  $\text{BiFeO}_\text{3}$ has drawn a great attention over last several decades
due to its promising multiferroic character. In the ground state the bulk
$\text{BiFeO}_\text{3}$ is found to be in the rhombohedral phase. However, it
has been possible to stabilize $\text{BiFeO}_\text{3}$ with tetragonal
structure. The importance of tetragonal phase is due to its much larger value
of the electric polarization and the possible stabilization of ferromagnetism
as in the rhombohedral phase. Furthermore, the tetragonal structure of
$\text{BiFeO}_\text{3}$ has been reported with different $c/a$ ratio, opening
up the possibility of a much richer set of electronic phases. In this work, we
have used density functional theory based first-principle method to study the
ferromagnetic phase of the tetragonal $\text{BiFeO}_\text{3}$ structure as a
function of the $c/a$ ratio. We have found that as the $c/a$ ratio decreases
from $1.264$ to $1.016$, the tetragonal $\text{BiFeO}_\text{3}$ evolve from a
ferromagnetic semiconductor to a ferromagnetic metal, while passing through a
\emph{half-metallic} phase. This evolution of the electronic properties becomes
even more interesting when viewed with respect to the volume of each structure.
The most stable half-metallic phase initially counter-intuitively evolve to the
magnetic-semiconducting phase with a reduction in the volume, and after further
reduction in the volume it finally becomes a metal. So far, this type of metal
to insulator transition on compression was known to exist only in alkali
metals, especially in Lithium, in heavy alkaline earth metals, and in some
binary compound.
