Symmetry Origins of Chiral Magnon Splitting

Updated 9 April 2026

The paper demonstrates that symmetry restrictions in magnetic materials induce chiral magnon splitting with measurable gaps up to 30 meV.
The methodology integrates group theory, spin Hamiltonian modeling, and first-principles calculations to reveal momentum-dependent non-degeneracy and topological edge states.
The findings highlight controlled magnon transport and electrical tunability, paving the way for advanced spintronic and magnonic device applications.

Symmetry-Principled Origins of Chiral Magnon Splitting

Chiral magnon splitting refers to the momentum-dependent non-degeneracy of magnon branches with opposite handedness (“chirality”) in magnetic materials whose symmetry properties lack certain sublattice-exchanging or inversion operations. Unlike conventional antiferromagnets (AFMs), where spin compensation in real space enforces twofold degeneracy at each wavevector, altermagnets and certain symmetry-reduced collinear magnets can display magnon bands split according to handedness, without net magnetization or applied field. The symmetry classification and mechanism of this phenomenon, its universal fingerprints, and its implications for topological magnonics and spintronics, have been illuminated using a range of analytical, group-theoretical, and first-principles techniques across both insulating and metallic systems.

1. Symmetry Constraints and Microscopic Spin Hamiltonians

The fundamental origin of chiral magnon splitting lies in the structure of the crystal and the associated magnetic (spin layer) group symmetry. In compensated collinear systems—canonical AFMs, but also a broad class of so-called “altermagnets”—the two sublattices (A,B) are not always related by pure translations or inversion. Instead, they may be connected by improper rotations, mirrors, or screw axes coupled with spin rotation or time-reversal, leading to a magnetic layer group that lacks conventional Kramers degeneracy for spin excitations (Xie et al., 21 Jan 2026, Kravchuk et al., 7 Apr 2025).

The minimal spin Hamiltonian that captures spontaneous chiral splitting is

$H = \sum_{\langle ij \rangle} J_{AB}(R_{ij})\; \mathbf{S}_{Ai} \cdot \mathbf{S}_{Bj} + \sum_{\langle\langle ij \rangle\rangle \in A} J_A(R_{ij})\; \mathbf{S}_{Ai} \cdot \mathbf{S}_{Aj} + \sum_{\langle\langle ij \rangle\rangle \in B} J_B(R_{ij})\; \mathbf{S}_{Bi} \cdot \mathbf{S}_{Bj}$

where $J_{AB}$ are inter-sublattice exchanges and $J_A$ , $J_B$ are intra-sublattice interactions that may differ by symmetry (Xie et al., 21 Jan 2026). The sublattice-inequivalence encoded in $J_A \neq J_B$ for at least one $R$ is the essential requirement for magnon band splitting.

A more specific form relevant to hexagonal D $_{6h}$ (NiAs-type) altermagnets such as CrSb and MnTe includes “g-wave” next-nearest-neighbor (NNN) exchanges:

$H_{\rm alt} \sim (\tilde J_2 - \tilde J_1) \left[ \mathbf{S}_A \cdot \hat D \mathbf{S}_A - \mathbf{S}_B \cdot \hat D \mathbf{S}_B \right]$

with $\hat D = \partial_y\partial_z(\partial_y^2-3\partial_x^2)$ , transforming as a fourth-order (“g-wave”) irreducible representation of D $_{6h}$ (Kravchuk et al., 7 Apr 2025, Liu et al., 2024). The symmetry dictates both the presence and the precise momentum dependence of the splitting.

2. Chiral Magnon Splitting: Group-Theoretic Analysis and General Formulas

In reciprocal space, the magnon Hamiltonian generically reduces to a $J_{AB}$ 0 (A/B) quadratic bosonic form:

$J_{AB}$ 1

where $J_{AB}$ 2 encodes the real and imaginary contributions from symmetric and antisymmetric exchange. In centrosymmetric AFMs, $J_{AB}$ 3 is real, so both branches are degenerate. In altermagnets, the imaginary (e.g., “g-wave”) component $J_{AB}$ 4, which is odd under certain improper operations, lifts the degeneracy:

$J_{AB}$ 5

The symmetry properties of $J_{AB}$ 6 determine where in the Brillouin zone the splitting is maximal or vanishing. For D $J_{AB}$ 7, $J_{AB}$ 8 transforms as $J_{AB}$ 9, enforcing node lines (“nodal planes”) and sixfold sign-changing patterns (Kravchuk et al., 7 Apr 2025, Beida et al., 12 May 2025).

