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arXiv:cond-mat/9908134 · Physical review. B, Condensed matter

Low-energy excitations of spin-Peierls chains with modified bond impurities

David Augier, José A. Riera, Didier Poilblanc

Published Mar 1, 2000• 10 citations
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Abstract

The introduction of modified bond defects in spin-Peierls systems is investigated in a model of antiferromagnetic Heisenberg spin chains coupled to adiabatic phonons. Generically, new low-energy magnetic or nonmagnetic excitations appear below the bulk spin gap energy. When two adjacent bonds are modified, these excitations can be interpreted in terms of bound states of a soliton with the localized spin 1/2 located on the impurity site. It is shown that the confining potential occurs even in the case of isolated chains.

DOI
10.1103/physrevb.61.6741

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The introduction of modified bond defects in spin-Peierls systems is investigated in a model of antiferromagnetic Heisenberg spin chains coupled to adiabatic phonons. Generically, new low-energy magnetic or nonmagnetic excitations appear below the bulk spin gap energy. When two adjacent bonds are modified, these excitations can be interpreted in terms of bound states of a soliton with the localized spin 1/2 located on the impurity site. It is shown that the confining potential occurs even in the case of isolated chains.
The role of the spin-phonon coupling in spin-Peierls chains doped with spin-0 or spin-1 impurities is investigated by various numerical methods such as exact diagonalization, quantum Monte Carlo simulations and Density Matrix Renormalization Group. Various treatments of the lattice, in a fully quantum mechanical way, classically in the adiabatic approximation or using a fixed three-dimensional dimerization pattern are compared. For an isolated chain, strong bonds form between the two spin-1/2 sites next to the impurity site, leading to the appearance of magneto-elastic solitons. We also show that these excitations do not bind to spin-0 impurities but are weakly attracted by spin-1 impurities. However, the interchain elastic coupling generates an effective confining potential at the non-magnetic impurity site which can lead to the formation of soliton-impurity bound states. We also predict that a soliton and an antisoliton bound to two impurities on the same chain can annihilate each other when the separation between the impurities is smaller than a critical value depending on the interchain elastic constant.
We investigate the occurrence of singlet bound states in the Raman spectrum of dimerized spin 1/2 chains by exact diagonalization and density matrix renormalization-group techniques. We predict that several bulk $\ensuremath{\delta}$ peaks could be observed in pure systems. Furthermore, we show that additional low-energy lines arise from nonmagnetic impurity doping. These features are interpreted in terms of soliton-antisoliton and soliton-impurity bound states, respectively. Energies and spectral weights associated with these bound states are sensitive to lattice relaxation effects. Our results are discussed in the context of the inorganic spin-Peierls compound CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ and quantitatively compared to recent Raman experiments.
The role of dynamical magnetoelastic coupling in spin-Peierls chains is investigated by numerical and analytical techniques. We show that a Heisenberg spin chain coupled to dynamical optical phonons exhibits a transition towards a spontaneously dimerized state in a wide range of parameter space. The low-energy excitations are characterized as solitons. No binding between solitons occurs in the isolated spin-phonon chain and the dynamical spin structure factor shows a broad magnon dispersion. However, elastic interchain coupling can lead to the formation of bound states.
The s=1 Heisenberg antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with J'\ensuremath{\ne}J at the center of an even-length open chain is considered. Using the density-matrix renormalization-group method we find that, for sufficiently strong or weak J', a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on s=1/2 chain-end excitations, both in the weak- and strong-coupling limit. In a region around the uniform limit, J'=J, no states are found with energy below the Haldane gap. Second, a s=1/2 impurity at the center of an otherwise even-length open chain is considered. The coupling to the s=1/2 impurity is varied. Bound states in the Haldane gap are found only for sufficiently weak (antiferromagnetic) coupling. For a s=1/2 impurity coupled with a strong (antiferromagnetic) bond, no states are found in the Haldane gap. Our results are in good qualitative agreement with recent experiments on doped NENP and Y2{\mathrm{Y}}_{2}Y2​BaNiO5{\mathrm{BaNiO}}_{5}BaNiO5​.
Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with an impurity bond are investigated in terms of domain-wall excitations by means of analytical methods as well as a method of numerical diagonalization. It is shown that 1) the impurity bond brings about a massive triplet mode in the Haldane gap, 2) the triplet state comprises three of the four ground states of an open chain, 3) the excited states with the domain wall trapped at the impurity bond, including the massive triplet mode, exhibit a Néel-type configuration of the magnetic moment around the impurity bond. On the basis of the present results, we propose a new energy versus magnetic-field diagram.
Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with an impurity bond are investigated in terms of domain-wall excitations by means of analytical methods as well as a method of numerical diagonalization.It is shown that 1) the impurity bond brings about a massive triplet mode in the Haldane gap, 2) the triplet state comprises three of the four ground states of an open chain, 3) the excited states with the domain wall trapped at the impurity bond, including the massive triplet mode, exhibit a Néel-type configuration of the magnetic moment around the impurity bond.On the basis of the present results, we propose a new energy versus magnetic-field diagram.