Mn-based alloys exhibit unique properties in the spintronics materials possessing perpendicular magnetic anisotropy (PMA) beyond the Fe and Co-based alloys. It is desired to figure out the quantum physics of PMA inherent to Mn-based alloys, which have never been reported. Here, the origin of PMA in ferrimagnetic Mn_{3− δ} Ga ordered alloys is investigated to resolve antiparallel-coupled Mn sites using x-ray magnetic circular and linear dichroism (XMCD/XMLD) and a first-principles calculation. We found that the contribution of orbital magnetic moments in PMA is small from XMCD and that the finite quadrupole-like orbital distortion through spin-flipped electron hopping is dominant from XMLD and theoretical calculations. These findings suggest that the spin-flipped orbital quadrupole formations originate from the PMA in Mn_{3− δ} Ga and bring the paradigm shift in the researches of PMA materials using x-ray magnetic spectroscopies.