Orbital-frustration-induced ordering in semiconductor alloys

It is well known that ternary zinc-blende semiconductors are always more stable in the chalcopyrite (CH) structure than the Cu-Au (CA) structure because the CH structure has a large Coulomb interaction and a reduced strain energy. Surprisingly, an experimental study showed that the $\mathrm{ZnFeS}{\mathrm{e}}_{2}$ alloy takes the CA order as the ground-state structure, which is consistent with our density functional theory calculations showing that the CA order has lower energy than the CH order for $\mathrm{ZnFeS}{\mathrm{e}}_{2}$. We reveal that the orbital degree of freedom of a high-spin $\mathrm{F}{\mathrm{e}}^{2+}$ ion $({d}^{6})$ in the tetrahedral crystal field plays a key role in stabilizing the CA order. First, the spin-minority $d$ electron of the $\mathrm{F}{\mathrm{e}}^{2+}$ ion tends to occupy the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like orbital instead of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$-like orbital because of its large negative Coulomb energy. Second, for a nearest-neighboring $\mathrm{F}{\mathrm{e}}^{2+}$ pair, two spin-minority $d$ electrons with occupied ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like orbitals on the plane containing the Fe-Fe bond have lower electronic kinetic energies. Both conditions can be satisfied in the CA ordered $\mathrm{ZnFeS}{\mathrm{e}}_{2}$ alloy, whereas there is an orbital frustration in the CH structure. Our results suggest that the orbital degree of freedom provides a new way to manipulate the structure and properties of alloys.