Antiferromagnetic exchange in two-leg spin-1/2 ladders

Extraction of antiferromagnetic (AF) exchange constants J and J' in two-leg spin-1/2 nearest-neighbour (NN) Heisenberg ladders from experimental magnetic spin susceptibility (chi)(T) data is studied, where J' is the NN exchange constant in the rungs and J is that in the legs. Two low-T (T much less than J/k(B)) approximations of Troyer, Tsunetsugu, and Wurtz [Phys. Rev. B 50, 13515 (1994)] for (chi)(T) of the isolated spin-1/2 two-leg ladder with J'/J = 1 are shown to be accurate to similar to 10% when extrapolated to T similar to J/k(B). The variations in the magnetic excitation dispersion relation parameters [which enter the low-T expression of Troyer et al. for (chi)(T)] for J'/J = 1 are inferred from previous theoretical results. Next, the values of the maxima in (chi)(T) = (max)(chi) from many numerical calculations in the literature for various nonfrustrated spin-1/2 NN Heisenberg antiferromagnets are considered. The values of the product (max)(chi)z(eff) are found to depend systematically and almost uniqely on an effective magnetic coordination number z(eff) 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 (max)(chi) values. Finally, a mean-field-type expression for (chi)(T) for arbitrary quasi-low-dimensional spin-1/2 Heisenberg antiferromagnets is derived, using the above (max)(chi) phenomenology as input, which allows the influence of intersystem coupling on (chi)(T) to be evaluated. These results, and the (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 (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'/J similar to 0.5, contrary to the expectation that J'/J approximate to 1, and that J is very large (similar to 2000 K), similar to the value of J in the linear-chain cuprate Sr2CuO3.