A Self-Adaptive Spin-Constrained First-Principles Approach for Excited Magnetic States

The profound impact of excited magnetic states on the intricate interplay between electron and lattice behaviors in magnetic materials is a topic of great interest. Unfortunately, despite the significant strides made in first-principles methods, accurately tracking these phenomena remains a challenging and elusive task. The crux of the challenge lies in characterizing the magnetic configuration of an excited state using density functional theory, a first-principle approach that is rooted in the system's ground state. We propose a versatile, self-adaptive spin-constrained density functional theory formalism. By iteratively optimizing the constraining field alongside the electron wave function during energy minimization, we obtain an accurate potential energy surface that captures both the longitudinal and transverse variations of magnetization in itinerant ferromagnetic Fe. Moreover, this technique allows us to identify the subtle coupling between magnetic moments and other degrees of freedom by tracking energy variation, providing new insights into the intricate interplay between magnetic interactions, electronic band structure, and phonon dispersion curves in single-layered CrI₃. This methodology represents a significant breakthrough in our ability to probe the complex properties of magnetic systems.