We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.
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