  In order to demonstrate that atomic Fermi gas is a good experimental reality
in studying unsolved problems in frustrated interacting-spin systems, we
numerically examine the Mott core state emerged by loading two-component atomic
Fermi gases on triangular optical lattices. Consequently, we find that plateau
like structures are observable in the Mott core polarization as a function of
the population imbalance. These plateau states are caused by a flexibility that
the surrounding metallic region absorbs the excess imbalance to keep the
plateau states inside the Mott core. We also find spin patterns peculiar to the
plateau states inside the Mott core.
