Cross-over from an incommensurate singlet spiral state with a vanishingly small spin-gap to a valence bond solid state in dimerized frustrated ferromagnetic spin-chains

Cliò Efthimia Agrapidis; Stefan-Ludwig Drechsler; Jeroen van den Brink; Satoshi Nishimoto

doi:10.1103/PhysRevB.95.220404

paper

Cross-over from an incommensurate singlet spiral state with a vanishingly small spin-gap to a valence bond solid state in dimerized frustrated ferromagnetic spin-chains

arXiv:1612.07609 · doi:10.1103/PhysRevB.95.220404

Abstract

Motivated by the magnetic properties of the spin-chain compounds LiCuSbO $_{4}$ $\equiv$ LiSbCuO $_{4}$ and Rb $_{2}$ Cu $_{2}$ Mo $_{3}$ O $_{12}$ , we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM)( $J_{1}, J_{1}^{'} < 0$ ) and next-nearest-neighbor antiferromagnetic ( $J_{2} > 0$ ) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at $2 α = β / (1 + β)$ , where $α$ is the frustration ratio $J_{2} /∣ J_{1} ∣$ and $β$ the degree of dimerization $J_{1}^{'} / J_{1}$ .In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO $_{4}$ . For larger $α$ , corresponding to Rb $_{2}$ Cu $_{2}$ Mo $_{3}$ O $_{12}$ , and smaller $β$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps.

4 pages, 5 figures

Cross-over from an incommensurate singlet spiral state with a vanishingly small spin-gap to a valence bond solid state in dimerized frustrated ferromagnetic spin-chains

Abstract

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