Ultrafast spin relaxation in two-dimensional (2D) magnets is a cutting-edge topic in next-generation spintronics. Among existing 2D magnets, $\mathrm{F}{\mathrm{e}}_{3\text{−}x}{\mathrm{GaTe}}_2$ (FGT) is one of the few systems exhibiting room-temperature ferromagnetism and strong perpendicular magnetic anisotropy. However, the role of Fe-deficient non-stoichiometric nature in FGT remains poorly understood. In this work, we investigate the effect of nonstoichiometry (i.e., $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}$ vacancies, $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ vacancies, and $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}-\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ covacancies) on the ultrafast spin dynamics of FGT by combining first-principles-based nonadiabatic molecular dynamics (NAMD) with phonon spectrum analysis. We identify two distinct spin relaxation pathways arising by the competition between spin orbit coupling (SOC) and electron phonon coupling (EPC): (1) a two-step process mediated by SOC and SOC-EPC occurring within and between Fe sites (path1), and (2) a direct EPC-driven $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}\text{−}3d$ spin-up to $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}\text{−}3d$ spin-up transition (path2). The latter pathway dominates the ultrafast relaxation, yielding a characteristic relaxation time of $\sim 100$ fs in $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$-deficient systems. Different Fe-vacancy configurations can modify the SOC- and EPC-assisted relaxation pathways: $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ vacancies enhance EPC and accelerate spin decay; $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}$ vacancies suppress EPC and prolong spin lifetimes, while $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}\text{−}\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ co-vacancies provide a balanced modulation. These results indicate that Fe vacancies can modify the ultrafast spin-relaxation timescale and the associated electronic relaxation pathways in two-dimensional FGT.

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• Ferromagnetism
• Ultrafast magnetization dynamics
• 2-dimensional systems
• Density functional calculations
• Molecular dynamics