Inverse Orbital Rashba Effect in Interfaces

• The inverse orbital Rashba effect is an orbital-to-charge conversion process at inversion-broken interfaces where nonequilibrium orbital angular momentum is transformed into a measurable charge current.
• It involves chiral orbital textures induced by symmetry breaking and orbital hybridization, with Berry-phase enhancements near avoided band crossings amplifying the response.
• Experimental studies in Pt/CuOx heterostructures reveal interface sensitivity and reciprocity asymmetry, offering insights for future orbitronic device engineering.

The inverse orbital Rashba effect (IORE) denotes an orbital-to-charge conversion process at an inversion-broken interface: a nonequilibrium orbital angular momentum (OAM) accumulation, or an interfacial orbital current arriving at such a boundary, is converted into a measurable charge current. In experimental orbitronics this reciprocal interconversion is often discussed as the inverse orbital Rashba-Edelstein effect (IOREE), especially in Pt/CuOx-based heterostructures where spin pumping or thermal spin injection is used to generate the incoming angular momentum flux (Santos et al., 7 Oct 2025, Santos et al., 2022). The subject sits at the intersection of orbital Rashba physics, interfacial symmetry breaking, multiorbital hybridization, and spin-orbital entanglement, and its interpretation depends strongly on whether one is discussing interfacial conversion, bulk orbital Hall conversion, or the multiorbital origin of Rashba textures themselves.

1. Definition, scope, and terminology

The orbital Rashba effect (ORE) is the orbital counterpart of the spin Rashba effect: it is the formation of chiral orbital-moment textures in momentum space for surface or interface states, and it can occur even without spin-orbit coupling (SOC). In the surface formulation based on $sp$ hybridization, broken inversion symmetry activates orbital hybridization and produces an effective Hamiltonian

$$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$

with $\hat{\mathbf{L}}$ the orbital angular momentum operator and $\alpha_{\mathrm{OR}}$ the orbital Rashba constant (Go et al., 2016). Within that framework, understanding ORE sets the stage for inverse manifestations, including orbital Edelstein responses and orbital-to-charge conversion at surfaces and interfaces.

The terminology is not fully uniform across the literature. In the Te/Au(100) interface study, the “inverse orbital Rashba effect” is discussed as a regime in which spin splitting results in orbital polarization, rather than OAM causing spin splitting; in that system the authors conclude that the atomic SOC is stronger than the inversion-symmetry-breaking energy scale, and that OAM and spin orientations are anti-parallel in the split branches, which they identify as a hallmark of the inverse ORE regime (Geldiyev et al., 2023). In a separate multiorbital band-structure usage, the “inverse orbital Rashba effect” refers to the mapping of spin structure back onto orbital texture: SOC couples spin to different orbital components, and the orbital makeup of the Bloch states determines the local spin helicity (Liu et al., 2016). In contemporary orbitronic transport experiments, by contrast, IORE usually refers more narrowly to interfacial orbital-to-charge conversion (Santos et al., 7 Oct 2025).

This terminological plurality is central to the field. A common misconception is to treat all “inverse orbital Rashba” usages as equivalent. They are related by the same underlying orbital texture physics, but they do not designate a single experimental observable.

2. Microscopic origin in orbital Rashba physics

The microscopic basis of IORE lies in the same orbital texture formation that underpins the ORE. In surface alloys such as BiAg$_2$, broken inversion symmetry activates $s$-$p_z$ hybridization through a surface potential gradient $\mathcal{E}_z$, and downfolding yields the orbital Rashba term. A key consequence is that orbital-coherent surface states acquire a $z$-directed electric polarization tied to the orbital chirality, so orbital texture is not merely a momentum-space pattern but an electrically polarizable interfacial degree of freedom (Go et al., 2016).

Berry-phase orbital magnetization is decisive for the magnitude of this response. In BiAg$_2$, the atom-centered approximation and the modern Berry-phase theory agree near $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$0, but near band crossings or gaps the Berry-phase theory predicts gigantic enhancements and sometimes singular behavior in the orbital moment, one order of magnitude larger than the atom-centered approximation. This establishes that interfacial orbital accumulation can be strongly amplified by wavefunction geometry near avoided crossings and topological features (Go et al., 2016).

At low-symmetry interfaces the ORE is intrinsically anisotropic. For a Te monolayer on Au(100), the $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$1 point has $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$2 symmetry, and the spin splitting is described by

$$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$3

The observed Rashba parameter is highly anisotropic, with $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$4 along $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$5 and $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$6 along $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$7. The accompanying tight-binding analysis shows that without inversion symmetry breaking, OAM is quenched and no spin splitting occurs; inversion symmetry breaking enables finite OAM, and SOC then converts that OAM texture into spin splitting (Geldiyev et al., 2023). This is the microscopic reason IORE is interface-sensitive: the orbital texture is created by symmetry breaking and hybridization at the boundary itself.

