Dimensional crossover in the magnetic properties of highly anisotropic antiferromagnets.

Abstract

Magnetic properties of highly anisotropic perovskites based on copper oxide planes have commonly been interpreted in terms of the free-spin-wave approximation to a Heisenberg model. For this model, we calculate the N\'eel temperature, the magnetic moment, the spin-wave velocity, and the first-nearest-neighbor instantaneous spin correlator by varying the anisotropy ratio \ensuremath{\epsilon}=${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/${\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}$ between the intraplane and interplane effective exchange couplings at three different levels of approximation: the ordinary free-spin-wave, the Tyablikov random-phase approximation (RPA), and a modified RPA obtained by adapting Callen original decoupling procedure. In all cases, we find that the crossover from three to two dimensions occurs at \ensuremath{\epsilon}\ensuremath{\approxeq}${10}^{\mathrm{\ensuremath{-}}3}$. By interpreting the available experimental data for ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ with our calculations, we also find that the value of \ensuremath{\epsilon} verges on the two-dimensional side, although it can vary by a factor ${10}^{2}$ depending on the approximation. Our results call for more accurate experimental determination and theoretical interpretation of the temperature-dependent magnetic excitations in the perovskite compounds. Their two-dimensional character favors, in fact, the existence of local magnetic excitations that outlive the disappearance of long-range order, as shown by the calculated behavior of the first-nearest-neighbor instantaneous spin correlator.