  We have deposited polycrystalline Re doped $(Fe_{65}Co_{35})_{100-x}Re_{x}$
(0 $\leq$ x $\leq$ 12.6 at\%) thin films grown under identical conditions and
sandwiched between thin layers of Ru in order to study the phenomenon of spin
pumping as a function of Re concentration. In-plane and out-of-plane
ferromagnetic resonance spectroscopy results show an enhancement of the Gilbert
damping with an increase in Re doping. We found evidence of an increase in the
real part of effective spin mixing conductance
[Re($g^{\uparrow\downarrow}_{eff}$)] with the increase in Re doping of 6.6
at\%, while a decrease is evident at higher Re doping. The increase in
Re($g^{\uparrow\downarrow}_{eff}$) can be linked to the Re doping induced
change of the interface electronic structure in the non-magnetic Ru layer and
the effect interfacial spin-orbit coupling has on the effective spin-mixing
conductance. The lowest and highest values of
Re($g^{\uparrow\downarrow}_{eff}$) are found to be 9.883(02) $nm^{-2}$ and
19.697(02) $nm^{-2}$ for 0 at\% and 6.6 at\% Re doping, respectively. The
saturation magnetization decreases with increasing Re doping, from 2.362(13) T
for the undoped film to 1.740(03) T for 12.6 at\% Re doping. This study opens a
new direction of tuning the spin-mixing conductance in magnetic
heterostructures by doping of the ferromagnetic layerr, which is essential for
the realization of energy efficient operation of spintronic devices.
