Inverse Orbital Hall Effect Overview

• IOHE is the orbital-angular-momentum counterpart to spin Hall effects, converting injected orbital currents into transverse charge signals.
• It employs diverse experimental architectures, from magnetic trilayers to ultrafast optical setups, to isolate and quantify orbital-to-charge conversion.
• Quantitative studies reveal thickness-dependent diffusion and sign reversals in materials like Ge, Ti, and various 4d metals, distinguishing IOHE from spin effects.

The inverse orbital Hall effect (IOHE) is the orbital-angular-momentum analogue of the inverse spin Hall effect: an injected orbital current, with a given orbital polarization, is converted into a transverse charge current in a conducting layer. In current orbitronics literature, IOHE is treated as the reciprocal of the orbital Hall effect (OHE), but with an important caveat emphasized in transport surveys: unlike spin, orbital angular momentum is not strictly conserved in a crystal field, so OHE/IOHE reciprocity can be locally violated even if it remains globally consistent with Onsager reciprocity (Xu et al., 2023, Costa et al., 10 Jun 2025). Experimentally, IOHE has been identified in quasi-dc spin-pumping and spin-Seebeck measurements, in thickness-dependent orbital diffusion studies, in ultrafast terahertz emitters, and in all-optical semiconductor probes, establishing orbital-to-charge conversion as a distinct transport channel rather than a mere byproduct of spin conversion (Vojkovic et al., 2 Mar 2026, Xu et al., 2022).

1. Reciprocal framework and defining relations

In the standard phenomenology, IOHE converts an orbital angular momentum current into a transverse electrical current. A commonly used form is

$$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{OH}}\,(\mathbf{J}_L \times \hat{\mathbf{o}}_L),$$

where $\mathbf{J}_L$ is the orbital current, $\hat{\mathbf{o}}_L$ is the orbital polarization direction, and $\theta_{\mathrm{OH}}$ is the orbital Hall angle (Vojkovic et al., 2 Mar 2026). Closely related papers also write the inverse conversion as

$$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$

with

$$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$

making explicit the link between the observed charge response, the orbital Hall conductivity, and the electrical conductivity (Santos et al., 2024).

This formulation parallels the inverse spin Hall effect (ISHE),

$$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$

but the literature repeatedly stresses that orbital transport is not simply a spin-transport copy with $s$ replaced by $L$. In transition metals, the orbital Hall conductivity can exceed the spin Hall conductivity, so the inverse conversion can dominate even when the conventional spin Hall response is weak (Xu et al., 2023). That distinction is central to the interpretation of experiments in Ru, Ti, Ge, Zr, CuO, and several 4d metals, where the observed charge signals are either too large, of the wrong sign, or too long-ranged to be explained by ISHE alone (Santos et al., 7 Oct 2025).

A further conceptual extension concerns ordered systems. In antiferromagnets and anisotropic ferromagnets, the orbital Hall angle is argued to require a tensorial rather than scalar description, in direct analogy with anomalous spin Hall physics. In that framework, the conventional cross-product form describes only the nonmagnetic limit, while additional order-parameter-dependent terms enable anomalous inverse orbital Hall responses in geometries where conventional IOHE would vanish (Abrão et al., 2024).

2. Conversion chains and experimental architectures

The most widely used transport architecture is the magnetic-insulator trilayer typified by YIG/Pt/NM. In that scheme, thermal or dynamic magnetic excitation in YIG first creates a spin current, the spin current is absorbed by Pt, and because Pt has strong spin–orbit coupling, part of the spin flow is converted into an orbital current in Pt. That orbital current then propagates into the top nonmagnetic layer, where IOHE converts it into a measurable charge current (Xu et al., 2023). The same logic underlies YIG/Pt(2)/X(5) surveys across 19 transition metals, where $X$ functions as the final orbital-to-charge converter and Pt acts as the spin–orbital converter and injector (Costa et al., 10 Jun 2025).

A second major platform uses direct orbital pumping into the detector layer. In $\mathbf{J}_L$0, ferromagnetic resonance drives coherent precession in CoFeB, which pumps orbital angular momentum into CuO. The resulting nonequilibrium orbital accumulation diffuses through the oxide, and CuO converts part of that orbital current into a transverse dc voltage $\mathbf{J}_L$1 through IOHE (Vojkovic et al., 2 Mar 2026). Related semiconductor structures such as YIG/Pt(2)/Ge($\mathbf{J}_L$2) and YIG/W(2)/Ge($\mathbf{J}_L$3) use Pt or W not as the final detector but as spin–orbit converters that inject a coupled spin-orbital current into Ge, where the orbital component is converted to charge (Santos et al., 2024).

