We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component 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 the intercomponents. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.
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