Magnon-Driven Anomalous Hall Effect

Updated 5 July 2026

Magnon-driven anomalous Hall effect is defined as a transverse transport phenomenon arising from spin excitations and dynamics instead of conventional charge deflection.
It involves mechanisms such as Dzyaloshinskii-Moriya interactions, coherent magnon chirality, and electron-magnon scattering that modulate thermal and electronic conductivity.
Experimental studies in both insulating and metallic magnets, like Lu2V2O7, demonstrate that spin-wave dynamics and chirality crucially determine the Hall response.

Magnon-driven anomalous Hall effect denotes a class of transverse transport phenomena in which magnons, magnon scattering, or coherent magnon dynamics generate a Hall-type response without a conventional Lorentz-force mechanism. In insulating magnets, the effect appears most directly as a transverse thermal conductivity $\kappa_{xy}$ carried by neutral spin-wave quasiparticles; in metallic ferromagnets and altermagnets, magnons can also induce or reshape an electronic anomalous Hall conductivity through spin-flip scattering, dipolar spin waves, or coherently excited chiral Néel dynamics [(Onose et al., 2010); (Yamamoto et al., 2015); (0911.3134); (Liu et al., 20 Mar 2026)]. The literature therefore spans thermal Hall transport of neutral bosons, extrinsic-like electronic anomalous Hall responses mediated by spin excitations, and nonequilibrium Hall phenomena whose symmetry is controlled by magnon chirality rather than by the equilibrium magnetic order alone.

1. Conceptual scope and taxonomy

The subject is unified by a common structural feature: a transverse response arises from magnetic order and spin dynamics rather than from the ordinary Hall deflection of charge carriers by an external magnetic field. In the thermal setting, this is the magnon Hall effect or anomalous Righi-Leduc effect; in the electronic setting, it is an anomalous Hall effect driven by electron-magnon coupling or by coherent chiral magnon motion [(Madon et al., 2014); (Onose et al., 2010); (Liu et al., 20 Mar 2026)].

Regime	Hall observable	Microscopic origin
Insulating ferromagnet	$\kappa_{xy}$	Dzyaloshinskii-Moriya-induced complex magnon hopping
Uniform ferromagnetic metal	$\sigma_{xy}$	Skew scattering by dipolar magnons or electron-magnon scattering
Coherently driven altermagnet	Electronic Hall current	Chirality of Néel-order precession

This taxonomy already shows that “magnon-driven” does not identify a single microscopic mechanism. The term covers band-geometric transport of magnons with an effective gauge field, diffusive magnon spin transport with anomalous Hall terms, and scattering-induced Hall effects in which the decisive asymmetry resides in a collision kernel rather than in Berry curvature. A plausible implication is that the field is best organized by carrier type and microscopic origin, not by a single phenomenological label.

2. Canonical realization: thermal Hall transport of magnons in pyrochlore ferromagnets

The canonical experimental realization is the observation of a magnon Hall effect in the insulating ferromagnet Lu $_2$ V $_2$ O $_7$ , reported as the first experimental observation of a Hall effect carried by magnons in an electrical insulator (Onose et al., 2010). The measured quantities were the longitudinal thermal conductivity $\kappa_{xx}$ and the transverse thermal Hall conductivity $\kappa_{xy}$ . Because Lu $_2$ V $_2$ O $\kappa_{xy}$ 0 is an insulating ferromagnet, the heat current below $\kappa_{xy}$ 1 K is carried only by phonons and magnons, with the electronic thermal conductivity estimated to satisfy

$\kappa_{xy}$ 2

below 100 K (Onose et al., 2010).

The central observation is that a finite thermal Hall signal appears below the Curie temperature $\kappa_{xy}$ 3 K, $\kappa_{xy}$ 4 rises sharply below $\kappa_{xy}$ 5, peaks around 50 K, and saturates at low magnetic field, while the signal is small above 80 K where ferromagnetic order is absent (Onose et al., 2010). The transverse response depends mainly on the spontaneous magnetization, so it is an anomalous thermal Hall effect rather than an ordinary field-linear Hall effect. This established that neutral quasiparticles can support a Hall response even though there are no mobile charge carriers.