3. Reciprocal conversion and its distinction from adjacent effects

In the experimental transport formulation, IORE is the reciprocal of orbital Rashba accumulation: an interfacial OAM density is converted into a charge current. In YIG/Pt/NM heterostructures, ferromagnetic resonance spin pumping or the spin Seebeck effect injects a spin current from YIG into Pt; because Pt hosts spin-orbital intertwined states, part of that injected spin current is converted into an orbital current, which can propagate to the adjacent interface and accumulate there. At a Pt/CuOx boundary, where inversion symmetry is broken and orbital hybridization is strong, this interfacial OAM density is converted into a measurable charge signal and parameterized by an IORE efficiency $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$8 (Santos et al., 7 Oct 2025).

This interfacial conversion must be distinguished from the inverse orbital Hall effect (IOHE). IORE is an interface effect and is dominant in YIG/Pt/CuOx; IOHE is a bulk effect in which an orbital current in a metallic or semiconducting overlayer is converted into a transverse charge current throughout the material. The distinction is operational: in CuOx-capped Pt structures the enhancement is interfacial and insensitive to whether CuOx is above or below Pt, whereas in Ti and Ge the signals depend on thickness and can be analyzed using orbital diffusion lengths, indicating bulk orbital transport (Santos et al., 7 Oct 2025).

The Pt/CuOx experiments further sharpen the distinction between IORE and spin-only inverse conversion. In YIG/Pt/CuOx, a pronounced inverse spin Hall effect-like signal is observed, but only part of it is explained by the inverse spin-orbital Hall effect in Pt; the additional enhancement relative to YIG/Pt is attributed to the inverse orbital Rashba-Edelstein effect at the Pt/CuOx interface mediated by spin-orbital entangled states in Pt (Santos et al., 2022). A second misconception is therefore to identify every extra voltage in such trilayers with the inverse spin Hall effect. The control structures show that an interfacial orbital channel is required.

4. Experimental realizations and quantitative benchmarks

The most developed IORE platform is the YIG/Pt/CuOx family, but neighboring systems are essential because they separate interfacial and bulk orbital conversion channels.

Platform	Probe	Reported outcome
YIG/Pt/CuOx	SP-FMR, SSE	4–5× signal enhancement; $$H_{\mathrm{OR}}(\mathbf{k})=\frac{\alpha_{\mathrm{OR}}}{\hbar}\,\hat{\mathbf{L}}\cdot(\hat{\mathbf{z}}\times\mathbf{k}),$$9
YIG/Pt/Ti	SP-FMR, SSE	positive IOHE; $\hat{\mathbf{L}}$0, $\hat{\mathbf{L}}$1
YIG/Pt/Ge	SP-FMR, SSE	negative IOHE; $\hat{\mathbf{L}}$2, $\hat{\mathbf{L}}$3
Pt/CuOx magnon devices	nonlocal $\hat{\mathbf{L}}$4	$\hat{\mathbf{L}}$5; $\hat{\mathbf{L}}$6

In YIG/Pt(2)/CuOx(3), spin-pumping ferromagnetic resonance and spin Seebeck measurements show a $\hat{\mathbf{L}}$7 enhancement relative to YIG/Pt(2), and the IORE efficiency parameter is estimated as $\hat{\mathbf{L}}$8 for Pt/CuOx. By contrast, YIG/Pt(2)/Ti and YIG/Pt(2)/Ge display thickness-dependent signals identified with IOHE: Ti yields positive signals and a positive orbital Hall angle, while Ge yields negative signals and sign reversal, consistent with a negative orbital Hall angle (Santos et al., 7 Oct 2025).

The earlier YIG(40 nm)/Pt($\hat{\mathbf{L}}$9)/CuOx(3 nm) study provided the first clear experimental evidence for the reciprocal process of orbital torque. The spin-pumping signal increases by a factor of $\alpha_{\mathrm{OR}}$0 compared with YIG/Pt, and the longitudinal spin Seebeck signal increases by a factor of $\alpha_{\mathrm{OR}}$1. The enhancement peaks for $\alpha_{\mathrm{OR}}$2 and disappears for large $\alpha_{\mathrm{OR}}$3, where the signal coincides with YIG/Pt, demonstrating that the extra contribution is interfacial rather than bulk. Substituting unoxidized Cu with MgO capping removes the enhancement, while AlOx also yields enhancement, reinforcing the role of interfacial inversion-symmetry breaking (Santos et al., 2022).

