Low-energy structure of the homometallic intertwining double-chain ferrimagnets A₃Cu₃(PO₄)₄ (A=Ca,Sr,Pb)

Motivated by the homometallic intertwining double-chain ferrimagnets A₃Cu₃(PO₄)₄ (A=Ca,Sr,Pb), we investigate the low-energy structure of their model Hamiltonian H=∑_n[J₁(S_n:1+S_n:3)+J₂(S_n+1:1+S_n−1:3)]∙S_n:2, where S_n:l stands for the Cu²⁺ ion spin labeled l in the nth trimer unit, with particular emphasis on the range of bond alternation 0<J₂∕J₁<1. Although the spin-wave theory, whether up to O(S¹) or up to O(S⁰), claims that there exists a flatband in the excitation spectrum regardless of bond alternation, a perturbational treatment, as well as the exact diagonalization of the Hamiltonian, reveals its weak but nonvanishing momentum dispersion unless J₂=J₁ or J₂=0. Quantum Monte Carlo calculations of the static structure factor further convince us of the low-lying excitation mechanism, elucidating similarities and differences between the present system and alternating-spin linear-chain ferrimagnets.