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

Article 
ADS 

Google Scholar
 

Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1259 (2015).

Article 
ADS 

Google Scholar
 

Manchon, A. et al. Current-induced spin–orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 035004 (2019).

Article 
ADS 
MathSciNet 

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 
ADS 

Google Scholar
 

Go, D., Jo, D., Kim, C. & Lee, H. W. Intrinsic spin and orbital Hall effects from orbital texture. Phys. Rev. Lett. 121, 086602 (2018).

Article 
ADS 

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, 104410 (2022).


Google Scholar
 

Burgos Atencia, R., Agarwal, A. & Culcer, D. Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect. Adv. Phys. X 9, 2371972 (2024).


Google Scholar
 

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

Article 
ADS 

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 
ADS 

Google Scholar
 

Go, D. & Lee, H.-W. Orbital torque: torque generation by orbital current injection. Phys. Rev. Res. 2, 013177 (2020).

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

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
 

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).

Article 

Google Scholar
 

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

Article 

Google Scholar
 

Gao, T. et al. Control of dynamic orbital response in ferromagnets via crystal symmetry. Nat. Phys. 20, 1896–1903 (2024).

Article 

Google Scholar
 

Gupta, R. et al. Harnessing orbital Hall effect in spin–orbit torque MRAM. Nat. Commun. 16, 130 (2025).

Article 
ADS 

Google Scholar
 

Sala, G., Wang, H., Legrand, W. & Gambardella, P. Orbital Hanle magnetoresistance in a 3d transition metal. Phys. Rev. Lett. 131, 156703 (2023).

Article 
ADS 

Google Scholar
 

Ding, S., Noël, P., Krishnaswamy, G. K. & Gambardella, P. Unidirectional orbital magnetoresistance in light-metal–ferromagnet bilayers. Phys. Rev. Res. 4, 033167 (2022).

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Hayashi, H. & Ando, K. Orbital Hall magnetoresistance in Ni/Ti bilayers. Appl. Phys. Lett. 123, 172401 (2023).

Article 
ADS 

Google Scholar
 

Aguilar-Pujol, M. X. et al. Orbital Hall conductivity and orbital diffusion length of vanadium thin films by Hanle magnetoresistance. Newton 1, 10 (2025).

Article 

Google Scholar
 

Hayashi, H., Go, D., Haku, S., Mokrousov, Y. & Ando, K. Observation of orbital pumping. Nat. Electron. 7, 646–652 (2024).

Article 

Google Scholar
 

El Hamdi, A. et al. Observation of the orbital inverse Rashba–Edelstein effect. Nat. Phys. 19, 1855–1861 (2023).

Article 

Google Scholar
 

Wang, H. et al. Orbital pumping in ferrimagnetic insulators. Phys. Rev. Lett. 134, 126701 (2025).

Article 
ADS 

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 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Rang, M. & Kelly, P. J. Orbital Hall effect in transition metals from first-principles scattering calculations. Phys. Rev. B 111, 125121 (2025).

Article 
ADS 

Google Scholar
 

Mankovsky, S. & Ebert, H. Spin and orbital Hall effect in nonmagnetic transition metals: extrinsic versus intrinsic contributions. Phys. Rev. B 110, 184417 (2024).

Article 
ADS 

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 
ADS 
MathSciNet 

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 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Sohn, J., Lee, J. M. & Lee, H.-W. Dyakonov–Perel-like orbital and spin relaxations in centrosymmetric systems. Phys. Rev. Lett. 132, 246301 (2024).

Article 
ADS 
MathSciNet 

Google Scholar
 

Peng, S. et al. Unconventional scaling of the orbital Hall effect. Nat. Mater. 24, 1749–1755 (2025).

Article 

Google Scholar
 

Sun, H. & Vignale, G. Orbital magnetic moment dynamics and Hanle magnetoresistance in multilayered two-dimensional materials. Phys. Rev. B 111, L180408 (2025).

Article 
ADS 

Google Scholar
 

Vélez, S. et al. Hanle magnetoresistance in thin metal films with strong spin–orbit coupling. Phys. Rev. Lett. 116, 016603 (2016).

Article 
ADS 

Google Scholar
 

Raes, B. et al. Spin precession in anisotropic media. Phys. Rev. B 95, 085403 (2017).

Article 
ADS 

Google Scholar
 

Hobbs, D., Hafner, J. & Spišák, D. Understanding the complex metallic element Mn. I. Crystalline and noncollinear magnetic structure of α-Mn. Phys. Rev. B 68, 014407 (2003).

Article 
ADS 

Google Scholar
 

Mott, N. F. & Davis, E. A. Electronic Processes in Non-Crystalline Materials (Clarendon, 1979).