A universal linear spin-wave formula is:

$J_A$ 0

yielding $J_A$ 1-wave, $J_A$ 2-wave, or higher-order angular dependence, dictated by the underlying motif of sublattice-inequivalent exchange (Xie et al., 21 Jan 2026, Liu et al., 2024, Siam et al., 11 Jul 2025).

3. Topological Magnon Bands and Edge States

Broken symmetry not only produces chiral magnon splitting but can also drive topological magnon phases. In particularly symmetry-reduced bilayer or 2D altermagnets, the combination of exchange anisotropies (e.g., $J_A$ 3), layered structures, and Dzyaloshinskii–Moriya interaction (DMI) lead to band structures with nonzero Berry curvature and integer spin Chern number ( $J_A$ 4) (Yuan et al., 29 Jan 2026, Mella et al., 2024).

These topological magnons host robust chiral or helical edge modes, with wavefunctions of the form

$J_A$ 5

where the edge localization $J_A$ 6 and circular phonon content $J_A$ 7 reflect polarization-momentum locking. The edge state propagation direction is protected by the nontrivial Chern topology and is robust to disorder unless the bulk gap closes (Mella et al., 2024).

4. Experimental Signatures and Material Realizations

Direct evidence for chiral magnon splitting has been obtained in altermagnetic $J_A$ 8-MnTe, where inelastic neutron scattering resolves two distinct magnon peaks with up to $J_A$ 9 meV splitting, displaying the predicted $J_B$ 0-wave nodal pattern across the Brillouin zone (Liu et al., 2024). In CrSb, LSWT yields splitting up to $J_B$ 1 meV, with TD-DFPT calculations giving even larger ( $J_B$ 230 meV) values; the effect appears primarily along high-symmetry $J_B$ 3– $J_B$ 4– $J_B$ 5 paths dominated by body-diagonal exchange paths with distinct spin-orbit (Zhang et al., 17 Mar 2025, Beida et al., 12 May 2025). In FeF $J_B$ 6, high-resolution neutron studies demonstrate that the mixed effect of altermagnetic splitting and long-range dipolar interactions can be disentangled, with the latter dominating except at special momentum planes (Sears et al., 7 Jan 2026).

Table: Representative Experimental Systems

Material	Space Group	Splitting Symmetry	Max $J_B$ 7	Experimental Access
$J_B$ 8-MnTe	P6 $J_B$ 9/mmc	$J_A \neq J_B$ 0-wave	$J_A \neq J_B$ 1 meV	Neutron scattering
CrSb	P6 $J_A \neq J_B$ 2/mmc	$J_A \neq J_B$ 3-wave	9–30 meV	LSWT, TD-DFPT
FeF $J_A \neq J_B$ 4	P4 $J_A \neq J_B$ 5/mnm	$J_A \neq J_B$ 6-wave	$J_A \neq J_B$ 7eV	Polarized neutron
V $J_A \neq J_B$ 8WS $J_A \neq J_B$ 9 bilayer	P $R$ 0m	$R$ 1-wave	$R$ 2	First-principles calc.

5. Symmetry-Driven Selectivity and Electric Field Control

Symmetry also dictates both where chiral splitting is symmetry-forbidden (protection of degeneracies along certain nodal planes) and where it can be switched on or off by external fields. In systems with PT symmetry, the two magnon chiralities are degenerate unless sublattice symmetry is broken by a perturbation odd under inversion but even under time-reversal. Application of an out-of-plane electric field $R$ 3 induces a hidden-site dipole that tunes $R$ 4, yielding large and reversible splitting, up to $R$ 5 meV for $R$ 6 V/Å in Cr $R$ 7CBr $R$ 8 (Ni et al., 22 Jan 2026, Xie et al., 21 Jan 2026). The sign of the splitting, and thus the handedness of the magnon population, is tunable with $R$ 9.

