Topological Magnetic Phases and Magnon-Phonon Hybridization in the Presence of Strong Dzyaloshinskii-Moriya Interaction

TL;DR

This work investigates a 2D honeycomb magnet with nearest-neighbor ferromagnetic exchange, next-nearest-neighbor Dzyaloshinskii–Moriya interaction, and an external Zeeman field, across weak-to-strong DMI. Using classical energy minimization and linear spin wave theory, it shows a DMI-driven transition from ferromagnetic order to a $120^rac{ ext{}^ ext{0}}\circ$ noncollinear ground state, with a Zeeman-field-induced crossover to noncoplanar textures. In the strong-D phase, the magnon spectrum splits into six bands with nontrivial Chern numbers that evolve with $D$ and $h$, and the anomalous thermal Hall conductivity $\kappa_{xy}$ tracks topological transitions. A quadratic magnon-phonon coupling emerges only in the strong-D phase due to noncollinear spin textures, producing topologically hybrid magnon-phonon bands and opening gaps near band crossings. Overall, the study highlights how strong DMI reshapes ground states, enriches magnon topology, and enables magnon-phonon hybrids with potential spintronic applications.

Abstract

In recent years, the interplay between quantum magnetism and topology has attracted growing interest, both for its fundamental importance and its technological potential. Topological magnons, quantized spin excitations with nontrivial band topology, hold particular promise for spintronics, offering routes to robust, low-dissipation devices for next-generation information processing and storage. While topological magnons in honeycomb ferromagnets with weak next-nearest-neighbor Dzyaloshinskii-Moriya interactions (DMI) have been extensively investigated, the strong-DMI regime remains largely unexplored. In this work, we examine topological magnetic phases and magnon-phonon hybridization in a two-dimensional magnetic system with strong DMI. We show that strong DMI drives a transition from a ferromagnetic ground state to a 120$^\circ$ noncollinear order. An additional Zeeman field further induces noncoplanar spin textures, giving rise to a diverse set of topological phases. We demonstrate that these topological phases can be directly probed through the anomalous thermal Hall effect. Finally, we find that the spin-spin interactions in the strong-$D$ phase enable magnon-phonon coupling that yields hybridized topological bands, whereas such coupling vanishes in the weak-$D$ phase.

Figures (8)

• Figure 1: Classical ground state phases.(a) Gray arrows represent the DMI. Black vectors $\boldsymbol{a}_1^\prime$ and $\boldsymbol{a}_2^\prime$ indicate the small unit cell for the weak-$D$ phase. Red vectors $\boldsymbol{a}_1$ and $\boldsymbol{a}_2$ mark the large unit cell for the strong-$D$ phase. Within the large unit cell, blue arrows show an example of 6-spin configuration in the strong-$D$ phase with $\phi_1=0$, $\phi_2=\frac{\pi}{3}$, and $D>0$. (b) Ground-state order parameter $M^z$ as a function of $D$ and $h/|J|$. The red dashed line marks the analytic phase boundary, $D_c$ from Eq. \ref{['criti']}. (c) Order parameter $M^z$ versus $D$ for selected values of $h$. (d) In-plane components of the spin structure factor, $S^x(\textbf{k})=S^y(\textbf{k})$, and $z$ component, $S^z(\textbf{k})$, in the strong-$D$ phase. Black and red arrows indicate the unit vectors in $\boldsymbol{k}$ space, for the weak-$D$ and strong-$D$ phases, respectively. Black and red dashed lines indicate the Brillouin zone for the weak-$D$ and strong-$D$ phases, respectively. The parameters used are $D/|J|=0.8$ and $h/|J|=0.3$, corresponding to the yellow star in the phase diagram, panel (b).
• Figure 2: Zero-point energy and magnon bands.(a) Zero-point energy (per unit cell) as a function of $\phi_2-\phi_1$ in the strong-$D$ phase. The parameters used are $D/|J|=0.8$ and $h/|J|=0.3$. (b) High-symmetry points in momentum space used in panels (c,d). (c-d) Magnon bands in the strong-$D$ phase with $\phi_2=\phi_1$: (c) $D/|J|=0.8$, $h/|J|=0.3$. The inset shows the band gap between $E_6$ and $E_5$. The green numbers are band indices. (d) $D/|J|=0.8$, $h=0$. Green circles mark additional band degeneracies compared with panel (c).
• Figure 3: Topological phase diagram.(a, b) Topological characteristics in the phase diagram for the strong-$D$ phase: (a) $C_3$ and $C_2+C_1$; (b) $C_6$, $C_5$, and $C_4$. (c, d) Chiral edge states numbers in the strong-$D$ phase: (c) $v_2$; (d) $v_5$ and $v_4$. The yellow stars indicate the parameters $D/|J| = 0.8$ and $h/|J| = 0.3$ used in Fig. \ref{['fig:2']}(c).
• Figure 4: Magnon Thermal Hall conductivity.(a)$\kappa_{xy}$ as a function of $D$ and $h$. (b)$\kappa_{xy}$ versus $D$ for selected values of $h$. (c)$\kappa_{xy}$ and $d\kappa_{xy}/dh$ at $D/|J|=0.8$ versus $h$. The dashed lines indicate the parameters at which topological phase transitions occur, as shown in Fig. \ref{['fig:2']}(b,c). (d) Temperature dependence of $\kappa_{xy}$ with different values of $D$ and $h$. The dashed line indicates $T=J/k_B$. Panels (a-c) are calculated at $T=J/k_B$.
• Figure 5: Magnon-phonon coupling.(a) Schematic illustration of magnon-phonon hybrid excitations. (b) Decoupled and coupled bands for $K_1/|J|=5$, $K_2/|J|=1$, and $\partial D_{ij}/\partial r_{ij}=0.3$. (c) Decoupled and coupled magnon-phonon bands for $K_1/|J|=10$, $K_2/|J|=2$, and $\partial D_{ij}/\partial r_{ij}=0.4$. Panels (b-c) are calculated using $M=1$, $D/|J|=0.8$, $h/|J|=0.3$ and $\partial J_{ij}/\partial r_{ij}=0$. In the decoupled case, the pink and green lines denote the magnon and phonon bands, respectively. When the coupling is turned on, the color represents the relative weights of the spin and lattice vibrations: pink (green) indicates a predominantly spin (lattice) character, while gray denotes strong magnon-phonon hybridization.