Ciuchi, S., Di Sante, D., Dobrosavljević, V. & Fratini, S. The origin of Mooij correlations in disordered metals. npj Quantum Mater. 3, 44 (2018).

Article 
ADS 

Google Scholar
 

Gunnarsson, O., Calandra, M. & Han, J. E. Colloquium: saturation of electrical resistivity. Rev. Mod. Phys. 75, 1085–1099 (2003).

Article 
ADS 

Google Scholar
 

Allen, P. B. & Chakraborty, B. Infrared and dc conductivity in metals with strong scattering: nonclassical behavior from a generalized Boltzmann equation containing band-mixing effects. Phys. Rev. B 23, 4815 (1981).

Article 
ADS 

Google Scholar
 

Hall, L. A. & Germann, F. E. E. Survey of Electrical Resistivity Measurements on 8 Additional Pure Metals in the Temperature Range 0 to 273 K (US National Bureau of Standards, 1970).

Liu, X. J., Liu, X. & Sinova, J. Scaling of the anomalous Hall effect in the insulating regime. Phys. Rev. B 84, 075210 (2011).


Google Scholar
 

Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

Article 
ADS 

Google Scholar
 

Bouma, D. S. et al. Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron–germanium. Phys. Rev. B 101, 014402 (2020).

Article 
ADS 

Google Scholar
 

Bass, J. & William, P. P.Jr 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 
ADS 

Google Scholar
 

Freeman, R., Zholud, A., Dun, Z., Zhou, H. & Urazhdin, S. Evidence for Dyakonov–Perel-like spin relaxation in Pt. Phys. Rev. Lett. 120, 067204 (2018).

Article 
ADS 

Google Scholar
 

Schirrmeister, F., Kahnt, H. & Feltz, A. Frequency-dependent conductivity and the time distribution function of hopping events. Phys. Status Solidi A 104, 523–530 (1987).


Google Scholar
 

Bobbert, P. A., Wagemans, W., van Oost, F. W. A., Koopmans, B. & Wohlgenannt, M. Theory for spin diffusion in disordered organic semiconductors. Phys. Rev. Lett. 102, 156604 (2009).

Article 
ADS 

Google Scholar
 

Baker, W. J., Keevers, T. L., Lupton, J. M., McCamey, D. R. & Boehme, C. Slow hopping and spin dephasing of Coulombically bound polaron pairs in an organic semiconductor at room temperature. Phys. Rev. Lett. 108, 267601 (2012).

Article 
ADS 

Google Scholar
 

Yu, Z. G. Spin–orbit coupling, spin relaxation and spin diffusion in organic solids. Phys. Rev. Lett. 106, 106602 (2011).

Article 
ADS 

Google Scholar
 

Harmon, N. J. & Flatté, M. E. Spin relaxation in materials lacking coherent charge transport. Phys. Rev. B 90, 115203 (2014).

Article 
ADS 

Google Scholar
 

Kubo, R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn 12, 570–586 (1957).

Article 
ADS 
MathSciNet 

Google Scholar
 

Wetzelaer, G. A. H., Koster, L. J. A. & Blom, P. W. M. Validity of the Einstein relation in disordered organic semiconductors. Phys. Rev. Lett. 107, 066605 (2011).

Article 
ADS 

Google Scholar
 

Coehoorn, R. & Bobbert, P. A. Effects of Gaussian disorder on charge carrier transport and recombination in organic semiconductors. Phys. Status Solidi A 211, 2265–2279 (2012).


Google Scholar
 

Kordt, P. et al. Parameter-free continuous drift–diffusion models of amorphous organic semiconductors. Phys. Chem. Chem. Phys. 17, 22778–22787 (2015).

Article 
ADS 

Google Scholar
 

Upreti, T. et al. Experimentally validated hopping-transport model for energetically disordered organic semiconductors. Phys. Rev. Appl. 12, 034039 (2019).

Article 

Google Scholar
 

Kimata, M., Nozaki, D., Niimi, Y., Tajima, H. & Otani, Y. Spin relaxation mechanism in a highly doped organic polymer film. Phys. Rev. B 91, 224422 (2015).

Article 
ADS 

Google Scholar
 

Yu, Z. G. Suppression of the Hanle effect in organic spintronic devices. Phys. Rev. Lett. 111, 016601 (2013).

Article 
ADS 

Google Scholar
 

Yu, Z. G. Spin–orbit coupling and its effects in organic solids. Phys. Rev. B 85, 115201 (2012).

Article 
ADS 

Google Scholar
 

Harmon, N. J. & Flatté, M. E. Distinguishing spin relaxation mechanisms in organic semiconductors. Phys. Rev. Lett. 110, 176602 (2013).

Article 
ADS 

Google Scholar