Dynamics of polar vortex crystallization

Vortex crystals are commonly observed in ultra-thin ferroelectrics. However, a clear physical picture of origin of this topological state is currently lacking. Here, we show that vortex crystallization in ultra-thin Pb(Zr0.4,Ti0.6)O3 films stems from the softening of a phonon mode and can be thus described as a SU(2) symmetry-breaking transition. This result sheds light on the topology of the polar vortex patterns and bridges polar vortices with smectic phases, spin spirals, and other modulated states. Finally, we predict an ac-field driven resonant switching of the vortex tube orientation which could enable new low-power electronic technologies.