Ferroelectric flux-closures, which exhibit closed head-to-tail continuous electric dipoles, are very promising in high density storage, because data storage in these domain patterns may avoid the problem of “cross-talk”. For the purpose of the data bits to be addressable, nanoscale flux-closures should be periodic.

In a recent study published in Nano Letters, a research team led by Prof. MA Xiuliang and Prof. ZHU Yinlian from Institute of Metal Research, Chinese Academy of Sciences (IMR, CAS) recently established the phase diagram of the layer-by-layer two-dimensional flux-closure arrays versus the thickness ratio of adjacent ferroelectric PbTiO₃ films.

Based on the one-dimensional flux-closure array (Science, 2015) discovered by the team, they recently artificially produced a series of PbTiO₃/SrTiO₃ multilayers grown on GdScO₃ (001)_pc substrate with multiple periodicities.

By tuning the thickness ratio of adjacent PTO layers, they have obtained two configurations of the flux-closure array: one features with 180^o domain walls perpendicular to the interfaces and another with 180^o domain walls parallel to the interfaces.

With methods of aberration-corrected scanning transmission electron microscopic imaging and phase field modeling, they have established the phase diagram of the two-dimensional flux-closure arrays versus the thickness ratio of adjacent PbTiO₃ films, in which energy competitions play dominant roles.

The growth of these flux-closures makes a great step toward the realization of ferroelectric nanoscale devices with exotic properties.

Figure: Identification of 2D regularly arranged veritcal and horizontal flux-closure quadrants. (a) Out-of-plane lattice strain maps of the PbTiO₃/SrTiO₃ multilayers; (b) Total energy density in the multilayered PbTiO₃/SrTiO₃ systems as the function of the thickness ratio of adjacent PbTiO₃ layers. (Image by IMR)