Magnon Orbital Angular Momentum (OAM)

• Magnon Orbital Angular Momentum (OAM) is the orbital component carried by spin waves, characterized by spatial phase structures, vortex-like excitations, and Berry connection effects.
• Research demonstrates techniques such as spin-to-OAM conversion, analytic and micromagnetic validation in confined geometries, and gauge invariant averaging to resolve observable quantities.
• Applications include mode multiplexing, skyrmion manipulation via OAM transfer, and hybrid magnon–phonon systems that bridge orbital dynamics with magnetoelectric and topological effects.

Searching arXiv for papers on magnon orbital angular momentum and closely related formulations. Magnon orbital angular momentum (OAM) denotes the orbital component of angular momentum carried by spin-wave excitations in magnetic media. In contrast to the spin angular momentum associated with magnon spin precession, magnon OAM is tied to spatial phase structure, wave-front twisting, azimuthal mode circulation, or wave-packet self-rotation, depending on the physical setting and formalism. The subject spans several distinct but partially overlapping research lines: twisted magnons in confined nanostructures and arrays (Li et al., 2022, Jiang et al., 2019), Bloch-band and Berry-geometric OAM in lattice magnets (Fishman et al., 2022, Fishman et al., 2022, Fishman, 2023, Fishman et al., 2023, Jeon et al., 27 Mar 2026), spatiotemporal vortex beams with transverse OAM in textured nanostrips (Xie et al., 16 Mar 2026), quantized dipolar-magnon OAM in magnetodipolar resonators (Kamenetskii, 2024), spectroscopic observation of azimuthal spin-wave OAM (Valet et al., 9 Mar 2025), and hybrid-boson and finite-temperature formulations that aim to clarify the proper definition of orbital dynamics for neutral bosonic quasiparticles (To et al., 30 Sep 2025, Tang et al., 1 Oct 2025).

1. Conceptual scope and definitions

The modern literature does not treat magnon OAM as a single universally equivalent object. Rather, several definitions coexist, each adapted to a different physical regime. In confined cylindrical or disk geometries, spin-wave eigenmodes with azimuthal phase dependence $e^{in\phi}$ are identified as OAM eigenstates, with the orbital quantum number related to the azimuthal mode index by $l=n-1$ in nanodisks and nanocylinders (Li et al., 2022, Jiang et al., 2019). In these settings, OAM is associated with vortex-like spatial phase structure and, in some formulations, with an operator built from the phase of the dynamical magnetization (Jiang et al., 2019).

In lattice and Bloch-band problems, the relevant quantity is a momentum-space orbital moment or orbital angular momentum of magnon bands. A widely used expression takes the form

${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$

which emphasizes the connection to the Berry connection of the magnon Bloch eigenstate $|u_n(\vk)\rangle$ (Fishman et al., 2022). However, unlike the Berry curvature, this $\vk$-resolved quantity is not generally gauge invariant under $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$, a fact that led to later gauge-invariant constructions (Fishman, 2023, Fishman et al., 2023).

A further distinction appears in work comparing thermodynamic and wave-packet formulations. In a Kagome antiferromagnet with negative vector chirality, the orbital magnetic moment (OMM), defined thermodynamically from the field derivative of band energy, and the wave-packet OAM, defined from the operator

$$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$

are quantitatively distinct in equilibrium, even though their Nernst coefficients are nearly identical in transport (Jeon et al., 27 Mar 2026). This distinction is central to current debates about what constitutes the physically measurable orbital degree of freedom of magnons.

A related strand of work argues that a proper theory for magnon OAM must respect magnon neutrality and bosonic statistics. In that formulation, magnon OAM does not generate a magnetic moment and instead couples through the Aharonov–Casher effect to electric-field gradients. The finite-temperature OAM contains both self-rotation and topological contributions: $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$ where $\mathcal{L}_n(\bm{k})$ is the self-rotation part and $\Omega_n(\bm{k})$ the Berry-curvature term (Tang et al., 1 Oct 2025).

