  In this report, we present structural, electronic, magnetic and transport
properties of Co-rich spin gapless semiconductor CoFeCrGa using both
theoretical and experimental techniques. The key advantage of Co-rich samples
$\mathrm{Co_{1+x}Fe_{1-x}CrGa}$ is the high Curie temperature (T$\mathrm{_C}$)
and magnetization, without compromising the SGS nature (up to x = 0.4), and
hence our choice. The quaternary Heusler alloys $\mathrm{Co_{1+x}Fe_{1-x}CrGa}$
(x = 0.1 to 0.5) are found to crystallize in LiMgPdSn-type structure having
space group $F\bar{4}3m$ (\# 216). The measured Curie temperature increases
from 690 K (x = 0) to 870 K (x = 0.5). Observed magnetization values follow the
Slater-Pauling rule. Measured electrical resistivity, in the temperature range
of 5-350 K, suggests that the alloys retain the SGS behavior up to x = 0.4,
beyond which it reflects metallic character. Unlike conventional
semiconductors, the conductivity value ($\mathrm{\sigma_{xx}}$) at 300 K lies
in the range of 2289 S $\mathrm{cm^{-1}}$ to 3294 S $\mathrm{cm^{-1}}$, which
is close to that of other reported SGS materials. The anomalous Hall effect is
comparatively low. The intrinsic contribution to the anomalous Hall
conductivity increase with x, which can be correlated with the enhancement in
chemical order. The anomalous Hall coefficient is found to increase from 38
S/cm for x = 0.1 to 43 S/cm for 0.3. Seebeck coefficients turn out to be
vanishingly small below 300 K, another signature for being SGS. All the alloys
(for different x) are found to be both chemically and thermally stable.
Simulated magnetization agrees fairly with the experiment. As such Co-rich
CoFeCrGa is a promising candidate for room temperature spintronic applications,
with enhanced T$\mathrm{_C}$, magnetic properties and SGS nature.
