Finite-temperature topological magnons in honeycomb ferromagnets with sublattice asymmetries

TL;DR

This work revisits magnon topology in honeycomb ferromagnets by incorporating magnon-magnon interactions through a self-consistently renormalized spin-wave theory and introducing sublattice-symmetry breaking via unequal easy-axis anisotropy and potentially unequal sublattice magnetizations. The main result is that temperature can induce a transition from a trivial to a Chern-insulating magnon phase, with band gaps closing and reopening at the K or K' points and nontrivial Berry curvature emerging, while edge states appear above a finite critical temperature and the thermal Hall conductivity does not reliably signal the transition. The study provides a realistic mechanism for finite-temperature magnon topology and highlights the crucial role of MMIs and sublattice asymmetry in magnonics, although higher-order corrections near Tc may modify precise phase boundaries. The findings suggest new avenues for temperature-tunable magnonic devices based on topological edge modes in honeycomb magnets.

Abstract

The Comment [Y.-M. Li, B. Wei, and K. Chang, Phys. Rev. Lett. 132, 219601 (2024)] pointed out that it is incorrect to predict the temperature-driven topological phase transition of Dirac magnons in honeycomb ferromagnets with Dzyaloshinskii-Moriya interactions based on the theory in Lu et al. [Y.-S. Lu, J.-L. Li, and C.-T. Wu, Phys. Rev. Lett. 127, 217202 (2021)]. Here we propose that by breaking the sublattice symmetries in honeycomb ferromagnets, increasing temperature could induce topological transitions from the trivial phase at zero temperature based on the linear spin wave theory to the Chern insulating phase above a critical temperature without changing any spin-spin interactions. The key to the finite-temperature topological magnons is considering the magnon-magnon interactions (MMIs) at a mean-field level. A self-consistently renormalized spin wave theory is employed to include self-energy corrections from MMIs, guaranteeing that the critical temperatures for topological transitions are below the Curié temperatures. Across the critical temperatures, the magnon band gap closes and reopens at K or K? points in the Brillouin zone, accompanied by nontrivial Berry curvature transitions. However, in stark contrast to the work of Lu et al. [Phys. Rev. Lett. 127, 217202 (2021)], the topological transitions cannot be revealed by the thermal Hall effect of magnons. Our work provides a realistic scheme for achieving a finite-temperature topological phase in honeycomb ferromagnets.

Figures (6)

• Figure 1: The honeycomb ferromagnets with NNN DMIs. The candidate materials includes the CrI$_{3}$, VI$_{3}$, etc. $\nu_{ij}=\pm 1$ characterizes the sign of DMIs with the sign dependent on the relative positions between two local spins, illustrated in the figure. $\delta_{i}$ and $\beta_{i}$ ($i$=1,2,3) denote the three nearest neighboring and next-nearest-neighboring vectors, respectively.
• Figure 2: (a) The phase diagram in the $K_{2}-D$ plane at zero temperature $T=0$. The order parameter is the Chern number of the upper magnon band. (b) The magnon bands at $T=0$ with three different value of $K_{2}$. The bandgap closes and reopens near $\mathbf{K}$ point. (c) The magnon bands at $T=0$ with another three larger $K_{2}$. The bandgap closes and reopens near $\mathbf{K}^{\prime}$ point. In (b) and (c), $D=0.03$. (d) The sublattice magnetization with respect to the temperature for $K_{2}=0$. (e) The phase diagram in the $K_{2}-D$ plane at finite temperature $T=1.75$. The while dashed lines denote the phase boundaries at zero temperature from (a). (f) The phase diagram in the $K_2-T$ plane at given DMI strength $D=0.03$. In all the panels, the other parameters are given by $S_{1} = S_{2} = 1.5$, $K_{1} = 0.5$, $I=-0.05$ and $J = -1$.
• Figure 3: (a) The magnon energies at $\mathbf{K}$ point with respect to the temperature at $K_{2}=0.2$. (b) The magnon energies at $\mathbf{K}^{\prime}$ point with respect to the temperature at $K_{2}=0.7$. (c-d) The magnon Berry curvature distribution in log scale $\Gamma(\Omega_1^z) = \text{sign}(\Omega_1^z)\text{log}_{10}(1+|\Omega_1^z|)$ at $T=0$ (c) and $T=1.75$ for $K_{2}=0.2$. (e-f) The zigzag ribbon band at $T=0$ and $T=1.75$ for $K_{2}=0.2$.
• Figure 4: The thermal Hall conductivity in the unit $k_{B}J/\hbar$ with respect to the temperature for three different $K_{2}$.
• Figure 5: (a) The phase diagram in the $K_{2}-D$ plane at $T=0$. (b) The phase diagram in the $K_{2}-D$ plane at $T=1.75$ . (c) The phase diagram in the $K_2-T$ plane with $D=0.03$. We set $S_{1} =1.5$, $S_{2}=2$ and $K_1 = 0.5$, $I=-0.05$, $J = -1$ for all calculations.