$text{BiFeO}_text{3}$ 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.
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