Ultrafast platforms replace microwave or thermal pumping with femtosecond photoexcitation. In NM/Ni bilayers, ultrafast optical excitation generates a ballistic orbital current in Ni, which is injected into an adjacent nonmagnetic metal and converted into a transient charge current detected through terahertz emission (Xu et al., 2022). In Co/Ti, Co/Mn, Co/Ru, and Fe/Pt/W heterostructures, the emitted THz pulse serves as a time-domain proxy for orbital-to-charge conversion, with stack order and thickness controlling whether IOHE cooperates with or competes against ISHE (Wang et al., 2023, Chao et al., 4 Feb 2026).

An all-optical route has also been reported in bulk silicon. Using near-infrared pump–terahertz probe spectroscopy and time-resolved THz polarimetry on $\mathbf{J}_L$4-thick undoped Si, a long-lived helicity-dependent anomalous Hall conductivity was isolated from the field-induced circular photogalvanic effect. Because the response is robust against pump photon energy and silicon has very weak spin–orbit coupling, the results are interpreted as suggesting the emergence of IOHE in silicon through optically injected orbital angular momentum (Shirai et al., 22 Dec 2025).

3. Diffusion, thickness dependence, and quantitative transport

Thickness dependence is the main operational test used to separate direct IOHE from competing channels such as ISHE, current shunting, and sink effects. In YIG(40)/Pt(1.5)/Ru($\mathbf{J}_L$5), the longitudinal spin Seebeck current at $\mathbf{J}_L$6 K increases from about $\mathbf{J}_L$7 nA in YIG/Pt to about $\mathbf{J}_L$8 nA in YIG/Pt/Ru(4), while spin pumping produces a trilayer signal more than ten times larger than the Pt-only sample. As $\mathbf{J}_L$9 increases, both SSE and SP signals rise and then saturate at around $\hat{\mathbf{o}}_L$0 nm (Xu et al., 2023). The corresponding one-dimensional spin–orbit diffusion description resolves the total current into

$\hat{\mathbf{o}}_L$1

with the Ru ISHE term taken to be negligible because Ru has weak spin–orbit coupling. Within that model, $\hat{\mathbf{o}}_L$2 grows rapidly and becomes the dominant term, while the “orbital sink effect” in Ru makes only a partial contribution by suppressing orbital backflow into Pt (Xu et al., 2023).

CuO bilayers provide a more explicit orbital diffusion model. The orbital chemical potential obeys

$\hat{\mathbf{o}}_L$3

with interfacial current continuity at the FM|NM interface and zero orbital current at the outer CuO surface. The charge-current density is written as

$\hat{\mathbf{o}}_L$4

and thickness integration gives

$\hat{\mathbf{o}}_L$5

Experimentally, the CuO series spans $\hat{\mathbf{o}}_L$6 and $\hat{\mathbf{o}}_L$7 nm, with a very small mostly asymmetric signal at $\hat{\mathbf{o}}_L$8 nm, a visible symmetric component by $\hat{\mathbf{o}}_L$9–$\theta_{\mathrm{OH}}$0 nm, and dominant symmetric voltages from $\theta_{\mathrm{OH}}$1 to $\theta_{\mathrm{OH}}$2 nm. Fitting yields $\theta_{\mathrm{OH}}$3 and $\theta_{\mathrm{OH}}$4, and the reported converted charge currents are of order tens of nA for thicknesses from $\theta_{\mathrm{OH}}$5 to $\theta_{\mathrm{OH}}$6 nm (Vojkovic et al., 2 Mar 2026).

Ge establishes the opposite sign case. In YIG/Pt(2)/Ge($\theta_{\mathrm{OH}}$7), the effective Ge contribution is defined as

$\theta_{\mathrm{OH}}$8

and its thickness dependence is fit by

$\theta_{\mathrm{OH}}$9

As Ge is added, the signal drops and for $$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$0 nm nearly saturates to zero, indicating cancellation of the Pt baseline by a negative Ge orbital-to-charge contribution. The extracted diffusion length is about $$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$1 for spin-pumping ferromagnetic resonance and about $$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$2 for the longitudinal spin Seebeck effect (Santos et al., 2024).

Antiferromagnetic IrMn shows a related saturation behavior in YIG/Pt(2)/Ir$$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$3Mn$$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$4($$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$5), where the signal grows and then saturates with IrMn thickness. The fit yields an orbital/spin diffusion length of about $$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$6 nm, consistent with diffusive transport in the converting layer (Abrão et al., 2024).

4. Materials dependence, sign structure, and distinction from related effects

Sign is one of the most important discriminants in IOHE experiments. In the YIG/Pt/NM trilayer framework, Pt has positive spin Hall conductivity and acts as a positive spin-to-orbit converter, while Ru has a positive orbital Hall conductivity; the Ru-generated orbit-to-charge current therefore adds constructively to the Pt-generated signal (Xu et al., 2023). This sign logic also explains why replacing Ru by Ta or W still enhances SSE and SP signals even though Ta and W have spin Hall signs opposite to Pt: a pure ISHE picture would predict cancellation or suppression, whereas the reported enhancement is consistent with orbital Hall conductivities of the same sign as Pt in the authors’ discussion (Xu et al., 2023).

