Vortex structure transformation of BaTiO3 nanoparticles through the gradient function

Abstract

Phase field method has been used to simulate the vortex structures in BaTiO3 (BTO) nanoparticles. Through the modulation of the gradient coefficients, vortices are found to transform in a path of monoclinic MA→orthorhombic→monoclinic MC→tetragonal. Although the gradient coefficients vary significantly, the change in gradient energy is remarkably small. The simulation results show that the rotation and magnitude reduction in polarization dipoles increase the bulk energy, which induces the vortex transformation process in BTO nanoparticles. Moreover, the existence of monoclinic phase is a necessity to start the polarization rotation as well as the vortex transformation process.