Inverse Orbital Hall Effect (iOHE)

• iOHE is the orbital analogue of the Hall effect where an injected orbital angular momentum current is converted into a transverse charge current via orbital Berry curvature and orbital textures.
• Experimental techniques such as ultrafast terahertz emission, spin pumping, and spin-Seebeck measurements quantify conversion efficiencies, orbital diffusion lengths, and material-dependent sign reversals.
• Diverse materials—including Ni-based heterostructures, transition metals, and semiconductors—demonstrate iOHE, highlighting its universality and potential for orbitronic device applications.

Inverse Orbital Hall Effect (iOHE), also written IOHE, is the Onsager-reciprocal conversion of an injected orbital angular-momentum current into a transverse charge current. In the direct orbital Hall effect, a longitudinal electric field produces a transverse flow of orbital angular momentum through orbital Berry curvature or orbital textures in Bloch bands; in the inverse process, a nonequilibrium orbital current or orbital polarization produces an electrical response, distinct from the spin-based inverse spin Hall effect (ISHE) (Xu et al., 2022, Xu et al., 2023). Since 2022, iOHE has been identified in ultrafast terahertz-emission experiments, spin-pumping and spin-Seebeck heterostructures, transition-metal oxides, ferromagnets, antiferromagnets, and semiconductors, with both conventional and anomalous forms now under active study (Xu et al., 2022, Abrão et al., 2024, Shirai et al., 22 Dec 2025).

1. Definition and formalism

The standard phenomenology of iOHE is the orbital analogue of ISHE. In the notation of Kang et al., an orbital-current density satisfies

$$j^{(L)}_\alpha(t)=\sigma^L_{\alpha\beta}E_\beta(t),$$

and inverse conversion in a nonmagnetic layer is written as

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$

or explicitly

$$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$

In vector form, related works write

$J_c=\theta_O\,J_o\times \hat s$

or

$$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$

depending on the adopted polarization convention (Xu et al., 2022, Vojkovic et al., 2 Mar 2026, Santos et al., 9 Jul 2025).

Across the literature, the orbital current is denoted either $J_o$ or $J_L$. The direct OHE is commonly attributed to orbital Berry curvature of $d$-electron or $p$-derived bands, and several works emphasize that it can remain large even when spin–orbit coupling is weak, because the underlying orbital texture is not reducible to spin Hall physics (Xu et al., 2023, Santos et al., 2024, Kumar et al., 2024). In this sense, iOHE is not merely a relabelled ISHE: the injected current carries orbital angular momentum rather than spin angular momentum, and the conversion efficiency is parameterized by an orbital Hall conductivity or orbital Hall angle rather than a spin Hall conductivity or spin Hall angle (Costa et al., 10 Jun 2025, Santos et al., 7 Oct 2025).

Several papers also formulate iOHE through orbital diffusion. In CuO, for example, the orbital chemical potential $\mu_L(z)$ obeys

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$0

and the induced voltage is

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$1

which rises in thin films and saturates for $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$2 (Vojkovic et al., 2 Mar 2026). In Ru-based terahertz emitters, the depth-dependent orbital current is modeled as

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$3

giving a total converted charge current

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$4

which directly links thickness-dependent terahertz amplitude to orbital transport length scales (Chao et al., 4 Feb 2026).

2. Foundational demonstration through light-induced terahertz emission

The first clear demonstration of iOHE in the present experimental literature was reported by Kang et al. using femtosecond-laser-induced terahertz emission from Ni-based heterostructures (Xu et al., 2022). In that work, Ni(10 nm) films and Ni(10 nm) capped by Cu, Ta, or Pt were excited by 800 nm pulses of $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$5 fs duration at $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$6 kHz. The central microscopic picture was that a time-dependent orbital polarization $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$7 in Ni launches a pulsed orbital current

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$8

into the adjacent nonmagnetic metal, which then converts part of that pulse into a transverse charge current radiating a broadband THz field (Xu et al., 2022).

The decisive observation was a sign reversal of the THz waveform when a Cu, Ta, or Pt cap layer was added to Ni. The bare Ni film emitted a THz burst whose polarity matched its anomalous Hall conductivity, whereas all three NM/Ni bilayers produced the same reversed polarity despite Cu’s near-zero spin Hall angle and Ta’s spin Hall angle opposite to Pt. This ruled out a purely ISHE-based interpretation and identified orbital-to-charge conversion in the capping layer as the dominant mechanism (Xu et al., 2022).

