Phase diagram in strained epitaxial BaTiO$_3$/SrTiO$_3$ superlattices studied by ultraviolet Raman spectroscopy*

Strain effect on phase transitions in nanoscale BaTiO$_3$/SrTiO$_3$ ferroelectric superlattices (SLs) has been studied by ultraviolet (UV) Raman scattering. A series of coherently strained (BaTiO$_3$)$_8$/(SrTiO$_3$)$_4$ SLs have been grown by molecular beam epitaxiy on rare earth scandate (GdScO$_3$, DyScO$_3$, SmScO$_3$, NdScO$_3$) and SrTiO$_3$ substrates. This allowed a systematic strain variation in the SLs. UV Raman data allowed the determination of the ferroelectric phase transition temperature ($T_c$) and indicated the presence of different ferroelectric phases with out-of-plane and in-plane components of polarization in SLs, depending on strain and temperature. Experimental Raman results are supported by first-principles calculations of structural instabilities in BaTiO$_3$/SrTiO$_3$ SLs and thermodynamic phase-field modeling of phase diagrams and ferroelectric polarization as a function of temperature and strain.