  Using density functional theory (DFT) with local density approximation (LDA)
and generalized gradient approximation (GGA) correlation functionals, the
electronic and magnetic structures of cubic BaFeO$_{3}$ in the ferromagnetic
(FM) and antiferromagnetic (AFM) states are studied. Our LDA/GGA and
LDA$+U$/GGA$+U$ results show that cubic BFO has a FM ground state, in agreement
with recent experimental works. Two types of Jahn-Teller (JT) distortions,
denoted as JT1 and JT2, are considered. We find FM to ferrimagnetic (FIM) and
FM to AFM magnetic phase transitionn in the JT1 and JT2 type of distortions,
respectively. Larger strains are required for the FM-AFM transition as compared
to the FM-FIM. DFT$+U$ calculations also show that the magnetic moments
dramatically decrease at large strains due to strong overlapping between the Fe
and O atoms. The origins of these transitions is discussed in terms of a
competition between double exchange and superexchange interactions. Oxygen and
Fe displacements are therefore responsible for the magnetic phase transitions
and the reduction of the magnetic moments.
