Using neutron diffraction under pressure at room temperature, we observed that pyrrhotite undergoes a ferrimagnetic to paramagnetic transition at about 2.8 GPa. Complete demagnetization of remanence at the same pressure is confirmed in an independent experiment. Such a process provides a quantitative explanation of the magnetic structure of the Martian Southern Hemisphere assuming that pyrrhotite is the major magnetic mineral and that our static experiments can be extrapolated to dynamic pressure conditions. Indeed, the 3 GPa isobaric line during the two large impacts of Argyre and Hellas separates the magnetized and unmagnetized zones. We also infer a reinterpretation of Martian meteorites paleomagnetic signal.