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., 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).
Go, D., Jo, D., Kim, C. & Lee, H.-W. Intrinsic spin and orbital Hall effects from orbital texture. Phys. Rev. Lett. 121, 086602 (2018).
Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).
Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).
Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213 (2015).
Kimura, T., Otani, Y., Sato, T., Takahashi, S. & Maekawa, S. Room-temperature reversible spin Hall effect. Phys. Rev. Lett. 98, 156601 (2007).
Zheng, Z. et al. Magnetization switching driven by current-induced torque from weakly spin–orbit coupled Zr. Phys. Rev. Res. 2, 013127 (2020).
Lee, D. et al. Orbital torque in magnetic bilayers. Nat. Commun. 12, 6710 (2021).
Lee, S. et al. Efficient conversion of orbital Hall current to spin current for spin–orbit torque switching. Commun. Phys. 4, 234 (2021).
Hayashi, H. et al. Observation of long-range orbital transport and giant orbital torque. Commun. Phys. 6, 32 (2023).
Go, D. & Lee, H.-W. Orbital torque: torque generation by orbital current injection. Phys. Rev. Res. 2, 013177 (2020).
Sunko, V. et al. Maximal Rashba-like spin splitting via kinetic-energy-coupled inversion-symmetry breaking. Nature 549, 492–496 (2017).
Park, S. R., Kim, C. H., Yu, J., Han, J. H. & Kim, C. Orbital-angular-momentum based origin of Rashba-type surface band splitting. Phys. Rev. Lett. 107, 156803 (2011).
Bhowal, S. & Vignale, G. Orbital Hall effect as an alternative to valley Hall effect in gapped graphene. Phys. Rev. B 103, 195309 (2021).
Cysne, T. P. et al. Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides. Phys. Rev. Lett. 126, 056601 (2021).
Zhang, L. & Niu, Q. Angular momentum of phonons and the Einstein–de Haas effect. Phys. Rev. Lett. 112, 085503 (2014).
Khomskii, D. I. & Streltsov, S. V. Orbital effects in solids: basics, recent progress, and opportunities. Chem. Rev. 121, 2992–3030 (2020).
Rückriegel, A. & Duine, R. A. Long-range phonon spin transport in ferromagnet–nonmagnetic insulator heterostructures. Phys. Rev. Lett. 124, 117201 (2020).
Neumann, R. R., Mook, A., Henk, J. & Mertig, I. Orbital magnetic moment of magnons. Phys. Rev. Lett. 125, 117209 (2020).
Zhang, L.-c. et al. Imprinting and driving electronic orbital magnetism using magnons. Commun. Phys. 3, 227 (2020).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Ghosh, S. & Grytsiuk, S. in Solid State Physics Vol. 71 (ed. Stamps, R. L.) 1–38 (Elsevier, 2020).
Go, D., Jo, D., Lee, H.-W., Kläui, M. & Mokrousov, Y. Orbitronics: orbital currents in solids. Europhys. Lett. 135, 37001 (2021).
Bhowal, S. & Satpathy, S. Intrinsic orbital moment and prediction of a large orbital Hall effect in two-dimensional transition metal dichalcogenides. Phys. Rev. B 101, 121112 (2020).
Phong, V. T. et al. Optically controlled orbitronics on a triangular lattice. Phys. Rev. Lett. 123, 236403 (2019).
Tokatly, I. Orbital momentum Hall effect in p-doped graphane. Phys. Rev. B 82, 161404 (2010).
Ding, S. et al. Harnessing orbital-to-spin conversion of interfacial orbital currents for efficient spin–orbit torques. Phys. Rev. Lett. 125, 177201 (2020).
Kim, J. et al. Nontrivial torque generation by orbital angular momentum injection in ferromagnetic-metal/Cu/Al2O3 trilayers. Phys. Rev. B 103, L020407 (2021).
Haney, P. M., Lee, H.-W., Lee, K.-J., Manchon, A. & Stiles, M. D. Current induced torques and interfacial spin–orbit coupling: semiclassical modeling. Phys. Rev. B 87, 174411 (2013).
Manchon, A. et al. Current-induced spin–orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 035004 (2019).
Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189–193 (2011).
Liu, L. et al. Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).
Sala, G. & Gambardella, P. Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures. Phys. Rev. Res. 4, 033037 (2022).
Go, D. et al. Theory of current-induced angular momentum transfer dynamics in spin–orbit coupled systems. Phys. Rev. Res. 2, 033401 (2020).
Xiao, J., Liu, Y. & Yan, B. in Memorial Volume for Shoucheng Zhang (eds Lian, B. et al.) 353–364 (World Scientific Publishing, 2021).
Stamm, C. et al. Magneto-optical detection of the spin Hall effect in Pt and W thin films. Phys. Rev. Lett. 119, 087203 (2017).
Mak, K. F., Xiao, D. & Shan, J. Light–valley interactions in 2D semiconductors. Nat. Photon. 12, 451–460 (2018).
Han, S., Lee, H.-W. & Kim, K.-W. Orbital dynamics in centrosymmetric systems. Phys. Rev. Lett. 128, 176601 (2022).
Saitoh, E. et al. Observation of orbital waves as elementary excitations in a solid. Nature 410, 180–183 (2001).
Chakraborty, J., Kumar, K., Ranjan, R., Chowdhury, S. G. & Singh, S. R. Thickness-dependent fcc–hcp phase transformation in polycrystalline titanium thin films. Acta Mater. 59, 2615–2623 (2011).
Marui, Y., Kawaguchi, M. & Hayashi, M. Optical detection of spin–orbit torque and current-induced heating. Appl. Phys. Express 11, 093001 (2018).
Fowles, G. R. Introduction to Modern Optics 2nd edn (Dover Publications, 1989).
You, C. Y. & Shin, S. C. Derivation of simplified analytic formulae for magneto‐optical Kerr effects. Appl. Phys. Lett. 69, 1315–1317 (1996).
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).
Salemi, L., Berritta, M., Nandy, A. K. & Oppeneer, P. M. Orbitally dominated Rashba–Edelstein effect in noncentrosymmetric antiferromagnets. Nat. Commun. 10, 5381 (2019).
Osgood Iii, R., Bader, S., Clemens, B. M., White, R. & Matsuyama, H. Second-order magneto-optic effects in anisotropic thin films. J. Magn. Magn. Mater. 182, 297–323 (1998).
Montazeri, M. et al. Magneto-optical investigation of spin–orbit torques in metallic and insulating magnetic heterostructures. Nat. Commun. 6, 8958 (2015).
Fan, X. et al. All-optical vector measurement of spin-orbit-induced torques using both polar and quadratic magneto-optic Kerr effects. Appl. Phys. Lett. 109, 122406 (2016).
Papaconstantopoulos, D. A. Handbook of the Band Structure of Elemental Solids (Springer, 2015).
Shanavas, K., Popović, Z. S. & Satpathy, S. Theoretical model for Rashba spin–orbit interaction in d electrons. Phys. Rev. B 90, 165108 (2014).
Tanaka, T. et al. Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals. Phys. Rev. B 77, 165117 (2008).
Jo, D., Go, D. & Lee, H.-W. Gigantic intrinsic orbital Hall effects in weakly spin–orbit coupled metals. Phys. Rev. B 98, 214405 (2018).
Shi, J., Zhang, P., Xiao, D. & Niu, Q. Proper definition of spin current in spin–orbit coupled systems. Phys. Rev. Lett. 96, 076604 (2006).