2. Twisted magnons in confined nanostructures

Twisted magnons are spin-wave states carrying longitudinal OAM, typically characterized by screw-type phase dislocations and azimuthal phase dependence. A concrete generation protocol was developed for a magnetic nanostrip attached to a nanodisk, where plane-wave magnons excited in the strip are converted into nanodisk twisted-magnon eigenmodes through spin-to-orbital angular momentum conversion (Li et al., 2022). The driving mechanism is resonant: a sinusoidal magnetic field excites planar magnons in the strip, and when they enter the disk, a twisted mode with selected azimuthal and radial quantum numbers $l=n-1$0 is excited by choosing the drive frequency appropriately (Li et al., 2022).

The nanodisk spectrum was solved analytically from the linearized Landau–Lifshitz–Gilbert equation. The magnetostatic potential is written as

$l=n-1$1

and the dispersion relation in the disk takes the form

$l=n-1$2

with boundary conditions

$l=n-1$3

The relation $l=n-1$4 connects the orbital quantum number to the Bessel-function order (Li et al., 2022). Theory and micromagnetic simulations were reported to agree well for the eigenfrequencies and mode profiles.

A notable numerical result is that the conversion rate from planar magnons to twisted magnons is approximately a universal constant of around $l=n-1$5, and is insensitive to the radial and azimuthal quantum numbers over the range studied (Li et al., 2022). In one-dimensional nanodisk arrays, the intensity of twisted magnons decays approximately as

$l=n-1$6

with the decay length $l=n-1$7 decreasing as either the azimuthal quantum number $l=n-1$8 or the radial quantum number $l=n-1$9 increases; the OAM encoding, however, remains preserved during propagation (Li et al., 2022). The same work states that under the parameters used, each disk supports many distinct twisted-magnon modes below ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$0 GHz, suggesting mode multiplexing based on ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$1 indices (Li et al., 2022).

An earlier theoretical treatment in magnetic nanocylinders established that spin-wave eigenmodes are eigenstates of an OAM operator along the cylinder axis, again with

${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$2

for modes with azimuthal dependence ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$3 (Jiang et al., 2019). That study further proposed a “magnetic tweezer” effect: twisted magnons generated in a YIG nanocylinder and injected into an exchange-coupled chiral nanodisk can transfer OAM to a skyrmion, causing steady-state gyration whose direction follows the sign of the injected magnon OAM (Jiang et al., 2019). For ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$4, the skyrmion falls into the disk center, whereas opposite signs ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$5 yield opposite rotation senses (Jiang et al., 2019). This established OAM transfer from magnonic vortices to topological magnetic textures as a concrete dynamical consequence of magnon OAM.

3. Band-structure OAM in collinear and noncollinear magnets

A major development was the recognition that magnon OAM can emerge in collinear magnets without requiring spin-orbit coupling or noncollinear magnetic order. For ferromagnetic and antiferromagnetic zig-zag and honeycomb lattices, nonzero OAM arises when the magnetic unit cell contains two inequivalent sites and the exchange network is nontrivial (Fishman et al., 2022). In this framework, the orbital operator in momentum space is

${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$6

and the band-resolved OAM is derived after diagonalizing the spin-wave Hamiltonian (Fishman et al., 2022).

The central result is that OAM is largest at avoided crossings or band extrema and vanishes for a Bravais lattice or symmetric exchange pattern (Fishman et al., 2022). In the ferromagnetic zig-zag chain, for example, ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$7 is odd in ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$8, vanishes when ${\cal L}_{zn}(\vk )=-\frac{i \hbar}{2} \{ \vk \times \langle u_n(\vk )| \nabla_{\vk} u_n(\vk ) \rangle \} \cdot \hat{z},$9, and becomes maximal near avoided crossings when $|u_n(\vk)\rangle$0 (Fishman et al., 2022). In the ferromagnetic honeycomb lattice without Dzyaloshinskii–Moriya (DM) interaction, OAM already exists because of the two-sublattice structure, and peaks at the Dirac points (Fishman et al., 2022).

