We study the effect of anisotropy of spin-
S impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-
S impurity. Based on the results, we find that the types of spin-
S impurities are classified into two groups: (i) nonmagnetic and
S=1 impurities enhance only short-range antiferromagnetic correlation and (ii)
S=21 and
S>1 impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of
S=21 impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ
S=21 impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in
SrCu0.99Co0.01O2 is
S=23.
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
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.
We study the properties of one-dimensional gapped Heisenberg antiferromagnets in the presence of a strong staggered magnetic field. For these systems we predict a universal form for the staggered magnetization curve. This function, as well as the effect the staggered field has on the energy gaps in longitudinal and transversal excitation spectra, is determined from the universal form of the effective potential in
O(3)-symmetric
(1+1)-dimensional field theory. Our theoretical findings are in excellent agreement with recent neutron scattering data on
R2BaNiO5 (
R= magnetic rare earth) linear-chain mixed spin antiferromagnets.
We present a
31P NMR study of the coupled spin
21 ladder compound
BiCu2PO6. 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
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/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 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.We report
63Cu nuclear magnetic resonance and muon spin rotation measurements on the
S=1/2 antiferromagnetic Heisenberg spin chain compound
Sr1.9Ca0.1CuO3. An exponentially decreasing spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound
Sr0.9Ca0.1CuO2, and it confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling ${J}^{\ensuremath{'}}$. Our results therefore suggest that the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain is induced by a local bond disorder of the intrachain exchange coupling
J. A low-temperature upturn of ${T}_{1}^{\ensuremath{-}1}$ evidences growing magnetic correlations. However, zero-field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound, which is most likely suppressed by the opening of the spin gap.