Orbital Hall Transition: Mechanisms & Insights

• Orbital Hall Transition is a multifaceted phenomenon marked by shifts from spin-dominated to orbital-dominated transport, manifesting as insulating, reciprocal conversion, or topological regimes.
• Analytical approaches include k-space Berry curvature, real-space interatomic flux analysis, and tight-binding models to quantify orbital Hall conductivity.
• Experimental diagnostics of OHT involve measurements like orbital Kerr rotation, torque efficiency, and temperature-dependent crossover behaviors in mesoscopic systems.

Searching arXiv for the core literature on Orbital Hall Transition and closely related orbital Hall physics. Search query: "Orbital Hall Transition orbital Hall effect arXiv" Orbital Hall Transition (OHT) denotes a family of transition-like phenomena centered on orbital Hall transport rather than a single universally standardized critical point. Across the literature, the term is used for the onset of an orbital Hall insulating regime when the chemical potential enters a gap, for reciprocal orbital-to-charge conversion in the inverse orbital Hall effect, for orbital-to-spin conversion that generates torque in heterostructures, for an orbital counterpart accompanying the integer quantum Hall transition, and for entry into a topological orbital Hall phase diagnosed in the projected orbital angular momentum spectrum (Canonico et al., 2020, Wang et al., 2023, Pessoa et al., 6 Jul 2025, Wang et al., 2024). In all of these usages, the transported quantity is orbital angular momentum or orbital magnetic moment, and a recurring theme is that a finite orbital Hall response can persist where the spin Hall response vanishes or is negligible (Canonico et al., 2020, Bhowal et al., 2021).

1. Nomenclature and conceptual scope

The term “Orbital Hall Transition” is not used in a single way across the arXiv literature. In several works it labels a crossover or onset in transport; in others it is tied to topological or critical behavior. This nonuniformity is itself a defining feature of the topic.

Usage of OHT	Representative meaning	arXiv id
Gap-driven onset	Entry into an orbital Hall insulating phase with finite orbital Hall conductivity in the gap	(Canonico et al., 2020)
Reciprocal conversion	Orbital current converted into charge current through the inverse orbital Hall effect	(Wang et al., 2023)
Torque conversion	Orbital Hall current converted into spin-active torque or magnetoresistance	(Lee et al., 2021, Mahapatra et al., 12 Nov 2025)
Quantum Hall partner transition	Orbital transport fluctuates alongside the integer quantum Hall transition	(Pessoa et al., 6 Jul 2025)
Topological transition	Ordinary orbital Hall response becomes a topological orbital Hall phase	(Wang et al., 2024)

A common misconception is to treat OHT as a universal symmetry-breaking phase transition. Multiple studies explicitly argue otherwise. In mesoscopic disorder problems, the relevant behavior is a disorder-driven crossover between transport regimes rather than a sharp thermodynamic transition (Barbosa et al., 2 Jul 2025). In quantum Hall settings, the orbital Hall response may accompany the quantum Hall state without defining a separate phase boundary (Göbel et al., 2024). In broader first-principles and modern-theory treatments, “transition” is often best understood as a qualitative change in the dominant angular-momentum transport channel or in the microscopic origin of the orbital Hall effect, rather than as a universal topological critical point (Pezo et al., 2022).

2. Gap-driven orbital Hall insulating regimes

One major meaning of OHT is the onset of an orbital Hall insulator. In H-phase transition metal dichalcogenide monolayers such as MoS$_2$ and WSe$_2$, the semiconducting gap supports a large, finite orbital Hall conductivity plateau while the spin Hall conductivity vanishes. The response is carried by atomic orbital angular momentum rather than spin, so a longitudinal electric field drives a transverse orbital current even in an insulating state. In the three-band description, the relevant transition-metal orbitals are $d_{z^2}$, $d_{xy}$, and $d_{x^2-y^2}$ on the triangular lattice imposed by $D_{3h}$ symmetry. The underlying texture is written as

$$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$

and the in-plane component near $K$ and $K'$ is described as Dresselhaus-like. The effect survives even without spin-orbit coupling, and in the gap one has a finite $\sigma_{OH}^z$ together with vanishing $_2$0. In the Kubo-Bastin formulation, the two responses differ only by the transverse current operator,

$_2$1

which makes explicit that the insulating response is a Berry-curvature phenomenon weighted by orbital angular momentum (Canonico et al., 2020).

