Transitions from a Kondo-like diamagnetic insulator into a modulated ferromagnetic metal in $\bm{\mathrm{FeGa}_{3-y}\mathrm{Ge}_y}$

One initial and essential question of magnetism is whether the magnetic properties of a material are governed by localized moments or itinerant electrons. Here we expose the case for the weakly ferromagnetic system FeGa$_{3-y}$Ge$_y$ wherein these two opposite models are reconciled, such that the magnetic susceptibility is quantitatively explained by taking into account the effects of spin-spin correlation. With the electron doping introduced by Ge substitution, the diamagnetic insulating parent compound FeGa$_3$ becomes a paramagnetic metal as early as at $ y=0.01 $, and turns into a weakly ferromagnetic metal around the quantum critical point $ y=0.15 $. Within the ferromagnetic regime of FeGa$_{3-y}$Ge$_y$, the magnetic properties are of a weakly itinerant ferromagnetic nature, located in the intermediate regime between the localized and the itinerant dominance. Our analysis implies a potential universality for all itinerant-electron ferromagnets.