- Open Access
Current-induced spin and orbital polarization in the ferroelectric Rashba semiconductor GeTe
Phys. Rev. Research 7, 043329 – Published 24 December, 2025Erratum Phys. Rev. Research 8, 039004 (2026)
DOI: https://doi.org/10.1103/py8f-zk2d
Abstract
The Edelstein effect is a promising mechanism for generating spin and orbital polarization from charge currents in systems without inversion symmetry. In ferroelectric materials, such as germanium telluride (GeTe), the combination of bulk Rashba splitting and voltage-controlled ferroelectric polarization provides a pathway for electrical control of the sign of the charge-spin conversion. In this work, we investigate current-induced spin and orbital magnetization in bulk GeTe using Wannier-based tight-binding models derived from ab initio calculations and semiclassical Boltzmann theory. Employing the modern theory of orbital magnetization, we demonstrate that the orbital Edelstein effect entirely dominates its spin counterpart. This difference is visualized through the spin and orbital textures at the Fermi surfaces, where the orbital moment surpasses the spin moment by one order of magnitude. Moreover, the orbital Edelstein effect remains largely unaffected in the absence of spin-orbit coupling, highlighting its distinct physical origin compared to the spin Edelstein effect.
Physics Subject Headings (PhySH)
Erratum
Erratum: Current-induced spin and orbital polarization in the ferroelectric Rashba semiconductor GeTe [Phys. Rev. Research 7, 043329 (2025)]
Article Text
References (79)
- E. Rashba and V. I. Sheka, Symmetry of energy bands in crystals of wurtzite type II. Symmetry of bands with spin-orbit interaction included [in Russian], Fiz. Tverd. Tela: Collect. Pap. 2, 162 (1959).
- G. Bihlmayer, O. Rader, and R. Winkler, Focus on the Rashba effect, New J. Phys. 17, 050202 (2015), English translation of Ref. [1] in the Supplemental Material.
- E. Rashba, Properties of semiconductors with an extremum loop. 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop, Sov. Phys. Solid State 2, 1109 (1960).
- Y. Bychkov and E. Rashba, Properties of a 2D electron gas with lifted spectral degeneracy, JETP 39, 78 (1984).
- Y. A. Bychkov and E. I. Rashba, Oscillatory effects and the magnetic susceptibility of carriers in inversion layers, J. Phys. C 17, 6039 (1984).
- D. Di Sante, P. Barone, R. Bertacco, and S. Picozzi, Electric control of the giant Rashba effect in bulk GeTe, Adv. Mater. 25, 509 (2013).
- S. Picozzi, Ferroelectric Rashba semiconductors as a novel class of multifunctional materials, Front. Phys. 2, 10 (2014).
- C. Rinaldi, J. C. Rojas-Sánchez, R. N. Wang, Y. Fu, S. Oyarzun, L. Vila, S. Bertoli, M. Asa, L. Baldrati, M. Cantoni, J.-M. George, R. Calarco, A. Fert, and R. Bertacco, Evidence for spin to charge conversion in GeTe(111), APL Mater. 4, 032501 (2016).
- C. Rinaldi, S. Varotto, M. Asa, J. Sławińska, J. Fujii, G. Vinai, S. Cecchi, D. Di Sante, R. Calarco, I. Vobornik, G. Panaccione, S. Picozzi, and R. Bertacco, Ferroelectric control of the spin texture in GeTe, Nano Lett. 18, 2751 (2018).
- S. Varotto, L. Nessi, S. Cecchi, J. Sławińska, P. Noël, S. Petrò, F. Fagiani, A. Novati, M. Cantoni, D. Petti, E. Albisetti, M. Costa, R. Calarco, M. Buongiorno Nardelli, M. Bibes, S. Picozzi, J.-P. Attané, L. Vila, R. Bertacco, and C. Rinaldi, Room-temperature ferroelectric switching of spin-to-charge conversion in germanium telluride, Nat. Electron. 4, 740 (2021).
- L. Vojáček, M. Chshiev, and J. Li, Domain wall migration-mediated ferroelectric switching and Rashba effect tuning in GeTe thin films, ACS Appl. Electron. Mater. 6, 3754 (2024).
- A. G. Aronov and Y. B. Lyanda-Geller, Nuclear electric resonance and orientation of carrier spins by an electric field, JETP Lett. 50, 431 (1989).
- V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun. 73, 233 (1990).
- A. Johansson, J. Henk, and I. Mertig, Theoretical aspects of the Edelstein effect for anisotropic two-dimensional electron gas and topological insulators, Phys. Rev. B 93, 195440 (2016).
- S. Leiva-Montecinos, J. Henk, I. Mertig, and A. Johansson, Spin and orbital Edelstein effect in a bilayer system with Rashba interaction, Phys. Rev. Res. 5, 043294 (2023).
- I. Gaiardoni, M. Trama, A. Maiellaro, C. Guarcello, F. Romeo, and R. Citro, Edelstein effect in isotropic and anisotropic Rashba models, Condens. Matter 10, 15 (2025).
- A. Dey, A. K. Nandy, and K. Saha, Current-induced spin polarisation in Rashba–Dresselhaus systems under different point groups, New J. Phys. 27, 013024 (2025).
- Y. Ando, T. Hamasaki, T. Kurokawa, K. Ichiba, F. Yang, M. Novak, S. Sasaki, K. Segawa, Y. Ando, and M. Shiraishi, Electrical detection of the spin polarization due to charge flow in the surface state of the topological insulator , Nano Lett. 14, 6226 (2014).
- K. Kondou, R. Yoshimi, A. Tsukazaki, Y. Fukuma, J. Matsuno, K. S. Takahashi, M. Kawasaki, Y. Tokura, and Y. Otani, Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators, Nat. Phys. 12, 1027 (2016).
