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arXiv:cond-mat/9609038 · Journal of the Physical Society of Japan

Effects of Nonmagnetic Impurity Doping on Spin Ladder System

Youichirou Iino, Masatoshi Imada

Published Dec 15, 1996• 39 citations
arXivHTMLPDF

Abstract

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 $SrCu_{2}O_{3}$. Temperature dependence of AF susceptibility shows power-law-like but weaker divergence than the single chain AFH in the temperature range studied.

DOI
10.1143/jpsj.65.3728

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Low-Temperature Properties of the Randomly Depleted Heisenberg Ladder

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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.
Effects of nonmagnetic impurity doping in a spin ladder system with a spin gap are investigated by the exact diagonalization as well as by the variational Monte Carlo calculations. Substantial changes in macroscopic properties such as enhancements in spin correlations and magnetic susceptibilities are observed in the low impurity concentration region, which are caused by the increase of low-energy states. These results suggest that small but finite amount of nonmagnetic impurity doping relevantly causes the reduction or the vanishment of the spin gap. This qualitatively explains the experimental result of Zn-doped SrCu2_{2}2​O3_{3}3​ where small doping induces gapless nature. We propose a possible scenario for this drastic change as a quantum phase transition in a spin gapped ladder system due to spinon doping effects.
We present a quantum Monte Carlo study for Heisenberg spin-12\frac{1}{2}21​ two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu${}_{1\ensuremath{-}x}$Znx{}_{x}x​)2{}_{2}2​O3{}_{3}3​, where a large broadening of the 65{}^{65}65Cu NMR lines has been observed in experiment at low temperatures but far above the N\'eel 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=0.001x=0.001x=0.001 and x=0.0025x=0.0025x=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.
Magnetic correlations are studied in a two-leg Hubbard ladder doped with nonmagnetic impurities using finite temperature quantum Monte Carlo (FTQMC) method. A number of relevant macroscopic quantities calculated as a function of temperature T and impurity concentration are found to exhibit significantly renormalized behavior, a feature noted in many experiments. The uniform magnetic susceptibility χ0(T) for the impurity doped system shows a cusplike behavior followed by a sharp increase at lower temperatures, signaling the formation of impurity induced free magnetic moments, while it diminishes rapidly for the pure system. The spin correlations are found to increase in the vicinity of an impurity. To investigate the effect of nonmagnetic impurities on the spin wave modes in the system, spin wave velocity vsw is calculated as a function of impurity concentration. The result shows that vsw is reduced by nonmagnetic impurities, indicating softening of the modes. Simulations are performed slightly away from half filling and kinetic energy of the electrons in the neighborhood of an impurity site is calculated to study the interplay between impurities and holes. However, contrary to previous experimental observations on two dimensional lattices where nonmagnetic impurities reduce hole mobility, no noticeable effect of impurity on the mobility of the neighboring electrons is found in our calculation.
We discuss the effects of nonmagnetic impurities (static holes) in the S=1/2S=1/2S=1/2 Heisenberg model on a two-dimensional (2D) square lattice, and on two- and three-leg ladders. Results of quantum Monte Carlo simulations show that a free localized moment is induced around an isolated impurity only in the spin-gapped two-leg ladder, in agreement with previous theoretical expectations. The localization length of the S=1/2S=1/2S=1/2 impurity moment in a two-leg ladder with isotropic couplings is $\ensuremath{\approx}1.5$ lattice spacings. In gapless ladders (odd number of legs) and in the 2D lattice, no free moments are induced. However, in the 2D system, which has antiferromagnetic long-range order at T=0T=0T=0 and a gap for longitudinal fluctuations, the impurity leads to a localized distortion of the magnetization in the direction of the broken symmetry, with total Sz=1/2.{S}^{z}=1/2.Sz=1/2. The shape of the distortion is in close agreement with previous spin-wave calculations. For all the systems, a staggered moment is induced by the impurity. For the gapped two-leg ladder this is exponentially localized within a length equal to the spin correlation length of the ladder ($\ensuremath{\approx}3.2$ lattice spacings). For the three-leg ladder, the integrated staggered moment diverges as the system size goes to infinity, but the staggered magnetization at a given site appears to vanish. In 2D, we discuss the behavior seen in finite systems both with and without additional symmetry-breaking mechanisms. We also discuss the effect of impurities on the NMR Knight shift and the bulk magnetic susceptibility.
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 $\mathrm{Cu}({\mathrm{NO}}_{3}{)}_{2}\ensuremath{\cdot}2.5{\mathrm{H}}_{2}\mathrm{O}$, CuWO4{\mathrm{CuWO}}_{4}CuWO4​, (VO)2P2O7(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}(VO)2​P2​O7​, and Sr14Cu24O41,{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},Sr14​Cu24​O41​, in ladder materials such as SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​, in the spin-Peierls systems CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ and NaV2O5{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}NaV2​O5​, 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 N\'eel order observed in SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ 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 Cu2(C5H12N2)2Cl4{\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}Cu2​(C5​H12​N2​)2​Cl4​ will not present N\'eel order at small Zn concentrations.
Low-temperature thermodynamic properties of the spin-1/2 Heisenberg ladder system with non-magnetic impurities are discussed using an effective Hamiltonian for the impurity-induced spins in the background of a spin liquid with a gap. It is shown that the uniform susceptibility shows Curie-like behavior in high-, intermediate-, and low-temperature regimes, with three different Curie constants. The ratio of specific heat to temperature, C/T, is divergent in the low-temperature limit, reflecting a singular distribution of the effective couplings among the impurity spins.