Orbital Pumping: Angular Momentum in Heterostructures

• Orbital pumping is the generation of orbital-angular momentum currents from dynamic magnetization, driven by ferromagnetic resonance, acoustic waves, and other perturbations.
• It enables the conversion of orbital currents into charge signals via inverse orbital Hall and interfacial Rashba–Edelstein effects, underscoring the impact of material interfaces and spin–orbit coupling.
• Quantitative studies with Ni/Ti, YIG-based heterostructures, and two-dimensional materials demonstrate orbital pumping's key role in reciprocal angular-momentum transfer for advanced spintronic and phononic applications.

Orbital pumping is the generation of an orbital-angular-momentum current from a time-dependent magnetic system into an adjacent material. In its standard form, a precessing ferromagnet under ferromagnetic resonance emits an orbital current into a neighboring nonmagnet, in direct analogy with spin pumping; more generally, the term now includes orbital-current injection driven by coherent and thermal magnons, surface acoustic waves, chiral phonons, and adiabatic orbital dynamics, together with reciprocal conversion processes such as the inverse orbital Hall effect and interfacial inverse orbital Rashba–Edelstein conversion (Hayashi et al., 2023, Ning et al., 2024, Wu et al., 4 Nov 2025).

1. Definition and conceptual scope

In the conventional spin-pumping picture, a time-dependent magnetization injects a pure spin current into an adjacent layer. Orbital pumping extends this logic to orbital angular momentum: a dynamic magnetization, or in some formulations a dynamic orbital moment, injects an orbital current $J_{\rm orb}$ or $J_L$ into a nonmagnetic conductor, semiconductor, or interface where it can be converted into charge current by the inverse orbital Hall effect (IOHE) or by an interfacial inverse orbital Rashba–Edelstein effect (IOREE) (Santos et al., 2023). In this sense, orbital pumping is routinely described as the orbital counterpart of spin pumping and as the Onsager-reciprocal phenomenon of orbital torque (Ning et al., 2024).

Several formulations distinguish orbital pumping from a mere copy of spin pumping. In the metallic-ferromagnet theory of Go et al., orbital pumping requires spin–orbit coupling in the ferromagnet because orbital angular momentum couples to the magnetization indirectly through $$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$, and the effect vanishes as $\lambda_{\rm SOC}\to0$ (Go et al., 2023). By contrast, Han et al. generalized adiabatic orbital pumping to include both orbital angular momentum (OAM) currents and orbital angular position (OAP) currents, the latter having no spin counterpart (Han et al., 2023). A further extension is evanescent orbital pumping, where coherent magnetization dynamics pumps orbital current into adjacent semiconductors through Zeeman coupling between the AC stray field and electron orbitals without relying on spin–orbit coupling (Cai et al., 8 Apr 2025).

The concept therefore spans several related but not identical objects: pumped orbital currents generated by magnetization dynamics in metallic bilayers, spin–orbital coupled currents whose orbital component survives in weak-SOC detectors, lattice-driven orbital currents generated by phonon–orbital coupling, and adiabatic orbital currents that include higher-rank orbital transport channels. This suggests that “orbital pumping” is best understood as a family of reciprocal angular-momentum-transfer phenomena rather than a single microscopic mechanism.

2. Microscopic and phenomenological frameworks

A common phenomenological starting point writes the pumped orbital current in the same kinematic form as spin pumping,

$$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$

with $g_{\uparrow\downarrow}^{\rm orb}$ the orbital-mixing conductance. For small-angle precession at angular frequency $\omega$, the cycle-averaged current becomes

$$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$

and orbital diffusion in the nonmagnet yields an effective thickness-dependent conductance $$g_{\uparrow\downarrow}^{\rm orb}(t)=g_\infty^{\rm orb}[1-\mathrm{sech}(t/\lambda_L)]$$ with orbital coherence length $\lambda_L$ (Zhang et al., 19 Nov 2025). In the earlier Ni/Ti orbital-pumping experiment, the instantaneous emitted orbital-current density was parameterized as

$J_L$0

where the $J_L$1 term provides the dc component at ferromagnetic resonance (Hayashi et al., 2023).