A closely related formulation appears in gapped graphene, where the phenomenon usually called the valley Hall effect is recast as an orbital Hall effect. The key replacement is the ambiguous valley label by the orbital magnetic moment, which is a genuine observable over the entire Brillouin zone. The orbital Hall conductivity is then defined as a full-Brillouin-zone integral of orbital Berry curvature rather than a valley-restricted integral with an arbitrary cutoff. In this description, the conductivity is maximal when the Fermi level lies in the gap and decreases when it moves into the bands, while Kerr-rotation edge signals are interpreted as accumulation of opposite orbital moments rather than abstract valley polarization. The $_2$2 limit yields a singular change in orbital response as the gap closes, which suggests a transition-like reorganization of the orbital sector even though the work does not formalize a separate OHT criticality (Bhowal et al., 2021).

Monolayer TMDs provide a further extension in which the orbital Hall plateau is correlated with higher-order topology. In 2H compounds protected by $_2$3 symmetry and in 1T compounds classified by a $_2$4 invariant, linear-response calculations show finite orbital Hall conductivity plateaus inside the insulating gap while the spin Hall conductivity vanishes there. In the 2H family the in-gap response is dominated by $_2$5, whereas in centrosymmetric 1T systems finite $_2$6 can also appear. The resulting picture is not that OHT is an autonomous universal topological transition; rather, the orbital Hall plateau is a transport manifestation of the same symmetry-organized electronic structure that yields higher-order topological features (Costa et al., 2022).

A more explicit transition into an orbital Hall insulating phase appears in a generalized three-band triangular-lattice model. There, tuning the symmetry-breaking hoppings and spin-orbit coupling produces four phases, and the full TMD-like phase is $_2$7-trivial yet retains a nonzero orbital Hall conductivity inside the gap with orbital Chern number $_2$8. In that regime the spin Hall response vanishes in the gap, but orbital transport survives, which is one of the clearest operational meanings of OHT as a change from spin-dominated to orbital-dominated gap transport (Barbosa et al., 2023).

3. Microscopic description and transport formalisms

The formal structure of OHT is inherited from the orbital Hall effect itself. In modern linear-response language, the orbital Hall conductivity is written as

$_2$9

with orbital current operator

$d_{z^2}$0

This formulation highlights the same interband coherence structure that underlies spin Hall physics, but with orbital angular momentum as the transported feature. In projected-feature formulations of the topological orbital Hall effect, the corresponding current operator appears as $d_{z^2}$1, and the Hall response is related to the feature curvature of the occupied subspace (Pezo et al., 2022, Wang et al., 2024).

A central controversy concerns the definition of orbital current itself. In the atomic center approximation, the orbital moment is treated as localized near atomic cores. The modern-theory treatment shows that this can be qualitatively adequate near the gap of wide-band-gap semiconductors such as monolayer MoS$d_{z^2}$2, where the intra-atomic contribution dominates, but it can fail badly in narrow-gap semiconductors and especially in metals, where inter-atomic or interstitial contributions become crucial. In Pt and V, for example, the total orbital Hall response is systematically smaller than the intra-atomic estimate because of strong cancellations across the dense band manifold. This establishes that OHT, when discussed as a change in orbital transport character, can also refer to a shift in the dominant microscopic origin of the response: intra-atomic in some systems, inter-atomic in others (Pezo et al., 2022).

A complementary real-space perspective comes from first-principles scattering calculations based on wave-function matching with a tight-binding MTO basis. In that approach, the relevant transported quantity is an interatomic flux of orbital angular momentum,

$d_{z^2}$3

and intraatomic fluxes are explicitly excluded because they do not transfer angular momentum between sites. Within this transport definition, the orbital Hall angle and resistivity are both approximately linear in temperature in the equipartition regime, so $d_{z^2}$4 is only weakly temperature dependent. The calculated conductivities are large and material dependent: for bulk Cr $d_{z^2}$5, while Ti, V, and Pt are reported as approximately $d_{z^2}$6, $d_{z^2}$7, and $d_{z^2}$8 in units of $d_{z^2}$9, and Cu is much smaller at approximately $d_{xy}$0 (Rang et al., 2024).

