  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.
