Abstract
The orbital Hall effect1 refers to the generation of electron orbital angular momentum flow transverse to an external electric field. Contrary to the common belief that the orbital angular momentum is quenched in solids, theoretical studies2,3 predict that the orbital Hall effect can be strong and is a fundamental origin of the spin Hall effect4,5,6,7 in many transition metals. Despite the growing circumstantial evidence8,9,10,11, its direct detection remains elusive. Here we report the magneto-optical observation of the orbital Hall effect in the light metal titanium (Ti). The Kerr rotation by the orbital magnetic moment accumulated at Ti surfaces owing to the orbital Hall current is measured, and the result agrees with theoretical calculations semi-quantitatively and is supported by the orbital torque12 measurement in Ti-based magnetic heterostructures. This result confirms the orbital Hall effect and indicates that the orbital angular momentum is an important dynamic degree of freedom in solids. Moreover, this calls for renewed studies of the orbital effect on other degrees of freedom such as spin2,3,13,14, valley15,16, phonon17,18,19 and magnon20,21 dynamics.
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References
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).
Acknowledgements
H.-W.L. acknowledges P. Haney for the discussion on the crystal field effect on orbital relaxation. D.J. was supported by the Global PhD Fellowship Program by National Research Foundation of Korea (grant no. 2018H1A2A1060270). D.J., K.-H. Kim and H.-W.L. were supported by the Samsung Science and Technology Foundation (BA-1501-51). Y.-G.C., K.-H. Ko and G.-M.C. were supported by the National Research Foundation of Korea (2022R1A2C1006504). H.G.P. and B.-C.M. were supported by the KIST institutional programme and the National Research Foundation of Korea (NRF) programmes (2022M3I7A2079267 and 2020M3F3A2A01081635). C.K. was supported by the Institute for Basic Science in Korea (Grant No. IBS-R009-G2, IBS-R009-D1) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A3B1077234). Device fabrication was supported in part by Advanced Facility Center for Quantum Technology at Sungkyunkwan University.
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Y.-G.C., D.J. and K.-H. Ko contributed equally to this work. C.K. initiated the project, and H.-W.L. and G.-M.C. supervised the study. Y.-G.C. performed the measurement and analysis for the orbital accumulation in Ti and Pt films. K.-H. Ko performed the measurement and analysis of the orbital torque in the Ti/Ni bilayer. D.J. and D.G. prepared a theoretical formulation of the MOKE analysis. D.J. carried out the tight-binding calculations of the spin and orbital Hall conductivities of bulk Ti, analysed the MOKE signals theoretically and calculated the current-induced torque in the Ti/Ni bilayer. K.-H. Kim calculated the effective orbital Hall conductivity of Ti. K.-H. Ko, Y.-G.C. H.G.P. and B.-C.M. fabricated samples and characterized their optical, electrical and magnetic properties.
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Extended data figures and tables
Extended Data Fig. 1 The crystalline structure of Ti films.
XRD θ-2θ scan of Ti films with the thickness of 27 (black line), 45 (red line), 63 (blue line), and 90 nm (green line). The XRD peaks at 38.4o and 44.3o indicate the (111) and (200) peaks of the face-centered-cubic phase of Ti, respectively.
Extended Data Fig. 2 Schematic illustration of magneto-optical Kerr effect setup with electrical current injection.
Ti:sapphire laser generates a probing beam, and its direction is indicated with red triangle arrows. The probing beam is linearly polarized with the polarization direction parallel to the optical table by passing through a polarizer (Pol). Two dichroic mirrors (DM) are used for optical imaging with a CCD camera, and they are removed. The probing beam is reflected by a 5:5 beam splitter (BS) and enters an objective lens (Obj.). The beam is shifted for the off-centered incidence on the objective lens pupil to make the grazing angle of 25o with s-polarization. The reflected probing beam is collected again by the objective lens, and it is focused by another lens onto the balanced detector. Before the detector, the beam passes through a quarter-wave plate (QWP, only for the imaginary part measurement), a half-wave plate (HWP), and a Wollaston prism (WP). Polarization rotation is measured in terms of the subtracted voltage output at a pair of Si detectors, and the signal is sent to the lock-in amplifier. A current source generates an AC electric current, and the polarity of the AC current is controlled automatically by a computer-controlled relay switch. Reference signal from the current source is sent to the lock-in amplifier.
