Magnetic ordering and exchange interactions in multiferroic $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$

We report our first-principles calculations on multiferroic $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$. The total energy results for different spin and structural configurations reveal that the ground state of $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$ in its ideal structure is antiferromagnetic but it is likely to have a possible site disorder of Fe and Ga atoms between octahedral Ga sites and Fe sites, which is consistent with previous experimental observations. Examining the exchange interactions among Fe atoms at either Ga or Fe sites in $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$, we conclude that the net magnetic moments observed in experiments may arise from Fe atoms occupying the Ga sites. Despite the $d^5$ configuration of Fe ions in $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$, significant orbital magnetic moments are found to exist and their origin is attributed to the local distortion of oxygen octahedra as well as the Fe off-centering present in the system.

Figure 1

(Color online) (a) Schematic drawing of the $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$ crystal structure. Light green, dark green, bright yellow, dark yellow, and red spheres correspond to Ga(1), Ga(2), Fe(1), Fe(2), and O, respectively. The unit cell contains 40 atoms and has the $P_c{2}_{1}n$ space group. (b) Local environments of Fe(1), Fe(2), Ga(1), and Ga(2) sites and their magnetic configurations assuming that Fe occupies either of the Ga sites.

Figure 2

(Color online) PDOS of Fe atoms (a) at Ga(2), (b) Fe(1), and (c) Fe(2) sites of $\mathrm{Ga}\mathrm{Fe}{\mathrm{O}}_3$. Fermi level is set to be zero.