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arXiv:0912.4353 · Physical Review B

Impurity effects in coupled-ladder BiCu2PO6 studied by NMR and quantum Monte Carlo simulations

Libu K. Alexander, Julien Bobroff, A. V. Mahajan, B. Koteswararao, Nicolas Laflorencie, Fabien Alet

Published Feb 24, 2010• 26 citations
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Abstract

We present a $^{31}\text{P}$ NMR study of the coupled spin $\frac{1}{2}$ ladder compound ${\text{BiCu}}_{2}{\text{PO}}_{6}$. In the pure material, intrinsic susceptibility, and dynamics show a spin gap of about $\ensuremath{\Delta}\ensuremath{\approx}35--40\text{ }\text{K}$. Substitution of nonmagnetic Zn or magnetic Ni impurity at Cu site induces a staggered magnetization which results in a broadening of the $^{31}\text{P}$ NMR line while susceptibility far from the defects is unaffected. The effect of Ni on the NMR line broadening is twice that of Zn, which is consistent with quantum Monte Carlo calculations assuming that Ni couples ferromagnetically to its adjacent Cu. The induced moment follows a $1/T$ temperature dependence due to the Curie-type development of the moment amplitude while its extension saturates and does not depend on impurity content or nature. This allow us to verify the generically expected scenario for impurity doping and to extend it to magnetic impurity case: in an antiferromagnetically correlated low-dimensional spin system with antiferromagnetic correlations, any type of impurity induces a staggered moment at low temperature, whose extension is not linked to the impurity nature but to the intrinsic physics at play in the undoped pure system, from one-dimensional to two-dimensional systems.

DOI
10.1103/physrevb.81.054438

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Nonmagnetic impurities in spin-gapped and gapless Heisenberg antiferromagnets

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We discuss the effects of nonmagnetic impurities (static holes) in the $S=1/2$ 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 $S=1/2$ 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 $T=0$ 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 ${S}^{z}=1/2.$ 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.

