Anomalous Inverse Orbital Hall Effect

• AIOHE is an orbital-to-charge conversion mechanism activated by order parameters like magnetic or Néel order, enabling responses in geometries where conventional IOHE is forbidden.
• Experiments in antiferromagnetic and ferromagnetic heterostructures, as well as ultrafast THz-emitter studies, show significant enhancements and non-additive behavior driven by anisotropy and stacking order.
• The phenomenon is underpinned by orbital magnetization, Berry curvature, and tensorial formulations that differentiate orbital from spin contributions, highlighting its robust material-dependence.

Searching arXiv for papers on anomalous inverse orbital Hall effect and related IOHE work. Anomalous Inverse Orbital Hall Effect (AIOHE) denotes an orbital-to-charge conversion process in which an orbital current generates a transverse charge current under conditions where the conventional inverse orbital Hall effect (IOHE) would be symmetry-forbidden or qualitatively altered by magnetic order, anisotropy, or other order parameters. Across recent experiments and theory, AIOHE appears in several related settings: as an order-parameter-enabled inverse Hall response in magnetic and antiferromagnetic heterostructures (Abrão et al., 2024, Santos et al., 9 Jul 2025); as a transport manifestation of current-induced orbital magnetization in nonmagnetic topological systems (Wang et al., 2024); and as an effective description of non-additive orbital-to-charge conversion in ultrafast terahertz emitters based on engineered multilayers (Zhou et al., 9 Feb 2026, Chao et al., 4 Feb 2026). The unifying theme is that orbital angular momentum, rather than spin, acts as the relevant transported or induced degree of freedom, and that its conversion into charge is controlled by symmetry, interfacial conversion, and the sign and magnitude of the orbital Hall response.

1. Definition and conceptual scope

The IOHE refers to the conversion of orbital angular momentum currents into transverse charge currents in a nonmagnetic metal, enabled by strong spin-orbit coupling in the converting medium (Zhou et al., 9 Feb 2026). In its conventional form, the geometry parallels the inverse spin Hall effect (ISHE): an orbital current with polarization transverse to its flow is converted into a charge current via a cross-product-like relation. A representative expression used for IOHE is

$$J_c = \frac{2e}{\hbar} \, \theta_{OH} \, (\mathbf{J}_L \times \hat{L}),$$

where $\mathbf{J}_L$ is the orbital current density, $\hat{L}$ the orbital polarization direction, and $\theta_{OH}$ the orbital Hall angle (Santos et al., 7 Oct 2025).

AIOHE is used in the recent literature in more than one, partially overlapping sense. In magnetic systems, it denotes an anomalous inverse conversion enabled by a magnetic order parameter, so that charge conversion becomes allowed even when the current flow and orbital polarization are collinear, a geometry forbidden for conventional IOHE (Abrão et al., 2024, Santos et al., 9 Jul 2025). In transport studies on few-layer TaIrTe$_4$, the term is also used for current-induced orbital magnetization and the resultant transverse electromotive response, with the observed orbital anomalous Hall effect (OAHE) interpreted as a transport manifestation of AIOHE (Wang et al., 2024). In orbitronic and THz-emitter studies, the “anomalous” character often refers to non-additive enhancement, sign reversal, or stacking-order-sensitive deviations from a simple spin-only picture (Zhou et al., 9 Feb 2026, Santos et al., 7 Oct 2025, Chao et al., 4 Feb 2026).

This broader usage suggests that AIOHE is best understood not as a single narrowly defined mechanism, but as a family of orbital inverse Hall responses in which magnetic order, orbital magnetization, symmetry lowering, or multilayer conversion pathways qualitatively modify conventional IOHE.

2. Symmetry, tensors, and magnetic-order-enabled conversion

A central theoretical development is the extension of the Hall-angle description from the conventional antisymmetric rank-2 form to a rank-3 tensor in ordered magnets. In antiferromagnetic systems, anomalous spin and orbital Hall phenomena were analyzed by promoting the Hall angle to

$$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$

with explicit dependence on the Néel vector $\mathbf{n}$ (Abrão et al., 2024). The same logic is applied to the orbital Hall angle, allowing anomalous inverse orbital Hall terms that are absent in nonmagnetic symmetry analysis.

