First-principles calculation of helical spin order in iron perovskite SrFeO${}_3$ and BaFeO${}_3$

Motivated by the recent discovery of ferromagnetism in cubic perovskite BaFeO${}_3$ under small magnetic field, we investigate spin order in BaFeO${}_3$ and isostructural SrFeO${}_3$ by first-principles calculation. On-site Coulomb and exchange interactions are necessary for the helical spin order consistent with experiments. SrFeO${}_3$ exhibits stable G-type helical order, while A- and G-type helical orders in BaFeO${}_3$ 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.

Figure 1

The $\phi$ dependence of the total energy difference per unit cell, $\Delta E\left(\phi \right)\equiv E\left(\phi \right)-E(\phi =0)$, obtained by the LSDA in SrFeO${}_3$. For the definition of $\phi$, see the text.

Figure 2

The $\phi$ dependence of the total energy difference per unit cell, $\Delta E\left(\phi \right)\equiv E\left(\phi \right)-E(\phi =0)$, obtained by LSDA + $U$ in SrFeO${}_3$ and BaFeO${}_3$. For the definition of $\phi$, see the text.

Figure 3

Density of states (DOS) of BaFeO${}_3$ in the FM state calculated by LSDA + $U$ with $U=3.0$ eV and $J=0.6$ eV. The positive side of the DOS denotes the up-spin DOS, while the negative side denotes the down-spin DOS. Dotted vertical line at zero energy represents the Fermi energy $E_F$. (a) DOS of Fe 3$d$ $t_{2g}$ and $e_g$ orbitals. (b) DOS of O 2$p$ orbitals.

Figure 4

The $\phi$ dependence of the total energy difference relative to $\phi =0$, $\Delta E\left(\phi \right)$ of model (2). (a) SrFeO${}_3$ and (b) BaFeO${}_3$. Parameters denoted in each panel are taken so that the minimum of the energy is located at experimentally observed $\phi$ (see text). The G (A) -type helical spin order is represented by a solid black (broken red) line.