The microscopic explanation is tied to the pyrochlore lattice. Lu $\kappa_{xy}$ 6V $\kappa_{xy}$ 7O $\kappa_{xy}$ 8 is a network of corner-sharing tetrahedra, the midpoints of the V–V bonds are not inversion centers, and a Dzyaloshinskii-Moriya interaction is therefore allowed: $\kappa_{xy}$ 9 The effective spin Hamiltonian is

$\sigma_{xy}$ 0

and for spin waves the magnon transfer amplitude acquires a complex phase,

$\sigma_{xy}$ 1

In this formulation the DM term acts as a vector potential, serves as an “orbital magnetic field” for magnons, and converts the spin-wave Hamiltonian into a tight-binding Hamiltonian with phase factors (Onose et al., 2010).

This picture is the magnonic analogue of the intrinsic anomalous Hall effect in metallic ferromagnets: the Hall response is generated not by an external deflection force but by spin-orbit-induced phases in the quasiparticle dynamics. The low-temperature theory gives a thermal Hall conductivity proportional to the DM strength $\sigma_{xy}$ 2 and dependent on the Zeeman gap and Bose occupation, and the fit to the data at 20 K yields

$\sigma_{xy}$ 3

which was taken to be reasonable for a transition-metal oxide (Onose et al., 2010). The high-field decrease of $\sigma_{xy}$ 4 was interpreted as Zeeman suppression of the magnon population, strengthening the magnonic interpretation over phonon-based alternatives.

3. Band geometry, anomalous Righi-Leduc transport, and dipolar magnon Hall responses

A broader thermal framework was developed by formulating the magnon Hall effect as an anomalous Righi-Leduc effect in ferromagnets. In this language, the heat-current response is organized by the same symmetry reduction that underlies anomalous Hall and planar Hall transport in charge systems: magnetization acts as an axial vector that partially breaks time-reversal symmetry and full rotational symmetry, while preserving rotations about the magnetization axis (Madon et al., 2014). The phenomenological thermal transport tensor is written as

$\sigma_{xy}$ 5

where the symmetric off-diagonal terms encode the planar Righi-Leduc response and the antisymmetric off-diagonal terms encode the anomalous Righi-Leduc response (Madon et al., 2014).

Experiments on NiFe and YIG showed transverse thermal signals in both a metallic ferromagnetic conductor and an insulating ferromagnet, with in-plane magnetization producing $\sigma_{xy}$ 6-periodic signals associated with the planar Righi-Leduc term and out-of-plane magnetization producing $\sigma_{xy}$ 7-periodic signals associated with the anomalous Righi-Leduc term (Madon et al., 2014). The measured angular signals in NiFe/Pt and YIG/Pt have opposite phase, explained by the sign of the thermocouple coefficient, with NiFe/Pt having $\sigma_{xy}$ 8 and YIG/Pt having $\sigma_{xy}$ 9 (Madon et al., 2014). The work argued that these thermal Hall-like signatures are universal in ferromagnets and not restricted to chiral lattices.

A more microscopic dipolar route was developed for YIG thin films with a magnetic field perpendicular to the film. There the relevant modes are forward-volume magnetostatic spin waves, and dipole-dipole interactions generate anomalous terms in the bosonic Bogoliubov–de Gennes Hamiltonian, producing squeezed or elliptic magnon states and a non-zero Berry curvature (Gunnink et al., 2021). In the diffusive regime the spin current takes the form

$_2$ 0

so the transport contains both a longitudinal diffusive part $_2$ 1 and an anomalous Hall part $_2$ 2 (Gunnink et al., 2021).

