Emergent Topology in Kagome Ferromagnets

TL;DR

This work addresses emergent topology in a two-dimensional kagome ferromagnet by coupling Dzyaloshinskii-Moriya-induced canting to a scalar spin chirality term through a topological orbital susceptibility $\kappa^{TO}$. Using linear spin-wave theory, the authors derive a momentum-space magnon Hamiltonian $\tilde{\mathcal{H}}(\mathbf{k}) = \mathcal{H}_J(\mathbf{k}) + \mathcal{H}_{DM}(\mathbf{k}) + \mathcal{H}_{\chi}(\mathbf{k}) + \mathcal{H}_Z(\mathbf{k})$ for the three kagome sublattices and analyze the momentum-space orbital texture $\mathbf{L}(\mathbf{k})$, its curl, and the Berry curvature $\Omega_n(\mathbf{k})$. They show that noncoplanar spin textures alone do not guarantee topology; a finite $\kappa^{TO}$ coupling of scalar chirality $\chi_{ijk}$ activates a nonzero Berry curvature, with momentum-space skyrmions acting as sources of geometric phase and yielding nonzero Chern numbers. The Berry phase $\gamma$ links local curvature hotspots to the global Chern number, and a global lattice rotation angle $\theta$ leaves the band energies invariant while redistributing Berry curvature, enabling geometry-driven control of topological magnon transport. Overall, the paper establishes a direct link between lattice geometry, chirality, and magnon topology, suggesting tunable topological phases and potential magnonic devices controlled by spin-orbit, chirality, and geometric orientation.

Abstract

We investigate the emergence of a topological magnon phase in a two-dimensional kagome ferromagnet with Dzyaloshinskii-Moriya interaction (DMI) and scalar spin chirality. By incorporating a chiral interaction term proportional to the scalar triple product chi_ijk = S_i (S_j x S_k), we examine how the interplay between DMI and the topological orbital coupling kappa_TO gives rise to geometric phase, nontrivial Berry curvature, and quantized Chern numbers in the magnon bands. Using a momentum-space representation and linear spin-wave theory, we compute the orbital texture, its vorticity, and the Berry curvature across the Brillouin zone. We show that noncoplanar spin textures, driven by finite DMI, form momentum-space skyrmions that act as sources of geometric curvature. Importantly, we demonstrate that DMI alone is insufficient to break time-reversal symmetry; only the presence of finite scalar chirality terms allows the system to develop a nonzero Berry phase and topological transport signatures. We further explore the effect of a global plaquette rotation, showing that while the band structure remains invariant under this unitary transformation, the Berry curvature and Chern number are modulated, highlighting the geometric sensitivity of the topological response. Our results establish a direct correspondence between the lattice geometry, chirality, and magnon topology, providing a route toward tunable topological phases in frustrated magnetic systems.

Figures (5)

• Figure 1: Orbital Texture as a Function of DMI Strength. (a) For $D = 0$, the spin configuration remains strictly coplanar. This leads to a highly ordered and mirror-symmetric orbital texture in momentum space, characterized by smoothly varying pseudospin vectors (arrows) and the absence of winding or topological defects. (b) At $D = 1$, The DMI breaks the coplanar alignment in the spin texture, breaking time-reversal symmetry and enabling finite scalar spin chirality $\chi_{ijk}$.
• Figure 2: Curl of Orbital Texture Reveals Momentum-Space Vorticity. (a) At $D = 0$, the system is coplanar, and the orbital texture is irrotational—resulting in vanishing curl across the Brillouin zone. (b) When $D = 1$, the onset of noncoplanar structure generates vortex–antivortex structures with finite positive and negative curl values, shown as blue and red regions.
• Figure 3: Berry Curvature and Emergent Quantum Geometry. (a) At $D = 0$, despite the presence of orbital texture, the system retains coplanar structure and time-reversal symmetry. As a result, the Berry curvature $\Omega(\mathbf{k})$ — which measures the quantum geometric twist of Bloch eigenstates — is identically zero throughout the Brillouin zone. (b) At finite DMI ($D = 1$), the system is noncoplanar and scalar chirality become active, leading to nontrivial Berry curvature patterns.
• Figure 4: Berry phase $\gamma$ as a function of DMI strength $D$, scalar chirality coupling $\kappa^\text{TO}$, and plaquette orientation angle $\theta$. (a) $\kappa^\text{TO} = 0$ (black line) yields $\gamma = 0$, even at finite $D$, confirming that the spin moments being noncoplanar alone is insufficient to generate a topological response. $\kappa^\text{TO} = 0.30$ (blue line), results in finite $\gamma$, antisymmetric about $D = 0$. (b) For fixed $\kappa^\text{TO} = 0.30$ and finite DMI $D = 0.10 \,\text{meV}$, the Berry phase $\gamma$ varies smoothly and periodically with the plaquette orientation angle $\theta$, illustrating the geometric sensitivity of the eigenstate structure.
• Figure 5: Chern number maps for two plaquette orientations. (a) $\theta = 0^\circ$. (b) $\theta = 30^\circ$. For $D = 0$, $C = 0$ for all $\kappa^\text{TO}$, consistent with coplanar symmetry. For $D > 0$, distinct topological regimes appear depending on $\theta$, illustrating how lattice geometry influences topological classification.