  The spin order in cubic perovskite SrFeO3 and BaFeO3 under high pressure is
studied by density functional theory (DFT) calculation with local spin density
approximation plus Hubbard U (LSDA+U). At ambient pressure, A-type and G-type
helical spin orders are almost degenerate in BaFeO3 whose lattice constant is
3.97{\AA} . When the lattice constant is reduced to 3.85 {\AA} which is same as
the lattice constant of SrFeO3 at ambient pressure, G-type helical spin order
becomes stable, being consistent with SrFeO3. This is because superexchange
interaction is enhanced as compared with double exchange interaction. Phase
transition from helical spin state to ferromagnetic state in both SrFeO3 and
BaFeO3 takes place if the lattice constant is further reduced to 3.70 {\AA}.
This is because reduced local spin moment weakens the contribution from
superexchange interaction. Our result agrees with recent experimental result of
BaFeO3 under high pressure. Additionally, our calculation predicts that
half-metal BaFeO3 at ambient pressure will become a good metal under high
pressure
