Hierarchy and scaling behavior of multi-rank domain patterns in ferroelectric K0.9Na0.1NbO3 strained films.

The formation process of a ferroelectric multi-rank domain pattern in the thickness range of 7-52 nm is investigated for monoclinic K0.9Na0.1NbO3 strained epitaxial films on (110) NdScO3 substrates. Although the elastic strain energy density is degenerated for two pseudocubic orientations, a distinctive hierarchy of domain evolution is observed with exclusive in-plane a1a2 domains for very thin films and the retarded onset of a ferroelectric MC phase at larger film thickness. This is accompanied by a thickness dependent transformation from stripe domains to a herringbone pattern and, eventually, for the thickest film, to a checkerboard-like structure. These transformations in the domain arrangement and width are correlated to energetic aspects as depolarization field and anisotropic strain relaxation in the film. While for the MC domains plastic strain relaxation is throughout observed, the a1a2 domains show a two-step strain relaxation mechanism starting with an in-plane elastic shearing, which is followed by plastic lattice relaxation. Our results highlight a pathway for engineering and patterning of periodic ferroelectric domain structures.