Electronic, magnetic, and optical properties of bulk and surface structures of Fe₃O₄

Identifying a transparent ferromagnetic material is crucial for enabling the next generation of multifunctional electronic and spintronic devices. In this study, we explore the magnetic behavior of bulk Fe₃O₄ using first-principles calculations. Our results reveal that Fe₃O₄ adopts a ferrimagnetic ground state, primarily due to the uneven distribution of iron atoms between its octahedral and tetrahedral lattice sites. The electronic structure analysis confirms that Fe₃O₄ exhibits a half-metallic character, supported by spin-resolved band structures and density of states. We also examine the surface stability of three low-index planes (001), (110), and (1,1,1) under various terminations. Among them, the Fe tet₁ and Fe-oct₂ terminations on the (111) surface emerge as the most energetically favorable. Both terminations maintain a ferrimagnetic ground state. Interestingly, while the Fe-tet1surface preserves the half-metallic nature observed in the bulk, the Fe-Oct₂ surface transitions to a direct band gap semiconductor with an energy gap of 0.52 eV. In addition, we investigate the optical response of both the bulk material and the stable Fe-tet₁ and Fe-Oct₂ surface terminations. The bulk Fe₃O₄ exhibits a peak refractive index of 2.93 and a visible-range reflectivity of 0.26. In comparison, the dielectric response is notably reduced for both surface terminations. Specifically, the refractive index reaches maximum values of 1.88 for Fe-tet₁ and 1.96 for Fe-Oct₂ in the visible spectrum. Additionally, the reflectivity coefficients for these surfaces in the visible range are 0.11 and 0.12, indicating their optical transparency. These values are more than ten times less than those reported for MoS₂ monolayers. Our findings suggest that Fe-tet₁ and Fe-Oct₂ surfaces exhibit relatively large refractive indices with optical transparency in the visible frequencies, which can be utilized for spintronics and optoelectronics device applications at high temperatures.