Phase diagrams of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3∕\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ superlattices from first principles

A first-principles-based technique is used to determine the temperature versus misfit strain phase diagram of epitaxially grown (001) $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3∕\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ superlattices of different periods. Short superlattices exhibit a phase diagram that resemble that of (001) $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ thin films under short-circuit-like conditions. On the other hand, original domain patterns with unusual atomistic features occurred in the longer superlattices. The reason behind such a dramatic difference between short and longer superlattices is discussed.

Figure 1

(Color online) Temperature versus misfit strain phase diagram of the ultrashort $(n=2)$ ${\left[\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\right]}_2∕{\left[\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\right]}_2$ superlattice. The solid line displays the boundary between the $r_c$ and $r_{aa}$ states.

Figure 2

(Color online) Temperature versus misfit strain phase diagram of the longer $(n=10)$ ${\left[\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\right]}_{10}∕{\left[\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\right]}_{10}$ superlattice.

Figure 3

(Color online) Structure of domains in (a) phase I, (b) phase II, (c) phase III, and (d) phase IV in ${\left[\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\right]}_{10}∕{\left[\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\right]}_{10}$ superlattice. The left-hand parts show the dipoles in all the different (001) planes (top view). The right-hand parts display the dipole distribution in a given plane that contains the $z$ axis, except for panel (c) that displays two adjacent $\left(1\overline{1}0\right)$ planes in order to see the variation in sign of the $z$-component of the dipoles in the BT layers when moving along $\left[1\overline{1}0\right]$. $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ and $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ layers are indicated in these right-hand parts. The cyan (gray) and blue (black) arrows represent dipoles having a $z$ component being positive and negative, respectively.