Inverse orbital Hall effect and orbitronic terahertz emission observed in the materials with weak spin-orbit coupling

Materials with spin-orbit coupling support spin (S) and orbital (L) angular momentum channels that can generate transverse spin and orbital currents under an applied electric field. While strong-SOC nonmagnetic materials exhibit efficient charge–spin and spin–charge interconversion via the spin Hall effect (SHE) and inverse spin Hall effect (ISHE), the orbital contribution has been less explored. Recent theory and experiments have revealed that weak-SOC metals can host a sizable orbital Hall effect (OHE), enabling charge-to-orbital current conversion and subsequent orbital-to-spin transfer in adjacent ferromagnets, giving rise to orbital torques. However, the inverse orbital Hall effect (IOHE)—the conversion of orbital current to charge current—has remained elusive, as has leveraging IOHE for orbitronic terahertz (THz) emission. This study investigates whether IOHE occurs in weak-SOC metals (Ti, Mn), how it can be detected via ultrafast THz emission, and how device stacking can enhance and control orbitronic THz output.

Prior work established SHE/ISHE in heavy metals and topological materials, enabling spin–orbit torque devices and spintronic THz emitters. Theoretical predictions and experimental observations have identified large intrinsic OHE in weak-SOC metals (e.g., Ti, Mn), and demonstrated orbital-to-spin conversion and orbital torque in FM/NM bilayers. Long-range orbital transport has been reported in some metals, and ultrafast THz emission is a sensitive probe of spin/orbit-charge conversion. Nevertheless, direct observation of IOHE and its role in THz emission had not been conclusively shown, motivating the present study.

Sample preparation: Films were sputtered at room temperature on Al2O3 (0001) substrates in an ultrahigh vacuum magnetron sputtering system. An MgO (5 nm) capping layer prevented oxidation. Argon working pressure was 2.5 mTorr. Structures fabricated included: Co (2 nm)/X (4–60 or 4–20 nm) with X = Ti or Mn for IOHE studies; Co (2 nm)/W (2 nm)/X (4–100 nm) to test enhancement via strong-SOC W; Co (2 nm)/Ti (4–100 nm)/W (2 nm) and Ti (4–100 nm)/Co (2 nm)/W (2 nm) to probe cooperation/competition between IOHE and ISHE. Reference samples: Co (2)/W (2), Co (2)/Pt (2), Co (2)/MgO (5), Ti (4)/MgO (5), Mn (4)/MgO (5), MgO (5). THz emission spectroscopy: A home-built setup used a Ti:sapphire oscillator (800 nm center wavelength, 100 fs pulses, 2 W average power, 80 MHz repetition). The pump beam excited the sample at normal incidence; the emitted THz field was detected by electro-optic sampling using a 2 mm ZnTe (110) crystal and a probe beam. An in-plane magnetic field of 50 mT was applied. Measurements were at room temperature in dry air. Normalization of THz signals: The emitted THz field E_THz was normalized by the FM laser absorbance A_FM and the THz radiation impedance Z: E = E_THz/(A_FM Z). For bilayers, Z = Z0/(1+n+Z0(σ_FM t_FM + σ_NM t_NM)); for trilayers, Z = Z0/(1+n+Z0(σ_FM t_FM + σ_NM1 t_NM1 + σ_NM2 t_NM2)). The normalized signal scales with the spin/orbit-charge conversion: E = α(θ_SH J_S + θ_OH J_L). The THz peak-to-peak amplitude ΔP_K was used to compare efficiencies across samples. Experimental design logic: In Co/X (X=Ti, Mn), fs-laser excited Co generates J_S and J_L (via SOC). In X, J_S produces J_c via ISHE with θ_SH,Ti/Mn < 0 and very small magnitude, whereas J_L injected into X converts to J_c via IOHE with sign set by C_Co θ_OH,Ti/Mn (>0), allowing polarity analysis to distinguish IOHE from ISHE. Inserting W (strong SOC, large |θ_SH|, negative) between Co and X supplies an additional J_S (and effectively large J_L via SOC coupling), enabling enhanced J_c from both ISHE (in W) and IOHE (in X). Layer order and thickness variations were used to tune relative phases and magnitudes of IOHE vs ISHE contributions.

