Motivated by the recent discovery of ferromagnetism in cubic perovskite BaFeO3 under small magnetic field, we investigate spin order in BaFeO3 and isostructural SrFeO3 by first-principles calculation. On-site Coulomb and exchange interactions are necessary for the helical spin order consistent with experiments. SrFeO3 exhibits stable G-type helical order, while A- and G-type helical orders in BaFeO3 are almost degenerate at a short propagating vector with a tiny energetic barrier with respect to ferromagnetic spin order, explaining ferromagnetism under a small field. The results are consistent with the model calculation in which negative charge-transfer energy is explicitly taken into account.

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