A more explicit reciprocity-based phenomenology treats orbital pumping as the inverse of orbital torque. In a bilayer $J_L$2, interfacial and bulk spin–orbital conversion enter through orbit–spin and spin–orbit mixing conductances. The pumped orbital current density is then

$J_L$3

where $J_L$4 is the spin–orbit mixing conductance related by Onsager reciprocity to the coefficient governing orbital torque (Ning et al., 2024). This formulation emphasizes that orbital pumping depends not only on orbital-current generation inside the ferromagnet but also on interfacial transmission, orbital backflow, and spin–orbit interconversion.

Microscopic linear-response theories resolve the origin of the pumping coefficients. In adiabatic perturbation theory for $J_L$5 ferromagnets,

$J_L$6

with $J_L$7 computed from Kubo–Bastin expressions involving torque operators and Green’s functions (Go et al., 2023). First-principles calculations for bcc Fe, hcp Co, and fcc Ni yield orbital-to-spin pumping ratios ranging from 5 to 15 percent, smallest in Fe and largest in Ni, and show that $J_L$8 scales linearly with spin–orbit coupling while spin pumping is essentially independent of SOC (Go et al., 2023).

A separate Keldysh–Wigner formulation for metallic heterostructures derives dc pumped spin and orbital densities from the antisymmetric part of the adiabatic response tensor and concludes that orbital pumping can be as significant as spin pumping when spin–orbit coupling is present in the ferromagnet (Pezo et al., 2024). In that framework orbital injection is favored in metals with $J_L$9 states close to the Fermi level, such as Ti, Pt, and W, and is quenched in materials lacking such states, such as Cu and Au (Pezo et al., 2024).

The most expansive theory is the adiabatic pumping formalism of Han et al., where the pumped particle current in orbital space decomposes into OAM and OAP sectors,

$$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$0

The corresponding OAM current contains the usual $$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$1 structure, while the OAP current generates sizable $$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$2 harmonics in the transverse voltage, a predicted signature absent in spin pumping (Han et al., 2023).

3. Driving mechanisms and source geometries

The experimentally dominant source geometry remains ferromagnetic resonance in metallic bilayers. In Ni/Ti, coherent precession of Ni pumps an orbital current into Ti that is detected through the IOHE, providing the first direct observation of orbital pumping (Hayashi et al., 2023). Related spin–orbital pumping experiments use YIG or Py as the resonant magnetic source and Pt, W, Ti, CuOx, Ge, Zr, or IrMn-containing stacks as transport and conversion layers (Santos et al., 2023).

Magnetic insulators extend the phenomenon beyond itinerant metallic ferromagnets. In Bi-doped yttrium iron garnet (BiYIG), both coherent and thermal magnons generate pure orbital currents detected in Cu$$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$3, Pt, Cr, and Cu devices; comparative measurements on YIG and BiYIG indicate that the origin of the orbital pumping in BiYIG/Cu$$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$4 is the dynamics of the orbital magnetization in the magnetic insulator (Wang et al., 13 Jun 2025). Thermal pumping also appears in YIG/Pt/Ge structures, where a vertical thermal gradient drives a spin–orbital current whose orbital component survives in Ge and is converted by a negative IOHE (Santos et al., 2024).

Lattice dynamics have introduced a distinct class of orbital pumping. In light-metal/ferromagnet bilayers on $$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$5 Y-cut LiNbO$$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$6, a surface acoustic wave (SAW) generates orbital current in the light metal through an acoustic orbital Hall effect, while SAW-driven ferromagnetic resonance pumps orbital angular momentum from the ferromagnet back into the nonmagnet; the pumped current is converted into a dc voltage by the inverse acoustic orbital Hall effect (Wu et al., 4 Nov 2025). The same theme is sharpened in chiral-phonon experiments, where field-even voltages track vorticity-sensitive orbital currents generated in the nonmagnet and field-odd voltages track magnetization-driven acoustic pumping from the ferromagnet (Rovirola et al., 9 Dec 2025).

Theoretical work has also pushed orbital pumping into regimes not mediated by conventional SOC. Evanescent orbital pumping uses the photonic spin of an AC stray field to define the orbital polarization injected into a semiconductor, while a transverse orbital Hall current emerges from orbital texture and does not suffer from orbital torque (Cai et al., 8 Apr 2025). In two-dimensional Janus rare-earth dichalcogenides, first-principles calculations predict strong in-plane orbital pumping currents $$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$7 driven by magnetization dynamics through inverse orbital torkance tensors, with nontrivial orbital polarization set by crystal symmetry and $$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$8-orbital physics (Zeer et al., 1 Feb 2025).

