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Physical review. B, Condensed matter

Impurity-induced staggered polarization and antiferromagnetic order in spin- 12 Heisenberg two-leg ladder compound SrCu2O3: Extensive Cu NMR and NQR studies

Shigeki Ohsugi, Y. Tokunaga, Kenji Ishida, Yoshitaka KITAOKA, Masaki Azuma, Yoshinobu Fujishiro, M. Takano

Published Aug 1, 1999• 37 citations
Publisher

Abstract

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 ${S}_{0}.$

DOI
10.1103/physrevb.60.4181

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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 SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ (Sr123). We have carried out comprehensive NMR and NQR investigations on three impurity-doped systems, Sr(Cu1\ensuremath−xMx)2O3(M=Zn,Ni)\mathrm{Sr}({\mathrm{Cu}}_{1\ensuremath{-}x}{M}_{x}{)}_{2}{\mathrm{O}}_{3} (M=\mathrm{Z}\mathrm{n},\mathrm{}\mathrm{Ni})Sr(Cu1\ensuremath−x​Mx​)2​O3​(M=Zn,Ni) with x< 0.02x<~0.02x< 0.02 and Sr1\ensuremath−xLaxCu2O3{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}Sr1\ensuremath−x​Lax​Cu2​O3​ 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 \ensuremathξ0{\ensuremath{\xi}}_{0}\ensuremathξ0​ was theoretically predicted as \ensuremathξ0/a\ensuremath∼3\ensuremath−8,{\ensuremath{\xi}}_{0}/a\ensuremath{\sim}3\ensuremath{-}8,\ensuremathξ0​/a\ensuremath∼3\ensuremath−8, where a is the lattice spacing between the Cu sites along the leg. However, a correlation length \ensuremathξs/a{\ensuremath{\xi}}_{s}/a\ensuremathξs​/a estimated from the IISP along the leg was found to be much longer than \ensuremathξ0/a{\ensuremath{\xi}}_{0}/a\ensuremathξ0​/a in x=0.001x=0.001x=0.001 and 0.005. The notable result is that \ensuremathξs/a{\ensuremath{\xi}}_{s}/a\ensuremathξs​/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), \ensuremathξs/a\ensuremath∼50{\ensuremath{\xi}}_{s}/a\ensuremath{\sim}50\ensuremathξs​/a\ensuremath∼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\ensuremathμB0.04{\ensuremath{\mu}}_{B}0.04\ensuremathμB​ at 1.4 K along the a axis. By assuming that exponential decay constants of AF moments are equivalent to \ensuremathξs/a{\ensuremath{\xi}}_{s}/a\ensuremathξs​/a's for the IISP, the size of an AF moment next to the impurity is deduced as SAF\ensuremath∼1/4.{S}_{\mathrm{AF}}\ensuremath{\sim}1/4.SAF​\ensuremath∼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 TN=J0exp(\ensuremath−DAV/(\ensuremathξs/a)){T}_{N}{=J}_{0}\mathrm{exp}(\ensuremath{-}{D}_{\mathrm{AV}}/({\ensuremath{\xi}}_{s}/a))TN​=J0​exp(\ensuremath−DAV​/(\ensuremathξs​/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 \ensuremathξs/a{\ensuremath{\xi}}_{s}/a\ensuremathξs​/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​.
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