An atomistic model approach parameterized from first-principles calculations is used to investigate size and shape effects on the polarization field in isolated stress-free PbTiO 3 nanoparticles. The study was carried out by molecular dynamics simulations in free-standing nanodots of cylindrical, spherical, and ellipsoidal shapes. We show that in cylinders with diameter equal to height, the size-induced transformation from the vortex to the flux-closure domain configuration causes an anomaly in the behavior of the toroidal moment and the volume of the system. During this transformation, the vortex core evolves into domain walls while the resulting structure is stabilized due to the nonhomogeneous distribution of polarization and strain inside the domains. A similar behavior is observed in elongated cylinders, spheres, and spheroids. The increment in the diameter/height relation of the nanoparticles gives rise to a succession of topological transformations that include multi-vortex configurations, ferroelectric bubble states, and multi-domain patterns. While the transformation path for flat cylinders is similar to the one previously obtained for cuboids, the thinner edge region of the spheroids prevents the stabilization of one-and twobubble states. Despite this last difference, our results indicate that the polarization pattern of a nanoparticle depends more on its aspect ratio than on its shape.
Ferroelectric materials manifest unique dielectric, ferroelastic, and piezoelectric properties. A targeted design of ferroelectrics at the nanoscale is not only of fundamental appeal but holds the highest potential for applications. Compared to two-dimensional nanostructures such as thin films and superlattices, one-dimensional ferroelectric nanowires are investigated to a much lesser extent. Here, we reveal a variety of the topological polarization states, particularly the vortex and helical chiral phases, in loaded ferroelectric nanowires, which enable us to complete the strain–temperature phase diagram of the one-dimensional ferroelectrics. These phases are of prime importance for optoelectronics and quantum communication technologies.
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