Abstract Spin Matrix theory (SMT) limits provide a way to capture the dynamics of the AdS/CFT correspondence near BPS bounds. On the string theory side, these limits result in non-relativistic sigma models that can be interpreted as novel non-relativistic strings. This SMT string theory couples to non-relativistic U(1)-Galilean background geometries. In this paper, we explore the relation between pp-wave backgrounds obtained from Penrose limits of AdS5 × S5, and a new type of U(1)-Galilean backgrounds that we call flat-fluxed (FF) backgrounds. These FF backgrounds are the simplest possible SMT string backgrounds and correspond to free magnons from the spin chain perspective. We provide a catalogue of the U(1)-Galilean backgrounds one obtains from SMT limits of string theory on AdS5 × S5 and subsequently study large charge limits of these geometries from which the FF backgrounds emerge. We show that these limits are analogous to Penrose limits of AdS5 × S5 and demonstrate that the large charge/Penrose limits commute with the SMT limits. Finally, we point out that U(1)-Galilean backgrounds prescribe a symplectic manifold for the transverse SMT string embedding fields. This is illustrated with a Hamiltonian derivation for the SMT limit of a particle.