The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J c is connected by rungs with antiferromagnetic bond J r . The numerical calculation is made for the system of 12 ×2 sites by Lanczos method. The ratio of J c / J r is considered to be 0.6–1.0 in order to discuss the experimental work for ladders of Cu 2+ ions in oxide compounds Sr 14- x Ca x Cu 24 O 41 . In addition to the Raman edge about J r corresponding twice the singlet-triplet spin gap, the characteristic structure appears around 2 or 3 times of J r i.e. 3 or 5 times the spin-gap. We concentrate our attention on characteristic features of excited levels, transitions to which are Raman-active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the picture of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.
Characteristic properties of excited states in anitiferromagnetic ladder systems with spin-1/2 are investigated in relation with the theoretical analysis of the quite asymmetric shape of the peak for twice the spin gap Δg in magnetic Raman spectra. Here, the structure of exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which legs with antiferromagnetic bond Jc is connected by rungs with antiferromagnetic bond Jr. The singlet ground state in this system can be expressed as the ordering of singlet dimers on rungs in the ladder for Jc/Jr →+0. In fact, the value of 0.1 is adopted to be the ratio of Jc /Jr in order to discuss the experimental work of the magnetic Raman spectra for the ladder of V4+ ions in the oxide compound CaV2O5 reported in Konstantinović et al., Phys. Rev. B61 (2000), 15185. As for this peak of 2Δg , quite an asymmetric observed shape is explained by the present calculation. According to the analysis of spectra, we discuss the expression of excited states by triplet dimers on rungs: The dominant contribution of the pair of triplet dimers on adjacent rungs to the corresponding state for 2Δg peak is pointed out.
Extraction of antiferromagnetic (AF) exchange constants J and J\ensuremath{'} in two-leg spin-1/2 nearest-neighbor (NN) Heisenberg ladders from experimental magnetic spin susceptibility \ensuremath{\chi}(T) data is studied, where J\ensuremath{'} is the NN exchange constant in the rungs and J is that in the legs. Two low-T (T\ensuremath{\ll}J/
kB) approximations of Troyer, Tsunetsugu, and W\"urtz [Phys. Rev. B 50, 13 515 (1994)] for \ensuremath{\chi}(T) of the isolated spin-1/2 two-leg ladder with J\ensuremath{'}/J=1 are shown to be accurate to \ensuremath{\sim}10% when extrapolated to T\ensuremath{\sim}J\ensuremath{'}/
kB. The variations in the magnetic excitation dispersion relation parameters [which enter the low-T expression of Troyer et al. for \ensuremath{\chi}(T)] for J\ensuremath{'}/J1 are inferred from previous theoretical results. Next, the values of the maxima in \ensuremath{\chi}(T)\ensuremath{\equiv}${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$ from many numerical calculations in the literature for various nonfrustrated spin-1/2 NN Heisenberg antiferromagnets are considered. The values of the product ${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$
zeff are found to depend systematically and almost uniqely on an effective magnetic coordination number
zeff, defined in the text, but are nearly independent of the dimensionality of the spin lattice and of the magnitude of any gap in the magnetic excitation spectrum. This observation allows accurate bounds on the exchange coupling constants in arbitrary quasi-low-dimensional spin-1/2 antiferromagnets to be inferred from experimental ${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$ values. Finally, a mean-field-type expression for \ensuremath{\chi}(T) for arbitrary quasi-low-dimensional spin-1/2 Heisenberg antiferromagnets is derived, using the above ${\mathrm{\ensuremath{\chi}}}^{\mathrm{max}}$ phenomenology as input, which allows the influence of intersystem coupling on \ensuremath{\chi}(T) to be evaluated. These results, and the \ensuremath{\chi}(T) calculations of Barnes and Riera [Phys. Rev. B 50, 6817 (1994)] for isolated two-leg spin-1/2 Heisenberg ladders, are used to analyze the experimental \ensuremath{\chi}(T) data of Azuma et al. [Phys. Rev. Lett. 73, 3463 (1994)] for the spin-1/2 two-leg ladder compound
SrCu2O3. The analyses together suggest that J\ensuremath{'}/J\ensuremath{\sim}0.5, contrary to the expectation that J\ensuremath{'}/J\ensuremath{\approxeq}1, and that J is very large (\ensuremath{\sim}2000 K), similar to the value of J in the linear-chain cuprate
Sr2CuO3. \textcopyright{} 1996 The American Physical Society.
A comprehensive theoretical and experimental study is presented of the magnetic susceptibility versus temperature χ(T) of spin S = 1/2 two- and three-leg Heisenberg ladders and ladder oxide compounds. Extensive quantum Monte Carlo simulations of χ(T) were carried out for both isolated and coupled two-leg ladders with spatially anisotropic intraladder exchange. Accurate fits to these and related literature QMC data were obtained. We have also calculated the one- and two-magnon dispersion relations and the dynamical spin structure factor for anisotropic isolated 2 x 12 ladders. The exchange constants in the two-leg ladder compound SrCu2O3 are estimated from LDA+U calculations. We report the detailed crystal structure of SrCu2O3 and of the three-leg ladder compound Sr2Cu3O5. New experimental χ(T) data are reported for the two-leg ladder cuprates SrCu2O3 and LaCuO_{2.5}, and for the (nominally) two-leg ladder vanadates CaV2O5 and MgV2O5. The new and literature χ(T) data for these compounds and for Sr2Cu3O5 are modeled using our QMC χ(T) simulation fits, and the exchange coupling constants between the spins-1/2 are thereby estimated for each material. The surpisingly strong spatial anisotropy of the bilinear intraladder exchange constants in the cuprate compounds is discussed together with the results of other experiments sensitive to this anisotropy. Recent theoretical predictions are discussed including those which indicate that a four-spin cyclic exchange interaction within a Cu4 plaquette is important to determining the magnetic properties and which can significantly influence the exchange interactions estimated from χ(T) data assuming the presence of only bilinear exchange.
Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.