The proposed electrical detection scheme places four Permalloy strips on top of the YIG film in a Hall-bar geometry. The measurable Hall signal is the detector asymmetry

$_2$ 3

and the theory predicts that this signal tracks the Hall angle $_2$ 4 (Gunnink et al., 2021). The Hall angle is large at low temperature and decreases to a smaller constant at higher temperature; for fixed film thickness it rises with field at low fields, reaches a maximum around $_2$ 5 Oe in the numerics, and then decreases; and, most strikingly, increasing the film thickness can reverse its sign, with a thin film of $_2$ 6 giving a positive Hall angle over the shown field range and a thicker film with $_2$ 7 giving a negative Hall angle at low field (Gunnink et al., 2021). This established that dipolar interactions alone can generate a measurable magnon Hall effect in a nominally uniform ferrimagnetic insulator.

4. Scattering-driven and many-body mechanisms

A distinct line of work treats magnon-driven Hall transport as a scattering problem rather than a band-geometric anomalous-velocity problem. In field-polarized chiral magnets, Dzyaloshinskii-Moriya interaction generates three-magnon interactions that violate time-reversal symmetry and interfere with four-magnon scattering, thereby breaking microscopic detailed balance and causing thermal Hall currents without disorder or Berry curvature (Chatzichrysafis et al., 2024). The model Hamiltonian is

$_2$ 8

and in the dominant diagonal-scattering approximation the Hall response is encoded in the antisymmetric part $_2$ 9 of the collision kernel through

$_2$ 0

The resulting Hall angle is estimated as $_2$ 1 to $_2$ 2, with

$_2$ 3

and a corresponding three-dimensional value of roughly

$_2$ 4

for a layer spacing $_2$ 5 (Chatzichrysafis et al., 2024). This work explicitly argues that magnon interactions can be as significant as the band-geometric anomalous velocity.

In conducting ferromagnets, a magnon-driven electronic anomalous Hall effect can also arise from skew scattering by dipolar spin waves. A uniform ferromagnet without relativistic spin-orbit coupling was shown to support an AHE whose leading contribution is proportional to the chiral spin correlation of dynamical spin textures and is physically understood in terms of skew scattering by dipolar magnons (Yamamoto et al., 2015). The Hall term appears first at third order in the exchange coupling $_2$ 6, and the generalized spin-chirality formula contains

$_2$ 7

Dipolar interactions generate the required parity-odd chiral correlation through phase factors $_2$ 8 in the spin-flip magnon propagators, so the electronic Hall current originates from dynamical magnon chirality rather than from a static noncoplanar texture or from relativistic band spin-orbit coupling (Yamamoto et al., 2015). The numerical evaluation gives an approximate temperature dependence $_2$ 9 with $_7$ 0, and one fit is

$_7$ 1

(Yamamoto et al., 2015).

Electron-magnon scattering also reshapes the extrinsic anomalous Hall effect in a qualitatively different way from impurity or phonon scattering because magnons flip spin. In a two-dimensional Dirac model, magnon scattering is off-diagonal in spin space, whereas impurity and phonon scattering are spin-conserving, so the side-jump and skew-scattering sectors respond differently (0911.3134). If the only scattering mechanism is magnon scattering, the conventional skew scattering vanishes, the intrinsic skew scattering also vanishes after angular averaging, and the surviving extrinsic contribution is

$_7$ 2

This cancels the Fermi-energy-dependent part of

$_7$ 3

so the total Hall conductivity becomes

$_7$ 4

With both impurity and magnon scattering present, the crossover is controlled by

$_7$ 5

and the side-jump sector can acquire a strong temperature dependence because magnon population changes with temperature (0911.3134).

5. Coherent chiral magnons and nonequilibrium Hall transport in altermagnets

A recent nonequilibrium formulation proposes a magnon-driven anomalous Hall effect in altermagnets, arising from the coupling between coherently excited chiral magnons and chiral electronic motion (Liu et al., 20 Mar 2026). The central idea is that opposite local spin sublattices contribute opposite Berry curvatures in equilibrium, so the static AHE cancels or is strongly reduced, whereas a coherently precessing Néel vector introduces a time-dependent chirality for which the contributions from the two sublattices add constructively. The relevant dynamical quantity is the precession chirality

$_7$ 6

and the Hall response is

$_7$ 7

The Hall conductivity is therefore linear in magnon chirality rather than controlled by the equilibrium Néel order alone (Liu et al., 20 Mar 2026).