- IOHE observed in weak-SOC metals Ti and Mn via ultrafast THz emission from Co/X bilayers. Robust normalized THz signals appear for Co (2)/Ti (4–60 nm) and Co (2)/Mn (4–20 nm), indicating J_L → J_c conversion in X. - Polarity analysis discriminates IOHE from ISHE: Co/Ti and Co/Mn THz polarities are opposite to Co/W and identical to Co/Pt, inconsistent with ISHE given θ_SH,Ti and θ_SH,Mn are negative like W. Reported θ_SH values: θ_SH,Ti = −3.6×10^−4, θ_SH,Mn = −1.9×10^−3, θ_SH,W = −3.3×10^−1, θ_SH,Pt = +1.2×10^−1. Polarity matches the sign of C_Co θ_OH,Ti/Mn, evidencing IOHE-dominated emission. - Thickness dependence reveals orbital transport: In Co/Ti, normalized THz ΔP_K increases to a maximum at d_Ti = 40 nm and persists even at 60 nm, consistent with a long orbital diffusion length in Ti. In Co/Mn, signals are limited to 4–20 nm, indicating a shorter orbital diffusion length. - W insertion strongly enhances orbitronic THz emission: Co (2)/W (2)/X (4) with X = Ti or Mn exhibits ΔP_K increases more than an order of magnitude larger than Co/X and larger than Co/W. The enhancement arises from combined J_c,ISHE (in W) and J_c,IOHE (in X) with the same phase, as the W layer supplies a large angular momentum flow that is converted in X via IOHE. - Weak-SOC insertions (Ti or Mn) do not enhance: In Co/Ti/Mn and Co/Mn/Ti, ΔP_K differences relative to Co/Ti or Co/Mn are smaller than for Co/W/X, consistent with the absence of an additional strong-SOC source. - Cooperative and competitive regimes of IOHE and ISHE: • Co/Ti/W: J_c,ISHE (in W) and J_c,IOHE (in Ti) are 180° out of phase; ΔP_K varies with d_Ti and can reverse polarity. For sufficiently thick Ti (d_Ti > orbital spin diffusion blocking scale), J_S to W is suppressed; IOHE from Ti dominates, yielding small ΔP_K with opposite polarity. • Ti/Co/W: THz polarity matches Co/W. ΔP_K increases then decreases with d_Ti, peaking at d_Ti = 10 nm and exceeding Co/W, because J_c,ISHE (W) and J_c,IOHE (Ti) add in phase. - Control of orbitronic THz emission achieved via layer order and thickness, demonstrating tunable cooperation or competition between IOHE and ISHE contributions.

The experiments directly address whether orbital currents in weak-SOC metals can be converted into charge currents (IOHE) and detected via ultrafast THz emission. The observed THz signal polarities in Co/Ti and Co/Mn, opposite to Co/W and identical to Co/Pt despite Ti and Mn having negative θ_SH like W, rule out ISHE-dominant origins and support IOHE-dominated emission. The thickness dependence in Ti (maximum at 40 nm, persistence to 60 nm) indicates long-range orbital transport, whereas Mn exhibits shorter orbital diffusion, aligning with differing orbital relaxation in these metals. Introducing a strong-SOC W layer adjacent to the weak-SOC layer markedly boosts THz emission due to simultaneous ISHE in W and IOHE in Ti/Mn that add constructively, confirming that efficient spin–orbit interconversion pathways can amplify orbitronic emission. Conversely, when Ti or Mn is inserted without a strong-SOC source, no comparable enhancement occurs, indicating that large SOC is required to supply additional angular momentum flux. Layer order engineering (Co/Ti/W vs Ti/Co/W) tunes the phase relation between IOHE and ISHE, enabling constructive or destructive interference of the emitted THz field and offering a handle to maximize or modulate output. Collectively, these findings validate IOHE in weak-SOC metals, quantify its contribution to THz emission, and establish design principles for orbitronic THz emitters based on interplay between IOHE and ISHE.

This work demonstrates the inverse orbital Hall effect in weak-SOC metals Ti and Mn using ultrafast THz emission from Co/X bilayers, establishes that the THz signal polarity and thickness dependence are consistent with IOHE-dominated orbit-to-charge conversion, and reveals long orbital transport in Ti. Incorporating a thin W layer provides a strong-SOC source that significantly enhances orbitronic THz emission through cooperative IOHE (in Ti/Mn) and ISHE (in W). By engineering layer order and thickness, the phase and magnitude of IOHE and ISHE can be controlled to optimize THz output. These results illuminate IOHE mechanisms and provide guidelines for designing spin–orbitronic devices and high-performance THz emitters. Future work may quantify orbital Hall angles and diffusion lengths across materials, explore temperature and frequency responses, and extend designs to other weak-SOC metals and heterostructures.