Phase Field Simulations Of Ferroelectric And Multiferroic In Nanoscale

Nanoscale ferroelectrics and multiferroics have been actively investigated formany years. Nanoscale ferroelectrics and multiferroics often retain bulk properties,and even exhibit enhanced or novel properties including optoelectronic,electrochemical, electromechanical and magnetoelectric, properties, due to effects offinite size, surfaces and interfaces. Therefore, nanoscale ferroelectrics andmultiferroics play important roles in the fabrication and miniaturization of nanoscalefunctional devices. Vortex domain patterns in ferroelectrics and multiferroics havebeen extensively studied which exhibit distinct characteristics and novel couplingswith external fields, compared to the traditional ferroelectric domains.The phase field simulations are based on the time-depended Ginzburg-Landauequation, which takes the long-range elastic and electrostatic interactions. The phasefield model can study the evolution of the domain structure. In this paper, we conductfinite element method and finite difference method to solve phase field model whichsimulations of size effect on vortex domain configuration of barium titanate(ferroelectric) and bismuth ferrite(multiferroic) nanodot under open-circuit-likeelectrical boundary conditions，The main results are as follows。The barium titanate nanodot is divided into three dimensional10×10×n and nvaries from small to large,△x=△y=△z=0.4nm. The phase transition temperature andpolarization are going up when the size becomes large. When the size of bariumtitanate nanodot is small and from paraelectric phase to ferroelectric phase, the shapeis flat and the vortex domain is on the z axis. When the shape is cubic, the vortexdomain is rhombohedral domain pattern. When the size is large and the shape iscylindricity, the vortex domain is on the x or y axis. The vortex is very variety whenthe shape is near cubic, such as orthorhombic vortex domain pattern,4-vortics. Whenthe temperature is from ferroelectric phase to paraelectric phase, the domain patternis close to the domain pattern of cooling but the phase temperature between theferroelectric phase and the domain pattern near the cubic are different. According tocalculations, the temperature-size phase diagrams of cooling and warming can beobtained.The bismuth ferrite nanodot is divided into three dimensional10×10×n and nvaries from small to large,△x=△y=△z=0.5nm. When the temperature is fromparaelectric phase to ferroelectric phase and the size become large, the core of vortexdomain is from z axis to apical angle and from apical angle to straightedge, and in theend the core will come to x or y axis. The vortex domain pattern of bismuth ferritenanodot is relatively simple compare to domain pattern of barium titanate nanodot. In summary, the relationship between the domain patter and the size of thebismuth ferrite nanodot are systematically investigated in this paper, and thetemperature-size phase diagrams depict the fruitful vortex domain pattern of thenanodot. This paper also compendiously introduces the size effect of the bismuthferrite nanodot.