Theory of magnetic 3d transition metal dopants in gallium nitride

Using first-principles density functional theory (DFT) methods and size-converged supercell models, we analyze the electronic and atomic structure of magnetic 3d transition metal dopants in cubic gallium nitride (c-GaN). All stable defect charge states for Fermi levels across the full experimental gap are computed using a method that correctly resolves the boundary condition problem (without a jellium approximation) and eliminates finite-size errors. The resulting computed defect levels are not impacted by the DFT band-gap problem, they span a width consistent with the experimental gap rather than being limited to the single-particle DFT gap. All defects with electronically degenerate (half-metal) Td ground states are found to have significant distortions, relaxing to D2d structures driven by the Jahn-Teller instability. This leads to insulating ground states for all substitutional 3d dopants, refuting claims in the literature that +U or hybrid functional methods are required to avoid artificial half-metal results. Interpreting the dn atomic occupations within a crystal-field model and exchange splittings, we identify a systematic trend across the 3d transition metal series. Approaches to estimate excited-state energies as observed in photoluminescence from defect centers are assessed, ranging from a Koopmans-type single-particle energy interpretation to relaxed total energy differences in fully self-consistent DFT. The single-particle interpretations are found to be qualitatively predictive and the calculations are consistent with the limited available experimental data across the 3d dopant series. These results provide a baseline understanding to guide future studies and a conceptual framework within which to interpret new results.

Automated summary

Using first-principles density functional theory, this study analyzes the electronic and atomic structure of 3d transition metal dopants in cubic gallium nitride. The calculations accurately determine the stable defect charge states across the experimental gap without relying on approximations or finite-size errors. The results show that substitutional 3d dopants have insulating ground states due to significant distortions driven by the Jahn-Teller instability, refuting the need for +U or hybrid functional methods to avoid artificial half-metal results.