Van Hove Singularity and Phase Instability: Exploring the Role of Electron Correlation in the Magnetic Behavior of $\mathrm{Fe}_{16}\mathrm{N}_2$
The ordered iron nitride phase $\alpha''-\mathrm{Fe}_{16}\mathrm{N}_2$ is a promising candidate for environment-friendly, rare-earth-free permanent magnets due to its demonstrated giant saturation magnetization ($M_s$). However, first-principles electronic-structure calculations have struggled to consistently reproduce experimentally-observed high $M_s$, and have yielded highly variable magneto-crystalline anisotropy (MCA) values. In this work, we employ Density Functional Theory under the GGA+$U$ framework to study the effect of the Hubbard parameters $U$ and $J$ on the magnetic properties of $\mathrm{Fe}_{16}\mathrm{N}_2$. We demonstrate that the electronic structure exhibits high sensitivity to these parameters, specifically uncovering a van Hove singularity near the Fermi level ($E_F$), inherently tied to the material's structural and thermal phase instability. By linking this topological anomaly to the calculated magnetic properties, we demonstrate that the selection of $U$ not only tunes $M_s$ and MCA energy towards experimental values but also reveals an underlying electronic mechanism potentially responsible for the phase's metastability. This provides a framework for understanding the correlation-driven magnetic behavior of $\mathrm{Fe}_{16}\mathrm{N}_2$ and offers a pathway for optimizing its stability and performance in practical applications.