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 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.}

Figures (2)

• Figure 1: (Color online) Symmetric and distorted sawtooth chains with three different coupling(s) for each side of triangle. The filled circles show the lattice sites occupied by spins. The exchange coupling, the $XXZ$ anisotropy and DM interaction along the basal line (black) are $J_1$, $\Delta_1$ and $D_1$, respectively. Left (red) and right (blue) bonds along the zigzag line feature the parameters $J_2$, $\Delta_2$ and $D_2$ (red) and $J_3$, $\Delta_3$ and $D_3$ (blue), respectively. The symmetric case features the same bond angles $\theta$ for the left and right bonds of the triangle, while in the distorted chain they are $\theta_1$ and $\theta_2$, respectively. The basal line is chosen to be parallel to $x$-axis and electric field vector lies in $(x, y)$ plane.
• Figure 2: (Color online) Zero-temperature exact diagonalization results for the magnetization in the distorted sawtooth chain with KNB mechanism for the values of electric field magnitude, angle, $\theta_1$, $\theta_2$ given in the Eqs. (\ref{['eq:the_the_1']})-(\ref{['eq:the_the_3']}). All three sets of parameters lead to the same magnetization curve as they all correspond to the same Hamiltonian (\ref{['eq:ham_gen']}), namely $J_1=1, J_2=1, J_3=3$, $\Delta_1=\Delta_2=\Delta_3=1$ and $D_1=1, D-2=-2, D_3=-1$.