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Artificial ferrimagnetic [D022-Mn3Ga/Co2MnSi]N superlattices ([Mn3Ga/CMS]N SLs) combining perpendicular magnetic anisotropy as well as exceptional thermal and magnetic stability hold promises in functional spintronic devices. However, the relevant precession dynamics are still lacking. Here, we report on the magnetic dynamic properties in [Mn3Ga/CMS]5 SLs investigated by the time-resolved magneto-optical Kerr effect (TRMOKE) measurements. The magnetization precession process and magnetic damping constant (α0) of [Mn3Ga/CMS]5 SLs rely heavily on the thickness of Mn3Ga layer (tMn3Ga). In addition, α0 is found to be higher with increasing tMn3Ga, but is not simply scaled by the uniaxial magnetic anisotropy (Ku), which can be ascribed to the contribution of spin–orbit interaction combined with the additional contributions, like spin-pumping. Furthermore, a large Ku value of 1.33 Merg/cm3 and a low α0 of 0.022 have been simultaneously obtained in [Mn3Ga/CMS]5 SL with tMn3Ga = 1.5 nm. This study contributes to the design of high-performance spintronic devices based on [Mn3Ga/CMS]N SLs. [ABSTRACT FROM AUTHOR]