4. Detection, conversion channels, and experimental signatures

Electrical detection generally relies on converting the pumped orbital current into a transverse charge current. In spin–orbital pumping heterostructures with CuOx interfaces, the phenomenological detector response is

$$\hat H_{\rm SO}=\lambda \mathbf L\!\cdot\!\mathbf S$$9

so that bulk inverse spin Hall, bulk inverse orbital Hall, and interfacial inverse orbital Rashba–Edelstein contributions can all coexist and can add or subtract depending on sign conventions and interface chirality (Santos et al., 2023). In Ge detectors, by contrast, the defining relation is

$\lambda_{\rm SOC}\to0$0

and the observed signal reduction relative to Pt-only samples identifies a strong negative IOHE in Ge (Santos et al., 2024).

Because orbital pumping usually coexists with spin pumping and spin rectification, diagnostic symmetries are central. In Ni/Ti, the symmetric dc signal scales linearly with microwave power, inverts sign upon reversing $\lambda_{\rm SOC}\to0$1, and shows the angular dependence $\lambda_{\rm SOC}\to0$2, consistent with pumping followed by Hall-type conversion (Hayashi et al., 2023). In Nb-based bilayers, the separation of orbital pumping from spin pumping and spin rectification was achieved by exploiting opposite signs of the spin and orbital Hall angles in Nb, together with a decomposition

$\lambda_{\rm SOC}\to0$3

and by the different gap dependences $\lambda_{\rm SOC}\to0$4 and $\lambda_{\rm SOC}\to0$5 (Keller et al., 12 Feb 2025).

Acoustic experiments use additional symmetry filters. In SAW bilayers, the rectified acoustic orbital Hall voltage varies as $\lambda_{\rm SOC}\to0$6, and reversing the SAW propagation direction can shift $\lambda_{\rm SOC}\to0$7 by approximately $\lambda_{\rm SOC}\to0$8, reversing the sign of the four-fold signal; in chiral-phonon experiments, field-even voltages reverse with $\lambda_{\rm SOC}\to0$9, whereas field-odd voltages do not, thereby separating AOHE-like and acoustic-pumping-like channels (Wu et al., 4 Nov 2025, Rovirola et al., 9 Dec 2025).

A distinctive prediction of the OAM/OAP formulation is a sizable second-harmonic voltage. Because the OAP current contains $$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$0 pieces proportional to $$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$1, lock-in detection at $$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$2 provides, in that framework, an unambiguous marker of orbital pumping absent in ordinary spin pumping (Han et al., 2023).

Finally, reciprocity itself has been probed directly. In two-port scattering-parameter measurements on Ru/Ni, Ru/Pt/CoFeB, and Co/Cu/SiO$$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$3, the transmission coefficients satisfy

$$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$4

demonstrating reciprocal conversion between charge, orbital, and spin angular momenta in the same device platform (Erram et al., 10 Apr 2026).

5. Material platforms and quantitative trends

The present literature spans metallic ferromagnets, ferrimagnetic insulators, antiferromagnetic detectors, semiconductors, and acoustic heterostructures. Representative results are summarized below.

Platform	Representative result	Citation
Ni(5 nm)/Ti($$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$5)	First direct observation of orbital pumping; $$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$6; $$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$7 nm	(Hayashi et al., 2023)
YIG/Pt(2)/Ge($$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$8)	Negative IOHE in Ge; $$J_{\rm orb}(t)=\frac{\hbar}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\,\mathbf m\times\dot{\mathbf m},$$9 nm and $g_{\uparrow\downarrow}^{\rm orb}$0 nm	(Santos et al., 2024)
YIG/Pt(2)/IrMn(4)	Anomalous inverse orbital Hall signal $g_{\uparrow\downarrow}^{\rm orb}$1 nA; sevenfold enhancement $g_{\uparrow\downarrow}^{\rm orb}$2	(Abrão et al., 2024)
Si/Ti($g_{\uparrow\downarrow}^{\rm orb}$3)/Co(6 nm)	$g_{\uparrow\downarrow}^{\rm orb}$4; $g_{\uparrow\downarrow}^{\rm orb}$5 nm	(Zhang et al., 19 Nov 2025)
Ti/Ni SAW bilayer	$g_{\uparrow\downarrow}^{\rm orb}$6 at $g_{\uparrow\downarrow}^{\rm orb}$7 mT; $g_{\uparrow\downarrow}^{\rm orb}$8 nm; pumping length $g_{\uparrow\downarrow}^{\rm orb}$9 nm	(Wu et al., 4 Nov 2025)
BiYIG/Cu$\omega$0	Pure orbital-current detection; $\omega$1 nA/mW; Ar$\omega$2 etching increases $\omega$3 by $\omega$4	(Wang et al., 13 Jun 2025)
Zr/Pt/CFB	Enhanced effective spin–orbital Hall angle $\omega$5 versus $\omega$6 for Zr/CFB	(Kumar et al., 2024)