Ge is the clearest negative case. Its orbital Hall conductivity is reported as

$$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$7

while its spin Hall conductivity is tiny,

$$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$8

Correspondingly, direct YIG/Ge is tiny, with

$$\mathbf{J}_c = \theta_{\mathrm{OHE}}\,(\hat{\mathbf{o}}_L \times \mathbf{J}_L),$$9

yet orbital-to-charge conversion in hybrid Pt/Ge or W/Ge stacks is large enough to cancel the Pt reference signal (Santos et al., 2024). Ti is the opposite-sign metallic example: in YIG/Pt(2)/Ti($$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$0), SP-FMR and SSE signals increase with Ti thickness and then saturate, and a diffusive fit gives $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$1 nm and $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$2 (Santos et al., 7 Oct 2025).

The broadest materials comparison comes from the 19-transition-metal survey using YIG/X(5) and YIG/Pt(2)/X(5). There the total trilayer response is written as

$$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$3

with $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$4, and IOHE is extracted through subtraction. A representative example is Mo, for which the measured total in YIG/Pt(2)/Mo(5) is $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$5 nA, YIG/Pt(2) gives $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$6 nA, YIG/Mo(5) contributes $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$7 nA by ISHE, and the inferred IOHE is about $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$8 nA. The same survey reports IOHE above $$\theta_{\mathrm{OHE}} = \frac{2e}{\hbar}\frac{\sigma_{\mathrm{OHE}}}{\sigma_e},$$9 nA in Mo, about $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$0 nA in Zr, about $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$1 nA in Nb, strong positive IOHE in Ru, positive IOHE in Pd, negative IOHE around $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$2 nA in Ag, negative IOHE about $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$3 nA in Au, and essentially negligible spin-orbital conversion in Cu (Costa et al., 10 Jun 2025).

At the same time, several studies separate bulk IOHE from interfacial orbital-to-charge conversion. “Probing orbital currents through inverse orbital Hall and Rashba effects” distinguishes bulk IOHE from the inverse orbital Rashba effect (IORE), which is interfacial rather than bulk-like. In YIG/Pt(2)/CuOx(3), naturally oxidized Cu enhances the SP-FMR signal by about $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$4 and the SSE signal by about $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$5 relative to YIG/Pt(2), and that enhancement is attributed to interfacial orbital Rashba physics rather than bulk IOHE (Santos et al., 7 Oct 2025). Zr-based heterostructures make the same distinction from a different angle: in Zr/CFB, charge current is nearly independent of Zr thickness from $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$6 to $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$7 nm, and the paper concludes that the observed conversion is dominated by IOREE rather than bulk IOHE, even though IOHE is present conceptually (Kumar et al., 2024). A plausible implication is that reported “orbital-to-charge conversion” amplitudes are strongly conditioned by whether the active conversion is bulk, interfacial, or mixed.

5. Ultrafast and terahertz manifestations

Ultrafast THz emission experiments established IOHE on sub-picosecond time scales. In NM/Ni bilayers, femtosecond laser pulses generate an ultrafast orbital current in Ni, and Ta/Ni, Pt/Ni, and Cu/Ni all yield THz signals with the same polarity, opposite to the intrinsic THz emission from a Ni monolayer. Because Ta and Pt have opposite spin Hall angles and Cu has negligible spin Hall effect, that common polarity is inconsistent with an ISHE-only explanation and is taken as evidence that the nonmagnetic metal converts the injected orbital current into charge through IOHE (Xu et al., 2022). Pt-thickness studies in Ni(5 nm)/Pt show a maximum around $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$8 nm Pt, while Ta(4 nm)/Ni exhibits a threshold behavior in which the THz signal appears only above about $$\mathbf{J}_c = \frac{2e}{\hbar}\,\theta_{\mathrm{SH}}\,(\mathbf{J}_s \times \hat{\mathbf{s}}),$$9 nm Ni thickness (Xu et al., 2022).

Weak-SOC emitters broadened that picture. In Co(2 nm)/Ti($s$0–$s$1 nm) and Co(2 nm)/Mn($s$2–$s$3 nm), the observed THz emission is attributed mainly to $s$4 conversion because the spin Hall angles of Ti and Mn are tiny. The inserted W layer in Co(2 nm)/W(2 nm)/X, with $s$5Ti or Mn, provides an additional conversion channel and significantly enhances the orbitronic THz emission; the relative phase between ISHE in W and IOHE in Ti or Mn depends on layer order, so cooperation or competition can be engineered structurally (Wang et al., 2023).

