  We demonstrate the existence of a new type of spatially localized excitations
in the unitary Fermi gas: spin polarized droplets with a peculiar internal
structure involving the abrupt change of the pairing phase at the surface of
the droplet. It resembles the structure of the Josephson-$\pi$ junction
occurring when a slice of a ferromagnet is sandwiched between two
superconductors. The stability of the impurity is enhanced by the mutual
interplay between the polarization effects and the pairing field, resulting in
an exceptionally long-lived state. The prospects for its realization in
experiment are discussed.

Quantum Gases;Superconductivity