Phase separation in optical lattices in a spin-dependent external potential

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.