Skyrmion nucleus resolves the Landauer paradox

Abstract

Ferroelectric switching is among the most fundamental and widely studied symmetry-breaking processes in physics. However, the Landauer paradox asserts that an ideal single-domain ferroelectric should be kinetically unswitchable, because a three-dimensional reversed nucleus would carry a prohibitive depolarization penalty, leading to unphysically large coercive field (the electric field required to switch the polarization). Here we show that this long-standing paradox is resolved by topology. In defect-free PbTiO3, large-scale molecular dynamics simulations reveal that the intrinsic critical nucleus is a three-dimensional polar skyrmion. Its continuous polarization rotation and Néel-type boundary walls self-compensate bound charge, suppressing the depolarization energy by orders of magnitude and bringing the predicted coercive field into agreement with experiment. This topological nucleus further overturns the 60-year-old Janovec-Kay-Dunn law. We derive an analytical thickness-dependent coercive-field law governed by field-induced softening of the parent ferroelectric state and controlled by a single material descriptor. This framework captures diverse experimental trends across ferroelectric families and recasts the Kay-Dunn exponent of -2/3 as an effective finite-window behavior. These results establish polar topology as an organizing principle for intrinsic switching and suggest that hidden topological transition states may broadly shape nonequilibrium phase transformations traditionally understood as Landau-type symmetry breaking.