Enhancement of antiferromagnetic correlations induced by nonmagnetic impurities: Origin and predictions for NMR experiments

Spin models that have been proposed to describe dimerized chains, ladders, two-dimensional antiferromagnets, and other compounds are studied here when some spins are replaced by spinless vacancies, such as it occurs by Zn doping. A small percentage of vacancies rapidly destroys the spin gap, and their presence induces enhanced antiferromagnetic correlations near those vacancies. The study is performed with computational techniques which includes Lanczos, world-line Monte Carlo, and the density-matrix renormalization-group methods. Since the phenomenon of enhanced antiferromagnetism is found to occur in several models and cluster geometries, a common simple explanation for its presence may exist. It is argued that the resonating-valence-bond character of the spin correlations at short distances of a large variety of models is responsible for the presence of robust staggered spin correlations near vacancies and lattice edges. The phenomenon takes place regardless of the long distance properties of the ground state, and it is caused by a “pruning” of the available spin singlets in the vicinity of the vacancies. The effect produces a broadening of the low-temperature NMR signal for the compounds analyzed here. This broadening should be experimentally observable in the structurally dimerized chain systems $\mathrm{Cu}({\mathrm{NO}}_3{)}_2\cdot 2.5{\mathrm{H}}_2\mathrm{O}$, ${\mathrm{CuWO}}_4$, $(\mathrm{VO}{)}_2{\mathrm{P}}_2{\mathrm{O}}_7$, and ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},$ in ladder materials such as ${\mathrm{SrCu}}_2{\mathrm{O}}_3$, in the spin-Peierls systems ${\mathrm{CuGeO}}_3$ and ${\mathrm{NaV}}_2{\mathrm{O}}_5$, and in several others since it is a universal effect common to a wide variety of models and compounds. In addition, it is argued that the Néel order observed in ${\mathrm{SrCu}}_2{\mathrm{O}}_3$ upon Zn doping is induced by the local antiferromagnetic order discussed in this paper, enhanced by a favorable ratio between the actual Heisenberg couplings along chains and rungs, as reported in recent experimental literature. Based on this reasoning it is predicted here that other ladder materials such as Zn-doped ${\mathrm{Cu}}_2({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2{)}_2{\mathrm{Cl}}_4$ will not present Néel order at small Zn concentrations.