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 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 spectrum when n, is even and n(l) is odd (corresponding to n = 5, 9,...) and a gapped spectrum 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 almost-equal-to 1/2J for the simplest single-rung ladder (n = 3), in agreement with numerical estimates. We also present results of the dynamical structure factor S(q, omega). 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 Srn-1Cun+1O2n compounds with n = 3,7,11,..., will be frustrated quantum antiferromagnets with a quantum-disordered or spin-liquid ground state.