Thickness dependences further constrained the mechanism. In Ni(5 nm)/Pt($$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$9), the THz peak amplitude grew with Pt thickness, reached a maximum at $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$0 nm, and then decayed or saturated; the associated characteristic length was attributed to a ballistic propagation length of orbital angular momentum in Pt, $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$1 nm. No systematic temporal shift with $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$2 was observed, which argued against an interfacial Rashba–Edelstein origin and favored a bulk iOHE in Pt (Xu et al., 2022). In Ta(4 nm)/Ni($$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$3), THz emission appeared only for $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$4 nm, coinciding with the thickness needed to maintain ferromagnetic order under pump heating; this indicated that broken time-reversal symmetry in Ni was required to generate the pulsed orbital current (Xu et al., 2022).

The THz amplitude scaled linearly with pump fluence, consistent with a one-photon-driven process, and the measured spectra extended from $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$5 to $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$6 THz within the instrumental window (Xu et al., 2022). The paper therefore established both an ultrafast optical source of orbital current pulses and a direct THz-based detection scheme for their conversion into charge.

3. Spin pumping, Seebeck pumping, and diffusive orbital conversion

After the THz-emission discovery, a second major line of work used spin pumping and spin Seebeck geometries to inject orbital currents into nonmagnetic layers and detect the resulting dc voltages. In YIG/Pt/NM trilayers, the additional NM layer was shown to enhance the signal beyond what Pt alone produces, and quantitative thickness fits yielded orbital diffusion lengths and inverse orbital Hall angles for several transition metals (Xu et al., 2023).

For Ru, the spin-Seebeck signal in YIG(40)/Pt(1.5)/Ru($$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$7) rose rapidly up to $$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$8 nm and then saturated. Fitting gave

$$j^{(C)}_x(t)=\theta_{iOHE}\cdot j^{(L)}_y(t),\qquad j^{(C)}_y(t)=-\theta_{iOHE}\cdot j^{(L)}_x(t).$$9

The same framework produced

$J_c=\theta_O\,J_o\times \hat s$0

$J_c=\theta_O\,J_o\times \hat s$1

and

$J_c=\theta_O\,J_o\times \hat s$2

The work interpreted the comparable enhancement seen for Ru, Ta, W, and Cu as evidence that iOHE is a universal phenomenon in transition metals rather than a special property of one heavy metal (Xu et al., 2023).

An oxide realization was reported for Co$J_c=\theta_O\,J_o\times \hat s$3Fe$J_c=\theta_O\,J_o\times \hat s$4B$J_c=\theta_O\,J_o\times \hat s$5|CuO bilayers driven by ferromagnetic resonance. There the CuO thickness was varied from 2 to 30 nm, the symmetric voltage component $J_c=\theta_O\,J_o\times \hat s$6 grew rapidly from 2 nm and saturated above 10 nm, and the converted charge current reached $J_c=\theta_O\,J_o\times \hat s$7 nA around 5–15 nm. Fitting the orbital-diffusion model yielded an orbital diffusion length

$J_c=\theta_O\,J_o\times \hat s$8

and an orbital Hall angle

$J_c=\theta_O\,J_o\times \hat s$9

Broadband FMR also showed a small increase of the Gilbert damping $$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$0 from $$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$1 for 2 nm CuO to $$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$2 for 30 nm CuO, consistent with CuO acting as an orbital sink without strong spin absorption (Vojkovic et al., 2 Mar 2026).

A large comparative survey across 19 transition metals extended this SP-FMR strategy. In YIG/X(5) and YIG/Pt(2)/X(5), the orbital contribution was reported to overwhelmingly dominate over the spin response in many cases, clarifying the difficulty of disentangling ISHE and iOHE experimentally. The extracted orbital Hall conductivities often exceeded the spin Hall conductivities by large factors, especially in light 4d metals such as Mo, Zr, and Nb (Costa et al., 10 Jun 2025). This suggests that orbital pumping geometries are a sensitive route to iOHE precisely because the orbital channel can dominate even when the spin channel is small.

