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Flat bands in the J1−J2−J3 XXZ sawtooth chain

Vadim Ohanyan1,2, Johannes Richter3,4, Michael Sekania5,6, Lucas Giambattista7, Alexei Andreanov8,9, and Marcus Kollar7

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Phys. Rev. B 113, 214418 – Published 4 June, 2026

DOI: https://doi.org/10.1103/byv6-h2m2

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.

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Phys. Rev. B 113, 214418– Published 4 June, 2026
  • Received 20 November 2025
  • Revised 2 April 2026
  • Accepted 12 May 2026
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