Quantum Monte Carlo simulations for stacked spin-ladder systems containing low concentrations of nonmagnetic impurities: Application to the low-temperature broadening of NMR spectra in SrCu_2O_3

摘要

We present a quantum Monte Carlo study for Heisenberg spin-1/2 two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu_(1-x)Zn_x)_2O_3, where a large broadening of the ~(65)Cu NMR lines has been observed in experiment at low temperatures but far above the Neel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as x = 0.001 and x = 0.0025, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.