Abstract
The spin-$1/2$ Heisenberg chain with a ferromagnetic first-neighbor exchange coupling $J_1$ and an antiferromagnetic second-neighbor $J_2$ has a Haldane dimer ground state with an extremely small spin gap. Thus, the ground state is readily altered by perturbations. Here, we investigate the effects of XXZ exchange magnetic anisotropy of both the easy-axis and easy-plane types and an alternation in $J_1$ on the ground state, the spin gap, and magnetic properties of the frustrated ferromagnetic spin-$1/2$ chain. It is found that there are two distinct dimerized spin-gap phases, in one of which the spin gap and the magnetic susceptibility are extremely small around the SU(2) symmetric case and in the other they are moderately large far away from the SU(2) symmetric case. A small alternation in the amplitude of $J_1$ rapidly shortens the pitch of spin correlations towards the four-spin periodicity, as in the limit of $J_1/J_2\to0$. These effects are not sufficient to quantitatively explain overall experimentally observed magnetic properties in the quasi-one-dimensional spin-gapped magnetoelectric cuprate Rb$_2$Cu$_2$Mo$_3$O$_{12}$ that exhibits ferroelectricity stabilized by a magnetic field. Our results are also relevant to Cs$_2$Cu$_2$Mo$_3$O$_{12}$, where the ferromagnetic intrachain and antiferromagnetic interchain order has recently been found, in a single chain level. We also reveal the nature of symmetry-protected topological phase transitions in the model by mapping onto effective spin-1 chain models.
Highlights
We have shown that this phase is surrounded by the partially polarized ferromagnetic (PPF) phase, the up-up-down-down (UUDD) phase, and the isotropic dimer phase (D+)
Clear first-order phase transitions have been found at the D−-Partially polarized ferromagnetic (PPF) and PPF-UUDD phase
The nature of D−-UUDD and D−-D+ phase transitions has been explained as the Haldane-large-D and Haldane–Néel phase transitions, respectively, by mapping the original spin1/2 model in the strongly dimerized case onto an effective spin-1 XXZ chain model with single-ion anisotropy D
Summary
The frustrated spin-1/2 XXZ chain with a ferromagnetic first-neighbor exchange coupling J1 < 0 and an antiferromagnetic second-neighbor exchange coupling J2 > 0 has attracted considerable interest both for realizing nontrivial phases, including the vector-spin-chirality ordered phase [1] and the Haldane dimer phase [2], and for the relevance to quasi-onedimensional edge-sharing multiferroic cuprates [1], such as A2Cu2Mo3O12 (A=Rb, Cs) [3,4,5,6,7,8], LiCu2O2 [9,10,11,12], SrCuO2 [13], LiCuVO4 [14,15,16,17,18], LiCuSbO4 [19], Li2CuZrO4 [20], and PbCuSO4(OH)2 [21,22]. With increasing easy-plane exchange anisotropy, namely, decreasing z from unity, a gapless vector-chiral (VC) phase appears robustly [1] These states are susceptible to other weak perturbations. We investigate the effects of easy-plane and easy-axis exchange magnetic anisotropy and the bond alternation δ on the spin gap, the periodicity of dominant spin correlations, and the uniform magnetic susceptibility. These results will be useful for direct comparisons with experiments and preclude single-chain scenarios for Rb2Cu2Mo3O12.
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