  Composite materials comprised of ferroelectric nanoparticles in a dielectric
matrix are being actively investigated for a variety of functional properties
attractive for a wide range of novel electronic and energy harvesting devices.
However, the dependence of these functionalities on shapes, sizes, orientation
and mutual arrangement of ferroelectric particles is currently not fully
understood. In this study, we utilize a time-dependent Ginzburg-Landau approach
combined with coupled-physics finite-element-method based simulations to
elucidate the behavior of polarization in isolated spherical PbTiO3 or BaTiO3
nanoparticles embedded in a dielectric medium, including air. The equilibrium
polarization topology is strongly affected by particle diameter, as well as the
choice of inclusion and matrix materials, with monodomain, vortex-like and
multidomain patterns emerging for various combinations of size and materials
parameters. This leads to radically different polarization vs electric field
responses, resulting in highly tunable size-dependent dielectric properties
that should be possible to observe experimentally. Our calculations show that
there is a critical particle size below which ferroelectricity vanishes. For
the PbTiO3 particle, this size is 2 and 3.4 nm, respectively, for high- and
low-permittivity media. For the BaTiO3 particle, it is ~3.6 nm regardless of
the medium dielectric strength.
