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arXiv:cond-mat/9812174 · Physical review. B, Condensed matter

Soliton bound states in the Raman spectrum of pure and doped spin-Peierls chains

David Augier, Erik Schwartz Sørensen, José A. Riera, Didier Poilblanc

Published Jul 1, 1999• 27 citations
arXivHTMLPDF

Abstract

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 ${\mathrm{CuGeO}}_{3}$ and quantitatively compared to recent Raman experiments.

DOI
10.1103/physrevb.60.1075

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arXiv:cond-mat/0008321•Physical review. B, Condensed matter•Jan 22, 2001•20 citations
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 \ensuremathδ\ensuremath{\delta}\ensuremathδ 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 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.
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.
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.
The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h<hc1,h<{h}_{c1},h<hc1​, an incommensurate regime (hc1<h<hc2){(h}_{c1}<h<{h}_{c2})(hc1​<h<hc2​) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin-polarized phase above an upper critical field hc2.{h}_{c2}.hc2​. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.
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.
We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the ``dimer line'' with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, an additional phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those ``charged solitons'' are studied; exact solutions for N-hole bound states are presented.