Low temperature Correlation lengths of Bilayer Heisenberg Antiferromagnets and Neutron Scattering

The low temperature correlation length and the static structure factor are computed for bilayer antiferromagnets such as YBa2Cu3O6. It is shown that energy integrated two-axis scan in neutron scattering experiments can be meaningfully interpreted to extract correlation length in such bilayer antiferromagnets despite intensity modulation in the momentum perpendicular to the layers. Thus, precise measurements of the spin-spin correlation length can be performed in the future, and the theoretical predictions can be tested. It is also shown how the same correlation length can be measured in nuclear magnetic resonance experiments. PACS: 75.10.Jm, 74.72.Bk Typeset using REVTEX 1 Nearly thirty five years ago Birgeneau, Skalyo and Shirane [1] invented a neutron scattering method, known as the energy integrated two-axis scan (ETAS), whereby the spin-spin correlation lengths of layered magnets can be measured without explicitly measuring the dynamic structure factor for all energy and momentum transfers and then integrating over the energy, known as the three axis scan. Except for special circumstances, three axis scan to measure correlation length is difficult. The underlying principles of ETAS are an analog energy integration performed by using a special geometry and the reliance on the dominance of low energy scattering—the method is especially effective when the critical scattering dominates. In recent years, ETAS has served us well in unravelling the magnetic fluctuations of the parent compound of one of the high temperature superconductors, namely the La2CuO4 [2]. The experimental results are in excellent agreement with our theoretical understanding of these two-dimensional magnets [3]. Unfortunately, the method does not appear to be readily extendable 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 of using ETAS is an intensity modulation [4] with the momentum transfer perpendicular to the planes. It is the purpose of the present paper to (a) derive the low temperature properties of such bilayer antiferromagnets and (b) to show how ETAS can be extended to such bilayer antiferromagnets. It is hoped that future experiments using ETAS will be able to provide us with precise measurements of the antiferromagnetic correlation lengths in these materials, which should be of great help in understanding the magnetic flutuations of these bilayer superconductors. We also briefly remark how the same correlation length can be also measured by measuring the Cu relaxation rate in nuclear magnetic resonance (NMR) experiments. The Heisenberg model for a spin-S, nearest neighbor, square lattice, bilayer antiferromagnet is