4. Materials dependence, sign, and conversion efficiency

A defining feature of iOHE is that its sign and magnitude are strongly material dependent. The sign need not track the sign of the spin Hall effect, and several experiments were designed specifically to exploit that distinction. In the original Ni-based THz work, Cu, Ta, and Pt all yielded the same THz-emission polarity in NM/Ni bilayers despite different, and in Ta opposite, spin Hall angles; the sign was therefore assigned to the bulk orbital Hall conductivity of the NM layer rather than to the spin Hall conductivity (Xu et al., 2022).

Negative iOHE was identified in Ge thin films using YIG/Pt(2)/Ge($$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$3) and YIG/W(2)/Ge($$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$4) heterostructures. In spin-pumping measurements, the Ge-induced reduction was $$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$5 nA at $$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$6 nm, corresponding to 60% of the 600 nA ISHE signal in YIG/Pt(2), and for $$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$7 nm the net signal tended to zero, implying exact cancellation of Pt ISHE by Ge IOHE. Fits of the subtracted orbital signal to

$$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$8

gave

$$J_c=\frac{2e}{\hbar}\theta_{ioh}[J_o\times \hat z],$$9

and, in LSSE measurements,

$J_o$0

The effective orbital conversion angle defined from the current ratio was $J_o$1 at 2 nm and tended to $J_o$2 for thick Ge. The same work also noted that pure spin pumping in YIG/Ge(8) produces a signal only $J_o$3 of that in YIG/Pt(8), emphasizing that Ge’s spin-to-charge conversion is negligible while its orbital-to-charge conversion is large (Santos et al., 2024).

A later study using YIG/Pt(2)/Ti($J_o$4) and YIG/Pt(2)/Ge($J_o$5) extracted

$J_o$6

and

$J_o$7

In the same work, CuO$J_o$8/Pt interfaces produced a giant inverse orbital Rashba effect rather than a bulk iOHE: YIG/Pt(2)/CuO$J_o$9(3) enhanced the SP-FMR signal by $J_L$0 and the SSE signal by $J_L$1 over YIG/Pt(2), whereas YIG/Ti/CuO$J_L$2 was unchanged (Santos et al., 7 Oct 2025). This is an important boundary condition on interpretation: not every orbital-to-charge signal is a bulk iOHE, and thickness independence or strong interface selectivity can instead indicate an inverse orbital Rashba–Edelstein mechanism.

Fe provides another example of strong orbital-to-charge conversion in a weak-SOC metal. In anisotropy-free YIG/Pt(2 nm)/Fe(12 nm), subtracting the known Pt ISHE contribution left an Fe-origin iOHE of $J_L$3 nA, an order of magnitude larger than the spin-only ISHE in YIG/Fe. The same study quoted for Fe

$J_L$4

and noted that orbital Hall angles in Fe can exceed a few $J_L$5, whereas spin Hall angles in 3d metals are typically a few $J_L$6 or less (Santos et al., 9 Jul 2025).

5. Anomalous and tensor-generalized forms

The simplest iOHE symmetry assumes that the orbital polarization is transverse to the orbital-current direction. Several papers show that this is incomplete in magnetic and antiferromagnetic media, where additional order-parameter-dependent terms allow charge conversion even in geometries where the conventional signal vanishes.

In Fe films with induced uniaxial anisotropy, the inverse orbital Hall conductivity was written in tensor form as

$J_L$7

with

$J_L$8

The first term corresponds to conventional iOHE, whereas the further terms generate an anomalous inverse orbital Hall effect (AIOHE) in the presence of ferromagnetic order $J_L$9 (Santos et al., 9 Jul 2025). Experimentally, YIG/Pt(2)/Fe(12) with no anisotropy showed the conventional in-plane symmetry $d$0 and no detectable out-of-plane voltage. When Fe was grown obliquely under a 500 Oe in-plane field, a strong uniaxial anisotropy appeared with easy axis along $d$1 and anisotropy field $d$2 Oe. Under these conditions, YIG/Pt(2)/Fe$d$3(12) and YIG/Pt(2)/Fe$d$4(12) displayed out-of-plane anomalous signals of $d$5 nA and $d$6 nA, respectively, with sign reversal between $d$7 and $d$8 (Santos et al., 9 Jul 2025).

