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

On the basis of the recently determined crystallographic structure of the delafossite Y CuO2.5, we argue that the Cu-O network has nearly independent Δ chains, with however different interactions between the s = 1/2 spins, owing to the different angles, distances and coordinations of the Cu ions. Although band-structure calculations are still lacking, motivated by this observation we study here the 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, we show that the elementary excitation spectrum is the same for total spins Stot = 0 and 1, but not for Stot = 2, and has a gap only in the interval 0.48742(2) ≤Jbb/Jbv ≤1.53(1). The gap, dispersionless for Jbb = Jbv, acquires increasing k-dependence as the ratio Jbb/Jbv moves away from unity, with the minimum energy excitations for k = 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 the ground state as the difference between the interactions increases