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arXiv:cond-mat/9706170 · Journal of the Physical Society of Japan

Disappearance of the Spin Gap in a Zn-Doped 2-Leg Ladder Compound Sr(Cu1-xZnx)2O3

Masaki Azuma, Mikio Takano, Roger S. Eccleston

Published Mar 15, 1998• 40 citations
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Abstract

An inelastic neutron scattering study was performed on a Zn-substituted spin-1/2 Heisenberg 2-leg ladder compound Sr(Cu1-xZnx)2O3 (x < 0.04) to investigate nonmagnetic impurity effects on the quantum spin system with a large spin gap of about 400 K. The magnitude of the spin gap was found to be independent of Zn concentration, 33 meV, while the integrated magnetic scattering which corresponds to the singlet-triplet excitation decreased monotonically with increasing x. On account of the total-sum rule, this result supports the existence of a finite in-gap density of states at E = 0 which was suggested from the T-linear magnetic specific heat.

DOI
10.1143/jpsj.67.740

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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 ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ (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 $x<~0.02$ and ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ with $x<~0.03.$ 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 $W/T.$ 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 ${S}_{0}=1/2$ induced next to impurity on the rung for the Zn and Ni doping ${(S}_{0}=1/4$ for the La doping) creates the staggered spin polarization along the leg, which decreases exponentially from ${S}_{0}.$ 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 $x=0.001$ and 0.005. The notable result is that ${\ensuremath{\xi}}_{s}/a$ that was found to be T independent is scaled to mean distances ${D}_{\mathrm{AV}}=1/(2x)$ between the Zn and Ni impurities and ${D}_{\mathrm{AV}}=1/x$ between the La impurities. When ${D}_{\mathrm{AV}}=500$ for $x=0.001$ (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 ${T}_{N}(\mathrm{exp})=3$ K $(x=0.01)$ and 5.8 K $(x=0.02)$ quantitatively and predicts to be as small as ${T}_{N}=0.09$ K for $x=0.001$ using ${J}_{0}=2000$ K. On the other hand, there is no evidence of AF-LRO for the La doping $(x=0.02$ 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 $(x=0.01$ 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 ${T}_{N}$ is determined by a strength of the interladder interaction and a size of ${S}_{0}.$

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arXiv:1706.01262•Physical review. B./Physical review. B•Jun 28, 2017•11 citations
An inelastic neutron scattering study was performed on a Zn-substituted spin-1/2 Heisenberg 2-leg ladder compound Sr(Cu1-xZnx)2O3 (x < 0.04) to investigate nonmagnetic impurity effects on the quantum spin system with a large spin gap of about 400 K. The magnitude of the spin gap was found to be independent of Zn concentration, 33 meV, while the integrated magnetic scattering which corresponds to the singlet-triplet excitation decreased monotonically with increasing x. On account of the total-sum rule, this result supports the existence of a finite in-gap density of states at E = 0 which was suggested from the T-linear magnetic specific heat.
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.
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 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​.
Magnetic properties of SrCu2{\mathrm{Cu}}_{2}Cu2​O3{\mathrm{O}}_{3}O3​ and Sr2{\mathrm{Sr}}_{2}Sr2​Cu3{\mathrm{Cu}}_{3}Cu3​O5{\mathrm{O}}_{5}O5​, containing two-leg and three-leg S=12S=\frac{1}{2}S=21​ ladders made of antiferromagnetic Cu-O-Cu linear bonds, were investigated. The susceptibility of the two-leg ladder material, SrCu2{\mathrm{Cu}}_{2}Cu2​O3{\mathrm{O}}_{3}O3​, is characteristic of thermal excitation from a nonmagnetic ground state with a spin gap of about 420 K, while the susceptibility of Sr2{\mathrm{Sr}}_{2}Sr2​Cu3{\mathrm{Cu}}_{3}Cu3​O5{\mathrm{O}}_{5}O5​, containing three-leg ladders, reflects a gapless spin excitation spectrum. The temperature dependence of the nuclear-spin lattice relaxation rate, 1T1\frac{1}{{T}_{1}}T1​1​, of 63Cu^{63}\mathrm{Cu}63Cu NMR also indicates the existence of a spin gap only for SrCu2{\mathrm{Cu}}_{2}Cu2​O3{\mathrm{O}}_{3}O3​. The spin gap we observed for SrCu2{\mathrm{Cu}}_{2}Cu2​O3{\mathrm{O}}_{3}O3​ confirms a recent theoretical prediction for the magnetic behavior of spin = \textonehalf{} antiferromagnetically coupled Heisenberg chains.
We study the effect of nonmagnetic Zn2+{\mathrm{Zn}}^{2+}Zn2+ (spin-0) and magnetic Ni2+{\mathrm{Ni}}^{2+}Ni2+ (spin-1) impurities on the ground state and low-lying excitations of the quasi-one-dimensional spin-1/21/21/2 Heisenberg antiferromagnet Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ using inelastic neutron scattering, specific heat, and bulk magnetization measurements. We show that 1% Ni2+{\mathrm{Ni}}^{2+}Ni2+ doping in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ results in a sizable spin gap in the spinon excitations, analogous to the case of Ni doped SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​ previously reported [Simutis et al., Phys. Rev. Lett. 111, 067204 (2013)]. However, a similar level of Zn2+{\mathrm{Zn}}^{2+}Zn2+ doping in SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​, investigated here for comparison, did not reveal any signs of a spin gap. Magnetic ordering temperature was found to be suppressed in the presence of both Zn2+{\mathrm{Zn}}^{2+}Zn2+ and Ni2+{\mathrm{Ni}}^{2+}Ni2+ impurities; however, the rate of suppression due to Ni2+{\mathrm{Ni}}^{2+}Ni2+ was found to be much more pronounced than for Zn2+{\mathrm{Zn}}^{2+}Zn2+. Effect of magnetic field on the ordering temperature is investigated. We found that with increasing magnetic field, not only the magnetic ordering temperature gradually increases but the size of specific heat anomaly associated with the magnetic ordering also progressively enhances, which can be qualitatively understood as due to the field induced suppression of quantum fluctuations.