Taken together, these formalisms imply that OHT is not a single operator-level construction. Depending on context, it is formulated through orbital textures in $d_{xy}$1-space, through gauge-consistent orbital Berry curvature, through interatomic fluxes in real space, or through projected spectral topology. This suggests that any encyclopedic treatment of OHT must distinguish carefully between orbital accumulation, orbital current, and orbital-to-spin or orbital-to-charge conversion.

4. Reciprocal conversion, torque, and magnetoresistive OHT

In heterostructures and ultrafast experiments, OHT often denotes a conversion process rather than an insulating onset. The inverse orbital Hall effect is the reciprocal relation

$d_{xy}$2

which is the orbital analogue of SHE/ISHE reciprocity. In Co/Ti and Co/Mn bilayers under femtosecond pumping, Co generates spin and orbital angular momentum currents through spin–orbit transition, and Ti or Mn converts the orbital current into charge current through IOHE. Inserting W creates an additional ISHE channel and an additional orbital-current source, so in Co/W/X ($d_{xy}$3Ti or Mn) IOHE and ISHE add constructively, whereas in Co/Ti/W they can compete with a $d_{xy}$4 phase difference. In this literature, OHT is effectively the transition from orbital current to measurable charge current, detected through orbitronic terahertz emission (Wang et al., 2023).

A second usage identifies OHT with orbital-to-spin conversion that makes orbital Hall currents torque-active. In Cr-based heterostructures, the effective charge-to-spin conversion efficiency is written as

$d_{xy}$5

so the orbital Hall channel enters through the $d_{xy}$6 conversion coefficient $d_{xy}$7. Cr is chosen because theory predicts $d_{xy}$8 and $d_{xy}$9. In this setting, OHT is the experimentally realized $d_{x^2-y^2}$0 step that turns orbital Hall current into damping-like torque. The enhancement is substantial: at $d_{x^2-y^2}$1 K, $d_{x^2-y^2}$2 for Gd/Cr, compared with $d_{x^2-y^2}$3 for Co/Cr, and a Pt interfacial layer reverses the switching polarity in Cr/Pt/CoFeB stacks (Lee et al., 2021).

A third operational definition appears in light-metal/Ni bilayers, where OHT is the conversion of a transverse orbital Hall current into torque on a ferromagnet and into unidirectional orbital magnetoresistance. Hall-bar Ni/Ti devices and Ni/Cu/Ti variants are analyzed through simultaneous longitudinal and transverse second-harmonic measurements. The extracted orbital Hall torque efficiency $d_{x^2-y^2}$4 and normalized UOMR both increase with Ti thickness, indicating a bulk orbital Hall source in Ti, and insertion of a $d_{x^2-y^2}$5 nm Cu layer between Ni and Ti produces roughly a fivefold increase in both quantities relative to Ni/Ti or Ni/Cu controls. Lowering the temperature causes both the OHT efficiency and the UOMR to decrease nearly monotonically, and their nearly linear correlated temperature dependence is taken as evidence for a common orbital Hall mechanism (Mahapatra et al., 12 Nov 2025).

A broader heterostructure program generalizes this picture to 3d, 5d, and 4f metals. There, the transport chain is charge current $d_{x^2-y^2}$6 orbital Hall current $d_{x^2-y^2}$7 spin current $d_{x^2-y^2}$8 torque, and the measured damping-like response is described as a spin-orbital conductivity rather than a pure spin Hall conductivity. Cr exhibits a giant orbital Hall conductivity of the order of $d_{x^2-y^2}$9, Pt carries both strong orbital and spin Hall channels, and Gd or Tb spacers act as efficient orbital-to-spin converters, boosting Cr-generated torques by a factor of $D_{3h}$0 and reversing the sign of Pt-generated torques (Sala et al., 2022).

