Manchon, A. et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 035004 (2019).
Shao, Q. et al. Roadmap of spin–orbit torques. IEEE Trans. Magn. 57, 1–39 (2021).
Liu, L. et al. Spin–torque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).
Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189–193 (2011).
Jo, D., Go, D., Choi, G.-M. & Lee, H.-W. Spintronics meets orbitronics: emergence of orbital angular momentum in solids. npj Spintronics 2, 19 (2024).
Wang, P. et al. Orbitronics: mechanisms, materials and devices. Adv. Electron. Mater. 11, 2400554 (2024).
Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Orbitronics: the intrinsic orbital current in p-doped silicon. Phys. Rev. Lett. 95, 066601 (2005).
Kontani, H., Tanaka, T., Hirashima, D. S., Yamada, K. & Inoue, J. Giant intrinsic spin and orbital Hall effects in Sr2MO4 (M = Ru, Rh, Mo). Phys. Rev. Lett. 100, 096601 (2008).
Go, D., Jo, D., Kim, C. & Lee, H.-W. Intrinsic spin and orbital Hall effects from orbital texture. Phys. Rev. Lett. 121, 086602 (2018).
Go, D. & Lee, H.-W. Orbital torque: torque generation by orbital current injection. Phys. Rev. Res. 2, 013177 (2020).
Jo, D., Go, D. & Lee, H.-W. Gigantic intrinsic orbital Hall effects in weakly spin–orbit coupled metals. Phys. Rev. B 98, 214405 (2018).
Lee, D. et al. Orbital torque in magnetic bilayers. Nat. Commun. 12, 6710 (2021).
Choi, Y.-G. et al. Observation of the orbital Hall effect in a light metal Ti. Nature 619, 52–56 (2023).
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).
Ding, S. et al. Observation of the orbital Rashba–Edelstein magnetoresistance. Phys. Rev. Lett. 128, 067201 (2022).
Sala, G., Wang, H., Legrand, W. & Gambardella, P. Orbital Hanle magnetoresistance in a 3d transition metal. Phys. Rev. Lett. 131, 156703 (2023).
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).
Yang, Y. et al. Orbital torque switching in perpendicularly magnetized materials. Nat. Commun. 15, 8645 (2024).
Gupta, R. et al. Harnessing orbital Hall effect in spin–orbit torque MRAM. Nat. Commun. 16, 130 (2025).
Tang, P. & Bauer, G. E. W. Role of disorder in the intrinsic orbital Hall effect. Phys. Rev. Lett. 133, 186302 (2024).
Canonico, L. M., Garcia, J. H. & Roche, S. Orbital Hall responses in disordered topological materials. Phys. Rev. B 110, L140201 (2024).
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).
Mankovsky, S. & Ebert, H. Spin and orbital Hall effect in nonmagnetic transition metals: extrinsic versus intrinsic contributions. Phys. Rev. B 110, 184417 (2024).
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).
Rang, M. & Kelly, P. J. Orbital Hall effect in transition metals from first-principles scattering calculations. Phys. Rev. B 111, 125121 (2025).
Sohn, J., Lee, J. M. & Lee, H.-W. Dyakonov–Perel-like orbital and spin relaxations in centrosymmetric systems. Phys. Rev. Lett. 132, 246301 (2024).
Kabanov, V. V. & Shumilin, A. V. Impact of the impurity symmetry on orbital momentum relaxation and orbital Hall effect studied by the quantum Boltzmann equation. Phys. Rev. B 110, 235161 (2024).
Go, D. et al. Long-range orbital torque by momentum-space hotspots. Phys. Rev. Lett. 130, 246701 (2023).
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).
Hayashi, H. et al. Observation of long-range orbital transport and giant orbital torque. Commun. Phys. 6, 32 (2023).
Gao, T. et al. Control of dynamic orbital response in ferromagnets via crystal symmetry. Nat. Phys. 20, 1896–1903 (2024).
Moriya, H. et al. Observation of long-range current-induced torque in Ni/Pt bilayers. Nano Lett. 24, 6459–6464 (2024).
Zhu, L., Ralph, D. C. & Buhrman, R. A. Maximizing spin–orbit torque generated by the spin Hall effect of Pt. Appl. Phys. Rev. 8, 031308 (2021).
Niimi, Y. et al. Extrinsic spin Hall effect induced by iridium impurities in copper. Phys. Rev. Lett. 106, 126601 (2011).
Niimi, Y. et al. Giant spin Hall effect induced by skew scattering from bismuth impurities inside thin film CuBi alloys. Phys. Rev. Lett. 109, 156602 (2012).
Moriya, H., Musha, A., Haku, S. & Ando, K. Observation of the crossover between metallic and insulating regimes of the spin Hall effect. Commun. Phys. 5, 12 (2022).
Xu, X. et al. Giant extrinsic spin Hall effect in platinum–titanium oxide nanocomposite films. Adv. Sci. 9, 2105726 (2022).
Wang, P. et al. Giant spin Hall effect and spin–orbit torques in 5d transition metal–aluminum alloys from extrinsic scattering. Adv. Mater. 34, 2109406 (2022).
Lin, W. et al. Electric field control of the magnetic Weyl fermion in an epitaxial SrRuO3 (111) thin film. Adv. Mater. 33, 2101316 (2021).
Li, S. et al. Room temperature spin–orbit torque efficiency and magnetization switching in SrRuO3-based heterostructures. Phys. Rev. Mater. 7, 024418 (2023).
Ou, Y. et al. Exceptionally high, strongly temperature dependent, spin Hall conductivity of SrRuO3. Nano Lett. 19, 3663–3670 (2019).
Zhou, J. et al. Modulation of spin–orbit torque from SrRuO3 by epitaxial‐strain‐induced octahedral rotation. Adv. Mater. 33, 2007114 (2021).
Lu, Z. et al. Heterogeneous integration of single‐crystal SrRuO3 films with large spin Hall conductivity on silicon for spintronic devices. Adv. Funct. Mater. https://doi.org/10.1002/adfm.202500755 (2025).
Lee, S. A. et al. Tuning electromagnetic properties of SrRuO3 epitaxial thin films via atomic control of cation vacancies. Sci. Rep. 7, 11583 (2017).
Chen, H. et al. Tuning stoichiometry for enhanced spin–charge interconversion in transition metal oxides. Adv. Electron. Mater. 10, 2300666 (2024).
Tanaka, T. et al. Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals. Phys. Rev. B 77, 165117 (2008).
Gupta, K., Wesselink, R. J. H., Liu, R., Yuan, Z. & Kelly, P. J. Disorder dependence of interface spin memory loss. Phys. Rev. Lett. 124, 087702 (2020).
Zhu, L., Ralph, D. C. & Buhrman, R. A. Spin–orbit torques in heavy-metal–ferromagnet bilayers with varying strengths of interfacial spin–orbit coupling. Phys. Rev. Lett. 122, 077201 (2019).
Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213 (2015).
Lee, K.-S., Lee, S.-W., Min, B.-C. & Lee, K.-J. Threshold current for switching of a perpendicular magnetic layer induced by spin Hall effect. Appl. Phys. Lett. 102, 112410 (2013).
Koepernik, K. & Eschrig, H. Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B 59, 1743 (1999).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
Koepernik, K., Janson, O., Sun, Y. & Van Den Brink, J. Symmetry-conserving maximally projected Wannier functions. Phys. Rev. B 107, 235135 (2023).
Pezo, A., García Ovalle, D. & Manchon, A. Orbital Hall effect in crystals: interatomic versus intra-atomic contributions. Phys. Rev. B 106, 104414 (2022).