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arXiv:cond-mat/9802053 · Physical review. B, Condensed matter

Dynamical effects of phonons on soliton binding in spin-Peierls systems

David Augier, Didier Poilblanc, Erik Schwartz Sørensen, Ian K. Affleck

Published Oct 1, 1998• 43 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.58.9110

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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.
Abstract The role of dynamical magneto-elastic coupling in spin–Peierls chains is investigated by various numerical techniques. We show that, generically, a Heisenberg spin chain coupled to dynamical optical phonons exhibits a transition towards a spontaneously dimerized state. The low energy excitations are characterized as topological solitons. No binding between solitons occurs in the isolated spin–phonon chain. However, elastic interchain coupling can lead to the formation of bound states.
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 study a model of a spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an interchain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic spin-Peierls compound CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​.
We consider the ground state and the elementary excitations of an array of spin-Peierls chains coupled by elastic and magnetic interactions. It is expected that the effect of the magnetic interchain coupling will be to reduce the dimerization amplitude and that of the elastic coupling will be to confine the spin one-half solitons corresponding to each isolated chain. We show that this is the case when these interactions are not frustrated. On the other hand, in the frustrated case we show that the amplitude of dimerization in the ground state is independent of the strength of the interchain magnetic interaction in a broad range of values of this parameter. We also show that free solitons could be the elementary excitations when only nearest neighbor interactions are considered. The case of an elastic interchain coupling is analyzed on a general energetic consideration. To study the effect of the magnetic interchain interaction the problem is simplified to a two-leg ladder which is solved using DMRG calculations. We show that the deconfinement mechanism is effective even with a significantly strong antiferromagnetic interchain coupling.
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.