Absence of critical thickness for polar skyrmions with breaking the Kittel’s law

Abstract

Abstract The period of polar domain (d) in ferroics was commonly believed to scale with corresponding film thicknesses (h), following the classical Kittel’s law of d ∝ $$\sqrt{h}$$ h . Here, we have not only observed that this relationship fails in the case of polar skyrmions, where the period shrinks nearly to a constant value, or even experiences a slight increase, but also discovered that skyrmions have further persisted in [(PbTiO3)2/(SrTiO3)2]10 ultrathin superlattices. Both experimental and theoretical results indicate that the skyrmion periods (d) and PbTiO3 layer thicknesses in superlattice (h) obey the hyperbolic function of d = Ah + $$\frac{{{\mbox{B}}}}{h}$$ B h other than previous believed, simple square root law. Phase-field analysis indicates that the relationship originates from the different energy competitions of the superlattices with PbTiO3 layer thicknesses. This work exemplified the critical size problems faced by nanoscale ferroelectric device designing in the post-Moore era.