Semi-phenomenological analysis of neutron scattering results for quasi-two dimensional quantum anti-ferromagnet

The available results from the inelastic neutron scattering experiment performed on the quasi-two dimensional spin $\frac{1}{2}$ anti-ferromagnetic material $La_2 Cu O_4$ have been analysed theoretically. The formalism of ours is based on a semi-classical like treatment involving a model of an ideal gas of mobile vortices and anti-vortices built on the background of the N$\acute{e}$el state, using the bipartite classical spin configuration corresponding to an XY- anisotropic Heisenberg anti-ferromagnet on a square lattice. The results for the integrated intensities for our spin $\frac{1}{2}$ model corresponding to different temperatures, show occurrence of vigorous unphysical oscillations, when convoluted with a realistic spectral window function. These results indicate failure of the conventional semi-classical theoretical model of ideal vortex/anti-vortex gas arising in the Berezinskii-Kosterlitz-Thouless theory for the low spin magnetic systems. A full fledged quantum mechanical formalism and calculations seem crucial for the understanding of topological excitations in such low spin systems. Furthermore, a severe disagreement is found to occur at finite values of energy transfer between the integrated intensities obtained theoretically from the conventional formalism and those obtained experimentally. This further suggests strongly that the full quantum treatment should also incorporate the interaction between the fragile-magnons and the topological excitations. This is quite plausible in view of the recent work establishing such a process in XXZ quantum ferromagnet on 2D lattice. The high spin XXZ quasi-two dimensional antiferromagnet like $MnPS_3$ however follows the conventional theory quite well