  We calculate transverse spin susceptibility in the linear response method
based on the ground states determined in the quasi-particle self-consistent
$GW$ (QSGW) method. Then we extract spin wave (SW) dispersions from the
susceptibility. We treat bcc Fe, hcp Co, fcc Ni, and B2-type FeCo. Because of
the better description of the independent-particle picture in QSGW, calculated
spin stiffness constants for Fe, Co, and Ni give much better agreement with
experiments in QSGW than that in the local density approximation (LDA), where
the stiffness for Ni in LDA is two times bigger than the experiment. For Co,
both acoustic and optical branches of SWs agree with the experiment. As for
FeCo, we have some discrrepancy between the spin stiffness in QSGW and that in
the experiment. We may need further theoretical and experimental investigations
on the discrepancy.
