It is related to the spin wave dispersion relation and the domain wall width (with the proper rescaling). Therefore, it is very interesting constant. More fundamentally, it is linked to the local exchange and is related to the Curie temperature but this last is more difficult to extract.
Thank you for the answer.....for a particular ferromagnetic material does A change with applied external field. Because the domain wall width changes with field
Domain wall width depends on the effective magnetic anisotropy and the exchange stiffness. Therefore, applying the out-of-plane magnetic field leads to no change in the domain wall width. However, applying the in-plane field would offset the effective anisotropy, leading to the change in domain wall width. As for the another use of exchange stiffness, apart from influencing the domain wall width, it also affects the domain wall energy, which in turn, directly affects the average domain size in materials.