The Δ chain with different base–base and base–vertex interactions

Abstract

On the basis of the recently determined crystallographic structure of the delafossiteY CuO2.5, we argue that the Cu–O network has nearly independentΔ chains, with however different interactions between thes = 1/2 spins, owing to the different angles, distances and coordinations of the Cu ions. Althoughband-structure calculations are still lacking, motivated by this observation we study herethe sawtooth lattice for different ratios of the base–base and base–vertex interactions,Jbb/Jbv. By exact diagonalization and extrapolation to the infinite-size limit, weshow that the elementary excitation spectrum is the same for total spinsStot = 0 and 1,but not for Stot = 2, and has a gap only in the interval . The gap, dispersionless for Jbb = Jbv, acquires increasing k-dependence as the ratio Jbb/Jbv moves away from unity, with the minimum energy excitations fork = 0 (k = π)when Jbb/Jbv<1 (Jbb/Jbv>1). Finally, we show that the gap closure is related to the instability of the dimers in theground state as the difference between the interactions increases.