An antiferromagnetic generalization was reported in YIG/Pt/Ir$d$9Mn$p$0, where the scalar orbital Hall angle was promoted to a rank-3 tensor

$p$1

The converted charge current then becomes

$p$2

In out-of-plane geometry, conventional ISHE and iOHE vanish because $p$3, so any residual signal must arise from the anomalous tensor terms. The measured peak current in YIG/Pt(2 nm)/IrMn(4 nm) reached $p$4 nA at $p$5 mW, roughly seven times larger than the conventional iOHE in YIG/IrMn alone ($p$6 nA), and changed sign when the sample was flipped from $p$7 to $p$8 (Abrão et al., 2024).

These results establish that iOHE is not restricted to the conventional antisymmetric Hall form. In ferromagnets and antiferromagnets, magnetic order permits anomalous orbital Hall tensors, and out-of-plane detection geometries that null ordinary inverse Hall effects can instead become selective probes of orbital-order-parameter coupling (Abrão et al., 2024, Santos et al., 9 Jul 2025).

6. Ultrafast orbital transport and terahertz-emitter architectures

A major application domain for iOHE is ultrafast THz emission, where the emitted field is proportional to the time derivative of the transient sheet current, $p$9 (Zhou et al., 9 Feb 2026). In this setting, iOHE supplies an orbital-to-charge conversion channel complementary to ISHE, and stack design can make the two channels cooperate or compete.

Early weak-SOC examples were Co/Ti and Co/Mn bilayers, where femtosecond laser demagnetization in Co generated a spin current that was converted partly into an orbital current and then into charge in Ti or Mn via iOHE. In Co(2)/Ti($\mu_L(z)$0) and Co(2)/Mn($\mu_L(z)$1), the THz peak amplitude rose with thickness and persisted to large $\mu_L(z)$2, with the maximum normalized amplitude occurring around $\mu_L(z)$3 nm for Ti. Inserting a 2 nm W layer boosted the THz amplitude by more than one order of magnitude in Co/W/Ti and Co/W/Mn, and reordering the layers changed whether ISHE and iOHE added constructively or destructively (Wang et al., 2023).

Direct evidence for long-range orbital transport was obtained in Co/Ru heterostructures. In Co/Ru bilayers, the THz signal persisted up to $\mu_L(z)$4 nm and reversed polarity with magnetic field or pump side, behavior incompatible with ISHE because Ru’s spin Hall angle is approximately zero. The time delay followed

$\mu_L(z)$5

yielding

$\mu_L(z)$6

while amplitude fits gave

$\mu_L(z)$7

Broadband FMR on the same platform gave an effective orbital diffusion length

$\mu_L(z)$8

reinforcing the interpretation of Ru as a strong angular-momentum sink (Chao et al., 4 Feb 2026). In Co/Pt/Ru trilayers, constructive interference between ISHE in Pt and IOHE in Ru boosted the THz field by more than 30% relative to either mechanism alone, while reversed stacking orders suppressed the output (Chao et al., 4 Feb 2026).

A related trilayer realization used Fe/Pt/W. Despite the absence of detectable orbital contributions in Fe/Pt and Fe/W bilayers, Fe/Pt/W showed long-distance THz signal persistence up to $\mu_L(z)$9 nm, linear delay accumulation

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$00

with

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$01

and amplitude decay consistent with an orbital diffusion length

$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$02

The pulse width broadened from about 0.6 ps at $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$03 nm to about 0.8 ps at 100 nm, and the peak-to-peak EO-sampled field reached roughly 500–1000 V/m, on the order of two to three times the Fe/Pt bilayer reference. The interpretation was a two-step spin$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$04orbital$$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$05charge mechanism, with Pt converting spin current from Fe into orbital current and W converting that orbital current into charge through IOHE (Zhou et al., 9 Feb 2026). This result is notable because elemental Fe is usually regarded as an orbital-quenched ferromagnet; the trilayer architecture showed that strong IOHE can nevertheless emerge once a suitable spin-to-orbital converter and orbital-transport layer are inserted (Zhou et al., 9 Feb 2026).

