On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain

TL;DR

This paper investigates the conditions for flat magnon bands in a generalized XXZ sawtooth chain with Dzyaloshinskii-Moriya interactions, analyzing their properties and potential electric-field control.

Contribution

It derives algebraic constraints for flat bands in a generalized XXZ sawtooth chain with Dzyaloshinskii-Moriya interactions and explores electric-field-driven flat bands via magnetoelectric coupling.

Findings

Derived algebraic constraints for flat bands in the model.

Analyzed properties of flat magnon bands and localized states.

Mapped flat-band conditions to magnetoelectric parameters.

Abstract

We consider a generalization of the XXZ model on the sawtooth spin chain with Dzyaloshinskii-Moriya interactions in which all exchange constants (symmetric, antisymmetric, and axial anisotropy) are different for the three different bonds of each triangle. We derive and resolve algebraic constraints on the exchange constants ensuring the appearance of a flat band in the one-magnon spectrum. The properties of the corresponding flat magnon bands and localized magnon states are analyzed. We further construct the mapping of the flat-band conditions for the Dzyaloshinskii-Moriya constants onto the Katsura-Nagaosa-Balatsky parameters. Based on the mapping, the possibility of the electric-field-driven flat bands with the aid of the magnetoelectric coupling is examined.