On the estimate of the spin-gap in quasi-1D Heisenberg antiferromagnets from nuclear spin-lattice relaxation

We present a careful analysis of the temperature dependence of the nuclear spin-lattice relaxation rate $1\mathrm{/}{T}_1$ in gapped quasi-1D Heisenberg antiferromagnets. It is found that in order to estimate the value of the gap correctly from $1\mathrm{/}{T}_1$ the peculiar features of the dispersion curve for the triplet excitations must be taken into account. The temperature dependence of $1\mathrm{/}{T}_1$ due to two-magnon processes, is reported for different values of the ratio $r=J_{\perp }\mathrm{/}{J}_{\parallel }$ between the superexchange constants in a 2-leg-ladder. As an illustrative example we compare our results to the experimental findings for ${}^{63}Cu1\mathrm{/}{T}_1$ in the dimerized chains and 2-leg-ladders contained in Sr${}_{14}C{u}_{24}{O}_{41}$