Chirality-Selective Topological Magnon Transition

• The paper demonstrates that tuning DMI, anisotropy, or strain can flip the chirality of magnon bands and induce a reversible topological phase transition.
• It employs model Hamiltonians and the Holstein–Primakoff transformation to reveal Dirac gap closing and reopening at high-symmetry points with corresponding Chern number jumps.
• The study links the chirality flip to measurable thermal Hall effects, highlighting potential applications in robust magnonic and spintronic devices.

A chirality-selective topological magnon phase transition refers to a topological change in the magnon excitation spectrum of a magnetically ordered system, wherein the sense of chirality—encoded via Berry curvature and Chern number—of the magnon bands is controllably flipped. The transition is realized through the tuning of physical parameters, such as Dzyaloshinskii–Moriya interactions (DMI), anisotropies, or external perturbations, which couple to the underlying chiral symmetry of the lattice or spin texture. Across the transition, the bulk band gap at a high-symmetry point closes and subsequently reopens, with the Chern numbers of the bands and the direction of associated edge-state propagation (the chirality) changing sign. Such transitions give rise to a strong thermal Hall response and robust switching of magnon edge currents, forming the basis of topological magnonic devices and chirality-sensitive transport phenomena.

1. Theoretical Framework: Microscopic Origin and Model Hamiltonians

Chirality-selective topological magnon phase transitions are studied across a series of magnetic models, united by bosonic band structures hosting Dirac or Weyl nodes whose gap and resulting topology can be tuned by chirality-coupled interactions. The canonical example is the honeycomb ferromagnet with next-nearest-neighbor (NNN) Dzyaloshinskii–Moriya interaction (DMI) and sublattice-resolved anisotropy. The general form of the quadratic spin Hamiltonian is: $$H_{\rm mag} = -J\sum_{\langle i,j\rangle}\mathbf S_i\cdot\mathbf S_j + D_A\sum_{\langle\!\langle i,j\rangle\!\rangle\in A}\nu_{ij}\,{\bf\hat z}\cdot(\mathbf S_i\times\mathbf S_j) + D_B\sum_{\langle\!\langle i,j\rangle\!\rangle\in B}\nu_{ij}\,{\bf\hat z}\cdot(\mathbf S_i\times\mathbf S_j) - K_A\sum_{i\in A}(S_i^z)^2 - K_B\sum_{i\in B}(S_i^z)^2 - H\sum_i S_i^z$$ where $J$ is the isotropic NN Heisenberg coupling, $D_{A,B}$ denote DMI on A/B sublattices, and $K_{A,B}$ are sublattice-dependent easy-axis anisotropies (Kim et al., 2022).

Upon linearization (Holstein–Primakoff transformation), Fourier transform, and projection onto the magnon basis, the Hamiltonian admits a $2\times 2$ Bloch form

$$H_{\rm mag}(\mathbf{k}) = \varepsilon_0(\mathbf{k})\,{\mathbb I} + \mathbf{h}(\mathbf{k})\cdot{\boldsymbol\tau}$$

with the "mass" $h_z(\mathbf{k})$ governing Dirac gap opening at the $K/K'$ points. The DMI generates complex hopping analogous to the Haldane mass, while sublattice anisotropy breaks inversion symmetry.

In more complex or lower-symmetry systems, additional pseudo-dipolar interactions, boundary-injected chirality fields, noncollinear (Kitaev–$\Gamma$) exchange, and time-dependent (Floquet) driving augment the basis, but the critical structure persists: a mass term $m$ encoding chirality, a tuning parameter (anisotropy, strain, external current), and Berry curvature of the eigenmodes.

2. Topological Bandstructure: Chern Numbers, Berry Curvature, and Transition Criteria

The essence of the chirality-selective transition is the closure and reopening of a topological band gap, typically at a Dirac (or Weyl) point, accompanied by a quantized Chern number jump. The Berry curvature for band $n$ is given by

$$\Omega_n(\mathbf{k}) = -\frac{1}{2}\,\hat{\mathbf{n}}\cdot\Bigl(\partial_{k_x}\hat{\mathbf{n}}\times\partial_{k_y}\hat{\mathbf{n}}\Bigr)$$

where $$\hat{\mathbf{n}}(\mathbf{k})=\mathbf{h}(\mathbf{k})/|\mathbf{h}(\mathbf{k})|$$ in the simplest two-band cases (Kim et al., 2022, Lee et al., 2022).