An all-optical semiconductor implementation was later reported in bulk Si using NIR pump–THz probe polarimetry. Circularly polarized 900–1100 nm excitation generated a helicity-dependent anomalous Hall conductivity of photocarriers, detected after separating it from the field-induced circular photogalvanic effect. At $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$06 ps, the real part of $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$07 around 1 THz was approximately $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$08, $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$09, and $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$10 for 900, 950, and 1000 nm pumps, respectively. Normalized by the photoexcited carrier density $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$11 for 900 nm pump, the conductivity per carrier was $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$12, with Hall angle $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$13. The signal flipped sign with helicity, remained essentially flat from 1.12 to 1.38 eV photon energy, and showed no decay out to 100 ps, implying $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$14 ps. Because spin polarization in Si is expected to drop sharply beyond 0.1 eV above the indirect gap, the photon-energy independence was interpreted as ruling out an ISHE origin and suggesting iOHE in Si (Shirai et al., 22 Dec 2025).

7. Relation to spin Hall physics, common ambiguities, and outlook

A recurring theme in the iOHE literature is that orbital and spin channels are difficult to disentangle experimentally. Several control strategies now recur across the field: comparison with reference bilayers, front-versus-back illumination, stack reversal, angular symmetry analysis, thickness dependences, and subtraction of known ISHE backgrounds (Xu et al., 2022, Xu et al., 2023, Costa et al., 10 Jun 2025). These controls are necessary because a measured transverse voltage can contain ISHE, iOHE, anomalous Hall, and inverse orbital Rashba–Edelstein contributions simultaneously.

One common misconception is that strong spin–orbit coupling is a prerequisite for a strong orbital response. The opposite trend is emphasized repeatedly in the cited works: Ti, Mn, Zr, Fe, Cu, CuO, Ge, and Si all show sizable orbital signatures despite weak or moderate SOC, while Pt, although central as a spin–orbit converter or injector, does not universally dominate the orbital channel under all measurement conditions (Wang et al., 2023, Kumar et al., 2024, Costa et al., 10 Jun 2025, Shirai et al., 22 Dec 2025). Another misconception is that iOHE is always positive. Ge provides a clear negative example, with polarity opposite to Pt ISHE and magnitude comparable to the Pt signal once an orbital current is injected (Santos et al., 2024, Santos et al., 7 Oct 2025).

The available quantitative ranges are broad but internally consistent across platforms. Reported orbital diffusion lengths span sub-nanometer to few-nanometer scales in Pt, Ru, Ta, W, Ti, Ge, and Cu when extracted from dc pumping geometries, yet reach 20–30 nm in W and about 20 nm from THz data and 46 nm from FMR in Ru-based ultrafast emitters (Xu et al., 2022, Xu et al., 2023, Santos et al., 7 Oct 2025, Chao et al., 4 Feb 2026, Zhou et al., 9 Feb 2026). Reported conversion efficiencies include $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$15 in CuO, $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$16, $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$17, $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$18, and $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$19 in Ru THz emitters (Vojkovic et al., 2 Mar 2026, Xu et al., 2023, Santos et al., 7 Oct 2025, Chao et al., 4 Feb 2026). These values indicate that orbital-to-charge conversion is not a marginal correction to spintronics, but often a quantitatively competitive or dominant channel.

The outlook proposed in these works is correspondingly broad. Suggested directions include optimizing $$j^{(C)}_\alpha(t)=\theta_{iOHE}\cdot j^{(L)}_\alpha(t),$$20 and emission bandwidth through better modeling of light-driven orbital dynamics, exploring other 3d ferromagnets and low-dimensional systems with strong orbital Berry curvature, integrating transition-metal oxides for all-oxide orbitronic devices, extending all-optical detection to other low-SOC semiconductors, and using interface engineering to control the balance between bulk iOHE and interfacial orbital Rashba conversion (Xu et al., 2022, Vojkovic et al., 2 Mar 2026, Xu et al., 2023, Shirai et al., 22 Dec 2025). Taken together, the present literature suggests that iOHE has evolved from a reciprocal analogue of OHE into a broader transport framework connecting orbital pumping, anomalous tensor responses, and ultrafast charge generation across metals, oxides, magnets, and semiconductors.