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Inverse Orbital Hall Effect Discovered from Light-Induced Terahertz Emission

Recent progress in orbitronics reveals the possibility of using orbital current as an information carrier. The interconversion between orbital currents and charge currents is crucial for orbital information processing. Although orbital currents can be created from charge current via the orbital Hall effect, the conversion from orbital current into charge current has not yet been discovered experimentally, which is due to the lack of a reliable orbital current source and disturbance of the omnipresent inverse spin Hall effect. In this study, we generate ultrafast pulses of orbital current in magnetic bilayers and trilayers from femtosecond laser pulses. We demonstrate that by injecting orbital current pulses into nonmagnetic metals, the inverse orbital Hall effect of the nonmagnetic layer induces a transient charge current and emits terahertz electromagnetic pulses. The nonmagnetic metal layer acts as a converter of the orbital current into the charge current. The discovery of the inverse orbital Hall effect enables detection of orbital currents and opens a new route for developing future orbitronic devices.

The primary operations in spintronic devices consist of creating and detecting transport of spin angular momentum through space, namely, spin currents 1,2 . Spin current can be created and detected through conversion between charge and spin current, which is pivotal for integrating spintronic devices into modern electronic technology 3 .
The conversion from a charge current to a spin current has been studied extensively in systems with strong spin-orbit coupling 4,5 . The most successful example of the conversion mechanism is the spin Hall effect (SHE) for nonmagnetic metals containing heavy atoms [6][7][8][9] . For two-dimensional electron gases at Rashba interfaces and the surfaces or interfaces of topological insulators, the spin-charge conversion is named the Rashba-Edelstein effect (REE) [10][11][12][13] . In ferromagnet (FM)/nonmagnet (NM) heterostructures, the spin currents induced by SHE or REE are strong enough to reverse the magnetization 3,14 . Therefore, both SHE and REE have attracted much attention due to their technological significance in developing future magnetic storage devices.
Their inverse effects, namely, inverse SHE (ISHE) 15 and inverse REE (IREE) 16 , convert a spin current into a charge current . These effects have been widely utilized for detecting spin currents generated by other stimuli, such as the heat current 17 , the charge current 8,9 , and the spinpumping technique [18][19][20] . In recent years, ISHE and IREE have also been utilized to generate ultrafast charge pulses and develop efficient broadband spintronic terahertz emitters [21][22][23][24] .
Recent studies have highlighted the importance of the orbital degree of freedom in condensed matter physics and kicked off the emergent research field of orbitronics 25 . Orbitronics exploits the transport of orbital angular momentum through space, namely, the orbital current, as an information carrier in solid-state devices. Similar to SHE, it has been theoretically predicted and experimentally shown that a charge current can be converted into an orbital current ( Figure 1a) via the orbital Hall effect (OHE) [26][27][28][29][30][31][32][33] .
The orbital current cannot exert torque directly on magnetization due to the lack of direct coupling between the orbital current and the magnetization. However, spin-orbit coupling can convert the orbital current into spin current , thereby generating torque on the magnetization.
The conversion efficiency depends on the strength of spin-orbit coupling. Several studies have identified the spin torques originating from OHE in heterostructures with elements of strong spinorbit coupling, such as Ni, Pt, and Gd 31,32 .
According to the Onsager reciprocal relation, the inverse effect of the OHE should convert an orbital current into a charge current. To date, there has been no report of the inverse effect of OHE.
This is due to the lack of a reliable orbital current source and the disturbance of the omnipresent inverse spin Hall effect. In this paper, we provide strong evidence for conversion from a current orbital into a charge current through free-space terahertz emission. The new effect, which is similar to the inverse spin Hall effect, is named the inverse orbital Hall effect (IOHE) 25 . Thanks to the induced charge current, the IOHE provides a feasible approach for electrical characterization of the orbital current.
We adopt the following strategy to demonstrate the IOHE. First, we prepare high-quality magnetic multilayers by magnetron sputtering. All of the samples are protected with a capping layer of MgO (2 nm)/Ta (2 nm), which is omitted for simplicity. As shown in the schematic in Fig. 1b, femtosecond laser pulses are used to induce spin currents , which are partially converted into orbital currents by spin-orbit coupling in the magnetic layer. and are then injected into the nonmagnetic layer. We studied the ultrafast conversion of orbital current into charge current by IOHE in the nonmagnetic layer and the resulting emission of terahertz electromagnetic waves sampled using homemade terahertz time-domain spectroscopy.

IOHE in Ni/Cu bilayers
In a FM/NM heterostructure, femtosecond laser pulses trigger ultrafast demagnetization of the FM, leading to ultrafast spin current pulses flowing in the perpendicular direction. As proposed previously 32 , spin-orbit coupling, which is critical for achieving conversion from the spin current into the orbital current, lays the foundation for laser-induced orbital current pulses. In metals with high spin-orbit coupling, the charge current is generated according to = − , where − refers to the spin-orbital conversion efficiency 31 .
In ferromagnetic transition metals such as Fe, Co, and Ni, spin-orbit coupling increases with the atomic number. Ni is expected to have a higher spin-orbit conversion efficiency − than the other ferromagnetic transition metals. When the Ni/NM bilayer is demagnetized optically, large orbital current pulses are generated through the ferromagnetic Ni layer 27,30 .  for Cu, indicating that IOHE is a bulk phenomenon similar to ISHE.

