Insights into the bonding properties and magnetism of the Mn-B system with a physically constrained neural network functional

In this study, we explore the manganese borides (Mn-B) system, chiefly on its complex magnetic properties that are of extensive academic interest and of significant potential for applications in magnetism. We employed an approach by using a machine-learning trained, physically constrained neural network functional to reevaluate the Mn-B system comprehensively. This offers insights into several contentious aspects of the system from an enthalpy perspective, including the spin frustration in $\mathrm{M}{\mathrm{n}}_{2}\mathrm{B}$, the ground state of $\mathrm{Mn}{\mathrm{B}}_{2}$, and the ongoing debates about the synthesis and various phases of MnB and $\mathrm{Mn}{\mathrm{B}}_{4}$. Additionally, we establish a nearly linear relationship between the bonding strength and measured hardness in borides, which enhances the understanding of their mechanical properties with our proposed descriptor of bonding strength. Spin dynamics predictions highlight both discrepancies and consistencies related to the itinerant characteristics of magnetic moments, primarily driven by a high density of states of the magnetic atoms at the Fermi level (${E}_{\mathrm{F}}$). This suggests that traditional local-moment models may be inadequate for describing these itinerant magnetic systems. This work provides insight for understanding the bonding properties and magnetism of magnetic intermetallic compounds.