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Progress of Theoretical Physics Supplement

Infrared Optical Absorption Spectra in Cuprate Two-Leg Spin-Ladder Systems with a Cyclic Four-Spin Interaction

Kensuke Inaba, Sei-ichiro Suga

Published Jan 1, 2005• 1 citation
Publisher

Abstract

On the basis of a resonating valence-bond description, we investigate the excitation spectrum caused by the Raman process in cuprate two-leg spin ladders with a cyclic four-spin interaction. Owing to a cyclic four-spin interaction, the S = 0 three-triplet excitation energy is reduced and becomes smaller than the S = 0 two-triplet excitation energy around the end of the Brillouin zone. Possible interpretations for the change in the lowest-lying mode are discussed. We show that such a change in the lowest-lying mode yields the shoulder structure at the lower edge in the phonon-assisted optical absorption spectrum.

DOI
10.1143/ptps.159.128

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On the basis of a resonating valence-bond description, we investigate the excitation spectrum caused by the Raman process in cuprate two-leg spin ladders with a cyclic four-spin interaction. Owing to a cyclic four-spin interaction, the S = 0 three-triplet excitation energy is reduced and becomes smaller than the S = 0 two-triplet excitation energy around the end of the Brillouin zone. Possible interpretations for the change in the lowest-lying mode are discussed. We show that such a change in the lowest-lying mode yields the shoulder structure at the lower edge in the phonon-assisted optical absorption spectrum.
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We investigate the influence of a cyclic spin exchange Jcyc{J}_{\mathrm{cyc}}Jcyc​ on the one- and two-triplet excitations of an undoped two-leg S=1/2S=1/2S=1/2 ladder, using the density-matrix renormalization group (DMRG). The dispersion of the S=0S=0S=0 two-triplet bound state is dramatically reduced by Jcyc{J}_{\mathrm{cyc}}Jcyc​ due to a repulsion between triplets on neighboring rungs. In (La,Ca)14Cu24O41(\mathrm{La},\mathrm{Ca}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}(La,Ca)14​Cu24​O41​ a consistent description of both the spin gap and the SSS=0 bound state requires ${J}_{\mathrm{cyc}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}0.20--0.27$ and ${J/J}_{\ensuremath{\perp}}\ensuremath{\approx}1.25--1.35.$ With these coupling ratios the recently developed dynamical DMRG yields an excellent description of the entire S=0S=0S=0 excitation spectrum observed in the optical conductivity, including the continuum contribution.
This article summarizes and extends the recent developments in the microscopic modeling of the magnetic excitations in cuprate two-leg ladder systems. The microscopic Hamiltonian comprises dominant Heisenberg exchange terms plus an additional four-spin interaction which is about five times smaller. We give an overview over the relevant energies like the one-triplon dispersion, the energies of two-triplon bound states and the positions of multi-triplon continua and over relevant spectral properties like spectral weights and spectral densities in the parameter regime appropriate for cuprate systems. It is concluded that an almost complete understanding of the magnetic excitations in undoped cuprate ladders has been obtained as measured by inelastic neutron scattering, inelastic light (Raman) scattering and infrared absorption.
We investigate the dynamical properties of S=12S=\frac{1}{2}S=21​ two-leg spin-ladder systems. In a strong-coupling region, an isolated mode appears in the lowest excited states, while in a weak-coupling region, an isolated mode is reduced and the lowest excited states become a lower bound of the excitation continuum. We find in the system with equal intrachain and interchain couplings that due to a cyclic four-spin interaction, the distribution of the weights for the dynamical structure factor and characteristics of the lowest excited states are strongly influenced. The dynamical properties of the two systems proposed for SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ are also discussed.
In the framework of this thesis the infrared spectra of two-leg spin ladders were measured. This study presents the first determination of the magnetic contribution to the optical conductivity of spin ladders. A comparison between experiment and new theoretical calculations provided a comprehensive understanding of the magnetic spectrum of the undoped telephone-number compounds La(y)Ca(14-y)Cu(24)O(41). To be able to study the weak magnetic contribution to the spectra, it was necessary to measure not only the reflectance but in particular the transmittance of thin single crystals. When both quantities are known, one can directly calculate the optical conductivity. The low-temperature spectra were compared with results of three different theoretical approaches in close collaboration with the theory groups of Uhrig et al. from the University of Cologne and of Kopp et al. from the University of Augsburg. The excellent agreement between theory and experiment allowed us to identify the two sharp peaks in the mid-infrared range unambiguously as the signature of a true bound state of two triplets. The occurrence of bound states in spin ladders had been predicted already by several groups, but we provided the first experimental verification. Further spectral weight at higher frequencies was attributed to the multi-triplet continuum. The exchange couplings were derived, and the importance of the four-spin cyclic exchange was demonstrated. With increasing temperature especially the line shape for polarization along the legs changes considerably. The spectral weight of the continuum strongly grows, whereas the bound-state peaks lose weight. The resemblance between the measured room-temperature data of the S=1/2 ladder and theoretical results for the S=1 Haldane chain was discussed. The corresponding calculations were performed by Nunner et al. in Augsburg. Another main part of this thesis was to examine the influence of doping on the infrared spectra. We observed the same bound-state features in Sr(14)Cu(24)O(41) as in the undoped compounds, but we found additional structure in the spectra. Several scenarios were discussed in order to explain the new features, including the modulation of the exchange coupling along the legs due to the incommensurate structure and due to the charge order in the chains.
We study the two-leg Heisenberg ladder with four-spin cyclic interaction using the (dynamical) density-matrix renormalization-group method. We demonstrate the dependence of the low-lying excitations in the spin wave, staggered dimer order, and scalar-chirality order structure factors on the four-spin cyclic interaction. We find that the cyclic interaction enhances spin-spin correlations with wave vector around momentum $({q}_{x},{q}_{y})=(\frac{\ensuremath{\pi}}{2},0)$. Also, the presence of long-range order in the staggered dimer and scalar-chirality phases is confirmed by a $\ensuremath{\delta}$-function peak contribution of the structure factors at energy $\ensuremath{\omega}=0$.