short circuit. Surface charges with a controllable density are then applied to another two parallel surfaces of the nanodot. Under this CSC condition, a characteristic short-circuit current vs. time ( I – t ) curve related with the evolution of domain structure in a nanodot can be detected. The evolution paths and the characteristic short-circuit I – t curves of the degenerated vortex states in ferroelectric nanodots have been systematically revealed by our phase field simulations by solving the time-dependent Ginzburg–Landau (TDGL) equations. It is found that the degenerated vortex states exhibit distinct evolution features under the CSC condition. In the stages of placing electrodes and increasing surface charges, one, two, and zero short-circuit I – t peak(s) are observed in the nanodots with 〈100〉, 〈010〉 and 〈001〉 vortex states, respectively. Therefore, the unknown vortex states of a nanodot can be distinguished. We further investigate the effects of temperature and nanodot size on the characteristic I – t curves of the vortex states. The results show that the vortex states can be nondestructively distinguished by applying the CSC condition if the nanodot size is within a moderate range ( i.e. , 8–12 nm). Our study provides an alternative way of detecting the degenerated tetragonal vortex states in ferroelectric nanodots without the use of a scanning probe microscope, and also sheds light on the application of ferroelectric vortex domain structures in novel devices such as memories, sensors and actuators.
机译：在这里，我们提出了一种检测退化的四方涡流状态的方法（即，环形轴线通过施加可控表面电荷（CSC）条件来检测退化的四方涡流状态（即环形轴线沿X-，Y - 或Z-XIS）。将电极放置在纳米盖的两个平行表面上以形成短路。然后将具有可控密度的表面电荷施加到纳米孔的另一个两个平行表面。在该CSC条件下，可以检测与纳米型中的域结构的演化相关的特征短路电流与时间（I-T）曲线。通过求解时间依赖的Ginzburg-Landau（TDGL）方程，我们的相现场模拟系统地揭示了铁电纳米陶器中退化涡旋状态的演化路径和特征短路I-T曲线。结果发现退化的涡旋状态表现出CSC条件下的明显进化特征。在放置电极的阶段和增加的表面电荷，分别在具有<100> <010>和<001>涡旋状态的纳米蛋白中观察到一个，两个和零短路I-T峰值。因此，可以区分纳米型的未知涡流状态。我们进一步研究了温度和纳米液尺寸对涡旋状态的特征I-T曲线的影响。结果表明，如果纳米型尺寸在中等范围内（即8-12nm）内，则可以通过施加CSC条件来非破坏性地区分涡流状态。我们的研究提供了在不使用扫描探针显微镜的情况下检测铁电纳米型中的退化四方涡流状态的替代方法，并且还揭示了在新颖的设备中在诸如存储器，传感器和致动器的新颖装置中应用铁电涡流结构域结构。

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