  We report a successful combination of magnetic force linear response theory
with quasiparticle self-consistent GW method. The self-consistently determined
wavefunctions and eigenvalues can just be used for the conventional magnetic
force calculations. While its formulation is straightforward, this combination
provides a way to investigate the effect of GW self-energy on the magnetic
interactions which can hardly be quantified due to the limitation of current GW
methodology in calculating the total energy difference in between different
magnetic phases. In ferromagnetic $3d$ elements, GW self-energy slightly
reduces the $d$ bandwidth and enhances the interactions while the same
long-range feature is maintained. In antiferromagnetic transition-metal
monoxides, QSGW significantly reduces the interaction strengths by enlarging
the gap. Orbital-dependent magnetic force calculations show that the coupling
between $e_g$ and the nominally-empty $4s$ orbital is noticeably large in MnO
which is reminiscent of the discussion for cuprates regarding the role of
Cu-$4s$ state. This combination of magnetic force theory with quasiparticle
self-consistent GW can be a useful tool to study various magnetic materials.
