from the strongly attractive to the strongly repulsive regime of interactions [@partridge2006pairing; @iskin2007mixtures; @cazalilla2009ultracold; @jo2009itinerant; @cazalilla2009ultracold; @greif2013short; @cherng2007superfluidity; @sanner2012correlations]. For instance, referring to attractive particle imbalanced FF mixtures it has been shown that beyond a critical polarization the mixture forms a superfluid paired core being surrounded by a shell of unpaired fermions [@partridge2006pairing; @iskin2007mixtures]. Turning to the repulsive regime of interactions magnetization effects emerge. For increasing repulsion, a first order phase transition [@cazalilla2009ultracold] between paramagnetism and itinerant ferromagnetism [@jo2009itinerant; @cazalilla2009ultracold; @greif2013short; @cherng2007superfluidity; @sanner2012correlations] has been revealed. It has been argued that this transition can be described by the mean-field model of Stoner [@stoner1933lxxx; @snoke2009solid] for strongly short-range repulsively interacting fermions.

The majority of the above-mentioned studies has been focussed on the static properties of FF mixtures within a Hartree-Fock (HF) i.e. mean-field description in higher dimensions. Most importantly, the dynamical properties of FF mixtures are largely unexplored and especially the role of many-body (MB) effects is much less understood. An intriguing prospect here is whether magnetization or phase separation effects emerge during the nonequilibrium dynamics of FF mixtures. A widely used technique to induce the nonequilibrium dynamics is the so-called quantum quench [@polkovnikov2011colloquium; @langen2015ultracold], where the quantum evolution is generated 