For anomalous inverse conversion, a representative current relation is

$$J_k = \frac{2e}{\hbar}\left( \theta_1 + \theta_2 \right) \delta_{ki} n_j j_{33},$$

where $j_{33}$ denotes a current whose polarization and propagation are along the same direction (Abrão et al., 2024). This is precisely the configuration in which conventional IOHE and ISHE vanish by symmetry, but AIOHE and AISHE remain allowed because the order parameter supplies the additional axial structure.

A closely related tensor picture appears in anisotropic Fe films. There, the generalized Hall current is written as

$$J_{k} = \frac{2e}{\hbar} \sum_{i,j} \theta^{SH,OH}_{ij} j_{i,j}^{s,L},$$

and the anomalous terms become nonzero only when the system possesses a magnetic order parameter (Santos et al., 9 Jul 2025). For the out-of-plane anomalous geometry, the study gives

$\mathbf{J}_L$0

making the dependence on the magnetization component $\mathbf{J}_L$1 explicit (Santos et al., 9 Jul 2025).

These formulations establish the formal distinction between IOHE and AIOHE. IOHE requires the conventional transverse relation between current flow and orbital polarization. AIOHE requires an additional order parameter—magnetization in a ferromagnet or Néel vector in an antiferromagnet—that activates otherwise forbidden response channels.

3. Microscopic origins: orbital magnetization, Berry curvature, and quantum geometry

Several papers connect AIOHE-related phenomena to orbital magnetization and Berry curvature. In few-layer TaIrTe$\mathbf{J}_L$2, the observed linear anomalous Hall effect, nonlinear Hall effect, and nonreciprocal Hall effect are all attributed primarily to current-induced orbital magnetization rather than spin magnetization (Wang et al., 2024). The induced magnetization satisfies

$\mathbf{J}_L$3

with the magnetoelectric susceptibility tensor $\mathbf{J}_L$4, and the measured Hall resistance is taken to be proportional to the induced out-of-plane magnetization,

$\mathbf{J}_L$5

(Wang et al., 2024). Theoretical analysis further relates the orbital magnetization to the Berry-curvature dipole $\mathbf{J}_L$6 through

$\mathbf{J}_L$7

which explains why the effect is maximal when current is applied along the crystallographic $\mathbf{J}_L$8 axis, parallel to the dipole (Wang et al., 2024).

A more general geometric framework is provided by work on intrinsic Hall conductivities induced by the orbital magnetic moment (OMM). In a magnetic field, the band energy becomes

$\mathbf{J}_L$9

leading to a scattering-time-independent intrinsic Hall contribution

$\hat{L}$0

or, for $\hat{L}$1,

$\hat{L}$2

(Das et al., 2020). This work interprets the OMM-plus-Berry-curvature Hall response as the dissipationless mechanism underpinning AIOHE in non-centrosymmetric systems.

In magnetic Weyl semimetals, in-plane anomalous Hall response further underscores the orbital route to Hall conversion. For EuCd$\hat{L}$3Sb$\hat{L}$4, in-plane magnetic field induces out-of-plane orbital magnetization and Weyl-point splitting, yielding a Hall conductivity with threefold symmetry tied to the trigonal lattice (Nakamura et al., 2024). The Hall conductivity is connected to Berry curvature by

$\hat{L}$5

and in Weyl language,

$\hat{L}$6

(Nakamura et al., 2024). Although this work is framed as in-plane anomalous Hall effect rather than AIOHE, it provides direct evidence that orbital magnetization and Berry curvature can generate Hall responses outside conventional spin-driven scenarios.

4. Experimental realizations in magnetic heterostructures

Experiments on ordered magnetic heterostructures provide the clearest direct demonstrations of AIOHE in the narrow symmetry-based sense.

