We investigate the magnetic properties of the Cu-O planes in stoichiometric Sr n−1 Cu n+1 O 2n (n=3,5,7,...) which consist of CuO double chains periodically intergrown within the CuO 2 planes. The double chains break up the two-dimensional antiferromagnetic planes into Heisenberg spin ladders with n r = 1 2 (n − 1) rungs and n l = 1 2 (n + 1) legs and described by the usual antiferromagnetic coupling J inside each ladder and a weak and frustrated interladder coupling J ′ . The resulting lattice is a new two-dimensional trellis lattice. We first examine the spin excitation spectra of isolated quasi one dimensional Heisenberg ladders which exhibit a gapless spectra when n r is even and n l is odd ( corresponding to n=5,9,...) and a gapped spectra when n r is odd and n l is even (corresponding to n=3,7,...). We use the bond operator representation of quantum S = 1 2 spins in a mean field treatment with self-energy corrections and obtain a spin gap of ≈ 1 2 J for the simplest single rung ladder (n=3), in agreement with numerical estimates. We also present results of the dynamical structure factor S(q,ω). The spin gap decreases considerably on increasing the width of the ladders. For a double ladder with four legs and three rungs (n=7) we obtain a spin gap of only 0.1J. However, a frustrated coupling, such as that of a trellis lattice, introduced between the double ladders leads to an enhancement of the gap. Thus stoichiometric Sr n−1 Cu n+1 O 2n compounds with n=3,7,11,... will be frustrated quantum antiferromagnets with a quantum disordered or spin-liquid ground state.

A homologous series of cuprates, Sr, -Cu, + 02,, formed by introducing a parallel array of planar defects into the infmite-layer cuprate, SrCuOz, have been reported by Takano et al. In each CuO, plane line defects consisting of CuO double chains result. An analysis of the electronic properties of such planes demonstrates that the stoichiometric compounds with n = 3,7,11, ... will be frustrated quantum antiferromagnets and spin liquids. When lightly doped with holes the spin gap will remain and singlet superconductivity should occur on a separate but high temperature scale. This prediction may shed new light on the origin of the separate energy scales for the spin gap and superconductivity in other lightly doped cuprates.

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