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

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 case 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.