Negative Orbital Hall Effect Overview

• Negative Orbital Hall Effect is a quantum transport phenomenon where orbital angular momentum flows transversely with its Hall conductivity reversed relative to conventional behavior.
• It arises from the interplay of spin-orbit coupling, orbital texture, and extrinsic scattering, with experimental evidence in vanadium films showing σ_OH ≈ –1.46×10⁵ Ω⁻¹ m⁻¹.
• Strain engineering and band topology tuning enable innovative orbitronic devices that exploit reversed orbital torque for enhanced MRAM and neuromorphic computing.

The negative orbital Hall effect (OHE) is a transport phenomenon wherein the transverse flow of orbital angular momentum in response to an applied electric field is characterized by a Hall conductivity of opposite sign to the conventional orbital Hall signal. This effect has been theoretically predicted and experimentally observed in multiple material classes, including transition metals, semiconductors, and two-dimensional crystals. Negative OHE is invariably linked to underlying orbital texture, band topology, extrinsic scattering mechanisms, and competing intra-atomic/inter-atomic orbital responses. It fundamentally impacts the sign of orbital torque generated in heterostructures and the directionality of orbital current conversion in orbitronic devices.

1. Fundamental Mechanism of the Negative Orbital Hall Effect

Negative OHE arises from the generation of a transverse, charge-neutral flow of orbital angular momentum, J^O, in the presence of an electric field. In conventional settings, the sign of the orbital Hall conductivity is determined by the interplay of intrinsic (Berry curvature-mediated) and extrinsic (disorder-induced) contributions. In transition metals and semiconductors, deviations from atomic-center approximations and the detailed interplay between interatomic and intra-atomic orbital characters become decisive (Pezo et al., 2022).

A critical quantum-mechanical factor for negative OHE is the relative sign of orbital and spin angular momentum correlations, ⟨L * S⟩. When spin-orbit coupling (SOC) polarizes L antiparallel to S (for example, in J = 1/2 states of heavy metals), the resulting orbital Hall signal can become negative (Jung et al., 2014). Quantum corrections arising from band-diagonal matrix elements and non-commutativity between position and velocity operators further shift the sign of the OHE, as evidenced in topological antiferromagnets and massive Dirac systems (Liu et al., 9 Aug 2024).

2. Orbital Texture, Band Topology, and Symmetry Breaking

Negative OHE is closely linked to the momentum-space distribution of orbital angular momentum—orbital texture—and the associated band topology. Broken inversion symmetry generates robust momentum-resolved orbital moments, M(k), which can be valley locked and differ in sign between K and K′ points (Bhowal et al., 2020). The sign of OHE is then set by the relative weights and winding numbers of contributions from distinct projected orbital angular momentum (POAM) sectors (Wang et al., 1 Nov 2024).

Strain engineering can induce band inversion or transfer of OAM between valence and conduction bands, resulting in reversal of the orbital Chern number and flipping the sign of the orbital Hall conductivity (Ji et al., 2023). Layered and multilayered systems offer further tunability, as the anisotropy of the inverse effective mass tensor modifies the coupling of orbital magnetic moments to external fields and enables negative OHE in selected quantum transport regimes (Sun et al., 6 Aug 2024).

<table> <thead> <tr> <th>Physical Mechanism</th> <th>Negative OHE Origin</th> <th>Reference</th> </tr> </thead> <tbody> <tr> <td>Antiparallel L * S polarization</td> <td>Negative Hall conductivity σ_SH</td> <td>(Jung et al., 2014)</td> </tr> <tr> <td>Interatomic band mixing</td> <td>Sign reversal/cancellation of σ_OH</td> <td>(Pezo et al., 2022)</td> </tr> <tr> <td>Strain-induced band inversion</td> <td>Switching orbital Chern number sign</td> <td>(Ji et al., 2023)</td> </tr> <tr> <td>Quantum corrections from [r,v] noncommutativity</td> <td>Opposite sign compared to conventional OHE</td> <td>(Liu et al., 9 Aug 2024)</td> </tr> <tr> <td>Dominant extrinsic side-jump/skew scattering</td> <td>Experimentally observed sign reversal</td> <td>(Liu et al., 2023)</td> </tr> <tr> <td>Valley-orbital locking</td> <td>Antisymmetric orbital current response</td> <td>(Bhowal et al., 2020)</td> </tr> </tbody> </table>

3. Material Realizations and Experimental Observations

Negative OHE has been experimentally demonstrated in several systems. In Vanadium thin films, systematic transport measurements showed a negative damping-like torque (DLT) per unit electric field, with the sign opposite to that of Pt (Vijayan et al., 22 Aug 2025). The extracted orbital Hall conductivity in V is –(1.46 ± 0.09)(ħ/2e) × 10^5 Ω⁻¹ m⁻¹, and the orbital diffusion length exceeds 13 nm. The sign remains negative at all thicknesses and increases in magnitude for thicker films, indicating a robust and long-range diffusive regime.

In Germanium, the negative inverse orbital Hall effect (IOHE) was observed using orbital pumping in YIG/Pt(2)/Ge(t_Ge) and YIG/W(2)/Ge(t_Ge) heterostructures (Santos et al., 12 Mar 2024). The orbital-to-charge conversion in Ge exhibits a large magnitude (σ_OH ≈ –1270 ħ/e Ω·cm⁻¹), contrasting with its negligible spin-to-charge conversion. This sign reversal is corroborated by both coherent and incoherent pumping experiments, and by the hyperbolic tangent scaling of signal reduction with Ge thickness (diffusion length λ_Ge ≈ 4–7 nm).