The inverse side of this heterostructure physics is exposed in ferromagnetic-resonance spin-pumping measurements on YIG/X and YIG/Pt/X structures across $D_{3h}$1 transition metals. By comparing direct spin-to-charge conversion with Pt-mediated orbital injection, the inverse Hall signal in many materials is found to be overwhelmingly dominated by the orbital channel. In YIG/Pt(2)/Mo(5), for example, the total measured signal is $D_{3h}$2, the Pt reference contributes $D_{3h}$3, the Mo ISHE reference is $D_{3h}$4, and with $D_{3h}$5 the inferred IOHE contribution is approximately $D_{3h}$6. This establishes an OHT regime in which inverse Hall voltages are no longer mainly explained by spin Hall conversion but by orbital Hall conversion (Costa et al., 10 Jun 2025).

5. Topological, quantum Hall, and critical formulations

In the quantum Hall regime, the ordinary quantum Hall effect is accompanied by an orbital Hall effect because chiral edge states are orbital polarized. On a square lattice with Peierls substitution, Landau levels form in the bulk and skipping orbits appear at the edge. The key point is that edge channels carry out-of-plane orbital angular momentum $D_{3h}$7, so the quantum Hall state already contains an orbital Hall response. The charge Hall conductivity remains quantized, but the orbital Hall conductivity is finite, stepwise, and nonuniversal, and the orbital Hall resistivity scales approximately as $D_{3h}$8. This work explicitly rejects the notion that there is necessarily a separate OHT as an independent phase transition; instead, orbital Hall transport emerges as an accompanying response of the quantum Hall state (Göbel et al., 2024).

A distinct critical use of the term appears in a disordered four-terminal nanowire with orbital momentum-space texture. There the integer quantum Hall transition is accompanied by an orbital Hall transition, and both charge and orbital transmission coefficients fluctuate strongly as magnetic flux or Fermi energy is tuned through the plateau-transition regime. Using multifractal detrended fluctuation analysis on traces of length $D_{3h}$9, the study finds that both IQHT conductance fluctuations and OHT orbital-conductance fluctuations are multifractal; at disorder strength $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$0 eV the singularity spectrum is broad with $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$1. The authors interpret the multifractality as primarily disorder driven, with finite size weakening it in an intermediate regime before a second growth regime at stronger disorder. In this formulation, OHT is a partner critical phenomenon to IQHT (Pessoa et al., 6 Jul 2025).

A more explicitly topological definition is developed through the projected orbital angular momentum spectrum $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$2. In monolayers of group-IV elements, spin-orbit-coupling-induced band inversion reorganizes the occupied subspace into projected orbital sectors with nontrivial Chern numbers. The Wannier charge centers of these sectors wind nontrivially, and the orbital Hall conductivity forms a plateau within the band gap as a direct consequence of the Chern number carried by the projected spectrum. Boundary manifestations include gapless states in the projected orbital spectrum and nonzero orbital textures at the edges. In this setting, OHT means the transition from an ordinary orbital Hall regime to a topological orbital Hall phase (Wang et al., 2024).

Weyl engineering yields yet another transition concept. In monolayer PtBi$$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$3, a type-II Weyl point dominated by orbitally distinct bands produces a strongly asymmetric orbital Berry-curvature distribution and an orbital Hall conductivity of about $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$4 at zero strain. Small biaxial tensile strain drives a type-II $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$5 type-I $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$6 type-II Weyl transition, and the OHC decreases to zero near $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$7 strain and then reverses sign. The process is assisted by a first-order structural phase transition between $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$8 and $$\vec{L}_{n,s}(\vec{k})=\sum_{\mu=x,y,z}\langle \psi^{\vec k}_{n,s}|L^\mu|\psi^{\vec k}_{n,s}\rangle \hat e_\mu,$$9 strain, where the out-of-plane thickness changes abruptly and the ferroelectric polarization jumps from $K$0 to $K$1 pC/m. Here OHT denotes a reversible sign switch of orbital Hall response driven by Weyl-point evolution and orbital-geometry reconstruction (Zhao et al., 9 Mar 2026).

