*$g_{eff}^{\uparrow \downarrow}$* are higher than the available literature values for the systems with Pt. Also, it should be noted here that the values of *$g_{r}^{\uparrow \downarrow}$* and *$g_{eff}^{\uparrow \downarrow}$* are large compared to the other reported low damping system viz. $Y_3Fe_5O_{12}/Pt$, $CoFeB/Pt$, and $Co_2MnSi/Pt$ \[43,44\]. Therefore, $CFMS/Pt$ system can be potential system for spin transfer torque and logic devices. In addition to the *$g_{r}^{\uparrow \downarrow}$*, spin interface transparency (*T*) is another parameter which is useful for spin-orbit torque-based devices. The value of *T* is affected by the electronics structure matching of FM and HM layers. We used the following expression for the calculation of *T* \[45\]

$$\label{q13}
    T = \frac{g_{r}^{\uparrow \downarrow} tanh(\frac{t_{Pt}}{2 \lambda_{Pt}})}{g_{r}^{\uparrow \downarrow} coth(\frac{t_{Pt}}{\lambda_{Pt}})+\frac{h\sigma_{Pt}}{2e^2\lambda_{Pt}}}$$

where *$\sigma_{Pt}$* is the conductivity of Pt layer. For *$t_{Pt}$*=20 nm, *T* is calculated to be 0.84 $\pm$ 0.02 by Eq.\[q13\], which is much higher than the values reported in the literature for $NiFe/Pt$ and $Co/Pt$ systems \[46\]. Further it is also higher than the recent low damping $Co_2FeAl$/Ta layers system (68 $\%$) \[46\]. It means that in $Co_2Fe_{0.4}Mn_{0.6}Si$/Pt system, matching of electronic structure is better than the other reported systems. We also calculated the $\Theta_{SH}$ for the Pt using the following expression \[2\]:

$$\label{q14}
