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

TL;DR

This paper studies the magnetic properties of Cu-O planes in specific cuprates, revealing how their structure leads to spin ladders with distinct gap behaviors, and provides theoretical estimates of the spin gap.

Contribution

It introduces a detailed analysis of spin ladders in cuprates with varying rung and leg numbers, using a bond operator mean field approach to estimate spin gaps.

Findings

Gapless spectra for even rungs and odd legs (n=5,9).

Gapped spectra for odd rungs and even legs (n=3,7).

Estimated spin gap of about half of J for the simplest ladder.

Abstract

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 $n_r=\frac{1}{2}(n-1)$ 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$^\prime$. 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.