Theory for low-lying excitations in the spin-Peierls systemCuGeO3

Abstract

Using the bosonization technique and self-consistent quantum theory, we study two branches of low-lying excitation in the spin-Peierls system CuGeO 3 with frustration. The energy gaps of triplet one-magnon excited state and singlet two-magnon bound state are calculated for a set of parameters appropriate to the compound CuGeO 3 . The calculated results are consistent with experimental data of CuGeO 3 . It is found that the energy gaps of the one-and two-magnon states increase with increasing either frustration or dimerization parameter. As the dimerization is increased, the binding energy of the singlet two-magnon bound state increases for smaller frustration, whereas it decreases for larger frustration. The power-law relation between the binding energy and the dimerization exists for small dimerization and at criticality ␣ϭ␣ c ϭ0.2411.

Analysis of a family of Heisenberg systems with simple eigenfunctions for the ground state and low lying excitations

“…We note that a two-magnon bound states have been reported 6 in the somewhat different context of a frustrated and dimerized Heisenberg chain; such bound states may explain the observation of two gaps in the spin-Peierls compound CuGeO 3 by inelastic neutron scattering.…”

“…This condition, implying a soft restoring force for lattice displacements, contrasts with the usual Peierls distortion ͑PD͒, where the magneto-elastic energy is linear on lattice displacements. 6 In addition, in contrast to PD, periodicity in these displacements is not required. However, the displacements ⌬ may be due to other reasons, beyond a spontaneous symmetry breaking.…”

“…[2][3][4][5][9][10][11][12] Although the MG-like exact ground states correspond to particular parameters of frustrated Heisenberg models, they are good reference points in order to understand the global behavior of some magnetic lattices, and eventually, to address some actual compounds, like the spin-Peierls system CuGeO 3 , 4,6 the planar lattice SrCu 2 ͑BO 3 ͒ 2 , 2,3,5 or other systems. 7 The excitation spectrum ͑ES͒ of frustrated systems is also a very active topic of theoretical and experimental investigation, 6 in order to elucidate, for example, the existence of a gap in the ES, the nature of the singlet and triplet excitations, the interaction between two excitations ͑eventually forming bounded states 6 ͒, and the effect of a large magnetic field 5 ͑which is also a sort of "probe" for the ES͒.…”

“…We note that the ES of MG-like systems is, usually, not simple to address. 4,6 We consider a lattice composed by magnetic clusters, linked among them by intermediate, spin atoms, which we shall call the "connectors." Each connector must have the same exchange interaction, J, with all the spins of the contiguous clusters.…”

Spin gap in doped dimerized chain near half-filling

“…The pairing ground state implies Bose condensation of the zero momentum mode, and the variational parameter is related to dynamical mass (or energy gap) generation. This method was also expanded to the 1D double-frequency SG model describing a dimerized and frustrated Heisenberg chain at zero temperature [25]. With it the properties of the ground state and the elementary excitation for the 1D spin model can be given analytically.…”