  We investigate the phase separation in one-dimensional Fermi gases on optical
lattices. The density distributions and the magnetization are calculated by
means of density-matrix renormalization method. The phase separation between
spin-up and spin-down atoms is induced by the interplay of the spin-dependent
harmonic confinement and the strong repulsive interaction between
intercomponent fermions. We find the existence of a critical repulsive
interaction strength above which the phase separation evolves. By increasing
the trap imbalance, the composite phase of Mott-insulating core is changed into
the one of ferromagnetic insulating core, which is incompressible and
originates from the Pauli exclusion principle.