Edge-resolved measurements in strip geometries also confirm negative OHE, where the accumulated orbital angular momentum at opposite boundaries takes on opposite signs, consistent with the theoretical lossy continuity/diffusion equations (Kiselev et al., 1 Jul 2025). Terahertz emission and high-frequency ST-FMR experiments in V/Ni and V/FeCoB stacks further validate the orbital origin and negative sign of the torque.

4. Theoretical Formulation and Quantum Corrections

The OHE is described by both semiclassical Berry-curvature formulations and full quantum Boltzmann/linear response frameworks. The general orbital Hall conductance can be split into intrinsic and extrinsic parts:

$$\sigma_{OH}^{tot} = \sigma_{OH}^{int} + \sigma_{OH}^{ext}$$

with typically

$\sigma_{OH}^{ext} \gg \sigma_{OH}^{int}$

in doped systems, due to side-jump and skew scattering (Liu et al., 2023).

Quantum corrections due to the full operator structure (intra-band matrix elements and position–velocity noncommutativity) can outweigh conventional terms, resulting in a sign reversal of OHE (Liu et al., 9 Aug 2024):

$$j_L = j_{conv} + \Delta j, \quad \Delta j = \Delta j_1 + \Delta j_2 + \Delta j_3$$

where $\Delta j_3$ (from $[r, v]$) can dominate, especially in topological antiferromagnets (e.g., CuMnAs) and massive Dirac systems. The resulting orbital current quantizes or reverses sign at higher energies, fundamentally altering the transport regime.

Advanced theoretical treatments also incorporate the distinction between intra-atomic and inter-atomic orbital contributions. Inter-atomic band mixing, sensitive to band ordering and Berry connection corrections, can lead to an overall negative OHE—contrary to the predictions of atomic-center approximations (Pezo et al., 2022).

5. Band Topology, Bulk-Boundary Correspondence, and Tunability

Band topology provides a unifying framework for OHE sign control. Analysis based on the projected orbital angular momentum (POAM) spectrum in group-IV monolayers demonstrates that the Chern number for each sector dictates the plateau value and sign of the orbital Hall conductivity (Wang et al., 1 Nov 2024):

$$\sigma_{xy}^{L_z} = \frac{e}{h} \sum_{i} \tilde{l}_i \mathcal{C}_i$$

Edge states in POAM-protected OHE systems exhibit nonzero and spatially oscillating orbital textures, with the sign of ⟨L_z⟩ changing across Dirac points or as chemical potential, strain, or gating are tuned (Ji et al., 2023, Wang et al., 1 Nov 2024). Strain-induced band inversion (Δ_τ – Dε changing sign in a k·p model) reverses the orbital Chern number (ĈLz) and the sign of OHE (Ji et al., 2023).

In artificial systems such as gapped bilayer graphene, the AC orbital Hall conductivity switches sign at a critical frequency proportional to the field-induced gap, further expanding practical tunability for negative OHE applications (Cysne et al., 7 Feb 2024).

6. Practical Implications and Device Applications

The negative OHE expands the design space for orbitronic and spin–orbitronic devices. Materials with high negative orbital Hall conductivity and long diffusion lengths—such as V, Ge, and certain topological insulators—can be leveraged for efficient, sign-reversible orbital torque generation in MRAM and neuromorphic computing (Vijayan et al., 22 Aug 2025, Gupta et al., 3 Apr 2024). The observed sign reversal, dependence on layer thickness, FM layer, and scattering environment suggests that device functionality (switching polarity, efficiency, power reductions) can be systematically controlled.

The reduction in spin-to-charge conversion in weak SOC semiconductors, coupled with large orbital-to-charge conversion in negative OHE systems, enables new paradigms for logic and memory devices where orbital angular momentum acts as a principal carrier for information transmission (Santos et al., 12 Mar 2024).

Experimental strategies for detection and exploitation of negative OHE include:

• Magneto-optical Kerr effect and XMCD for edge orbital accumulation.
• Hyperbolic tangent fitting of orbital-pumping signals and extraction of diffusion lengths.
• Frequency-dependent AC transport, terahertz emission, and spin-torque FMR for sign and magnitude determination.
• Strain engineering, chemical gating, and heterostructure design for topological sign switching.

7. Open Problems and Future Directions

Despite significant advances, several aspects of negative OHE remain under investigation:

• Quantitative ab initio modeling of inter-atomic and extrinsic contributions, especially in 3d transition metals, to clarify the mechanisms behind sign reversal and maximize device performance (Pezo et al., 2022, Liu et al., 2023).
• Systematic exploration of strain-driven, topological, or gating-induced OHC reversal for robust, tunable orbital circuits (Ji et al., 2023, Wang et al., 1 Nov 2024).
• Complete quantum-mechanical treatments and inclusion of non-Ohmic charge flow contributions in confined geometries, necessary for accurate modeling of real-world device responses (Liu et al., 9 Aug 2024, Kiselev et al., 1 Jul 2025).
• Experimental separation of intrinsic versus extrinsic OHE contributions, potentially employing AC transport or high-frequency probes to suppress disorder effects and isolate the negative OHE (Liu et al., 2023).
• Development of orbital-current-based magnetoresistive effects (e.g., orbital Hanle magnetoresistance) leveraging the anisotropic dynamics and magnetic-field interactions in multilayered structures (Sun et al., 6 Aug 2024).

The elucidation and control of negative orbital Hall currents underpin novel orbitronic devices and quantum transport regimes where the sign and magnitude of orbital angular momentum flows are engineered for functional advantage.