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We investigate the magnetic properties of the Cu-O planes in stoichiometricSr$_{n-1}$Cu$_{n+1}$O$_{2n}$ (n=3,5,7,...) which consist of CuO double chainsperiodically intergrown within the CuO$_2$ planes. The double chains break upthe two-dimensional antiferromagnetic planes into Heisenberg spin ladders with$n_r=\frac{1}{2}(n-1)$ rungs and $n_l=\frac{1}{2}(n+1)$ legs and described bythe usual antiferromagnetic coupling J inside each ladder and a weak andfrustrated interladder coupling J$^\prime$. The resulting lattice is a newtwo-dimensional trellis lattice. We first examine the spin excitation spectraof isolated quasi one dimensional Heisenberg ladders which exhibit a gaplessspectra when $n_r$ is even and $n_l$ is odd ( corresponding to n=5,9,...) and agapped spectra when $n_r$ is odd and $n_l$ is even (corresponding ton=3,7,...). We use the bond operator representation of quantum $S=\frac{1}{2}$spins in a mean field treatment with self-energy corrections and obtain a spingap of $\approx \frac{1}{2} J$ for the simplest single rung ladder (n=3), inagreement with numerical estimates.Comment: 21 pages, 5 figures upon request, REVTEX, ETH-TH/93-3

Spin ladders with spin gaps: A description of a class of cuprates