We present experimental results of transverse electron focusing measurements performed on an n-type GaAs based mesoscopic device consisting of one-dimensional (1D) quantum wires as injector and detector. We show that non-adiabatic injection of 1D electrons at a conductance of e$^2$/h results in a single first focusing peak, which on gradually increasing the injector conductance up to 2e$^2$/h , produces asymmetric two sub-peaks in the first focusing peak, each sub-peak representing the population of spin-state arising from the spatially separated spins in the injector. Further increasing the conductance flips the spin-states in the 1D channel thus reversing the asymmetry in the sub-peaks. On applying a source-drain bias, the spin-gap, so obtained, can be resolved thus providing evidence of exchange interaction induced spin polarisation in the 1D systems.
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