Noncollinear 3 k -type antiferromagnetic ground state and multipolar exchange interactions in uranium nitride

Understanding the fundamental properties of uranium nitride (UN) is critical for the development of accident-tolerant nuclear fuel and anticorrosion technology for uranium metal. Nevertheless, more complex magnetic configurations and possible multipolar interactions remain largely unexplored. Here, by combining the density functional theory with the magnetic multipolar Hamiltonian methods, and employing multiple calculational strategies such as the treatment of strong correlation interactions, regulation of spin-orbit coupling (SOC) magnitude, control of the $5f$ occupation matrix, constraint of magnetic orientation, and decomposition of magnetic interaction energy, we examined both collinear and noncollinear magnetic configurations in the UN compound. Typically, the local magnetic vectors in the $n\mathbf{k}$ ($n$ = 1--3) configurations were comprehensively evaluated. Our calculations showed that the SOC effect plays a decisive role in stabilizing the noncollinear multi-$\mathbf{k}$ states, with the longitudinal $3\mathbf{k}$ antiferromagnetic configuration identified as the magnetic ground state. We revealed that the magnetic quadrupole-quadrupole interaction contributes to the transverse $3\mathbf{k}$ configuration, while the magnetic dipole-dipole interaction contributes to the longitudinal $3\mathbf{k}$ configuration in UN. The theoretical framework presented, incorporating multiple strategies, offers valuable guidance for further studies on multi-$\mathbf{k}$ magnetic configurations in strongly correlated magnetic systems. Additionally, the interplay between SOC and multipolar magnetic interactions enhances our understanding of magnetic behavior in systems with highly localized $f$ electrons, such as actinide compounds.