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

TL;DR

This paper calculates the NMR relaxation rate of oxygen in a 2D quantum antiferromagnet, revealing how short-wavelength magnons influence relaxation and comparing theoretical predictions with experimental data.

Contribution

It provides a detailed two-loop order calculation of the relaxation rate, explicitly including two- and three-magnon scattering processes, and links theory with experimental observations.

Findings

The relaxation rate follows a T^3 and T^4 dependence at low temperatures.

Explicit coefficients for two- and three-magnon scattering are derived.

Experimental data confirms the presence of short-wavelength magnons.

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.