Electric-field driven flat bands in the distorted sawtooth chain via the Katsura-Nagaosa-Balatsky mechanism

TL;DR

This paper explores how electric fields can induce flat magnonic bands in a distorted sawtooth chain through the Katsura-Nagaosa-Balatsky mechanism, analyzing the effects of lattice distortion and field orientation.

Contribution

It derives conditions for electric-field induced flat bands in a generalized sawtooth chain with Dzyaloshinskii-Moriya interactions generated via the KNB mechanism, considering lattice distortion effects.

Findings

Electric field can induce flat magnonic bands in the distorted sawtooth chain.

Expressions for the electric-field strength needed to achieve flat bands are derived.

The dependence of the saturation field on lattice distortion angles is analyzed.

Abstract

We investigate flat magnonic bands in a generalized sawtooth-chain model in which three sets of exchange parameters (symmetric Heisenberg exchange, axial Ising anisotropy, and antisymmetric Dzyaloshinskii-Moriya (DM) exchange) are assigned independently to each side of the triangular plaquette. If the effective Dzyaloshinskii-Moriya (DM) interaction parameters are generated via the Katsura-Nagaosa-Balatsky (KNB) mechanism of magnetoelectricity, they become explicit functions of the electric-field magnitude and direction, as well as of the lattice geometry, which in the present casen is characterized by two bond angles. We focus on the situation in which these two angles are unequal, corresponding to a distortion of the triangular plaquette. Several electric-field induced flat-band scenarios in the distorted sawtooth chain are analyzed, and expressions are derived for the electric-field strength required to drive the one-magnon excitations into a flat-band regime when the field is aligned along the lattice bonds. The saturation field and its dependence on the distortion angle are also examined. Finally, we establish a mapping between the flat-band solutions for a general DM interaction and its specific KNB-induced form. \\~ \emph{This article is dedicated to the memory of Johannes Richter.}