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

We investigate the magnetic properties of the Cu-O planes in stoichiometric Srn−1Cun+1O2n (n=3,5,7,...) which consist of CuO double chains periodically intergrown within the CuO2 planes. The double chains break up the two-dimensional antiferromagnetic planes into Heisenberg spin ladders with nr = 1 2 (n − 1) rungs and nl = 12 (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 nr is even and nl is odd ( corresponding to n=5,9,...) and a gapped spectra when nr is odd and nl 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,