Fig. 4: Formation mechanism of antivortex in STO and its electric tuning via phase-field simulation.
From: Creating polar antivortex in PbTiO3/SrTiO3 superlattice
a The electrostatic and elastic energy densities (on the left) for (PTO)10/(STO)m heterostructures and the critical electric fields (on the right) under which the antivortex disappears. b The hysteresis loop of winding number of STO within (PTO)10/(STO)6 versus external electric field. The left and right insets show the polarization distributions of vortex–antivortex pair and single-domain state, respectively. c The spatial distribution of local permittivity in the middle plane of STO across the antivortex cores. The two peaks indicate the significant increase of the permittivity at the antivortex cores. d The average permittivity in the middle plane of STO versus the external electric field. The two abrupt changes of permittivity in the hysteresis loop are induced by the topological phase transition.
