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arXiv:cond-mat/9911271 · Physical review. B, Condensed matter

Magnetic order in ferromagnetically coupled spin ladders

Sergio D. Dalosto, José A. Riera

Published Jul 1, 2000• 17 citations
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Abstract

A model of coupled antiferromagnetic spin-1/2 Heisenberg ladders is studied with numerical techniques. In the case of ferromagnetic interladder coupling we find that the dynamic and static structure factor has a peak at $(\ensuremath{\pi},\ensuremath{\pi}/2)$ where the first (second) direction is along (transversal) to the ladders. In addition, we suggest that the intensity of this peak and the spin-spin correlation at the maximum distance along the ladder direction remain finite in the bulk limit for strong enough interladder coupling. We discuss the relevance of these results for magnetic compounds containing ladders coupled in a trellis lattice and for the stripe scenario in high-${T}_{c}$ superconducting cuprates.

DOI
10.1103/physrevb.62.928

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A model of coupled antiferromagnetic spin-1/2 Heisenberg ladders is studied with numerical techniques. In the case of ferromagnetic interladder coupling we find that the dynamic and static structure factor has a peak at (\ensuremathπ,\ensuremathπ/2)(\ensuremath{\pi},\ensuremath{\pi}/2)(\ensuremathπ,\ensuremathπ/2) where the first (second) direction is along (transversal) to the ladders. In addition, we suggest that the intensity of this peak and the spin-spin correlation at the maximum distance along the ladder direction remain finite in the bulk limit for strong enough interladder coupling. We discuss the relevance of these results for magnetic compounds containing ladders coupled in a trellis lattice and for the stripe scenario in high-Tc{T}_{c}Tc​ superconducting cuprates.
The Raman scattering spectra from magnetic excitations in an antiferromagnetic spin-12\frac{1}{2}21​ 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{\mathrm{CaV}}_{2}{\mathrm{O}}_{5}CaV2​O5​ and Sr14Cu24O41.{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.Sr14​Cu24​O41​.
We investigate weakly coupled spin-1/21/21/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (CH12N)CuBr4{(}_{\mathrm{C}}{\mathrm{H}}_{12}{\mathrm{N}}_{)}{\mathrm{CuBr}}_{4}(C​H12​N)​CuBr4​ (BPCB). We use a combination of numerical and analytical methods, in particular, the density-matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic-field dependence of the nuclear-magnetic-resonance relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore, we compute, using time-dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to describe directly the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid or onto a ttt-JJJ model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high-energy part of the spectrum that are potentially testable in future experiments.
We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C5H12N)2CuBr4\mathrm{(C_5H_{12}N)_2CuBr_4}(C5​H12​N)2​CuBr4​ (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean field approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.
Heisenberg antiferromagnetic spin ``ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO)2{)}_{2})2​P2{\mathrm{P}}_{2}P2​O7{\mathrm{O}}_{7}O7​. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-k0{\mathit{k}}_{0}k0​)2{)}^{2})2 (in the strong-coupling limit ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at k0{\mathit{k}}_{0}k0​=\ensuremath{\pi}, and a maximum between k1{\mathit{k}}_{1}k1​=\ensuremath{\pi}/2 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=0) and 0 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=\ensuremath{\infty}). We also give numerical results for the dynamical structure factor S(q,\ensuremath{\omega}), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.
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