Abstract We study the effect of impurities on the two types of spin-dimers in the hybrid chain-ladder spin 1/2 quantum magnet Sr Cu O . Four different impurities were used, namely, the non-magnetic Zn (0.0025 and 0.01 per Cu) and Al (0.0025 and 0.01 per Cu), and magnetic Ni (0.0025 and 0.01 per Cu) and Co (0.01, 0.03, 0.05 and 0.1 per Cu). These impurities were doped in high-quality single-crystals synthesized by the floating-zone method. The magnetic susceptibility of pristine Sr Cu O is analyzed rigorously to confirm that at low temperatures ( K), the ‘free’ spins in the chains undergo a long-distance dimerization as proposed in a recent study (Sahling et al 2015 Nat. Phys . 11 255). The effect of impurity on these dimers is analyzed by measuring the specific heat down to K. We found that even at the lower impurity concentration, the long-distance dimers are significantly severed but the quantum entangled spin dimerized state of the chains persists. On the other hand, the other type of spin dimers that form at relatively higher temperatures via an intervening Zhang–Rice singlet are found to be practically unaffected at the lower impurity concentration; but at 1% doping these dimers are considerably severed. The effect of Co impurity turned out to be most unusual displaying a strongly anisotropic response, and with a dimerization gap that suppresses faster along the chain/ladder direction than perpendicular to it as a function of increasing Co concentration.
The effects of spin-1 impurities introduced in dimerized antiferromagnetic spin chains are studied using Lanczos diagonalization and quantum Monte Carlo simulations. First, the magnitude of the interaction between a Ni ion replacing a Cu ion is derived for the case study system Cu-O-Cu. Then, it is shown that the introduction of
S=1 impurities leads to the suppression of the original spin gap of the dimerized system and to the enhancement of the antiferromagnetic correlations close to the impurity. These features are interpreted in terms of a valence bond picture of the ground state of both the pure and the doped system. The similitudes and differences between the underlying mechanisms that produce these effects in the cases of nonmagnetic and
S=1 impurities are analyzed. It is stressed that a singlet formed between the spin-1 impurity site and the two spin-1/2 neighbors spins behaves as an effective nonmagnetic vacancy which may be partially responsible for the enhancement of the antiferromagnetic correlations on the whole system. Implications of these results for experiment are also discussed.
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
SrCu2O3. Temperature dependence of AF susceptibility shows power-law-like but weaker divergence than the single chain AFH in the temperature range studied.
We present a quantum Monte Carlo study for Heisenberg spin-
21 two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu${}_{1\ensuremath{-}x}$Zn
x)
2O
3, where a large broadening of the
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=0.001 and
x=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.
The influence of nonmagnetic impurities on the spectrum and dynamical spin structure factor of a model for
CuGeO3 is studied. A simple extension to Zn-doped Sr
Cu2 O3 is also discussed. Using exact diagonalization techniques and intuitive arguments we show that Zn doping introduces states in the spin-Peierls gap of
CuGeO3. This effect can be understood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn doping according to the numerical data presented here. As recent numerical calculations have shown, similar arguments apply to ladders with nonmagnetic impurities simply replacing the tendency to dimerization in
CuGeO3 by the tendency to form spin singlets along the rungs in
SrCu2O3. \textcopyright{} 1996 The American Physical Society.
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 (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
S0=1/2 induced next to impurity on the rung for the Zn and Ni doping
(S0=1/4 for the La doping) creates the staggered spin polarization along the leg, which decreases exponentially from
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=0.001 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) between the Zn and Ni impurities and
DAV=1/x between the La impurities. When
DAV=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
TN(exp)=3 K
(x=0.01) and 5.8 K
(x=0.02) quantitatively and predicts to be as small as
TN=0.09 K for
x=0.001 using
J0=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
TN is determined by a strength of the interladder interaction and a size of
S0.