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arXiv:cond-mat/0405310 · Journal of Physics Condensed Matter

The effects of Zn impurity on the properties of doped cuprates in the normal state

Yun Song

Published May 14, 2004• 0 citations
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Abstract

We study the interplay of quantum impurity, and collective spinon and holon dynamics in Zn doped high-T$_c$ cuprates in the normal state. The two-dimensional t-t$^{\prime}$-J models with one and a small amount of Zn impurity are investigated within a numerical method based on the double-time Green function theory. We study the inhomogeneities of holon density and antiferromagnetic correlation background in cases with different Zn concentrations, and obtain that doped holes tend to assemble around the Zn impurity with their mobility being reduced. Therefore a bound state of holon is formed around the nonmagnetic Zn impurity with the effect helping Zn to introduce local antiferromagnetism around itself. The incommensurate peaks we obtained in the spin structure factor indicate that Zn impurities have effects on mixing the q=($π$, $π$) and q=0 components in spin excitations.

DOI
10.1088/0953-8984/16/21/018

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We study the interplay of quantum impurity, and collective spinon and holon dynamics in Zn doped high-Tc_cc​ cuprates in the normal state. The two-dimensional t-t′^{\prime}′-J models with one and a small amount of Zn impurity are investigated within a numerical method based on the double-time Green function theory. We study the inhomogeneities of holon density and antiferromagnetic correlation background in cases with different Zn concentrations, and obtain that doped holes tend to assemble around the Zn impurity with their mobility being reduced. Therefore a bound state of holon is formed around the nonmagnetic Zn impurity with the effect helping Zn to introduce local antiferromagnetism around itself. The incommensurate peaks we obtained in the spin structure factor indicate that Zn impurities have effects on mixing the q=(πππ, πππ) and q=0 components in spin excitations.
Local magnetic moments induced by a nonmagnetic impurity in the two-dimensional $t\ensuremath{-}J$ model are investigated by use of a Green function method in a finite-size system (50\ifmmode\times\else\texttimes\fi{}50=2500 sites). Local electron number and nearest-neighbor correlation functions are calculated self-consistently at each lattice point. A local electron number distribution shows that electrons form a bound state around an impurity site and the magnitude of the local moment is enhanced, whereas doped holes can be distributed only apart from the impurity site and destroy an antiferromagnetic spin configuration by their motion. This result is consistent with experimental results of Zn-doped high-Tc{T}_{c}Tc​ superconductors.
The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped high-Tc\text{high-}{T}_{c}high-Tc​ cuprate superconductors is studied using exact diagonalization of effective $t\ensuremath{-}J\text{-like}$ Hamiltonians describing low energy electronic excitations of the CuO2{\mathrm{CuO}}_{2}CuO2​ plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu 3d3d3d, Ni 3d3d3d, and O 2p2p2p orbitals. Our main findings are: (i) The width ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ of the pseudogap occurring in the many body density of states, and manifesting itself also in the c-axisc\text{-axis}c-axis infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is---for realistic values of the model parameters---weakly bound to the Ni site. This causes a slight increase of ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ with respect to the pure case. (iii) Based on this result and further results for 1--2 holes and 1--2 Ni impurities, we suggest that in the real Ni substituted CuO2{\mathrm{CuO}}_{2}CuO2​ plane ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the c-axisc\text{-axis}c-axis infrared conductivity data of Zn and Ni substituted (Sm,Nd)${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystals.
The effect of static impurities in a two-dimensional quantum antiferromagnet has been studied. Creation of a vacancy in an antiferromagnetic lattice yields an impurity Hamiltonian whose x-y part maps to single impurity Anderson model whereas the z-part becomes the X-ray singularity problem. The model is solved where one obtains a bound state giving rise to δ-function density of states. The z-part of the interaction makes this peak asymmetric which follows a power law. It has been argued that the bound state corresponds to a local moment in the system giving rise to Curie-like contribution to the susceptibility. The implications of the present model in the substitutional Zn doped high-T c oxides have been discussed.
The influence of nonmagnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ is studied. A simple extension to Zn-doped Sr Cu2{\mathrm{Cu}}_{2}Cu2​ O3{\mathrm{O}}_{3}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{\mathrm{CuGeO}}_{3}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{\mathrm{CuGeO}}_{3}CuGeO3​ by the tendency to form spin singlets along the rungs in SrCu2{\mathrm{SrCu}}_{2}SrCu2​O3{\mathrm{O}}_{3}O3​. \textcopyright{} 1996 The American Physical Society.
In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a bare impurity potential which is onsite and attractive, magnetic and single-particle properties have been calculated. The QMC results show that giant oscillations develop in the Knight shift response around the impurity site due to the short-range antiferromagnetic correlations. These results are useful for interpreting the NMR data on Li- and Zn-substituted layered cuprates.
We study the two-dimensional Hubbard model with nonmagnetic Zn impurities modeled by binary diagonal disorder using quantum Monte Carlo within the dynamical cluster approximation. With increasing Zn content we find a strong suppression of d-wave superconductivity and an enhancement of antiferromagnetic spin correlations. T(c) vanishes linearly with Zn impurity concentration. The spin susceptibility changes from pseudogap to Curie-Weiss-like behavior indicating the existence of free magnetic moments in the Zn doped system. We interpret these results within the resonating-valence-bond picture.