Antiferromagnetic heterostructures

In YIG/Pt/Ir$\hat{L}$7Mn$\hat{L}$8 structures studied by orbital pumping, strong anomalous inverse orbital Hall signals were observed in an out-of-plane configuration, where conventional IOHE/ISHE should vanish (Abrão et al., 2024). The key result is a sevenfold increase in the AIOHE signal compared to conventional effects. Specifically, for YIG/Pt(2)/Ir$\hat{L}$9Mn$\theta_{OH}$0(4), an out-of-plane signal of 271.6 nA was reported, compared with 37.5 nA in YIG/Ir$\theta_{OH}$1Mn$\theta_{OH}$2(4) (Abrão et al., 2024). The signal polarity reverses upon rotating the sample by $\theta_{OH}$3, and no AIOHE was detected in YIG/Pt(2)/Ti(4), indicating that the antiferromagnetic order parameter is essential.

The same study reports linear dependence on RF pumping power and thickness saturation at approximately 3–4 nm, consistent with a diffusive bulk mechanism and a spin-orbital diffusion length $\theta_{OH}$4 nm (Abrão et al., 2024). The interpretation is that YIG pumps spin current into Pt, Pt creates an entangled spin-orbital current via SOC, and the IrMn antiferromagnetic layer converts the orbital component into charge through an anomalous inverse mechanism enabled by the Néel vector.

Ferromagnetic Fe films with engineered anisotropy

In Fe films, AIOHE was observed in YIG/Fe and YIG/Pt/Fe structures fabricated by oblique deposition in a magnetic field to create strong uniaxial anisotropy (Santos et al., 9 Jul 2025). The anomalous character is again tied to out-of-plane geometries in which conventional inverse Hall effects are forbidden. Only samples with strong Fe anisotropy show nonzero spin-pumping FMR signals in the out-of-plane configuration; samples lacking anisotropy do not (Santos et al., 9 Jul 2025).

The magnitude of the out-of-plane signal scales with the strength of uniaxial anisotropy and reaches approximately 40 nA (Santos et al., 9 Jul 2025). The paper attributes the large orbital response to Fe’s low spin-orbit interaction and high orbital response, quoting $\theta_{OH}$5 and $\theta_{OH}$6 for Fe (Santos et al., 9 Jul 2025). In this interpretation, anisotropy engineering functions as the control parameter that turns AIOHE on and off by stabilizing the requisite magnetic order configuration.

Comparison of magnetic-order-enabled experiments

System	Order parameter enabling AIOHE	Key signature
YIG/Pt/Ir$\theta_{OH}$7Mn$\theta_{OH}$8	Néel vector in AF layer	Sevenfold signal increase in OOP geometry
YIG/Fe and YIG/Pt/Fe	Uniaxial-anisotropy-stabilized magnetization in Fe	Nonzero OOP signal only for strongly anisotropic Fe

These studies collectively establish the most restrictive definition of AIOHE: an anomalous inverse orbital Hall response enabled by magnetic order, detectable in geometries where conventional IOHE is symmetry-forbidden.

5. AIOHE-like behavior in THz emitters and ultrafast orbitronics

Ultrafast THz-emission spectroscopy has become a major experimental route for identifying orbital transport and inverse orbital conversion. In this context, the nomenclature often centers on IOHE, but several observations have anomalous features that place them within the broader AIOHE landscape.

Fe/Pt/W trilayers

In Fe/Pt/W trilayers, a pronounced enhancement of THz emission was observed despite Fe being an elemental ferromagnet with a quenched orbital moment (Zhou et al., 9 Feb 2026). In Fe/Pt and Fe/W bilayers, only conventional ISHE-based THz emission is seen; the THz amplitude decays rapidly with heavy-metal thickness, vanishing for thicknesses above about 15 nm, and neither peak delay nor pulse width changes significantly (Zhou et al., 9 Feb 2026). By contrast, in the trilayer, THz emission persists with increasing W thickness up to 100 nm, accompanied by systematic delay accumulation and pulse broadening (Zhou et al., 9 Feb 2026).

