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arXiv:cond-mat/0607753 · Physical Review B

Spin-polaron excitations in a doped Shastry-Sutherland model

Samir El Shawish, J. Bonča

Published Nov 17, 2006• 9 citations
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Abstract

Using variational algorithm on an infinite Shastry-Sutherland (SS) lattice we show that the introduction of a static nonmagnetic impurity into a dimerized ground state leads to a formation of a small, localized spin polaron surrounding the impurity site. Due to a particular symmetry of the SS lattice, the polaron is extremely anisotropic with a short spatial extent. The presence of nonmagnetic impurities leads to a formation of pronounced in-gap peaks in the dynamical spin structure factor, which we attribute to the spin-doublet excitations of a single unpaired spin $S=1∕2$ surrounded by triplet fluctuations. Our results are relevant for the description of $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ compound when doped with nonmagnetic atoms at Cu sites.

DOI
10.1103/physrevb.74.174420

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Absence of hole pairing in a simple t−J model on the Shastry-Sutherland lattice

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The Shastry-Sutherland model is a two-dimensional frustrated spin model whose ground state is a spin gap state. We study this model doped with one and two holes on a 32-site lattice using exact diagonalization. When ${t}^{\ensuremath{'}}>0,$ we find that the diagonal dimer order that exists at half-filling is retained at these moderate doping levels. No other order is found to be favored on doping. The holes are strongly repulsive unless the hopping terms are unrealistically small. Therefore, the existence of a spin gap at half-filling does not guarantee hole-pairing in the present case.

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Using variational algorithm on an infinite Shastry-Sutherland (SS) lattice we show that the introduction of a static nonmagnetic impurity into a dimerized ground state leads to a formation of a small, localized spin polaron surrounding the impurity site. Due to a particular symmetry of the SS lattice, the polaron is extremely anisotropic with a short spatial extent. The presence of nonmagnetic impurities leads to a formation of pronounced in-gap peaks in the dynamical spin structure factor, which we attribute to the spin-doublet excitations of a single unpaired spin S=1∕2S=1∕2S=1∕2 surrounded by triplet fluctuations. Our results are relevant for the description of SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ compound when doped with nonmagnetic atoms at Cu sites.
Controlled doping of SrCu2(BO3)2{\text{SrCu}}_{2}{({\text{BO}}_{3})}_{2}SrCu2​(BO3​)2​, a faithful realization of the Heisenberg spin-1/2 antiferromagnet on the Shastry-Sutherland lattice, with nonmagnetic impurities generates bound states below the spin gap. These bound states and their symmetry properties are investigated by exact diagonalization of small clusters and within a simple effective model describing a spinon submitted to an attractive extended potential. It is shown that Raman spectroscopy is a unique technique to probe these bound states. Quantitative theoretical Raman spectra are numerically obtained.
Configurations of singlets and triplets on the Shastry-Sutherland lattice (SSL) have been proposed in the literature as variational ground states of the Shastry-Sutherland model at a fixed magnetization M. We prove that isolated triplet excitations on the SSL are unstable if the coupling $\ensuremath{\alpha}$ falls below a critical value ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}2.0.$ The instability should be visible in the compound SrCu2(BO3)2,{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2},SrCu2​(BO3​)2​, where a coupling ${\ensuremath{\alpha}}^{*}=1.48$ is realized.
In this thesis, we investigated the spectral properties of polaronic quasiparticles resulting from the coupling of a charge carrier to the bosonic excitations of ordered environments. Holstein polarons, describing an electron locally coupled to dispersionless phonons, and spin polarons in hole-doped antiferromagnets are considered. The Green's function of the Holstein polaron in a lattice with various kinds of impurities is calculated using the momentum average approximation. The main finding is that the scenario where the mere effect of the coupling to phonons is to enhance the electron's effective mass is incomplete as the phonons are found to also renormalize the impurity potential the polaron interacts with. This formalism is applied first to the case of a single impurity and the range of parameters where the polaron's ground state is localized is identified. The lifetime of the polaron due to scattering from weak but extended disorder is then studied and it is shown that the renormalization of the disorder potential leads to deviation of the strong coupling results from Fermi's golden rule's predictions. Motivated by the hole-doped cuprate superconductors, the motion of a hole in a two-dimensional Ising antiferromagnet and its binding to an attractive impurity is studied next, based on a variational scheme that allows for configurations with a certain maximum number of spin flips. The role of the magnetic sublattices in determining the symmetry of the resulting bound states is discussed. Next, a more realistic model describing a hole in a CuO₂ layer which retains the O explicitly, is considered. By neglecting the fluctuations of the Cu spins and using a variational principle similar to that of the previous chapter, a semi-analytic solution for the Green's function of the hole in an infinite 2D lattice is constructed. The resulting quasiparticle dispersion shows the proper ground state and other features observed in experiments. The lack of importance of the background spin fluctuations is justified based on the hole's ability to move on the O sublattice without disturbing the Cu spins. Finally, the model is generalized to gauge the importance of other relevant O orbitals.
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=1S=1S=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=1S=1S=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.
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.
The Shastry-Sutherland model is a two-dimensional frustrated spin model whose ground state is a spin gap state. We study this model doped with one and two holes on a 32-site lattice using exact diagonalization. When ${t}^{\ensuremath{'}}>0,$ we find that the diagonal dimer order that exists at half-filling is retained at these moderate doping levels. No other order is found to be favored on doping. The holes are strongly repulsive unless the hopping terms are unrealistically small. Therefore, the existence of a spin gap at half-filling does not guarantee hole-pairing in the present case.