• Go, D. et al. Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp metals. Sci. Rep. 7, 46742 (2017).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Phong, V. T. et al. Optically controlled orbitronics on a triangular lattice. Phys. Rev. Lett. 123, 236403 (2019).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Orbitronics: the intrinsic orbital current in p-doped silicon. Phys. Rev. Lett. 95, 066601 (2005).

    Article 
    PubMed 

    Google Scholar
     

  • Go, D., Jo, D., Lee, H. W., Kläui, M. & Mokrousov, Y. Orbitronics: orbital currents in solids. EPL 135, 37001 (2021).

    Article 
    CAS 

    Google Scholar
     

  • Zutic, I., Fabian, J. & Das Sarma, S. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).

    Article 
    CAS 

    Google Scholar
     

  • Fert, A. Nobel lecture: origin, development, and future of spintronics. Rev. Mod. Phys. 80, 1517–1530 (2008).

    Article 
    CAS 

    Google Scholar
     

  • Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1260 (2015).

    Article 

    Google Scholar
     

  • Go, D., Jo, D., Kim, C. & Lee, H. W. Intrinsic spin and orbital Hall effects from orbital texture. Phys. Rev. Lett. 121, 86602 (2018).

    Article 
    CAS 

    Google Scholar
     

  • Kontani, H., Tanaka, T., Hirashima, D. S., Yamada, K. & Inoue, J. Giant orbital Hall effect in transition metals: origin of large spin and anomalous Hall effects. Phys. Rev. Lett. 102, 016601 (2009).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Salemi, L., Berritta, M., Nandy, A. K. & Oppeneer, P. M. Orbitally dominated Rashba–Edelstein effect in noncentrosymmetric antiferromagnets. Nat. Commun. 10, 5381 (2019).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Choi, Y. G. et al. Observation of the orbital Hall effect in a light metal Ti. Nature 619, 52–56 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Ding, S. et al. Observation of the orbital Rashba–Edelstein magnetoresistance. Phys. Rev. Lett. 128, 067201 (2022).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Ding, S. et al. Harnessing orbital-to-spin conversion of interfacial orbital currents for efficient spin–orbit torques. Phys. Rev. Lett. 125, 177201 (2020).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Liao, L. et al. Efficient orbital torque in polycrystalline ferromagnetic-metal/Ru/Al2O3 stacks: theory and experiment. Phys. Rev. B 105, 104434 (2022).

    Article 
    CAS 

    Google Scholar
     

  • Lyalin, I., Alikhah, S., Berritta, M., Oppeneer, P. M. & Kawakami, R. K. Magneto-optical detection of the orbital Hall effect in chromium. Phys. Rev. Lett. 131, 156702 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Bose, A. et al. Detection of long-range orbital-Hall torques. Phys. Rev. B 107, 134423 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Hayashi, H. et al. Observation of long-range orbital transport and giant orbital torque. Commun. Phys. 6, 32 (2023).

    Article 

    Google Scholar
     

  • Seifert, T. S. et al. Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten. Nat. Nanotechnol. 18, 1132–1138 (2023).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Mishra, S. S., Lourembam, J., Lin, D. J. X. & Singh, R. Active ballistic orbital transport in Ni/Pt heterostructure. Nat. Commun. 15, 4568 (2024).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Xu, Y. et al. Orbitronics: light-induced orbital currents in Ni studied by terahertz emission experiments. Nat. Commun. 15, 2043 (2024).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Xu, R. et al. Terahertz generation via the inverse orbital Rashba–Edelstein effect at the Ni/CuOx interface. Phys. Rev. Res. 7, L012042 (2025).

    Article 
    CAS 

    Google Scholar
     

  • Go, D. et al. Long-range orbital torque by momentum-space hotspots. Phys. Rev. Lett. 130, 246701 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Urazhdin, S. Symmetry constraints on orbital transport in solids. Phys. Rev. B 108, L180404 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Belashchenko, K. D. et al. Breakdown of the drift–diffusion model for transverse spin transport in a disordered Pt film. Phys. Rev. B 108, 144433 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Rang, M. & Kelly, P. J. Orbital relaxation length from first-principles scattering calculations. Phys. Rev. B 109, 214427 (2024).

    Article 
    CAS 

    Google Scholar
     

  • Zheng, Z. C. et al. Magnetization switching driven by current-induced torque from weakly spin–orbit coupled Zr. Phys. Rev. Res. 2, 013127 (2020).

    Article 
    CAS 

    Google Scholar
     

  • Boeglin, C. et al. Distinguishing the ultrafast dynamics of spin and orbital moments in solids. Nature 465, 458–461 (2010).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Idrobo, J. C. et al. Direct observation of nanometer-scale orbital angular momentum accumulation. Preprint at https://arxiv.org/abs/2403.09269 (2025).

  • Lee, S. et al. Efficient conversion of orbital Hall current to spin current for spin–orbit torque switching. Commun. Phys. 4, 234 (2021).