A complementary nonlocal magnon-transport realization uses Pt/CuOx electrodes on YIG. For $\alpha_{\mathrm{OR}}$4, the first-harmonic nonlocal signal increases from $\alpha_{\mathrm{OR}}$5 in Pt to $\alpha_{\mathrm{OR}}$6 in Pt/CuOx, and the second-harmonic response increases from $\alpha_{\mathrm{OR}}$7 to $\alpha_{\mathrm{OR}}$8. These measurements establish that Pt/CuOx interfaces enhance both magnon injection and detection through orbital Rashba-Edelstein conversion (Mendoza-Rodarte et al., 2024).

5. Reciprocity, efficiency asymmetry, and what is actually measured

A central result of the nonlocal Pt/CuOx magnon devices is that direct and inverse orbital Rashba-Edelstein efficiencies are not equal. Using the normalized responses

$\alpha_{\mathrm{OR}}$9

and comparing Pt/CuOx with Pt-only devices, the reported values at $_2$0 are $_2$1, $_2$2, and

$_2$3

The consequence is

$_2$4

so the inverse OREE efficiency is larger than the direct OREE efficiency by a factor of $_2$5 (Mendoza-Rodarte et al., 2024).

This observation matters because the spin Hall effect is commonly treated as symmetric between direct and inverse processes, whereas the Pt/CuOx data indicate a disparity in orbital Rashba-Edelstein conversion. The proposed interpretation is analogous to prior work on the Rashba-Edelstein effect, where asymmetry was attributed to different scattering times in interfacial and bulk states (Mendoza-Rodarte et al., 2024). A plausible implication is that IORE cannot be parameterized solely by the same effective length that describes charge-to-orbital conversion, even in a nominally reciprocal geometry.

What is measured is also not a pure orbital observable in the strict microscopic sense. In Pt-based structures the injected current is described as spin-orbital entangled, and the experimentally detected voltage contains contributions from the inverse spin-orbital Hall effect in Pt together with the interfacial IORE at Pt/CuOx. The empirical separation relies on thickness dependence, oxide controls, and the absence of analogous enhancement in Ti/CuOx structures (Santos et al., 2022).

6. Symmetry control, anisotropy, and emerging platforms

Low symmetry and field control strongly modulate orbital Rashba conversion. The Te/Au(100) interface shows that in-plane square-lattice symmetry and broken inversion symmetry enforce a remarkably anisotropic ORE, which then strongly modulates Rashba spin splitting. The direction with larger OAM, $_2$6, has the larger Rashba splitting, while the orthogonal direction $_2$7 has reduced OAM and smaller splitting (Geldiyev et al., 2023). This establishes orbital symmetry engineering as a direct route to tuning interfacial angular-momentum conversion.

The LaAlO$_2$8/SrTiO$_2$9 interface adds an all-electrical perspective. There, broken rotation and inversion symmetries allow an anisotropic linear-in-momentum orbital Rashba coupling that produces conductivity anisotropy at zero magnetic field. Scanning SQUID current imaging and global transport measurements show that the onset of this conductivity anisotropy coincides with the onset of the non-linear Hall effect at $s$0, indicating a common origin in momentum-space orbital textures. The work explicitly frames this as a foundation for all-electrical probing of orbital currents in two-dimensional systems (Persky et al., 13 Feb 2025).

Ferroelectric heterostructures extend the control space further. In PtSe$s$1/MoSe$s$2/LiNbO$s$3, first-principles calculations quantify both spin and orbital Rashba responses and their inverse counterparts under ferroelectric polarization reversal. In relation to CoFeB/PtSe$s$4/MoSe$s$5/LiNbO$s$6-based heterostructures investigated by S. Massabeau et al., the calculations show that reversing the LiNbO$s$7 polarization reverses the sign of both spin and orbital Rashba responses; the spin contribution shows $s$8 modulation in the THz signal, while the orbital contribution can change by up to $s$9 across different energies. The effective Rashba coefficient is reported as $p_z$0, and the orbital channel can match or exceed the spin channel in polarization dependence (Pezo et al., 19 Sep 2025).

Taken together, these results define IORE as a symmetry-governed, interface-centered orbital-to-charge conversion phenomenon whose magnitude depends on chiral OAM formation, Berry-phase enhancement, spin-orbital entanglement, and the balance between interfacial and bulk orbital transport. Its present experimental identity is clearest in Pt/CuOx trilayers, but its broader significance lies in providing a route to detect, quantify, and engineer orbital currents through purely electrical, magnonic, and ultrafast-optical observables.