  Spin semimetals are amongst the most recently discovered new class of
spintronic materials, which exhibit a band gap in one spin channel and
semimetallic feature in the other, thus facilitating tunable spin transport.
Here, we report Mn$_2$IrGa to be a candidate material for spin semimetal along
with giant coercivity and spin-valve characteristics using a combined
experimental and theoretical study. The alloy crystallizes in an inverse
Heusler structure (without any martensitic transition) with a para- to
ferri-magnetic transition at $T_\mathrm{C} \sim$ 243 K. It shows a giant
coercive field of about 8.5 kOe (at 2 K). The negative temperature coefficient,
relatively low magnitude and weak temperture dependance of electrical
resistivity suggest the semimetallic character of the alloy. This is further
supported by our specific heat measurement. Magnetoresistance (MR) confirms an
irreversible nature (with its magnitude $\sim$1\%) along with a change of sign
across the magnetic transition indicating the potentiality of Mn$_2$IrGa in
magnetic switching applications. In addition, asymmetric nature of MR in the
positive and negative field cycles is indicative of spin-valve characteristics.
Our ab-initio calculations confirm the inverse Heusler structure with
ferrimagnetic ordering to be the lowest energy state, with a saturation
magnetization of 2 $\mu_\mathrm{B}$. $<100>$ is found to be the easy magnetic
axis with considerable magneto-crystalline anisotropy energy. A large positive
Berry flux at/around $\Gamma$ point gives rise to an appreciable anomalous Hall
conductivity ($\sim$-180 S/cm).
