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We study the collective spin response and spin diffusion of an ultracold lithium Fermi gas artificially engineered in a fully ferromagnetic state, obtained by spatially segregating oppositely-oriented spins into two adjacent reservoirs. In this way, we show that strong repulsive interactions are sufficient to temporarily stabilize ferromagnetic correlations in a Fermi mixture. In particular, we reveal a substantial increase of the magnetic susceptibility of the gas while approaching the critical value of interaction. Correspondingly, we show that above the critical interaction a spin up-down domain wall can persist for a finite time, indicating the metastability of the ferromagnetic state. Such findings point to Stoner-like ferromagnetic instability driven only by short-range repulsion, and are consistent with our recent study of a repulsive Fermi liquid of polarons in strongly polarized Fermi gases. G. Valtolina, et al., |