Effective sublattice magnetization and Néel temperature in quantum antiferromagnets

Abstract

We present an analytic expression for the finite temperature sublattice magnetization which would be detected by inelastic neutron-scattering experiments performed on a two-dimensional square-lattice quantum Heisenberg antiferromagnet with short-range N\'eel order. Our expression, which has no adjustable parameters, is able to reproduce both the qualitative behavior of the phase diagram $M(T)\ifmmode\times\else\texttimes\fi{}T$ and the experimental values of the N\'eel temperature ${T}_{N}$ for either doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.15}$ and stoichiometric ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ compounds. Finally, we remark that by incorporating frustration and three-dimensional effects as perturbations is sufficient to explain the deviation of the experimental data from our theoretical curves.