Supplementary Material for "Collective Behavior in intrinsic polarization switching of PbTiO3 and Pb(Zr,Ti)O3"

The time evolution of polarization properties and dipolar pattern of PbTiO3 for different supercell sizes; The time evolution of the dipolar pattern of PbTiO3 single crystals on the xz plane at E = 20 MV/cm; Hypertoroidal moment for single vortex and zero vortex structures; The time evolution of x component of the polarization and the hypertoroidal moment for PbTiO3;The time evolution of the dipolar pattern of a different single unit cell layer on the xy plane for PbTiO3;The hypertoroidal moment as a function of time and the dipolar pattern with a different initial configuration for PbTiO3.