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

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 ∝ √(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 [(PbTiO 3 ) 2 /(SrTiO 3 ) 2 ] 10 ultrathin superlattices. Both experimental and theoretical results indicate that the skyrmion periods ( d ) and PbTiO 3 layer thicknesses in superlattice ( h ) obey the hyperbolic function of d = A h + /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 PbTiO 3 layer thicknesses. This work exemplified the critical size problems faced by nanoscale ferroelectric device designing in the post-Moore era.