Stability of polarization vortices within two interacting ferroelectric nanoparticles

The state of polarization vortices within a ferroelectric nanoparticle could be affected by the long-range electrostatic and elastic interactions from the neighboring particles. Phase field simulations were conducted to investigate the stability of polarization vortices within two interacting ferroelectric nanodots embedded in a non-ferroelectric medium. The interaction between these two nanodots can be neglected if the intermediate distance is larger than a critical distance, whereas the interaction becomes visible once the distance is smaller than that. Two separate vortices were observed to merge into one single vortex once an extreme state of perfect contact condition has been virtually achieved.