Strain-temperature phase diagram of BaZrO3 with antiferrodistortive distortions

Abstract

Barium zirconate ($\mathrm{BaZr}{\mathrm{O}}_{3}$) has attracted increasing attention due to its distinguished dielectric property and high chemical stability. As one kind of perovskite oxide, $\mathrm{BaZr}{\mathrm{O}}_{3}$ often exhibits a delicate interplay of lattice distortions and strain. In this work, the effect of strain on the ferroelectric and antiferrodistortive distortions in $\mathrm{BaZr}{\mathrm{O}}_{3}$ thin films is investigated at finite temperature by using density functional theory calculations and the first-principles based effective Hamiltonian method. It is found that due to the delicate balance between antiferrodistortive and ferroelectric distortions, polarization in $\mathrm{BaZr}{\mathrm{O}}_{3}$ thin films at absolute zero kelvin can be activated only under an in-plane tensile strain larger than 3.0%. The rotation of oxygen octahedra (antiferrodistortive distortion) is along the out-of-plane direction under the compressive strain and small tensile strain, whereas it changes to the in-plane direction when the tensile strain is larger than 0.3%. When the tensile strain increases to 4.1%, both rotation of oxygen octahedra and polarization are along the [110] direction. Furthermore, the temperature dependence of ferroelectric and antiferrodistortive distortions under different strains is investigated by using an effective Hamiltonian model. The strain-temperature phase diagram is calculated to identify the different distortions under different strains and temperatures.