The Chern number

$$C_n = \frac{1}{2\pi}\int_{\rm BZ}d^2k\,\Omega_n(\mathbf{k})$$

serves as the topological invariant classifying the phase. A bulk transition is triggered when the gap at $K$ or $K'$ closes: $$\Delta_K \pm 3\sqrt{3}\,\bar D = 0,\quad \text{or}\quad m=0$$ for average DMI $\bar D$ and sublattice-mass $m$ (Kim et al., 2022).

Critical tuning parameters across various implementations include:

• Sublattice anisotropy difference $\Delta_K = K_A - K_B$ (with DMI fixed)
• Boundary-injected chirality $\chi$ controlling $m(\chi)\sim\chi^3$ (Lee et al., 2022)
• Competing DMI and pseudo-dipolar exchange $F$ in honeycomb ferromagnets (Ni et al., 26 Dec 2025)
• Temperature-tuned self-energies in the presence of sublattice/asymmetric interactions (Li et al., 2022, Zhu et al., 2023)
• Strain amplitude or driving phase in Floquet-engineered magnets (Vidal-Silva et al., 2022, Martinez-Berumen et al., 27 Aug 2025)
• External magnetic field in noncollinear spin textures or skyrmion crystals (Diaz et al., 2019, Timofeev et al., 2023)

Generalized, the closing of the topological gap is described by the vanishing of a symmetry-breaking mass term dictating the chirality of the mode, with the Chern number changing by $\pm 1$ at each crossing.

3. Edge-State Chirality and Bulk–Boundary Correspondence

The hallmark of the topological phase is the emergence of chiral magnon edge modes, protected by the bulk Chern number and robust to disorder. In honeycomb and kagome ribbons, the number and direction of edge states correspond to the net Chern number across the gap (Kim et al., 2022, Ni et al., 26 Dec 2025, Alwan et al., 17 Oct 2025):

• For $(C_+,C_-)= (+1, -1)$, a single chiral edge mode bridges the magnon gap, with its propagation direction set by the sign of the DMI or scalar chirality.
• On crossing the phase boundary, the gap reopens with $(C_+,C_-)=(0,0)$ and no edge states.
• Entering the opposite chiral topological regime reverses the edge mode direction.

In noncollinear/large magnetic cell systems (e.g., triple-meron textures, skyrmion crystals), the transition involves a band inversion between distinct collective modes (e.g., breathing and anti-clockwise), transferring the topological edge-mode across magnon branches. The group velocity (chirality) of boundary magnon currents switches sign across the transition (Chen et al., 2023, Timofeev et al., 2023, Diaz et al., 2019).

4. Mechanisms for Tuning and Controlling the Transition

Chirality-selective topological transitions can be engineered or controlled via multiple routes:

• Sublattice symmetry breaking: Tuning the difference $\Delta_K$ competes with DMI, allowing access to both topological and trivial phases (Kim et al., 2022).
• Boundary chirality injection: Via spin Hall effect at the boundaries, injection of a controlled chirality $\chi$ accumulates a sublattice mass $m(\chi)\sim\chi^3$, inducing and flipping the Chern number, directly observable as a "shoulder" in the thermal Hall conductivity (Lee et al., 2022).
• Interaction-induced transitions: Many-body magnon-magnon interactions produce anomalous self-energy terms breaking effective time-reversal, with external fields or temperature shifting the magnonic Dirac mass; this leads to field- or temperature-driven transitions with sign reversal of the Hall effect (Mook et al., 2020, Li et al., 2022).
• Competing anisotropic exchanges: The balance between DMI and pseudo-dipolar interactions provides an additional tuning mechanism, unique to honeycomb geometry, with the possibility of a pseudo-orbital (valley) band inversion and sign change of $\kappa_{xy}$ (Ni et al., 26 Dec 2025).
• Floquet engineering and strain: Periodic (high-frequency) strain, phase-modulated DMI, or complex driving fields create effective chiral couplings; the relative phase or strain geometry controls the sign of the resulting mass and thus the edge-state chirality (Vidal-Silva et al., 2022, Martinez-Berumen et al., 27 Aug 2025).

In all cases, the mechanism relies on a synthetic or intrinsic mass term that couples to chirality (pseudospin, valley, or edge-mode) and can be continuously tuned to close and reopen gaps at high-symmetry points.