Extended Data Fig. 3 The decomposition of longitudinal and polar components of Kerr signals.
a, Probing light incidence angle dependence of the LMOKE signals of the Ti 90 nm sample. \({\theta }_{{\rm{K}}}^{{\rm{pos}}({\rm{neg}})}\) denoted by black squares (red circles) indicates the Kerr rotation with positive (negative) incidence angle. b, Decomposed polar (red circles) and longitudinal (black circles) components of the LMOKE signals. Red and black circle data denote \(({\theta }_{{\rm{K}}}^{{\rm{pos}}}+{\theta }_{{\rm{K}}}^{{\rm{neg}}})/2\) and \(({\theta }_{{\rm{K}}}^{{\rm{pos}}}-{\theta }_{{\rm{K}}}^{{\rm{neg}}})/2\), respectively. Red and black solid lines are guidelines for Oersted field and flat signal distributions, respectively.
Extended Data Fig. 4 Fabrication process of the sap/Ti (90 nm)/Si3N4 (55 nm)/Ti (90 nm)/Si3N4 (5 nm) device.
a, sapphire substrate. b, Sputtering a Ti (90 nm)/Si3N4 (5 nm) film and making a bar pattern with a photolithography process. c, Sputtering of a Si3N4 (50 nm) film to block the orbital current. d, Sputtering second Ti (90 nm) film and making a square island with e-beam lithography. After Ti deposition, Si3N4 (5 nm) is also sputtered on the device to prevent oxidation of the top Ti layer. e, Side view of the fabricated device and measurement scheme. The red and blue arrows indicate the orbital angular momentum of electrons. The black circle arrow is the Oersted field due to \({j}_{{\rm{c}}}\). Although the orbital current is blocked by the thick Si3N4 layer, the Oersted field reaches the upper Ti layer resulting in the Oersted-field-induced net magnetization. f, An optical image of the fabricated device.
Extended Data Fig. 5 The capping layer effect of the Kerr rotation.
The current-induced Kerr rotation (θK) in the (a) sapphire substrate/Ti (90 nm)/Si3N4 (5 nm) heterostructure and (b) sapphire substrate/Ti (90 nm)/Al2O3 (5 nm) heterostructure. The Ti layer is deposited from a single element target (purity of 99.99%) using a DC sputtering. The Si3N4 and Al2O3 layers are deposited from compound targets (purity of 99.95%) using RF sputtering. The black up-triangle and blue down-triangle are θK measurements with incident angles (ϕ) of +25o and −25o, respectively, at the channel center. The negative sign of the current density (jc) is obtained by switching the source and drain connections of the AC current source. The sign reversal of θK with ± incident angles indicates that θK comes from the y-component of magnetization. From the linear fit of θK as a function of jc, we determine the current-normalized θK of 43.1 ± 3 nrad and 49.7 ± 3 nrad at jc of 107 A cm−2 for (a) and (b), respectively.
Extended Data Fig. 6 Tight-binding calculation results for fcc Ti.
a, The electronic band structure of fcc Ti. b, The Fermi surfaces of fcc Ti. Note that there are two Fermi surfaces. The inner and outer surfaces are colored by purple and orange, respectively. c, The orbital texture on the outer Fermi surface. The color implies whether the wave function is more like \({d}_{{z}^{2}-{x}^{2}}\) than \({d}_{{zx}}\) (pink) or vice versa (green) for each crystal momentum k. d, k-resolved orbital Hall conductivity contribution from the outer Fermi surface. It is assumed that an electric field is along the x-direction. The orbital texture and the k-resolved orbital contribution for the inner Fermi surface are given in Figs. 1c and 1d, respectively. e, The orbital (blue) and spin (red) Hall conductivities as a function of the Fermi energy EF. The actual Fermi energy corresponds to EF = 0 eV.
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Choi, YG., Jo, D., Ko, KH. et al. Observation of the orbital Hall effect in a light metal Ti. Nature 619, 52–56 (2023). https://doi.org/10.1038/s41586-023-06101-9
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DOI: https://doi.org/10.1038/s41586-023-06101-9
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