This mechanism differs sharply from conventional equilibrium AHE. The response coefficient is even under reversal of the equilibrium Néel vector,

$_7$ 8

and the symmetry requirements are classified by a derived symmetry group in which time reversal is effectively identified with the identity (Liu et al., 20 Mar 2026). The work emphasizes that diagonal components such as $_7$ 9, $\kappa_{xx}$ 0, and $\kappa_{xx}$ 1 are symmetry-allowed under arbitrary rotational symmetry, so a Hall-type response can generically appear in the plane perpendicular to the magnon precession axis.

The microscopic treatment uses density-matrix perturbation theory and a relaxation-time kinetic equation,

$\kappa_{xx}$ 2

with the current obtained from

$\kappa_{xx}$ 3

The response is third order because it is bilinear in the electric field and the oscillating Néel order (Liu et al., 20 Mar 2026). A minimal lattice model with the symmetry of CrSb demonstrates that altermagnetic band splitting can exist without static AHE, while the magnon-driven coefficient, especially $\kappa_{xx}$ 4, remains finite. Upon rotating the Néel vector by an angle $\kappa_{xx}$ 5, the response obeys

$\kappa_{xx}$ 6

which matches the predicted dipolar dependence in Néel-vector space (Liu et al., 20 Mar 2026). This shows that coherent magnon chirality can bypass symmetry constraints that prohibit the equilibrium Hall effect.

A central boundary of the subject is that not every Hall response in a magnetic system is magnon-driven. The large anomalous Hall effect in non-collinear antiferromagnetic Mn $\kappa_{xx}$ 7Ge is a Berry-curvature-driven intrinsic electronic transport phenomenon arising from its chiral spin structure; the paper explicitly does not assign a central role to magnons, magnon Hall transport, or collective spin-wave excitations (Nayak et al., 2015). The Hall conductivity reaches about $\kappa_{xx}$ 8 at 2 K and about $\kappa_{xx}$ 9 at room temperature, and the effect is traced to momentum-space Berry-curvature hot spots near avoided crossings in the Mn 3d bands rather than to a magnonic mechanism (Nayak et al., 2015).

A second boundary concerns magnetic-texture-induced Hall effects. In Rashba systems coupled to localized spins, skew scattering by magnetic textures can produce an anomalous Hall conductivity proportional to the net magnetic monopole charge of the texture,

$\kappa_{xy}$ 0

with finite responses even for an in-plane ferromagnetic domain wall or a vortex (Mochida et al., 2022). This is a magnetic-texture Hall mechanism enabled by spin-orbit interaction and broken inversion symmetry, not a magnon Hall effect.

A third boundary concerns magnetotransport anomalies induced by an already existing anomalous Hall conductivity. When the ordinary Hall angle or anomalous Hall angle is not small, the anomalous Hall effect must be treated at the conductivity level rather than as a simple additive Hall resistivity, and tensor inversion then generates linear magnetoresistance, bowtie-shaped MR, nonlinear Hall resistance, and a $\kappa_{xy}$ 1-symmetric Hall component even in a single-band system (Zhao et al., 2022). These effects can mimic signatures sometimes associated with more exotic physics, but they are not themselves evidence for a magnon-driven mechanism.

Taken together, these distinctions clarify several recurrent misconceptions. Magnon-driven anomalous Hall transport need not involve mobile charge carriers, as in insulating thermal Hall experiments (Onose et al., 2010). It need not require relativistic electronic spin-orbit coupling, as in the dipolar-magnon mechanism in homogeneous ferromagnets (Yamamoto et al., 2015). It need not rely on Berry curvature of a single-magnon band, as shown by many-body skew scattering without disorder or Berry curvature (Chatzichrysafis et al., 2024). And it can exist even when the static anomalous Hall effect is forbidden by symmetry, provided that the relevant dynamical degree of freedom is the chirality of coherent Néel-order precession (Liu et al., 20 Mar 2026). These facts make the magnon-driven anomalous Hall effect less a single effect than a family of transverse transport phenomena whose common theme is chirality transfer from spin excitations to Hall response.