The NMR relaxation rate of O in undoped Sr_2CuO_2Cl_2: Probing two-dimensional magnons at short distances

Abstract

We calculate the nuclear relaxation rate of oxygen in the undoped quasi two-dimensional quantum Heisenberg antiferromagnet Sr_2CuO_2Cl_2 above the Neel temperature. The calculation is performed at two-loop order with the help of the Dyson-Maleev formulation of the spin-wave expansion, taking all scattering processes involving two and three magnons into account. At low temperatures T we find 1 / T_1 = c_1 T^3 + c_2 T^4 + O (T^5), and give explicit expressions for the coefficients c_1 (two-magnon scattering) and c_2 (three magnon scattering). We compare our result with a recent experiment by Thurber et al. and show that this experiment directly probes the existence of short-wavelength magnons in a two-dimensional antiferromagnet.