Exact results were subsequently obtained for the OAM at the corners of the Brillouin zone in honeycomb lattices (Fishman et al., 2022). For a ferromagnetic honeycomb lattice without DM interaction, both magnon bands take alternating values $|u_n(\vk)\rangle$1 at the symmetry-related corners (Fishman et al., 2022). With DM interaction, the band degeneracy is lifted and the corner values are dramatically modified: the lower band alternates between $|u_n(\vk)\rangle$2 and $|u_n(\vk)\rangle$3, while the upper band alternates between $|u_n(\vk)\rangle$4 and $|u_n(\vk)\rangle$5 (Fishman et al., 2022). For the antiferromagnetic honeycomb lattice, the corner OAM values depend on the anisotropy parameter $|u_n(\vk)\rangle$6, while the result is independent of the DM interaction: $|u_n(\vk)\rangle$7 (Fishman et al., 2022). That work also emphasized that the use of periodic lattice derivatives is essential; otherwise the OAM would diverge at Brillouin-zone corners (Fishman et al., 2022).

The noncollinear case adds Berry-curvature-driven orbital physics. In a Kagome antiferromagnet with negative vector chirality stabilized by $|u_n(\vk)\rangle$8, Berry curvature textures are strong and band selective, and the wave-packet OAM texture closely follows the Berry curvature, while the thermodynamic OMM shows sharp and field-sensitive behavior near the $|u_n(\vk)\rangle$9 point (Jeon et al., 27 Mar 2026). The total OAM remains almost unchanged as the external field varies, whereas the total OMM can switch sign with increasing $\vk$0 (Jeon et al., 27 Mar 2026). Yet the Nernst coefficients associated with OMM and OAM are nearly identical as functions of temperature and field, suggesting that orbital transport is governed mainly by band geometry rather than by the equilibrium distinction between the two observables (Jeon et al., 27 Mar 2026).

4. Gauge invariance and the observable content of magnon OAM

One of the most important conceptual issues is gauge dependence. The $\vk$1-resolved expression

$\vk$2

changes under $\vk$3 by the addition of $\vk$4, so it is not directly gauge invariant (Fishman, 2023). To remedy this, the angular average

$\vk$5

was introduced and shown to be gauge invariant because the added term integrates to zero for a single-valued gauge function (Fishman, 2023). A related disk average

$\vk$6

is also gauge invariant (Fishman, 2023).

In the ferromagnetic honeycomb lattice with next-nearest-neighbor DM interaction, $\vk$7 has opposite sign for the two magnon bands for all $\vk$8 in the first Brillouin zone, whereas without DM interaction the gauge-invariant angular average vanishes (Fishman, 2023). The same conclusion was sharpened using a harmonic expansion

$\vk$9

which shows that all harmonics except the angular average $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$0 can be gauged away (Fishman et al., 2023). In that sense, $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$1 is the only observable component of the magnon OAM in that formulation (Fishman et al., 2023).

This gauge-invariant program was applied to both ferromagnetic honeycomb and zig-zag lattices. In each case, $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$2 becomes nonzero only when DM interaction is present (Fishman et al., 2023). In the zig-zag model with $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$3, DM yields observable OAM, but for equal exchange interactions $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$4 the magnon bands remain degenerate along the Brillouin-zone boundaries $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$5, so the Chern numbers are ill-defined (Fishman et al., 2023). A revised model with $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$6 lifts the degeneracy and produces well-defined Chern numbers $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$7 (Fishman et al., 2023).

A common misconception is that any $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$8-resolved orbital angular momentum extracted from a Bloch eigenvector is directly observable. The gauge-invariance analyses argue against this and restrict observability to properly averaged quantities such as $|u_n(\vk)\rangle \to |u_n(\vk)\rangle e^{-i\lambda_n(\vk)}$9 (Fishman, 2023, Fishman et al., 2023). A plausible implication is that experimental claims about momentum-resolved magnon OAM require careful specification of gauge-fixing conventions or of the actual gauge-invariant observable being probed.