Physical review. B, Condensed matter•Nov 1, 1997•49 citations
We present a 31P^{31}\text{P}31P NMR study of the coupled spin 12\frac{1}{2}21​ ladder compound BiCu2PO6{\text{BiCu}}_{2}{\text{PO}}_{6}BiCu2​PO6​. In the pure material, intrinsic susceptibility, and dynamics show a spin gap of about \ensuremathΔ\ensuremath≈35−−40 K\ensuremath{\Delta}\ensuremath{\approx}35--40\text{ }\text{K}\ensuremathΔ\ensuremath≈35−−40 K. Substitution of nonmagnetic Zn or magnetic Ni impurity at Cu site induces a staggered magnetization which results in a broadening of the 31P^{31}\text{P}31P NMR line while susceptibility far from the defects is unaffected. The effect of Ni on the NMR line broadening is twice that of Zn, which is consistent with quantum Monte Carlo calculations assuming that Ni couples ferromagnetically to its adjacent Cu. The induced moment follows a 1/T1/T1/T temperature dependence due to the Curie-type development of the moment amplitude while its extension saturates and does not depend on impurity content or nature. This allow us to verify the generically expected scenario for impurity doping and to extend it to magnetic impurity case: in an antiferromagnetically correlated low-dimensional spin system with antiferromagnetic correlations, any type of impurity induces a staggered moment at low temperature, whose extension is not linked to the impurity nature but to the intrinsic physics at play in the undoped pure system, from one-dimensional to two-dimensional systems.
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.
We present the effect of Zn (S=0)(S=0)(S=0) and Cu (S=1/2)(S=1/2)(S=1/2) substitution at the Ni site of S=1S=1S=1 Haldane chain compound Y2BaNiO5.{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5}.Y2​BaNiO5​. 89Y{}^{89}\mathrm{Y}89Y nuclear-magnetic resonance (NMR) allows us to measure the local magnetic susceptibility at different distances from the defects. The 89Y{}^{89}\mathrm{Y}89Y NMR spectrum consists of one central peak and several less intense satellite peaks. The central peak represents the chain sites far from the defect. Its shift measures the uniform susceptibility, which displays a Haldane gap $\ensuremath{\Delta}\ensuremath{\approx}100\mathrm{K}$ and it corresponds to an antiferromagnetic (AF) coupling $J\ensuremath{\approx}260\mathrm{K}$ between the nearest neighbor Ni spins. Zn or Cu substitution does not affect the Haldane gap. The satellites, which are evenly distributed on the two sides of the central peak, probe the antiferromagnetic staggered magnetization near the substituted site. The spatial variation of the induced magnetization is found to decay exponentially from the impurity for both Zn and Cu for T>50K.T>50\mathrm{K}.T>50K. Its extension is found identical for both impurities and corresponds accurately to the correlation length $\ensuremath{\xi}(T)$ determined by Monte Carlo simulations for the pure compound. In the case of nonmagnetic Zn, the temperature dependence of the induced magnetization is consistent with a Curie law with an ``effective'' spin S=0.4S=0.4S=0.4 on each side of Zn. This staggered effect is quantitatively well accounted for in all the explored range by quantum Monte Carlo (QMC) computations of the spinless-defect-induced magnetism. In the case of magnetic Cu, the similarity of the induced magnetism to the Zn case implies a weak coupling of the Cu spin to the nearest-neighbor Ni spins. The slight reduction of about $20\ensuremath{-}30%$ of the induced polarization with respect to Zn is reproduced by QMC computations by considering an antiferromagnetic coupling of strength ${J}^{\ensuremath{'}}=0.1J\ensuremath{-}0.2J$ between the S=1/2S=1/2S=1/2 Cu spin and nearest-neighbor Ni spin. Macroscopic susceptibility measurements confirm these results as they display a clear Curie contribution due to the impurities nearly proportional to their concentration. This contribution is indeed close to that of two spin half for Zn substitution. The Curie contribution is smaller in the Cu case, which confirms that the coupling between Cu and near-neighbor Ni is antiferromagnetic.
We report characteristics of impurity-induced staggered polarization (IISP) and antiferromagnetic long-range order (AF-LRO) in the gapped spin-1/2 Heisenberg two-leg ladder compound SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ (Sr123). We have carried out comprehensive NMR and NQR investigations on three impurity-doped systems, $\mathrm{Sr}({\mathrm{Cu}}_{1\ensuremath{-}x}{M}_{x}{)}_{2}{\mathrm{O}}_{3} (M=\mathrm{Z}\mathrm{n},\mathrm{}\mathrm{Ni})$ with x< 0.02x<~0.02x< 0.02 and ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ with x< 0.03.x<~0.03.x< 0.03. Either the Zn or Ni impurity that is nonmagnetic depletes a single spin on the ladders, whereas the La impurity is believed to dope electrons onto the ladders. The width of the Lorentzian Cu NMR spectrum increases with the increase in impurity content x and follows the Curie-like temperature (T) dependence as W/T.W/T.W/T. The W's for the Zn- and Ni-doped samples (M doping) are larger than for the La-doped one (La doping). The NMR spectra were fit by assuming that unpaired spin S0=1/2{S}_{0}=1/2S0​=1/2 induced next to impurity on the rung for the Zn and Ni doping (S0=1/4{(S}_{0}=1/4(S0​=1/4 for the La doping) creates the staggered spin polarization along the leg, which decreases exponentially from S0.{S}_{0}.S0​. In Sr123, an instantaneous spin-correlation length ${\ensuremath{\xi}}_{0}$ was theoretically predicted as ${\ensuremath{\xi}}_{0}/a\ensuremath{\sim}3\ensuremath{-}8,$ where a is the lattice spacing between the Cu sites along the leg. However, a correlation length ${\ensuremath{\xi}}_{s}/a$ estimated from the IISP along the leg was found to be much longer than ${\ensuremath{\xi}}_{0}/a$ in x=0.001x=0.001x=0.001 and 0.005. The notable result is that ${\ensuremath{\xi}}_{s}/a$ that was found to be T independent is scaled to mean distances DAV=1/(2x){D}_{\mathrm{AV}}=1/(2x)DAV​=1/(2x) between the Zn and Ni impurities and DAV=1/x{D}_{\mathrm{AV}}=1/xDAV​=1/x between the La impurities. When DAV=500{D}_{\mathrm{AV}}=500DAV​=500 for x=0.001x=0.001x=0.001 (Zn doping), ${\ensuremath{\xi}}_{s}/a\ensuremath{\sim}50$ is estimated. The significantly broadened NQR spectrum has provided unambiguous evidence for the AF-LRO in the Zn and Ni doping (x=0.01 and 0.02). Rather uniform AF moments at the middle Cu sites between the impurities are estimated to be about $0.04{\ensuremath{\mu}}_{B}$ at 1.4 K along the a axis. By assuming that exponential decay constants of AF moments are equivalent to ${\ensuremath{\xi}}_{s}/a$'s for the IISP, the size of an AF moment next to the impurity is deduced as ${S}_{\mathrm{AF}}\ensuremath{\sim}1/4.$ We propose that these exponential distributions of IISP and AF moments along the two-leg suggest that an interladder interaction is in a weakly coupled quasi-one-dimensional (WC-Q1D) regime. The formula of ${T}_{N}{=J}_{0}\mathrm{exp}(\ensuremath{-}{D}_{\mathrm{AV}}/({\ensuremath{\xi}}_{s}/a))$ based on the WC-Q1D model explains TN(exp)=3{T}_{N}(\mathrm{exp})=3TN​(exp)=3 K (x=0.01)(x=0.01)(x=0.01) and 5.8 K (x=0.02)(x=0.02)(x=0.02) quantitatively and predicts to be as small as TN=0.09{T}_{N}=0.09TN​=0.09 K for x=0.001x=0.001x=0.001 using J0=2000{J}_{0}=2000J0​=2000 K. On the other hand, there is no evidence of AF-LRO for the La doping (x=0.02(x=0.02(x=0.02 and 0.03) down to 1.4 K, nevertheless their ${\ensuremath{\xi}}_{s}/a$'s are almost equivalent to those in the Zn and Ni doping (x=0.01(x=0.01(x=0.01 and 0.02). We remark that the Q1D-IISP is dramatically enhanced by the interladder interaction even though so weak, once the impurity breaks up the quantum coherence in the short-range resonating valence bond (RVB) state with the gap. On the one hand, we propose that TN{T}_{N}TN​ is determined by a strength of the interladder interaction and a size of S0.{S}_{0}.S0​.
Nuclear magnetic resonance and magnetization measurements were used to probe the magnetic features of single-crystalline Bi(Cu(1-x)Zn(x))(2)PO(6) with 0<x<0.05 at temperatures between 2.6 K and 300 K. The simple line shape of the (31)P NMR signals of the pristine compound changes considerably for x>0 and we present clear evidence for a temperature-dependent variation of the local magnetization close to the Zn sites. The generic nature of this observation is indicated by results of model calculations on appropriate spin systems of limited size employing quantum Monte Carlo methods.
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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.