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

Gong, Feng-Hui; Tang, Yun-Long; Wang, Yu-Jia; Chen, Yu-Ting; Wu, Bo; Yang, Li-Xin; Zhu, Yin-Lian; Ma, Xiu-Liang · Nat Commun · 2023

basic_science · Level V

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

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