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arXiv:cond-mat/0109095 · Physical review. B, Condensed matter

Absence of effective spins 12 induced by nonmagnetic impurities in a class of low-dimensional magnets

Bruce Normand, Frédéric Mila

Published Feb 12, 2002• 20 citations
arXivHTMLPDF

Abstract

We show that doping a Majumdar--Ghosh chain with non-magnetic impurities does {\it not} produce almost free spins 1/2. The difference between this system and other spin liquids, such as unfrustrated spin ladders, is illustrated in the context of the general dimerized, frustrated spin chain. By detailed analysis of the excitation spectra of finite chains with two impurities, we investigate the evolution of the screening affecting impurity-induced free spins, and of the sign and magnitude of their effective interactions. We comment on a possible connection to impurity-doping experiments in CuGeO_3.

DOI
10.1103/physrevb.65.104411

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We show that doping a Majumdar--Ghosh chain with non-magnetic impurities does {\it not} produce almost free spins 1/2. The difference between this system and other spin liquids, such as unfrustrated spin ladders, is illustrated in the context of the general dimerized, frustrated spin chain. By detailed analysis of the excitation spectra of finite chains with two impurities, we investigate the evolution of the screening affecting impurity-induced free spins, and of the sign and magnitude of their effective interactions. We comment on a possible connection to impurity-doping experiments in CuGeO_3.
The magnetic responses of a spin-1/21/21/2 ladder doped with nonmagnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by Sigrist and Furusaki [M. Sigrist and A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996)] and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte Carlo simulations gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response that is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature and with quantum Monte Carlo simulations at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2{}_{2}2​PO6{}_{6}6​ compound and other spin-gapped materials are briefly mentioned.
Effects of nonmagnetic impurity doping on an AF spin-1/2 Heisenberg ladder system are studied by the QMC method. A single nonmagnetic impurity induces a localized spin-1/2 moment accompanied by "static" and enhanced AF correlations around it. Small and finite concentration of impurities induces a remarkable change of magnetic and thermodynamic properties with gapless excitations. It also shows rather sharp but continuous crossover around the concentration of about 4%. Above the crossover concentration, all the spins are strongly coupled participating in the enhanced and rather uniform power-law decay of the antiferromagnetic correlation. Below the crossover, each impurity forms an antiferromagnetic cluster only weakly coupled each other. For random distribution of impurities, large Curie-like susceptibility accompanied with small residual entropy is obtained at low temperatures in agreement with recent experimental observation in Zn-doped SrCu2O3SrCu_{2}O_{3}SrCu2​O3​. Temperature dependence of AF susceptibility shows power-law-like but weaker divergence than the single chain AFH in the temperature range studied.
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We investigate antiferromagnetic spin ladders with nonmagnetic impurities by variational and numerical [Lanczos and density matrix renormalization group (DMRG)] methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchange interaction Jeff{\mathrm{J}}_{\mathrm{eff}}Jeff​, the magnitude of which depends on the impurity distance. The magnitude of Jeff{\mathrm{J}}_{\mathrm{eff}}Jeff​ is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to six impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.
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