  The core structure of multiply quantized vortices is theoretically
investigated in fermionic superfluid near Feshbach resonance. Under population
imbalance in two hyperfine spin states, the vortex core is filled in by the
``paramagnetic moment''. Here, we find the spatial oscillation of the
magnetization inside the core sensitively due to the topological structure of
the pairing field, in the range from the weak coupling regime to the unitary
limit. This magnetization inside the giant core reveals the winding number of
the vortex and directly results from the low-lying quasiparticle states bound
inside the core. It is therefore proposed that the density profile experiment
using phase contrast imaging can provide the spectroscopy of novel core level
structures in giant vortices. To help the understanding on these outcomes, we
also derive the analytic solution for the low-lying quasiparticle states inside
the core of a multiply quantized vortex.
