Few-magnon excitations in a frustrated spin-$S$ ferromagnetic chain with single-ion anisotropy

• URL: http://arxiv.org/abs/2401.14101v3
• Date: Wed, 17 Apr 2024 13:33:25 GMT
• Title: Few-magnon excitations in a frustrated spin-$S$ ferromagnetic chain with single-ion anisotropy
• Authors: Jiawei Li, Ye Cao, Ning Wu,
• Abstract summary: We study few-magnon excitations in a finite-size spin-$S$ chain with ferromagnetic nearest-neighbor interaction. We analytically identify in the $Delta'-D/|J'|$ plane the regions supporting the SI or NNN exchange two-magnon bound states.
• Score: 14.065256504065912
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\Delta=\Delta'=1$ ($\Delta$ and $\Delta'$ 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 $k=-\pi$, 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 $\Delta'-D/|J'|$ 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 $S\geq 1/2$. Finally, we numerically calculate the $n$-magnon spectra for $S=1/2$ with $n\leq5$ 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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