Theoretical analysis of neutron scattering results for quasi-two dimensional quantum anti-ferromagnet - possible role of Berezinskii - Kosterlitz - Thouless transition

Abstract

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. Use of a refined realistic spectral window function however, minimizes unwanted oscillations but, the negative values of integrated intensity still persist within the experimental range. These results indicate failure of the semi-classical theoretical model of ideal vortex/anti-vortex gas. A full quantum formalism and treatment seem essential for treating such low spin systems. Furthermore, a severe disagreement is found to occur between the integrated intensities at finite values of energy transfer obtained theoretically from the present 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 vortices/merons (and anti-vortices/anti-merons).