Pressure-induced ferromagnetism in cubic perovskite SrFeO${}_3$ and BaFeO${}_3$

The spin order in cubic perovskite SrFeO${}_3$ and BaFeO${}_3$ 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 BaFeO${}_3$ whose lattice constant is 3.97 Å. When the lattice constant is reduced to 3.85 Å, which is the same as the lattice constant of SrFeO${}_3$ at ambient pressure, G-type helical spin order becomes stable, being consistent with SrFeO${}_3$. This is because superexchange interaction is enhanced as compared with double-exchange interaction. Phase transition from helical spin state to ferromagnetic state in both SrFeO${}_3$ and BaFeO${}_3$ takes place if the lattice constant is further reduced to 3.70 Å. This is because reduced local spin moment weakens the contribution from superexchange interaction. Our result agrees with recent experimental result of BaFeO${}_3$ under high pressure. Additionally, our calculation predicts that half-metal BaFeO${}_3$ at ambient pressure will become a good metal under high pressure.

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 LSDA+$U$ for various lattice constant $a$ shown as numbers in SrFeO${}_3$. (a) G-type helical spin order; (b) A-type helical spin order. At ambient pressure, $a$ = 3.85 Å. For the definition of $\phi$, see 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+$U$ for various lattice constant $a$ shown as numbers in BaFeO${}_3$. (a) G-type helical spin order; (b) A-type helical spin order. At ambient pressure, $a$ = 3.97 Å. For the definition of $\phi$, see text.

Figure 3

The spin moment $M$ in BaFeO${}_3$ with G-type helical spin order obtained by LSDA+$U$ as a function of $\phi$ for several values of $a$.

Figure 4

Density of states (DOS) of BaFeO${}_3$ in the FM state calculated by LSDA+$U$ with $U=4.0$ eV and $J=0.9$ 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 level. Black solid line and red solid lines represent the DOS of Fe$t_{2g}$ and Fe$e_g$ orbitals, respectively. The partial DOS of O2$p$ orbitals is shown by solid blue line. (a) $a$ = 3.97 Å (ambient pressure). (b) $a$ = 3.70 Å (under pressure).

Figure 5

Band structure of ferromagnetic BaFeO${}_3$ calculated by LSDA+$U$. Solid and dotted lines represent spin-up and spin-down bands, respectively. (a) $a$ = 3.97 Å and (b) $a$ = 3.70 Å.