Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices

Abstract

We present a comprehensive theoretical study of the topological properties of triplon excitations in spin-1/2 dimer-singlet ground states defined on the maple leaf and star lattices. Our analysis is based on a model that includes Heisenberg interactions, Dzyaloshinskii-Moriya (DM) interactions, and an external magnetic field. In the absence of an in-plane DM vector, we demonstrate that the triplon Hamiltonian maps onto the magnon Hamiltonian of the Kagome lattice, inheriting its nontrivial topological characteristics, including Berry curvature and topological invariants such as the Z2 invariant and Chern numbers. This correspondence enables us to derive analytical expressions for the spin Nernst and thermal Hall conductivities at low temperatures. Furthermore, we explore the effects of realistic finite in-plane DM interactions, uncovering multiple topological transitions and a complex thermal Hall conductivity behavior, including potential sign reversals as functions of magnetic field and temperature. Using layer groups, we also provide a symmetry classification of the star and maple leaf lattices.

Figures (18)

• Figure 1: Schematic figures of (a) a maple-leaf and (b) a star lattice with three types of Heisenberg interactions $J_d$, $J_t$, and $J_h$ ($J^{\prime}_h$) commentfig1. In this figure, the thick blue bonds represent $J_d$ (dimer bond), the solid red bonds denote $J_t$, and the dotted green (dashed purple) bonds indicate $J_h$ ($J^{\prime}_h$). Both lattices (a) and (b) are equivalent in terms of the connectivity when $J^{\prime}_{h} = 0$, and thus we treat them simultaneously in the following sections. When the midpoint of each $J_d$ (thick blue) bond is identified as a single effective site, the lattice structures reduce to that of a Kagome lattice (c).
• Figure 2: Schematic picture of dimers in our model. The symbols $L$ and $R$ denote the left and right spins of each dimer (thick blue bond), and the indices 1, 2, and 3 are the sublattice indices. The coordinate system represented by $x$, $y$, and $z$ axes are also indicated in the figure.
• Figure 3: Schematic figure of the magnon system on a Kagome bilayer, which corresponds to the triplon system on maple-leaf and star lattices.
• Figure 4: The three bands of $H_{\mathrm{mag}} (\bm{k})$ (\ref{['Eq:single_Kagome']}). The parameters used in the plot are $J_t = 1.0$, $J_h = 0.1$, and (a) $D_z = 0$, (b) $D_z = 0.3$. The high-symmetry points in reciprocal space are denoted by $\Gamma = (0,0)$, $M = (\frac{\pi}{2}, \frac{\pi}{2\sqrt{3}})$, and $K = (\frac{\pi}{3}, \frac{\pi}{\sqrt{3}})$.
• Figure 5: Phase diagram of $H_{\mathrm{mag}}(\bm{k})$ (\ref{['Eq:single_Kagome']}) as a function of $J_t - J_h$ and $D_z$. The components of $\bm{C}^{\mathrm{mag}} = (C^{\mathrm{mag}}_1, C^{\mathrm{mag}}_2, C^{\mathrm{mag}}_3)$ are the Chern numbers of the magnon bands $\lambda_1 (\bm{k})$, $\lambda_2(\bm{k})$, and $\lambda_3(\bm{k})$, respectively.