  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$_{3-{\delta}}$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$_{3-{\delta}}$Ga and bring the paradigm shift in the researches of PMA
materials using x-ray magnetic spectroscopies.
