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

Sudha Gopalan; T. M. Rice; M. Sigrist

doi:10.1103/PhysRevB.49.8901

paper

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

arXiv:cond-mat/9312026 · doi:10.1103/PhysRevB.49.8901

Abstract

We investigate the magnetic properties of the Cu-O planes in stoichiometric Sr $_{n - 1}$ Cu $_{n + 1}$ O $_{2 n}$ (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 $n_{r} = \frac{1}{2} (n - 1)$ rungs and $n_{l} = \frac{1}{2} (n + 1)$ 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 $S = \frac{1}{2}$ spins in a mean field treatment with self-energy corrections and obtain a spin gap of $\approx \frac{1}{2} J$ for the simplest single rung ladder (n=3), in agreement with numerical estimates.

21 pages, 5 figures upon request, REVTEX, ETH-TH/93-39

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

Abstract

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