5. Spin–orbit coupling, dipolar magnons, and quantized azimuthal modes

Another research direction concerns OAM in dipolar or magnetostatic spin-wave systems. In quasi-two-dimensional ferrite disks supporting magnetodipolar-mode (MDM) oscillations, OAM appears together with spin angular momentum along the bias magnetic field, and the confined geometry yields quantized MDM energy levels (Kamenetskii, 2024). The power-flow circulation

$$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$0

defines the orbital contribution associated with chiral edge currents and circulating energy flow (Kamenetskii, 2024). The paper states that the OAM of the magnon is $$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$1, while also describing the quantum confinement in terms of a half-integer internal OAM associated with the boundary topology and $$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$2 orbital rotation (Kamenetskii, 2024). These resonances are interpreted as magnetoelectric states arising from the coupling of ferromagnetic and electric-polarization orders, with simultaneous violation of time-reversal and inversion symmetry in the near fields (Kamenetskii, 2024).

A distinct but related advance is the experimental evidence for magnon OAM in azimuthal spin waves. In a $$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$3-diameter, $$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$4 nm thick YIG disk, magnetic resonance force microscopy resolved field-dependent splitting of counter-rotating azimuthal spin-wave modes (Valet et al., 9 Mar 2025). Using a Noether-theorem-based field-theoretic formulation, the total angular momentum is decomposed as

$$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$5

with

$$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$6

(Valet et al., 9 Mar 2025). The observed splitting between modes identified as $$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$7 and $$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$8 was interpreted as spectroscopic evidence that the wavefront rotates rather than remaining stationary (Valet et al., 9 Mar 2025).

The underlying mechanism is the long-ranged dipole-dipole interaction, which couples right- and left-handed precessional components and acts as a magnetic-field-controllable spin-orbit interaction for magnons (Valet et al., 9 Mar 2025). The splitting is described by

$$\langle u_\mathbf{k}^n | \hat{l}^{(a)} | u_\mathbf{k}^n \rangle = \frac{\epsilon_{abc}}{4} \langle u_\mathbf{k}^n | (r_b v_c - v_b r_c) | u_\mathbf{k}^n \rangle,$$9

and matches the field dependence of the measured spectra (Valet et al., 9 Mar 2025). This provides a route to spectroscopic readout of OAM states without relying on direct imaging of the phase profile.

6. Vortex beams, hybrid quasiparticles, and interconversion with light

Magnon OAM is not limited to longitudinal vortex modes. In a ferromagnetic nanostrip containing a vortex domain wall, spatiotemporal magnonic vortex beams were predicted with transverse OAM perpendicular to the propagation direction (Xie et al., 16 Mar 2026). Planar spin waves at $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$0 GHz passing through the inhomogeneous magnetization texture are split and redirected into a zigzag-like propagation path, generating four stationary phase singularities with OAM values alternating spatially as $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$1 (Xie et al., 16 Mar 2026). The OAM associated with each singularity is computed from

$$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$2

where $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$3 and $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$4 is defined relative to the singularity (Xie et al., 16 Mar 2026). The phase dislocations are stationary because the beam is a coherent superposition of three discrete plane waves with identical frequency, a feature that contrasts with the moving dislocations of photonic and acoustic spatiotemporal vortex beams (Xie et al., 16 Mar 2026).

Hybridization with phonons introduces another layer of orbital physics. In strongly coupled magnon–phonon systems in two-dimensional antiferromagnets, two origins of OAM are distinguished: global rotational motion of the system and quantum geometry of the wavefunctions (To et al., 30 Sep 2025). The latter produces orbital dynamics even when the lattice is fixed. The orbital moment operator is written as

$$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$5

and the theory identifies intra-band OAM generated by time-parity symmetry breaking and inter-band OAM generated by virtual interband transitions near anti-crossings (To et al., 30 Sep 2025). In a honeycomb antiferromagnet such as MnPS$$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$6, out-of-plane phonon modes acquire finite OAM and spin moment via hybridization with magnons, and a transverse voltage $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$7 is proposed as an electrical probe of these orbital degrees of freedom (To et al., 30 Sep 2025). The paper states that a microvolt-scale transverse voltage is predicted and that the OAM contribution dominates at low magnetic fields (To et al., 30 Sep 2025).