These features are interpreted as evidence for orbital angular momentum transport in W, converted into charge current by IOHE, with constructive interference between ISHE in Pt and IOHE in W (Zhou et al., 9 Feb 2026). The extracted propagation velocity in W, 0.3–0.6 nm/fs, is slower than the approximately 1 nm/fs spin current in Fe/W, consistent with a distinct orbital transport channel (Zhou et al., 9 Feb 2026). The enhancement factor is defined as

$\theta_{OH}$9

where $_4$0 indicates non-additive cooperative enhancement (Zhou et al., 9 Feb 2026).

The significance for AIOHE is indirect but important. The results show that strong orbital inverse conversion can emerge even when the ferromagnetic source itself has a quenched orbital moment, provided an intermediate Pt layer performs spin-to-orbital conversion. This suggests that “anomalous” orbital inverse behavior need not require an intrinsically orbital-active ferromagnet.

Co/Ru and Co/Pt/Ru structures

A related THz study on Co/Ru heterostructures reports long-range orbital transport and IOHE in Ru, evidenced by persistent THz emission up to 50 nm Ru thickness, pulse delay, and broadening (Chao et al., 4 Feb 2026). The time delay is modeled as

$_4$1

with orbital flip time $_4$2–$_4$3 fs, group velocity $_4$4 nm/fs, and orbital diffusion length about 20 nm (Chao et al., 4 Feb 2026). In Co/Pt/Ru trilayers, THz emission is enhanced through constructive interference between ISHE in Pt and IOHE in Ru, while reversed stacking suppresses the output (Chao et al., 4 Feb 2026).

The paper does not distinctly use the term AIOHE, but it emphasizes stacking-order-dependent anomalous behavior: Co/Pt/Ru shows strong cooperative conversion, Co/Ru/Pt shows rapid attenuation with attenuation length $_4$5 nm, and Ru/Co/Pt shows partial destructive interference with signal vanishing at larger Ru thickness and $_4$6 nm (Chao et al., 4 Feb 2026). This suggests that in ultrafast multilayers, “anomalous inverse orbital Hall” can also refer to deviations from simple additive IOHE plus ISHE due to interfacial sequence and orbital transport asymmetry.

6. Materials trends, sign reversals, and orbital-dominant conversion

A striking theme across recent orbitronics is that orbital contributions can dominate even in weak-SOC systems, and that the sign of the orbital Hall response can reverse between materials.

Positive and negative IOHE signals

In YIG/Pt/NM trilayers investigated by spin pumping and spin Seebeck measurements, positive and negative IOHE signals were observed in Ti and Ge, respectively (Santos et al., 7 Oct 2025). In Ti, the IOHE is strong and positive, adding constructively to Pt-based ISHE. In Ge, the IOHE is strong and negative, reducing and nearly canceling the net current from Pt (Santos et al., 7 Oct 2025). The extracted parameters are $_4$7 nm, $_4$8, $_4$9 nm, and $$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$0, with near-zero spin Hall angle in both materials (Santos et al., 7 Oct 2025).

The coupled diffusive model used there is

$$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$1

for the interconverting layer, together with conventional diffusion equations in the outer layer (Santos et al., 7 Oct 2025). The study explicitly identifies AIOHE with positive or negative IOHE signals depending on the sign of the orbital Hall angle.

First-principles origin of sign changes

First-principles Wannier-interpolation calculations give a microscopic basis for such sign reversals. The position operator in the Wannier representation contains an orbital-dependent anomalous position,

$$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$2

with

$$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$3

(Go et al., 2023). This modifies the velocity operator to

$$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$4

which in turn changes the computed orbital Hall conductivity (Go et al., 2023).

The resulting orbital Hall conductivities are predicted to be negative in several group X and XI metals for which earlier studies predicted positive sign: Cu, Ag, Au, Pd, and nonmagnetic Ni (Go et al., 2023). Specific values given include $$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$5 for Cu, $$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$6 for Ag, $$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$7 for Au, and $$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$8 for Pd, in units of $$\theta_{ijk} = \theta_0 \epsilon_{ijk} + \theta_1 n_l \epsilon_{iln} \epsilon_{jnk} + \theta_2 n_i \epsilon_{ink} \epsilon_{jln},$$9 (Go et al., 2023). These sign reversals imply that anomalous inverse orbital responses may be highly sensitive to orbital overlap, interface chemistry, oxidation, and strain.

