Not yet reviewed by Pith; the record is open.

By using a multiscale approach based on first-principles density functional theory combined with atomistic spin dynamics, we investigate the electronic structure and magnetization dynamics of an inverse Heusler and a Heusler compound and their alloys, i. e. Mn$_{2-x}Z_x$CoAl and Mn$_{2-x}Z_x$VAl, where $Z$ = Mo, W, Os and Ru, respectively. A signature of the ferrimagnetic ordering of Mn$_{2}$CoAl and Mn$_{2}$VAl Heusler alloys is reflected in the calculated Heisenberg exchange constants. They decay very rapidly with the interatomic distance and have short range, which is a consequence of the existence of the finite gap in the minority spin band. The calculated Gilbert damping parameter of both Mn$_2$CoAl and Mn$_2$VAl is high compared to other half-metals, but interestingly in the particular case of the inverse Mn$_{2}$CoAl alloys and due to the spin-gapless semiconducting property, the damping parameters decrease with the doping concentration in clear contradiction to the general trend. Atomistic spin dynamics simulations predict ultrafast magnetisation switching in Mn$_{2}$CoAl and Mn$_{2}$VAl under the influence of an external magnetic field, starting from a threshold field of $2\text{T}$. Our overall finding extends with Heusler and inverse Heusler alloys, the class of materials that exhibits laser induced magnetic switching.