Interconversion between magnonic and optical angular momentum has also been demonstrated. In Brillouin light scattering from the Kittel mode in a YIG sphere, a Gaussian input beam with zero photonic OAM scatters into optical vortices with winding number $$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$8 (Hisatomi et al., 6 May 2025). The selection rule is governed by conservation of total angular momentum,

$$L = -\sum_{\bm{k},n} \left[\mathcal{L}_n(\bm{k}) b_n - \frac{4}{\beta \hbar } \Omega_n(\bm{k}) \ln (1-e^{-\beta\epsilon_n}) \right],$$9

where the Kittel-mode magnon contributes spin angular momentum but no magnon OAM because it is spatially uniform (Hisatomi et al., 6 May 2025). The experiment therefore does not directly probe OAM-carrying magnons, but it establishes that magnonic angular momentum can be converted into optical OAM at gigahertz bandwidths and suggests that vortex-magnon modes with intrinsic magnon OAM would lead to richer selection rules (Hisatomi et al., 6 May 2025).

7. Applications, controversies, and outlook

Several application motifs recur across the literature. Twisted magnons with distinct $\mathcal{L}_n(\bm{k})$0 quantum numbers are proposed as orthogonal data channels for spatial-division and frequency-division multiplexing in magnonic circuits (Li et al., 2022). OAM transfer to skyrmions provides a route to all-magnonic manipulation of topological textures, exemplified by the “magnetic tweezer” effect (Jiang et al., 2019). In dipolar disks and cavity settings, the combination of spin and orbital moments is linked to magnetoelectric states, strong light–matter interaction, and subwavelength magnetoelectric emitters (Kamenetskii, 2024). In band-topological magnets, the close connection between orbital dynamics and Berry curvature suggests implications for thermal Hall, spin Nernst, and orbital Nernst responses (Fishman et al., 2022, Jeon et al., 27 Mar 2026, Tang et al., 1 Oct 2025). Hybrid magnon–phonon systems extend these ideas toward phonon orbitronics and electrical detection schemes (To et al., 30 Sep 2025).

The principal controversies concern definition and observability. One issue is whether magnon OAM should be understood as a canonical, gauge-dependent Bloch-band quantity, a gauge-invariant angular average, a wave-packet self-rotation, a thermodynamic orbital magnetization, or a finite-temperature response quantity tied to electric-field gradients through the Aharonov–Casher effect (Fishman, 2023, Fishman et al., 2023, Jeon et al., 27 Mar 2026, Tang et al., 1 Oct 2025). Another issue is whether orbital motion of neutral bosons can be treated by analogy with electrons. The proper-theory formulation argues that it cannot: magnon OAM does not generate a magnetic moment and vanishes as $\mathcal{L}_n(\bm{k})$1 because of bosonic statistics, whereas some earlier approaches transplanted electronic orbital-magnetization logic too directly to magnons (Tang et al., 1 Oct 2025). By contrast, the Kagome study finds that thermodynamic OMM and wave-packet OAM are distinct in equilibrium but nearly indistinguishable in Nernst transport, which suggests that transport experiments alone may not discriminate between formulations (Jeon et al., 27 Mar 2026).

A further misconception is that magnon OAM necessarily requires spin-orbit coupling or noncollinear order. The collinear-honeycomb and zig-zag studies explicitly show that nontrivial exchange networks and two inequivalent sites per unit cell suffice to generate OAM (Fishman et al., 2022). Conversely, another misconception is that all twisted or azimuthal spin-wave patterns automatically imply a directly measurable OAM quantum number. The gauge-invariance studies caution that only appropriately averaged quantities are observable in Bloch-band settings (Fishman, 2023, Fishman et al., 2023), while the spectroscopic YIG-disk experiment shows that in confined axially symmetric systems counter-rotating OAM states can indeed be resolved directly through degeneracy lifting (Valet et al., 9 Mar 2025).

Taken together, the field has moved from initial demonstrations of twisted-magnon eigenstates and OAM-induced texture manipulation (Jiang et al., 2019, Li et al., 2022) to a broader framework in which magnon OAM is treated as a multifaceted orbital degree of freedom shaped by confinement, symmetry, topology, dipolar interactions, and quantum geometry. A plausible implication is that future progress will depend less on a single universal definition than on establishing precise correspondences between definition, symmetry class, probe, and device function in each magnonic platform.