5. Experimental Signatures and Physical Consequences

The dominant observable of chirality-selective topological magnon phase transitions is the magnon thermal Hall conductivity, $\kappa^{xy}$: $$\kappa^{xy} = -\,\frac{2k_B^2 T}{\hbar V}\,\sum_{n=\pm}\sum_{\mathbf{k}\in{\rm BZ}} \Omega^n(\mathbf{k})\,c_2\bigl[\rho_n(\mathbf{k})\bigr]$$ where $c_2(\rho)$ encodes magnon occupation statistics and $\Omega^n(\mathbf{k})$ is the Berry curvature (Kim et al., 2022, Lee et al., 2022). Across the chirality-selective transition, $\kappa^{xy}$ displays quantized sign changes or sharp "shoulders" as a function of the controlling parameter. Notable regimes include:

• Switching behavior: On passing from $(C_+,C_-)= (+1, -1)$ to $(-1,+1)$, $\kappa^{xy}$ reverses sign.
• Criticality: At the phase boundary, the magnon gap collapses, and $\kappa^{xy}\to 0$.
• Finite-temperature transitions: For thermally driven transitions, $\kappa^{xy}(T)$ exhibits abrupt jumps at the critical temperature $T_c$ (Li et al., 2022, Zhu et al., 2023).
• Edge transport: The directionality of edge-magnon propagation, observable via nonreciprocal transmission or local edge heating, provides a direct chirality indicator (Kim et al., 2022, Chen et al., 2023, Diaz et al., 2019).
• Magnon polarization/pseudospin: The flip of magnon chirality at the transition can be detected by polarized neutron or Raman scattering (Li et al., 2022).

In 3D chiral antiferromagnets or magnetic Weyl semimetals, the transition can be probed by anomalous Hall effect, node annihilation via ARPES, or by inspecting Weyl-node chirality dependencies in the electron-magnon self-energy (Sourounis et al., 2024, Owerre, 2018).

6. Representative Models and Material Platforms

A selection of key systems realizing chirality-selective topological magnon transitions is summarized below:

Lattice/model	Tuning parameter(s)	Phase transition/observable	Reference
Honeycomb ferromagnet (DMI, anisotropy)	$\Delta_K$, $\bar D$	Chern flip, $\kappa^{xy}$ sign change	(Kim et al., 2022)
Honeycomb (pseudo-dipolar, DMI)	$F$ (PDI), $D_z$ (DMI)	Valley inversion, $\kappa_{xy}$ sign change	(Ni et al., 26 Dec 2025)
magnon–magnon interaction (honeycomb/kag.)	$B$, $T$	Interaction-induced, field or thermal	(Mook et al., 2020)
Boundary chirality injection	$\chi$ (spin Hall current)	Chern flip, shoulder in $\kappa_{xy}$	(Lee et al., 2022)
Floquet/strain engineering (honeycomb/sq.)	Strain amplitude, driving phase	Chern and edge-mode chirality flipping	(Vidal-Silva et al., 2022, Martinez-Berumen et al., 27 Aug 2025)
Skyrmion crystal (chiral DMI, field)	$B$	Breather—rotational magnon band inversion	(Diaz et al., 2019, Timofeev et al., 2023)
Noncollinear Kitaev–$\Gamma$ materials	$\phi$, $h$	Sequential Chern jumps, edge-mode switches	(Chen et al., 2023)
Kagome ($XXZ$, field)	$\Delta$, $h$, $T$	Chiral symmetry breaking, topological plateaux	(Albarracín et al., 2020)
3D chiral AFM (uniaxial strain)	$\delta$ (strain)	Weyl-to-Chern transition, sign-chirality locking	(Owerre, 2018)
Magnetic Weyl systems (electron–magnon)	$T$, $g$ (coupling strength)	Chirality-dependent node annihilation, $\sigma_{xy}$	(Sourounis et al., 2024)

Materials hosting these transitions include 3d/4d/5d honeycomb and kagome magnets (e.g., $\alpha$-RuCl$_3$, Na$_2$IrO$_3$, CrI$_3$, Cu(1,3-bdc),$Fe$_2$Mo$_3$O$_8$, MnPS$_3$), chiral magnets (skyrmion hosts), and tailored artificial magnonic crystals.

7. Significance and Outlook

The chirality-selective topological magnon phase transition represents a key convergence of bosonic topological band theory and magnetic order, distinguished by the tunable, reversible control of chiral edge excitation transport in solid-state systems. Unlike electronic Chern transitions, magnonic transitions can be driven by non-magnetic means—strain, boundary currents, temperature, or engineered interaction terms—opening new avenues for low-power, robust spin transport and topological manipulation in magnonic and spintronic devices. The response functions, notably the magnon thermal Hall effect, provide a direct probe, and future research is anticipated to realize real-time, on-demand chirality switching (including via interface or Floquet effects), explore non-equilibrium topological phenomena, and extend the formalism to driven, disordered, and interacting multiband systems (Kim et al., 2022, Lee et al., 2022, Mook et al., 2020, Ni et al., 26 Dec 2025, Martinez-Berumen et al., 27 Aug 2025).