In addition, magnon splitting can be dynamically programmed via control over domain wall orientation (e.g., in AMDWs), where the magnitude and sign of $_{6h}$ 0 splitting can be switched by spin-orbit torque or spin-transfer torque, enabling flexible chiral magnon routing (Zeng et al., 4 Jan 2026).

6. Magnon-Phonon Hybridization and Chirality-Selective Coupling

In systems without inversion symmetry, magnons may hybridize with chiral phonons through symmetry-allowed, valley-selective magnetoelastic coupling. In the hexagonal Heisenberg–Kitaev– $_{6h}$ 1 model, only phonon modes with definite pseudoangular momentum $_{6h}$ 2 are symmetry-allowed to couple to a given magnon branch, leading to a valley-dependent magnon–polaron gap:

$_{6h}$ 3

with observation of unidirectional magnon-polaron edge states combining spin and lattice angular momentum (Mella et al., 2024). In layered zigzag AFMs such as FePSe $_{6h}$ 4, group theory enforces that only same-chirality magnon–phonon pairs can hybridize, producing chiral magnon polarons (chiMPs) at zero field; their circular polarization and branch-dependent Raman response are direct symmetry fingerprints (Cui et al., 2023).

7. Physical Consequences and Spintronic Implications

Chiral magnon splitting leads to a variety of novel and technologically relevant consequences:

Nonreciprocal magnon transport: Due to symmetry-driven non-degeneracy, magnons at a given frequency propagate only in certain crystallographic directions (rectification/diode effect) (Beida et al., 12 May 2025).
Momentum-resolved and anisotropic thermal Hall effect: The momentum dependence of the splitting, inherited from the underlying $_{6h}$ 5- or $_{6h}$ 6-wave symmetry, enables direction-selective spin and heat currents, as shown by the thermal Hall conductivity hot-spot structure (Yuan et al., 29 Jan 2026).
Electrical switching: The magnitude and sign of the splitting—and thus the direction of associated spin currents—can be toggled by external electric field, enabling magnonic logic and spin current control (Ni et al., 22 Jan 2026, Xie et al., 21 Jan 2026).
Topological protection: The resulting chiral edge states are protected as long as the topological gap, set by exchange and DMI anisotropies, remains open (Mella et al., 2024, Yuan et al., 29 Jan 2026).
Enhanced damping and device selectivity: In metallic altermagnets, the overlap of chiral magnon branches with Stoner continua allows spatial and directional filtering of magnon excitation lifetimes (Beida et al., 12 May 2025, Zhang et al., 17 Mar 2025).

A plausible implication is that symmetry-based design principles may be used to engineer magnon modes with targeted chirality, directionality, and robustness for applications in magnonic circuits, sensors, and low-power signal processing.

In summary, the symmetry-principled origin of chiral magnon splitting rests on the absence or reduction of certain sublattice- or inversion operations in the magnetic layer group, enabling sublattice-inequivalent exchange and thus momentum-dependent non-degeneracy of magnon modes. These effects are universally controlled by group-theoretical representations, encoded in the real-space and reciprocal-space form factors, and are manifest across a wide variety of material systems through direct measurements, ab-initio computations, and effective model analyses. This symmetry-driven physics underpins a wide array of nontrivial band topology, nonreciprocal transport, and electrical control, situating chiral magnon splitting as a core paradigm in contemporary quantum magnonics and spintronics (Mella et al., 2024, Kravchuk et al., 7 Apr 2025, Xie et al., 21 Jan 2026, Beida et al., 12 May 2025, Sears et al., 7 Jan 2026, Zhang et al., 17 Mar 2025, Liu et al., 2024, Cui et al., 2023, Yuan et al., 29 Jan 2026, Zeng et al., 4 Jan 2026, Siam et al., 11 Jul 2025).