Floquet engineering in collinear antiferromagnetic multilayers introduces a nonequilibrium version of the same idea. Circularly polarized light induces odd-parity $K$2-wave altermagnetism, drives band inversions, and produces QAHE phases with tunable Chern numbers up to $K$3. The orbital Hall conductivity evolves strongly across these phases because the orbital angular momentum texture and orbital Berry curvature are redistributed by the Floquet reconstruction. Notably, the OHE can be strongly enhanced even in a topologically trivial driven regime, and then change abruptly when topological band inversions occur. This makes OHT a distinct orbitally resolved transport signature that co-evolves with, but is not identical to, the QAHE (Tian et al., 12 Mar 2026).

6. Disorder, temperature, geometry, and experimental diagnostics

In mesoscopic transport, OHT is frequently observed as a disorder-driven crossover. A real-space tight-binding study of square and rectangular devices with $K$4 orbitals finds that disorder can significantly enhance the orbital Hall conductivity and even reverse its sign. In square devices, the orbital Hall current density follows

$K$5

with $K$6, and the orbital Hall angle obeys $K$7, which is interpreted as skew-scattering-dominated extrinsic OHE in the diffusive regime. In rectangular devices, the orbital current decays as

$K$8

allowing extraction of an orbital relaxation length. This work explicitly frames the phenomenon as a crossover from skew-scattering-dominated generation to a saturated or relaxation-dominated regime rather than a sharp thermodynamic OHT (Barbosa et al., 2 Jul 2025).

Temperature enters the subject in two apparently different ways that are not contradictory once the experimental context is separated from the bulk transport coefficient. In first-principles scattering calculations on disordered transition metals, the resistivity and orbital Hall angle are both approximately linear in temperature, so $K$9 is at most weakly temperature dependent (Rang et al., 2024). In contrast, in Ni/Ti-based torque measurements, the experimentally extracted orbital Hall torque efficiency and UOMR both decrease as temperature is lowered, which the authors attribute to a common mechanism involving orbital-current generation in the light-metal layer and its subsequent action on the ferromagnet (Mahapatra et al., 12 Nov 2025). This suggests that the observed temperature dependence of OHT-sensitive observables is strongly context dependent: intrinsic orbital Hall transport can remain robust while interface conversion and torque transduction vary more strongly.

Geometry and boundary conditions are equally central. In the triangular-lattice orbital Hall insulating phase, in-gap edge states can carry orbital angular momentum only for specific ribbon terminations, and their transport is not topologically protected against edge disorder in the same way as the edge states of a first-order topological insulator (Barbosa et al., 2023). In the higher-order topological TMD setting, corner states, zigzag-edge metallic states, and orbital pseudo-spin structure further link the observed orbital transport to the chosen cut and symmetry class (Costa et al., 2022). OHT therefore cannot be characterized solely by a bulk coefficient; edge termination, interface transparency, and structural symmetry all enter the operational definition.

Direct experimental detection of orbital Hall transport in a single nonmagnetic layer has been achieved in epitaxial Cr through current-modulated longitudinal MOKE. The measured Kerr signal scales linearly with current density, reaches $K'$0 nrad per $K'$1 in a $K'$2 nm Cr film, changes sign when the optical path is reversed, and vanishes upon $K'$3 sample rotation, consistent with in-plane orbital accumulation transverse to the current. Comparison with $K'$4 modeling yields an orbital diffusion length of $K'$5 nm and an orbital Hall angle of approximately $K'$6. This experiment does not identify a sharp OHT critical point, but it provides a direct surface-sensitive diagnostic of the orbital Hall channel that underlies many transition-like interpretations of OHT in heterostructures and mesoscopic devices (Lyalin et al., 2023).

The accumulated literature therefore presents OHT as a multiform concept whose unity lies in orbital Hall transport and whose diversity lies in what is considered to “transition”: the Fermi level into an orbital Hall insulator, an orbital current into charge or spin, a quantum Hall system into an orbital-critical regime, or a conventional orbital response into a topological or Weyl-engineered one. The most stable conclusion is that OHT is best treated as a family of orbital-transport transitions and crossovers organized by orbital texture, Berry curvature, symmetry, and conversion processes, rather than as a single universal phase transition.