Separation of IOHE and ISHE contributions in samples with light and heavy nonmagnetic metals
Unfortunately, for most FM/NM bilayers, the IOHE is often covered by the omnipresent ISHE.
To distinguish the two contributions, we chose NMs with positive (Pt), negative (Ta, W), and vanishing (Cu) spin Hall angles. Figure   To further confirm the orbital origin in Ni-based bilayers, we analyzed the dependence on the Ni thickness for the Ni/W(4 nm) bilayer in Figure 3a, where ISHE and IOHE are expected to coexist.
For Ni (2 nm)/W (4 nm), the waveform polarity was the same as that of CoFeB/W, indicating that the ISHE contribution exceeded the IOHE contribution. As the Ni thickness was increased above 4 nm, the THz waveform polarity was reversed, indicating that the IOHE contribution exceeded the ISHE contribution for sufficiently thick Ni. Because the orbital current drives the IOHE contribution, our results showed that the orbital current increased with the Ni thickness and suggested that the conversion from spin to orbital currents in a magnetic layer increases with its thickness above a threshold thickness, approximately 3-4 nm for Ni. This is an interesting element for the theory of spin-to-orbit conversion in a magnetic material.

Generation of orbital current assisted by Pt in FM/Pt/NM multilayers
Among nonmagnetic metals, Pt has strong spin-orbit coupling and facilitates the conversion between spin current and orbital current. In the following, spin and orbital current pulses are generated through the ferromagnetic Ni layer, and an additional orbital current is created by spinto-orbit conversion in a thin Pt insertion layer between FM and NM 27,30 . In a Ni(5 nm)/Pt(4 nm) bilayer, we replaced a portion of the Pt with a Cu (2 nm) layer and obtained Ni (5 nm)/Pt (2 nm)/Cu (2 nm). We compared the THz waveforms of Ni (5 nm)/Pt (4 nm) and Ni (5 nm)/Pt (2 nm)/Cu (2 nm). (Figure 3b) Surprisingly, the two samples showed similar amplitudes, which cannot be explained in the second sample by the ISHE of the added Cu because the spin Hall angle of the Cu is negligible or by the SHE in the Pt layer, which is thinner than the spin diffusion length of Pt. We conclude that, despite a smaller ISHE in the thinner Pt in the second sample and the relatively small orbital Hall angle in Cu 34 , the signal was at the same level because the orbital current was enhanced by crossing Pt to give a larger IOHE in Cu that compensated for the decrease in the Pt ISHE.
To verify the role of the Pt insertion layer in generating the orbital current from spin current, Ni was replaced by CoFeB in the trilayers. Note that CoFeB cannot generate a noticeable orbital current, as shown in the image in Fig. 4a. We measured the THz signals for CoFeB (2 nm [35][36][37] . If the results of FM/Pt/Cu were from intermixing of the PtCu alloy phase at the Pt/Cu interface, we should expect the interfacial alloy to have a high spin Hall angle . However, the peak amplitudes of the THz waveforms from Cu (2 nm)/Pt (2 nm) and Pt (2 nm)/Cu (2 nm)/Pt (1 nm), which should contain similar or even more PtCu alloy due to two Pt/Cu interfaces, were much weaker than that of Pt (2 nm)/Cu (2 nm) (Figure 4c). We conclude that the ISHE contribution due to the PtCu alloy phase cannot explain the results from the trilayer. The interfacial alloy phase is negligible in this study.

Conclusion
Orbitronics is an emerging and promising field of research in which our work introduces a new experimental method based on light-induced terahertz emission. A light-induced orbital current generated from a magnetic layer is converted into a charge current by IOHE in a nonmagnetic layer (NM = Cu, Ta, W or Pt) and gives rise to terahertz emission. We find terahertz emission of the same polarity with Cu, W, T and Pt despite the opposite SHE of Ta and W with respect to Pt. Ni appears to be an efficient emitter of orbital current, and the terahertz emission generated by IOHE (orbit-tocharge conversion) in NM dominates the emission by ISHE (spin-to-charge conversion). CoFeB is much less efficient than Ni for generation of orbital current, and in CoFeB/NM bilayers, the terahertz signal is dominated by the ISHE conversion of the light-induced spin current and presents opposite polarities for Ta and W compared to Pt, as well as a negligible signal for Cu. However, we found that inserting a thin Pt layer between CoFeB and NM converted the light-induced spin current in CoFeB into an orbit current by spin-to-orbit conversion. This orbit current injected into NM generates significant terahertz emission by IOHE in NM and leads to significant IOHE in NM as Cu or Au. All of our results with Ni/NM and FM/Pt/NM cannot be explained within the framework of ISHE.
In summary, light-induced terahertz emission in orbitronics reveals how light-induced orbital currents can be efficiently converted by IOHE into charge currents detected by terahertz emission and opens a new route for developing future devices using the orbital degree of freedom.