Few-magnon excitations in a frustrated spin-S ferromagnetic chain with single-ion anisotropy
Physical Review B(2024)
摘要
We study few-magnon excitations in a finite-size spin-S chain with
ferromagnetic nearest-neighbor (NN) interaction J>0 and antiferromagnetic
next-nearest-neighbor (NNN) interaction J'<0, in the presence of the
single-ion (SI) anisotropy D. We first reveal the condition for the emergence
of zero-excitation-energy states. In the isotropic case with Δ=Δ'=1
(Δ and Δ' are the corresponding anisotropy parameters), a
threshold of J/|J'| above which the ground state is ferromagnetic is
determined by exact diagonalization for short chains up to 12 sites. Using a
set of exact two-magnon Bloch states, we then map the two-magnon problem to a
single-particle one on an effective open chain with both NN and NNN hoppings.
The whole two-magnon excitation spectrum is calculated for large systems and
the commensurate-incommensurate transition in the lowest-lying mode is found to
exhibit different behaviors between S=1/2 and higher spins due to the
interplay of the SI anisotropy and the NNN interaction. For the commensurate
momentum k=-π, the effective lattice is decoupled into two NN open chains
that can be exactly solved via a plane-wave ansatz. Based on this, we
analytically identify in the Δ'-D/|J'| plane the regions supporting the
SI or NNN exchange two-magnon bound states near the edge of the band. In
particular, we prove that there always exists a lower-lying NN exchange
two-magnon bound state near the band edge for arbitrary S≥ 1/2. Finally,
we numerically calculate the n-magnon spectra for S=1/2 with n≤5 by
using a spin-operator matrix element method. The corresponding n-magnon
commensurate instability regions are determined for finite chains and
consistent results with prior literature are observed.
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