Orbital Hall conductivity and relaxation in thin films with variable disorder

Nature Physics (2026) Cite this article Electric-field-induced orbital angular momentum has emerged as a fundamental electronic degree of freedom in solid-state devices. It complements the spintronic functionalities used to sense and manipulate magnetic states. However, how orbital angular momentum evolves and relaxes in conductors with various degrees of structural and thermal order remain poorly understood. Here we demonstrate that the orbital Hall effect and orbital relaxation are robust and quantifiable in strongly disordered Mn thin films up to single-crystalline α-Mn. Using orbital Hanle magnetoresistance as a probe, we find that the orbital Hall conductivity scales linearly with electrical conductivity in the hopping-dominated regime from amorphous to polycrystalline films. This reveals a scaling behaviour analogous to the anomalous and spin Hall effects in bad metals. The orbital relaxation time, of the order of picoseconds, decreases with increasing crystalline order. Temperature-dependent measurements identify distinct relaxation channels. We observe in disordered films a crossover from on-site orbital dephasing to interorbital hopping with increasing temperature. In single-crystalline α-Mn, orbital relaxation is dominated by Elliott–Yafet-type scattering. Our findings establish orbital angular momentum as a structurally resilient degree of freedom and elucidate its relaxation dynamics across crystalline and disordered systems, thus enabling orbital control in different classes of materials.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data that support the findings of this study will be made available on the ETH Research Collection repository (https://doi.org/10.3929/ethz-c-000785607). Source data are provided with this paper.No custom code was used in this study.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).

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Lett. 110, 176602 (2013).Article ADS Google Scholar Download referencesThis research was supported by the Swiss National Science Foundation (Grant No. 200021-236524). M.-G.K. acknowledges support from the ETH Zürich internal funding programme (Career Seed Award 24-1 SEED-008). G.S. acknowledges support from the Swiss National Science Foundation (Grant No. PZ00P2_223542).These authors contributed equally: Min-Gu Kang, Federica Nasr.Department of Materials, ETH Zurich, Zurich, SwitzerlandMin-Gu Kang, Federica Nasr, Giacomo Sala, Richard Schlitz, Shilei Ding, Stefan Bartsch, Santos F. Alvarado & Pietro GambardellaDepartment of Quantum Matter Physics, University of Geneva, Geneva, SwitzerlandGiacomo SalaDepartment of Physics, University of Konstanz, Konstanz, GermanyRichard SchlitzElectron Microscopy Center, Empa – Swiss Federal Laboratories for Materials Science and Technology, Dubendorf, SwitzerlandMarta D. RossellSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarM.-G.K., F.N. and P.G. conceived the project and designed the experiments. M.-G.K. and F.N. grew the thin films, fabricated samples and performed the magnetotransport measurements. G.S., R.S., S.D., S.B. and P.G. assisted with the data analysis. M.D.R. performed the transmission electron microscopy measurements. S.F.A. provided input on the experimental infrastructure and methodology. M.-G.K. and P.G. interpreted the data and wrote the paper with input from all authors. All authors discussed the results and contributed to the final article.Correspondence to Min-Gu Kang or Pietro Gambardella.The authors declare no competing interests.Nature Physics thanks Samik Duttagupta, Henri Jaffres and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Temperature-dependent resistivity (\({\rho }_{{\rm{Mn}}}\)) of 10-nm-thick (a) amorphous Mn (4 mTorr of Ar sputtering pressure), (b) room temperature polycrystalline Mn, (c) textured Mn(211), and (d) epitaxial Mn(001). The red arrows serve as a guide to the eye to identify the resistivity minima.Source dataSupplementary Figs. 1–12, Table 1 and Notes 1–4.XRD intensity as a function of 2θ for epitaxial and textured Mn films.Orbital HMR as a function of magnetic field with fitted curves for Mn thin films with various degrees of crystallinity.Orbital Hall conductivity and relaxation time as a function of electrical conductivity with fitted curves for Mn films with various levels of static disorder.Orbital Hall conductivity and relaxation time as a function of electrical conductivity, with temperature as a tuning parameter, for Mn thin films.Electrical resistivity as a function of temperature for Mn films with various degrees of crystallinity.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsKang, MG., Nasr, F., Sala, G. et al. Orbital Hall conductivity and relaxation in thin films with variable disorder. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03334-zDownload citationReceived: 03 November 2025Accepted: 13 May 2026Published: 15 June 2026Version of record: 15 June 2026DOI: https://doi.org/10.1038/s41567-026-03334-zAnyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative