Exchange stiffness in Co${}_2$-based Heusler compounds

We determine the spin wave exchange stiffness $D$ and the exchange constant $A$ for the full Heusler compound \CFS using Brillouin light scattering spectroscopy. We find an extraordinarily large value of $D=715\pm 20$ meV \AA${}^2$ ($A=31.5\pm 1.0$ pJ/m) which is, to the best of our knowledge, only surpassed by the intermetallic compound Fe${}_{53}$Co${}_{47}$ (J. Appl. Phys. $\mathbf{\text{75}}$, 7021 (1994)). Furthermore, we provide a systematization of the exchange stiffnesses determined for a variety of Co${}_2$-based Heusler compounds. We find that for the investigated compounds, the exchange stiffness is a function of the valence electron concentration and the crystallographic ordering. The exchange stiffness increases when the valence electron concentration and/or the amount of the L2${}_1$ ordering increase. A qualitative explanation for the dependence on the valence electron concentration is provided.