  A theoretical study has been carried out to analyse the available results
from the inelastic neutron scattering experiment performed on a quasi-two
dimensional spin-1/2 ferromagnetic material $K_2CuF_4$. Our formalism is based
on a conventional semi-classical like treatment involving a model of an ideal
gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg
ferromagnet on a square lattice. The results for dynamical structure functions
for our model corresponding to spin-1/2, show occurrence of negative values in
a large range of energy transfer even encompassing the experimental range, when
convoluted with a realistic spectral window function. This result indicates
failure of the conventional theoretical framework to be applicable to the
experimental situation corresponding to low spin systems. A full quantum
formalism seems essential for treating such systems.
