Phase transitions and metastable states in stressed SrTiO$_{3}$ films

The sequence of the ground states in SrTiO$_{3}$ films subjected to epitaxial strain and fixed mechanical stress in the [001] and [110] directions is calculated from first principles within the density functional theory. Under the fixed-strain conditions, an increase in the substrate lattice parameter results in the following sequence of the ground states: $I$4$cm$ $\to$ $I$4/$mcm$ $\to$ $Ima$2 $\to$ $Cm$ $\to$ $Fmm$2 $\to$ $Ima$2(II). When moving to the fixed-stress conditions, the phase sequence changes significantly and depends on how the stress is applied. It is revealed that the simultaneous presence of two types of the lattice instability (the ferroelectric and structural ones) in strontium titanate leads to the formation of a whole system of metastable phases whose number increases abruptly under the fixed-stress conditions. The stability of these phases changes with pressure and phase transitions occur between them. The appearance of broad bistability regions in certain parts of the phase diagram enables the use of this phenomenon for developing nonvolatile phase-change memory.