    Article 

    Google Scholar
     

  • Lee, D. et al. Orbital torque in magnetic bilayers. Nat. Commun. 12, 6710 (2021).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Salemi, L. & Oppeneer, P. M. First-principles theory of intrinsic spin and orbital Hall and Nernst effects in metallic monoatomic crystals. Phys. Rev. Mater. 6, 095001 (2022).

    Article 
    CAS 

    Google Scholar
     

  • Go, D., Lee, H. W., Oppeneer, P. M., Blügel, S. & Mokrousov, Y. First-principles calculation of orbital Hall effect by Wannier interpolation: role of orbital dependence of the anomalous position. Phys. Rev. B 109, 174435 (2024).

    Article 
    CAS 

    Google Scholar
     

  • Kampfrath, T. et al. Terahertz spin current pulses controlled by magnetic heterostructures. Nat. Nanotechnol. 8, 256–260 (2013).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Yang, D. et al. Powerful and tunable THz emitters based on the Fe/Pt magnetic heterostructure. Adv. Opt. Mater. 4, 1944–1949 (2016).

    Article 
    CAS 

    Google Scholar
     

  • Seifert, T. et al. Efficient metallic spintronic emitters of ultrabroadband terahertz radiation. Nat. Photon. 10, 483–488 (2016).

    Article 
    CAS 

    Google Scholar
     

  • Torosyan, G., Keller, S., Scheuer, L., Beigang, R. & Papaioannou, E. T. Optimized spintronic terahertz emitters based on epitaxial grown Fe/Pt layer structures. Sci. Rep. 8, 1311 (2018).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Jungfleisch, M. B. et al. Control of terahertz emission by ultrafast spin–charge current conversion at Rashba interfaces. Phys. Rev. Lett. 120, 207207 (2018).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Zhou, C. et al. Broadband terahertz generation via the interface inverse Rashba–Edelstein effect. Phys. Rev. Lett. 121, 086801 (2018).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Zhang, S. et al. Nonrelativistic and nonmagnetic terahertz-wave generation via ultrafast current control in anisotropic conductive heterostructures. Adv. Photon. 5, 056006 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Ning, X. et al. Orbital diffusion, polarization, and swapping in centrosymmetric metals. Phys. Rev. Lett. 134, 026303 (2025).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Zhang, Q. et al. Terahertz emission from anomalous Hall effect in a single-layer ferromagnet. Phys. Rev. Appl. 12, 054027 (2019).

    Article 
    CAS 

    Google Scholar
     

  • Zhang, W. et al. Ultrafast terahertz magnetometry. Nat. Commun. 11, 4247 (2020).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Beaurepaire, E. et al. Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses. Appl. Phys. Lett. 84, 3465–3467 (2004).

    Article 
    CAS 

    Google Scholar
     

  • Veneri, A., Rappoport, T. G. & Ferreira, A. Extrinsic orbital Hall effect: orbital skew scattering and crossover between diffusive and intrinsic orbital transport. Phys. Rev. Lett. 134, 136201 (2025).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Liu, H. & Culcer, D. Dominance of extrinsic scattering mechanisms in the orbital Hall effect: graphene, transition metal dichalcogenides, and topological antiferromagnets. Phys. Rev. Lett. 132, 186302 (2024).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Tang, P. & Bauer, G. E. W. Role of disorder in the intrinsic orbital Hall effect. Phys. Rev. Lett. 133, 186302 (2024).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Liu, Q. & Zhu, L. Absence of orbital current torque in Ta/ferromagnet bilayers. Nat. Commun. 16, 8660 (2025).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Dewhurst, J. K., Shallcross, S., Gross, E. K. U. & Sharma, S. Substrate-controlled ultrafast spin injection and demagnetization. Phys. Rev. Appl. 10, 044065 (2018).

    Article 
    CAS 

    Google Scholar
     

  • Feng, Z. et al. Anomalous Nernst effect induced terahertz emission in a single ferromagnetic film. Nano Lett. 23, 8171–8179 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Malinowski, G. et al. Control of speed and efficiency of ultrafast demagnetization by direct transfer of spin angular momentum. Nat. Phys. 4, 855–858 (2008).

    Article 
    CAS 

    Google Scholar
     

  • Bass, J. & Pratt, W. P. Spin-diffusion lengths in metals and alloys, and spin-flipping at metal/metal interfaces: an experimentalist’s critical review. J. Phys. Condens. Matter 19, 183201 (2007).

    Article 

    Google Scholar
     

  • Lu, W. T. & Yuan, Z. Spin accumulation and dissipation excited by an ultrafast laser pulse. Phys. Rev. B 104, 214404 (2021).

    Article 
    CAS 

    Google Scholar
     

  • Levchuk, A. et al. Pump wavelength-dependent terahertz spin-to-charge conversion in CoFeB/MgO Rashba interface. Appl. Phys. Lett. 123, 012407 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Tao, Z. Data for the publication “Terahertz Emission Spectroscopy Evidences Sub-Nanometer Orbital Diffusion Lengths in Heavy Metals” published in Nature Nanotechnology (2026). The datasets are provided for Figures 2- 5. Zenodo https://doi.org/10.5281/zenodo.18365981 (2026).