Polarization rotation in Bi$_{\mathbf{4}}$Ti$_{\mathbf{3}}$O$_{\mathbf{12}}$ by isovalent doping at the fluorite sublattice

Bismuth titanate, Bi$_4$Ti$_3$O$_{12}$ (BiT), is a complex layered ferroelectric material that is composed of three perovskite-like units and one fluorite-like unit stacked alternatively along the $c$-direction. The ground state crystal structure is monoclinic with the spontaneous polarization (~50 $\mu$C/cm$^{2}$) along the in-plane $b$-direction. BiT typically grows along the $c$-direction in thin film form and having the polarization vector aligned with the growth orientation can be beneficial for several potential device applications. It is well known that judicious doping of ferroelectrics is an effective method in adjusting the magnitude and the orientation of the spontaneous polarization. Here, we show using first-principles density functional theory and a detailed phonon analysis that Bi atoms in the fluorite-like layers have significantly more impact on the magnitude and orientation of the spontaneous polarization vector as compared to the perovskite-like layer. The low energy hard phonon modes are characterized by fluorite-like layers experiencing transverse displacements and large changes in Born effective charges on Bi atoms. Thus, the breaking of symmetry caused by doping of Bi sites within the fluorite-like layer leads to the formation of uncancelled permanent dipole moments along the $c$-direction. This provides an opportunity for doping the Bi site in the fluorite-like layer. Isovalent dopants P, As, and Sb were studied. P is found to be most effective in the reorientation of the spontaneous polarization. It leads to a three-fold enhancement of the $c$-component of polarization and to a commensurate rotation of the spontaneous polarization vector by 36.2$^{\circ}$ towards the $c$-direction.