Putting DFT to the Test: A First-Principles Study of Electronic, Magnetic, and Optical Properties of Co₃O₄

First-principles density functional theory (DFT) and a many-body Green’s function method have been employed to elucidate the electronic, magnetic, and photonic properties of a spinel compound, Co₃O₄. Co₃O₄ is an antiferromagnetic semiconductor composed of cobalt ions in the Co²⁺ and Co³⁺ oxidation states. Co₃O₄ is believed to be a strongly correlated material, where the on-site Coulomb interaction (<i>U</i>) on Co d orbitals is presumably important, although this view has recently been contested. The suggested optical band gap for this material ranges from 0.8 to 2.0 eV, depending on the type of experiments and theoretical treatment. Thus, the correlated nature of the Co d orbitals in Co₃O₄ and the extent of the band gap are still under debate, raising questions regarding the ability of DFT to correctly treat the electronic structure in this material. To resolve the above controversies, we have employed a range of theoretical methods, including pure DFT, DFT+U, and a range-separated exchange–correlation functional (HSE06) as well as many-body Green’s function theory (i.e., the GW method). We compare the electronic structure and band gap of Co₃O₄ with available photoemission spectroscopy and optical band gap data and confirm a direct band gap of ca. 0.8 eV. Furthermore, we have also studied the optical properties of Co₃O₄ by calculating the imaginary part of the dielectric function (Im­(ε)), facilitating direct comparison with the measured optical absorption spectra. Finally, we have calculated the nearest-neighbor interaction (<i>J</i>₁) between Co²⁺ ions to understand the complex magnetic structure of Co₃O<sub>4