Spin-spin correlation lengths of bilayer antiferromagnets

– The spin-spin correlation length and the static structure factor for bilayer antiferromagnets, such as YBa2Cu3O6, are calculated using field theoretical and numerical methods. It is shown that these quantities can be directly measured in neutron scattering experiments using energy integrated two-axis scan despite the strong intensity modulation perpendicular to the layers. Our calculations show that the correlation length of the bilayer antiferromagnet diverges considerably more rapidly, as the temperature tends to zero, than the correlation length of the corresponding single layer antiferromagnet typified by La2CuO4. This rapid divergence may have important consequences with respect to magnetic fluctuations of the doped superconductors. A powerful method to measure the spin-spin correlation length of a layered magnet is the neutron scattering method known as the energy integrated two-axis scan (TAS). In recent years, TAS has been successfully applied to La2CuO4[1], which is the parent compound of one of the high temperature superconductors. This experimental technique is not readily extendable, however, to a wide class of high temperature superconductors with close magnetic bilayers or triple layers within the unit cell; a particularly important example is YBa2Cu3O6, which has a close pair of magnetic planes within the unit cell, but it is otherwise a square lattice spin S = 1/2 Heisenberg antiferromagnet. The reason for the difficulty is an intensity modulation[2] with the momentum transfer perpendicular to the planes. Thus, there have been no direct measurements of the correlation length despite considerable discussion of the importance of antiferromagnetic fluctuations in these materials. In the present paper, we use both the field theoretical approach[3] and the numerical quantum Monte Carlo (QMC) loop algorithm[4] to obtain the low temperature properties of bilayer antiferromagnets. We also show that in the experimentally relevant regime TAS can be extended to such antiferromagnets. Thus, it is hoped that the antiferromagnetic fluctuations can be explored more thoroughly in future measurements. This is likely to be important Typeset using EURO-LTEX 2 EUROPHYSICS LETTERS in understanding the magnetic properties of the superconductors obtained by doping these antferromagnetic parent compounds. The Heisenberg model for a spin-S bilayer antiferromagnet is H = J‖ ∑ 〈ij〉,p S (p) i · S (p) j + J⊥ ∑ i S (1) i · S (2) i . (1) The sum in the first term is over the nearest neighbor pairs on a square lattice in each plane, where the plane index p takes two values 1 and 2. The second term represents the coupling between the planes. The exchange constants J‖ and J⊥ are both positive. The low energy, long wavelength properties of the two dimensional Heisenberg model is welldescribed by the quantum O(3) nonlinear σ-model[3]. Here, we shall consider its generalization to coupled bilayers. The Euclidean action for this system can be written down on general symmetry grounds[3], but it can also be derived from a (1/S) expansion[5]. The action is