Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation on a frustrated ferromagnetic spin-$1/2$ chain

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 $J_1/J_2\to 0$. 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.

arXiv comment16 pages, 7 figures, 1 table, to appear in Phys. Rev. B

References in corpus (44)

• Entanglement spectrum of a topological phase in one dimension
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Detection of Symmetry Protected Topological Phases in 1D
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field
• Correlation between spin helicity and electric polarization vector in quantum-spin chain magnet LiCu${}_2$O${}_2$
• Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
• Numerical and approximate analytical results for the frustrated spin-1/2 quantum spin chain
• Confirmation of a one-dimensional spin-1/2 Heisenberg system with ferromagnetic first-nearest-neighbor and antiferromagnetic second-nearest-neighbor interactions in Rb${}_2$Cu${}_2$Mo${}_3$O${}_{12}$
• Ferroelectric Transition Induced by the Incommensurate Magnetic Ordering in LiCuVO4
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Spin waves and magnetic interactions in LiCu2O2
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Chiral order and electromagnetic dynamics in one-dimensional multiferroic cuprates
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Strongly reduced gap in the zigzag spin chain with a ferromagnetic interchain coupling
• Ground State Phase Diagrams of Frustrated Spin-S XXZ Chains: Chiral Ordered Phases
• Quantum spin liquid in frustrated one dimensional LiCuSbO4
• Zigzag spin chains with antiferromagnetic-ferromagnetic interactions: Transfer-matrix renormalization group study
• Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
• Relationship between Magnetic Structure and Ferroelectricity of LiVCuO4
• Magnetic properties and revisited exchange integrals of the frustrated chain cuprate PbCuSO${}_4$(OH)${}_2$ - linarite
• Thermodynamics of multiferroic spin chains
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Highly Dispersive Spin Excitations in the Chain Cuprate Li2CuO2
• Phase diagram of the XXZ chain with next-nearest-neighbor interactions
• Ferroelectricity from spin supercurrents in LiCuVO4
• Modified DMRG algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large $J_2/J_1$
• Quantum Fluctuations of Chirality in One-Dimensional Spin-1/2 Multiferroics: Gapless Dielectric Response from Phasons and Chiral Solitons
• Zigzag spin-S chain near ferromagnet-antiferromagnet transition point
• Unconventional Neel and dimer orders in a spin-1/2 frustrated ferromagnetic chain with easy-plane anisotropy
• Competing phases in spin-1/2 J1-J2 chain with easy-plane anisotropy
• Coexistence of valence-bond formation and topological order in the Frustrated Ferromagnetic $J_1$-$J_2$ Chain
• One- and three-dimensional quantum phase transitions and anisotropy in Rb${}_2$Cu${}_2$Mo${}_3$O${}_{12}$
• 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
• Numerical study of the frustrated ferromagnetic spin-1/2 chain
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Vector-spin-chirality order in a dimerized frustrated spin-1/2 chain
• Emergent spin-$1$ Haldane gap and ferroelectricity in a frustrated spin-$1/2$ ladder
• 133Cs-NMR study on aligned powder of competing spin chain compound Cs2Cu2Mo3O12

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• Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Few-magnon excitations in a frustrated spin-$S$ ferromagnetic chain with single-ion anisotropy
• Exploring Frustration Effects of Strongly Interacting Bosons via the Hall Response
• Competing magnetic phases in the frustrated spin-1/2 chain compound $\beta$-TeVO${}_4$ probed by NMR