Staggered-spin contribution to nuclear spin-lattice relaxation in two-leg antiferromagnetic spin-1/2 ladders

We study the nuclear spin-lattice relaxation rate $1\mathrm{/}{T}_1$ in the two-leg antiferromagnetic spin-1/2 Heisenberg ladder. More specifically, we consider the contribution to $1\mathrm{/}{T}_1$ from the processes with momentum transfer $(\pi ,\pi )$. In the limit of weak coupling between the two chains, this contribution is of activation type with gap $2\mathrm{\Delta }$ at low temperatures ($\mathrm{\Delta }$ is the spin gap), but crosses over to a slowly-decaying temperature dependence at the crossover temperature $T\approx \mathrm{\Delta }$. This crossover possibly explains the recent high-temperature NMR results on ladder-containing cuprates by T. Imai et al.