Several trends recur across these systems. First, strong orbital signatures are not confined to heavy metals. Ti, Cr, Zr, and Ge all appear as efficient orbital transport or conversion media despite weak or moderate SOC, because the relevant figures of merit are orbital Hall conductivity, phonon–orbital coupling, interfacial orbital transparency, and the presence of suitable $\omega$7- or $\omega$8-derived states near the Fermi level (Pezo et al., 2024). Second, Ni repeatedly appears as a favorable orbital source: first-principles calculations place the orbital-to-spin pumping ratio highest in Ni among Fe, Co, and Ni, and experiments report Ni/Ti signals much larger than Fe/Ti and Co/Ti (Go et al., 2023). Third, interfaces matter strongly: CuOx can enhance or suppress the measured charge current depending on the heavy metal, while BiYIG/Cu$\omega$9 and Ni/Cr or Ni/Ti data indicate that interfacial transparency can dominate overall pumping efficiency (Santos et al., 2023).

6. Controversies, unresolved issues, and future directions

The most immediate controversy concerns experimental identification. Keller et al. reported orbital-pumping-dominated positive voltages in Nb/Ni, distinguished from spin pumping by the sign difference between $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$0 and $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$1 and by angular and spatial diagnostics (Keller et al., 12 Feb 2025). By contrast, Bakare et al. found no detectable increase in Gilbert damping attributable to spin or orbital pumping from Ni to Nb in out-of-plane FMR, obtaining an upper limit $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$2 and concluding that angular-momentum pumping from Ni into Nb is at least an order of magnitude weaker than from FeV into Nb (Bakare et al., 13 Sep 2025). A plausible implication is that different observables—dc voltage versus damping enhancement—probe different combinations of interfacial transmission, orbital diffusion, and conversion efficiencies.

Several mechanism-level questions remain open. The Ni/Ti observation paper explicitly asked whether bulk IOHE or interface orbital Rashba–Edelstein conversion dominates orbital-to-charge conversion (Hayashi et al., 2023). The CuOx studies similarly show that interfacial orbital-charge conversion can reverse or enhance the net spin-pumping voltage depending on the heavy metal and the sign of the interfacial coefficient $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$3 (Santos et al., 2023). Antiferromagnetic systems introduce an additional complication: Abrão et al. argued that the orbital Hall angle must be generalized to a rank-3 tensor $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$4 to describe anomalous inverse orbital Hall effects controlled by the Néel vector (Abrão et al., 2024).

The scope of the phenomenon is also still expanding. Acoustic orbital pumping and chiral-phonon generation establish lattice dynamics as an efficient driver of orbital transport and suggest integrating phononic cavities, exploiting chiral phonons, and exploring other light-metal/ferromagnet pairs with larger $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$5 and $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$6 (Wu et al., 4 Nov 2025, Rovirola et al., 9 Dec 2025). Two-dimensional rare-earth dichalcogenides provide a first-principles route to in-plane orbital pumping dominated by $$\langle J_{\rm orb}\rangle=\frac{\hbar\omega}{4\pi}\,g_{\uparrow\downarrow}^{\rm orb}\sin^2\theta,$$7-orbital response (Zeer et al., 1 Feb 2025). Two-port measurements have already demonstrated reciprocity of charge–orbital–spin transport in a unified device geometry, which suggests a future experimental standard for comparing forward orbital torque and reciprocal orbital pumping on equal footing (Erram et al., 10 Apr 2026).

Taken together, the current record supports a technically precise but still evolving picture: orbital pumping is a reciprocal angular-momentum-transfer phenomenon whose magnitude can range from a minority correction to spin pumping to a comparable or even dominant channel, depending on SOC in the source magnet, orbital Hall conductivity and diffusion in the sink, interfacial orbital transparency, and whether the driving field is magnetic, thermal, or acoustic.