Dynamics of polar vortex crystal formation in ultra-thin ferroelectrics
2Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas, USA
Periodic stacking of polar vortex tubes with alternating vorticity in a crystal-like fashion was predicted to form in atomically thin Pb(Zr,Ti)O3 films [1] and then recently observed at room temperature in PbTiO3/SrTiO3 superlattices [2]. Such vortex tube crystals (VTC) spontaneously form with a delicate balance of elastic and electrostatic conditions [1-3] and are promising candidates for technological applications. VTC have been also shown to be the seeding ground for various topologically non-trivial states [3]. However, a comprehensive understanding of the origin of the VTC state is lacking. Using atomistic effective Hamiltonian [4] within Molecular Dynamics simulations conducted on ultra-thin Pb(Zr,Ti)O3 films, we show that:
· The origin of VTC lies in the softening of a single sub-terahertz phonon mode which is highly degenerate at high temperatures. This mode softens on cooling and becomes gapless at the VTC formation temperature.
· Such soft mode couples to an in-plane ac electric field enabling a resonant switching of the VTC even at low temperatures and magnitudes of the electric field.
Our findings provide fresh insight into the formation and properties of VTC where they can now be seen as waves instead of ensemble of ferroelectric domains. Such a viewpoint fundamentally relates polar topologies to spin counterparts. Furthermore, the THz resonant switching of polar vortices can possibly find a conceptually new functional application.
1. Lai, B.-K. et al. Electric-Field-Induced Domain Evolution in Ferroelectric Ultrathin Films. Phys. Rev. Lett. 96, 137602 (2006).
2. Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).
3. Nahas, Y. et al. Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics. Nat. Commun. 11, 5779 (2020).
4. Kornev, I., Fu, H. & Bellaiche, L. Ultrathin films of ferroelectric solid solutions under a residual depolarizing field. Phys. Rev. Lett. 93, 196104 (2004).
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