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

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 $J^{\prime }<0$, 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 $\Delta ={\Delta }^{\prime }=1$ ($\Delta$ and ${\Delta }^{\prime }$ are the corresponding anisotropy parameters), a threshold of $J/|J^{\prime }|$ 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 ${\Delta }^{\prime }-D/|J^{\prime }|$ 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 $S\ge 1/2$. Finally, we numerically calculate the $n$-magnon spectra for $S=1/2$ with $n\le 5$ 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.

18 pages, 11 figures, to appear in Physical Review B

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Cited by in corpus (1)

• Evolution of two-magnon bound states in a higher-spin ferromagnetic chain with single-ion anisotropy: A complete solution