Low-energy structure of the homometallic intertwining double-chain ferrimagnetsA3Cu3(PO4)4

Abstract

Motivated by the homometallic intertwining double-chain ferrimagnets A 3 Cu 3 ͑PO 4 ͒ 4 ͑A =Ca,Sr,Pb͒, we investigate the low-energy structure of their model Hamiltonian H = ͚ n ͓J 1 ͑S n:1 + S n:3 ͒ + J 2 ͑S n+1:1 + S n−1:3 ͔͒ · S n:2 , where S n:l stands for the Cu 2+ ion spin labeled l in the nth trimer unit, with particular emphasis on the range of bond alternation 0 Ͻ J 2 / J 1 Ͻ 1. Although the spin-wave theory, whether up to O͑S 1 ͒ or up to O͑S 0 ͒, 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 J 2 = J 1 or J 2 = 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.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB 2 Hubbard chains

“…066J, in full agreement with a similar spin-wave procedure [19]. Surprisingly, the estimated value from Exact Diagonalization (ED) [5]: ∆ f lat = 1.0004J, lies between these two theoretical values.…”

“…In the large-U regime, double occupancy is energetically unfavorable and the factor 2 − ρ iα is no longer needed in Eq. (19), i.e., S iα · n iα = p iα ρiα 2 , with ρ iα = 0 or 1. In this case, a proper perturbative analysis will allow us to study hole doping effects in Sec.…”

“…Lastly, by using the constraint as given in Eq. (19), we can identify the spin field {S iα } at the single occupied sites:…”

Coexistence of spin ordering on ladders and spin dimer formation in a new-structure-type compound Sr2Co3S2O3

“…The necklace ladder can be regarded as the inverse version of the 2-leg ladder (Fig. 4b) and is related to the Cu lattice in A 3 Cu 3 (PO 4 ) 4 ( A  = Ca, Sr, Pb)15. However, the combination of the 2-leg ladders and the necklace ladders by sharing legs constructs a hybrid spin ladder , which is, to our knowledge, a new type of N -leg spin ladders.…”

“…According to magnetic susceptibility measurements, it shows no magnetic ordering down to 1.8 K, while a field-induced phase transition is observed at about 1.5 T. Necklace ladders (see Fig. 1b), which can be regarded as 3-leg zigzag ladders, are so far not found in Co-based compounds but in some Cu-based materials like ferrimagnets A 3 Cu 3 (PO 4 ) 4 ( A  = Ca, Sr, Pb)15.…”