Fe/Pt/W trilayers show a different ultrafast signature of IOHE. Fe/Pt and Fe/W bilayers behave as conventional spin-dominated emitters: THz amplitude reaches a maximum at about $s$6 nm heavy-metal thickness, then decreases sharply and becomes nearly zero at $s$7 nm, with almost no change in pulse arrival time and no systematic pulse broadening. By contrast, Fe(2 nm)/Pt(2 nm)/W($s$8) maintains detectable emission even at $s$9 nm, while the THz peak arrival time shifts later and the pulse broadens with increasing W thickness. The extracted effective transport velocity in the trilayer is about $L$0–$L$1 nm/fs, compared with about $L$2 nm/fs in Fe/W bilayers, and the authors interpret the trilayer response as cooperation between ISHE in Pt and IOHE in W (Zhou et al., 9 Feb 2026).

Co/Ru-based emitters provide a closely related but quantitatively distinct long-range orbital transport case. In Co/Ru, the THz signal peaks around $L$3–$L$4 nm Ru but remains detectable even at $L$5 nm, and time-domain measurements reveal delayed and broadened THz waveforms with increasing Ru thickness. Fitting yields an effective orbital velocity $L$6, an orbital flip time of about $L$7–$L$8 fs, and an estimated orbital diffusion length $L$9 nm. In Co/Pt/Ru, constructive interference between ISHE in Pt and IOHE in Ru enhances the THz output, whereas reversed stack structures such as Co/Ru/Pt and Ru/Co/Pt suppress it (Chao et al., 4 Feb 2026).

6. Anomalous forms, magnetic order, and theoretical extensions

Ordered systems support anomalous inverse orbital Hall responses that are not captured by the conventional scalar Hall-angle picture. In YIG/Pt(2)/Ir$X$0Mn$X$1, the in-plane spin-pumping signal nearly doubles relative to YIG/Pt(2), consistent with orbital transport into IrMn and its conversion by IOHE. The more distinctive observation is in out-of-plane geometry, where conventional ISHE should vanish because $X$2, yet a large signal remains. For YIG/IrMn(4) the current is about $X$3 nA, whereas YIG/Pt(2)/IrMn(4) gives about $X$4 nA, an enhancement by more than seven times, and the paper attributes that enhancement to the anomalous inverse orbital Hall effect (AIOHE) in antiferromagnetic IrMn (Abrão et al., 2024). To rationalize such data, the orbital Hall angle is proposed to be expanded to a rank-3 tensor, schematically

$X$5

with the Néel vector supplying the required symmetry breaking (Abrão et al., 2024).

An analogous ferromagnetic version has been reported in Fe films with strong uniaxial anisotropy. There the paper gives $X$6 and $X$7, argues that Fe is favorable for orbital conversion despite weak SOC, and finds that YIG/Pt(2)/Fe(12) produces a signal about $X$8 times that of YIG/Pt(2) alone. The spin-orbital diffusion length in Pt is taken to be about $X$9 nm, and out-of-plane anomalous conversion appears only when Fe is made strongly uniaxial by oblique deposition in a $\mathbf{J}_L$00 Oe magnetic field (Santos et al., 9 Jul 2025). In this symmetry-based description, the anomalous charge current is tied to order-parameter-dependent tensor components rather than to the ordinary antisymmetric Hall form.

Microscopic theory for confined geometries does not yet present a full reciprocal IOHE formalism, but it supplies several ingredients directly relevant to IOHE interpretation. In a strip geometry, the OHE-generated orbital Hall current must vanish at the edges, producing opposite-sign orbital accumulation described by

$\mathbf{J}_L$01

The same work finds a Dykonov–Perel-like scaling for the effective OAM decay rate, with the long-time decay rate inversely proportional to the scattering rate in the DP regime, and identifies nonlocal contributions driven by the $\mathbf{J}_L$02 harmonic and by spatially varying electric fields (Kiselev et al., 1 Jul 2025). Because that paper does not explicitly formulate IOHE, any reciprocal interpretation remains inferential; however, it strongly suggests that orbital-to-charge conversion in finite devices should depend on confinement, boundary conditions, and non-Ohmic flow as much as on bulk orbital Hall conductivity.

Taken together, these anomalous and geometry-sensitive results indicate that IOHE is not restricted to the simplest bulk, nonmagnetic cross-product form. Magnetic order, interfacial symmetry breaking, finite-size constraints, and ultrafast nonequilibrium transport can all reshape how orbital angular momentum is converted into charge, and in several experimentally relevant regimes the orbital channel becomes larger, longer-ranged, or of different sign than the corresponding spin channel (Abrão et al., 2024, Santos et al., 9 Jul 2025, Kiselev et al., 1 Jul 2025).