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Employing first principles electronic structure calculations in conjunctionwith the frozen-magnon method we calculate exchange interactions, spin-wavedispersion, and spin-wave stiffness constants in inverse-Heusler-based spingapless semiconductor (SGS) compounds Mn$_2$CoAl, Ti$_2$MnAl, Cr$_2$ZnSi,Ti$_2$CoSi and Ti$_2$VAs. We find that their magnetic behavior is similar tothe half-metallic ferromagnetic full-Heusler alloys, i.e., the intersublatticeexchange interactions play an essential role in the formation of the magneticground state and in determining the Curie temperature, $T_\mathrm{c}$. Allcompounds, except Ti$_2$CoSi possess a ferrimagnetic ground state. Due to thefinite energy gap in one spin channel, the exchange interactions decay sharplywith the distance, and hence magnetism of these SGSs can be describedconsidering only nearest and next-nearest neighbor exchange interactions. Thecalculated spin-wave dispersion curves are typical for ferrimagnets andferromagnets. The spin-wave stiffness constants turn out to be larger thanthose of the elementary 3$d$-ferromagnets. Calculated exchange parameters areused as input to determine the temperature dependence of the magnetization and$T_\mathrm{c}$ of the SGSs. We find that the $T_\mathrm{c}$ of all compounds ismuch above the room temperature. The calculated magnetization curve forMn$_2$CoAl as well as the Curie temperature are in very good agreement withavailable experimental data. The present study is expected to pave the way fora deeper understanding of the magnetic properties of the inverse-Heusler-basedSGSs and enhance the interest in these materials for application in spintronicand magnetoelectronic devices.

First-principles calculations of exchange interactions, spin waves, and  temperature dependence of magnetization in inverse-Heusler-based spin gapless  semiconductors