Raman scattering cross section of spin ladders

Abstract

The Raman scattering spectra from magnetic excitations in an antiferromagnetic spin-1 2 two leg ladder is investigated for weak and strong interladder coupling. In the first case, a cusp in the Raman intensity is obtained at a frequency twice the gap. In the second case, a peak at twice the gap replaces the cusp. We discuss the relevance of our calculation to recent experiments on CaV2O5 and Sr14Cu24O41. Raman scattering is an experimental technique that has provided valuable informations about the spin dynamics in quasi-one dimensional antiferromagnets in the recent years. Since Raman scattering is sensitive to singlet excitations, this technique is complementary of neutron diffraction which is sensitive to triplet excitations. It has been used to probe spin 1/2 chains 1 , spin 1 chains 2 , spin Peierls systems 3-6 , and spin ladders 7-9 . In particular, Raman scattering has been very useful in the analysis of magnetic excitations in the spin-Peierls compound CuGeO 3 . The bosonized theory of dimerized spin 1/2 states that is believed to describe the dimerized low temperature phase of spin-Peierls systems predicts the appearance of a singlet bound state of two triplet excitations at an energy √ 3∆, where ∆ is the spin gap 10 . Such singlet bound state has been successfully observed in Raman scattering experiments on CuGeO 3 for T < T SP at an energy 1.79∆, close to the theoretical prediction. Moreover, the peak was not observed in the uniform phase(T > T SP ), showing that it is characteristic of the dimerized phase 4,11 . For T > T SP , a broad band of magnetic excitations is observed 4 . The theoretical analysis of magnetic Raman scattering is based on the FleuryLoudon Hamiltonian 12,13 , that describes the interaction of photons with magnetic excitations. There exists at present a certain amount of litterature on the theory of Raman scattering from dimerized spin chains, both analytical 10,14,15 and numerical 16 . The case of frustrated spin chains has also been investigated 17 , in relation with the Raman spectra of CuGeO 3 at T > T SP . The theory of Ref. 17 reproduced well the features of the spectrum at T > T SP 4 . The application of Raman scattering to probe the singlet excitations of two leg ladders is more recent 7-9 . In spin ladder systems, magnetic peaks in the Raman intensity were observed at twice the spin gap. From the theoretical point of view, some numerical calculations are available 18 , but no analytic expression of the Raman intensity has been derived so far. In order to fill this gap, we discuss in the present work the Raman spectrum of an antiferromagnetic spin-1/2 ladder. After recalling some basic results on the Fleury-Loudon theory of magnetic Raman scattering, we will consider first the Majorana fermion approach valid for weak coupling and then the Bond Operator Technique (BOT) valid for the strong coupling case. The Majorana fermions approach leads to a cusp in the Raman intensity at twice the gap, in disagreement with experiment. We discuss briefly what could be missing in the Ma...

Breathers and Raman scattering in a two-leg ladder with staggered Dzyaloshinskii-Moriya interaction

“…[66][67][68][69] For frequencies equal to approximately twice the spin gap, a threshold is obtained when interaction between magnons are neglected, 67,68 with the Raman intensity behaving as I R ͑͒ϳ͑ −2⌬͒ 1/2 . When interactions are added, a peak forms in the continuum, but the square root singularity at the edge persists.…”

“…[69][70][71] Turning to the ladder with Dzyaloshinskii-Moriya interaction, in the weak-coupling case, the threshold at twice the spin gap will be obtained from the contribution of antisymmetric modes a / a to the Raman intensity. 67 The symmetric modes will give extra peaks and thresholds but at energy scales small compared to the gap. In the following, we will compute the Raman intensity for frequencies smaller than 2J Ќ .…”

Two-magnon Raman scattering in spin ladders with exact singlet-rung ground state

“…Raman scattering in spin-ladders was theoretically studied in a number of papers (see [3], [12]- [15] and references therein). Following Sugai [16] we shall consider only the case when the incident and scattered light have parallel polarization directions both lying in the plane of the ladder and forming an angle θ with respect to vertical bonds.…”

“…where we have added the normalization factor 1 2N +1 [12]. Within the Fleury-Loudon-Elliot approach the effective Raman Hamiltonian H R (θ) have the following form [2], [3] (we also take into account interactions across diagonals): …”

Raman cross section of spin ladders

“…The dotted line in 1(a) depicts the bare Raman intensity [3] which results from neglecting the two-triplet on-site hard-core as well as the NN-attraction. Displaying two van-Hove singularities this spectrum fails to explain the observed magnetic line-shape.…”