A two-band model for magnetism is used to calculate the hardness constant in ferromagnetic systems. A band is narrow and degenerate, representing the "quasi-localized" electrons. The second is broad containing few traveling electrons. The transverse dynamic susceptibility is calculated in the random phase approximation (RPA). From the poles of susceptibility two spin wave modes are obtained: an acoustic mode and an optical mode. The value of the hardness constant of the acoustic spin wave is essential to satisfy the criterion of ferromagnetic stability at T = OK. It is shown that taking into account the interaction between inter-atomic exchange between electrons of the narrow bands is necessary for the hardness constant to assume the experimental value.
