  We report the structural, transport, electronic, and magnetic properties of
Co$_2$FeGa Heusler alloy nanoparticles. The Rietveld refinements of x-ray
diffraction (XRD) data with the space group Fm$\bar {3}$m clearly demonstrates
that the nanoparticles are of single phase. The particle size (D) decreases
with increasing the SiO$_2$ concentration. The Bragg peak positions and the
inter-planer spacing extracted from high-resolution transmission electron
microscopy image and selected area electron diffraction are in well agreement
with data obtained from XRD. The coercivity initially increases from 127~Oe to
208~Oe between D = 8.5~nm and 12.5~nm, following the D$^{-3/2}$ dependence and
then decreases with further increasing D up to 21.5~nm with a D$^{-1}$
dependence, indicating the transition from single domain to multidomain regime.
The effective magnetic anisotropic constant behaves similarly as coercivity,
which confirms this transition. A complex scattering mechanisms have been
fitted to explain the electronic transport properties of these nanoparticles.
In addition we have studied core-level and valence band spectra using
photoemission spectroscopy, which confirm the hybridization between $d$ states
of Co/Fe. Further nanoparticle samples synthesized by co-precipitation method
show higher saturation magnetization. The presence of Raman active modes can be
associated with the high chemical ordering, which motivates for detailed
temperature dependent structural investigation using synchrotron radiation and
neutron sources.
