  We consider repulsively-interacting cold fermionic atoms loaded on an optical
ladder lattice in a trapping potential. The density-matrix
renormalization-group method is used to numerically calculate the ground state
for systematically varied values of interaction U and spin imbalance p in the
Hubbard model on the ladder. The system exhibits rich structures, where a fully
spin polarized phase, spatially separated from other domains in the trapping
potential, appears for large enough U and p. The phase-separated ferromagnetism
can be captured as a real-space image of the energy gap between the
ferromagnetic and other states arising from a combined effect of Nagaoka's
ferromagnetism extended to the ladder and the density dependence of the energy
separation between competing states. We also predict how to maximize the
ferromagnetic region.