Silicon as a weak-SOC orbital platform

An additional indication of orbital-dominant inverse conversion comes from time-resolved THz polarimetry in silicon. There, a long-lived anomalous Hall conductivity of photocarriers depends on the helicity of near-infrared light, with magnitude comparable to GaAs despite silicon’s much weaker spin-orbit coupling (Shirai et al., 22 Dec 2025). The study argues that the photon-energy robustness rules out a spin-polarization-based origin and suggests the emergence of IOHE in Si (Shirai et al., 22 Dec 2025). The anomalous Hall conductivity is extracted via

$\mathbf{n}$0

and time-resolved separation of the field-induced circular photogalvanic effect from the long-lived light-induced anomalous Hall effect is essential (Shirai et al., 22 Dec 2025). Although not cast primarily as AIOHE, it reinforces the material trend that orbital conversion can dominate where spin-based explanations are untenable.

7. Interpretive issues, distinctions, and research directions

A recurring interpretive issue is that the label AIOHE is not used uniformly. At least three usages are now present in the literature.

First, in magnetic and antiferromagnetic heterostructures, AIOHE has a symmetry-specific meaning: inverse orbital Hall conversion activated by magnetic order, anisotropy, or Néel order, especially in out-of-plane geometries where conventional IOHE is forbidden (Abrão et al., 2024, Santos et al., 9 Jul 2025). This is the most formal and restrictive usage.

Second, in current-biased topological semimetals such as TaIrTe$\mathbf{n}$1, AIOHE is associated with current-induced orbital magnetization and its Hall readout, with the orbital anomalous Hall effect viewed as the transport manifestation of the inverse orbital response (Wang et al., 2024). This usage emphasizes magnetoelectric orbital polarization rather than injected orbital-current transport through a heterostructure.

Third, in THz-emitter and multilayer-orbitronics studies, “anomalous” often denotes non-additive enhancement, constructive or destructive interference with ISHE, thickness-dependent persistence far beyond spin diffusion lengths, or sign reversal due to orbital Hall angle polarity (Zhou et al., 9 Feb 2026, Chao et al., 4 Feb 2026, Santos et al., 7 Oct 2025). This broader language reflects the experimental reality that orbital transport and conversion are often inferred from deviations from spin-only models.

Several misconceptions are therefore best avoided. AIOHE is not simply “IOHE in any magnetic material”; rather, the anomalous qualifier usually indicates either order-parameter-enabled symmetry breaking or a qualitatively nonstandard orbital inverse response. Nor is strong SOC universally required. Some experiments use Pt as a spin-to-orbital converter, but large orbital responses are reported in low-SOC or weak-SOC systems such as Fe, Ti, Ge, Ru, and Si (Santos et al., 9 Jul 2025, Santos et al., 7 Oct 2025, Chao et al., 4 Feb 2026, Shirai et al., 22 Dec 2025). Conversely, the presence of a large Hall-like signal does not by itself distinguish spin from orbital origin; careful control of geometry, thickness dependence, polarity, photon-energy dependence, or time-domain signatures is required.

The emerging research direction is the consolidation of AIOHE across these currently distinct subfields. This suggests a future framework in which AIOHE encompasses tensorial inverse orbital conversion in ordered magnets, orbital-magnetization-driven Hall transport in low-symmetry materials, and ultrafast orbital-to-charge conversion in multilayers with engineered interfaces. The present literature indicates that the decisive ingredients are Berry-curvature-derived orbital response, sign-selective orbital Hall conductivity, and symmetry control through order parameters, crystal orientation, or stack design (Go et al., 2023, Das et al., 2020, Wang et al., 2024, Abrão et al., 2024, Zhou et al., 9 Feb 2026).