- J.-C. Rojas-Sánchez, S. Oyarzún, Y. Fu, A. Marty, C. Vergnaud, S. Gambarelli, L. Vila, M. Jamet, Y. Ohtsubo, A. Taleb-Ibrahimi, P. Le Fèvre, F. Bertran, N. Reyren, J.-M. George, and A. Fert, Spin to charge conversion at room temperature by spin pumping into a new type of topological insulator: α-Sn films, Phys. Rev. Lett. 116, 096602 (2016).
- A. Johansson, J. Henk, and I. Mertig, Edelstein effect in Weyl semimetals, Phys. Rev. B 97, 085417 (2018).
- B. Zhao, B. Karpiak, D. Khokhriakov, A. Johansson, A. M. Hoque, X. Xu, Y. Jiang, I. Mertig, and S. P. Dash, Unconventional charge–spin conversion in Weyl‐semimetal , Adv. Mater. 32, 2000818 (2020).
- T. Furukawa, Y. Watanabe, N. Ogasawara, K. Kobayashi, and T. Itou, Current-induced magnetization caused by crystal chirality in nonmagnetic elemental tellurium, Phys. Rev. Res. 3, 023111 (2021).
- F. Calavalle, M. Suárez-Rodríguez, B. Martín-García, A. Johansson, D. C. Vaz, H. Yang, I. V. Maznichenko, S. Ostanin, A. Mateo-Alonso, A. Chuvilin, I. Mertig, M. Gobbi, F. Casanova, and L. E. Hueso, Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires, Nat. Mater. 21, 526 (2022).
- B. Göbel, L. Schimpf, and I. Mertig, Chirality-induced orbital Edelstein effect in an analytically solvable model, Phys. Rev. Res. 7, 033180 (2025).
- D.C. Vaz, P. Noël, A. Johansson, B. Göbel, F. Y. Bruno, G. Singh, S. McKeown-Walker, F. Trier, L. M. Vicente-Arche, A. Sander et al., Mapping spin–charge conversion to the band structure in a topological oxide two-dimensional electron gas, Nat. Mater. 18, 1187 (2019).
- A. Johansson, B. Göbel, J. Henk, M. Bibes, and I. Mertig, Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to interfaces, Phys. Rev. Res. 3, 013275 (2021).
- M. Trama, V. Cataudella, C. A. Perroni, F. Romeo, and R. Citro, Tunable spin and orbital Edelstein effect at (111) / interface, Nanomaterials 12, 2494 (2022).
- S. Krishnia, L. Vojáček, T. D. C. S. C. Gomes, N. Sebe, F. Ibrahim, J. Li, L. M. Vicente-Arche, S. Collin, T. Denneulin, R. E. Dunin-Borkowski et al., Interfacial spin-orbitronic effects controlled with different oxidation levels at the Co/Al interface, Phys. Rev. Appl. 24, 024055 (2025).
- N. A. A. Pari, R. Jaeschke-Ubiergo, A. Chakraborty, L. Šmejkal, and J. Sinova, Nonrelativistic linear Edelstein effect in helical , Phys. Rev. B 112, 024404 (2025).
- A. Chakraborty, A. B. Hellenes, R. Jaeschke-Ubiergo, T. Jungwirth, L. Šmejkal, and J. Sinova, Highly efficient non-relativistic Edelstein effect in nodal -wave magnets, Nat. Commun. 16, 7270 (2025).
- M. Ezawa, Out-of-plane Edelstein effects: Electric field induced magnetization in -wave magnets, Phys. Rev. B 111, L161301 (2025).
- T. P. Cysne, F. S. M. Guimarães, L. M. Canonico, M. Costa, T. G. Rappoport, and R. B. Muniz, Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides, Phys. Rev. B 107, 115402 (2023).
- S. Lee, D. J. P. de Sousa, Y.-K. Kwon, F. de Juan, Z. Chi, F. Casanova, and T. Low, Charge-to-spin conversion in twisted heterostructures, Phys. Rev. B 106, 165420 (2022).
- J. Ingla-Aynés, I. Groen, F. Herling, N. Ontoso, C. K. Safeer, F. de Juan, L. E. Hueso, M. Gobbi, and F. Casanova, Omnidirectional spin-to-charge conversion in graphene/ van der Waals heterostructures, 2D Mater. 9, 045001 (2022).
- K. Tenzin, A. Roy, H. Jafari, B. Banas, F. T. Cerasoli, M. Date, A. Jayaraj, M. Buongiorno Nardelli, and J. Sławińska, Analogs of Rashba-Edelstein effect from density functional theory, Phys. Rev. B 107, 165140 (2023).
- L. Chirolli, M. T. Mercaldo, C. Guarcello, F. Giazotto, and M. Cuoco, Colossal orbital Edelstein effect in noncentrosymmetric superconductors, Phys. Rev. Lett. 128, 217703 (2022).
- T. Thonhauser, Theory of orbital magnetization in solids, Int. J. Mod. Phys. B 25, 1429 (2011).
- A. Johansson, Theory of spin and orbital Edelstein effects, J. Phys.: Condens. Matter 36, 423002 (2024).
- T. P. Cysne, L. M. Canonico, M. Costa, R. B. Muniz, and T. G. Rappoport, Orbitronics in two-dimensional materials, npj Spintron. 3, 39 (2025).
- T. Yoda, T. Yokoyama, and S. Murakami, Current-induced orbital and spin magnetizations in crystals with helical structure, Sci. Rep. 5, 12024 (2015).
- T. Yoda, T. Yokoyama, and S. Murakami, Orbital Edelstein effect as a condensed-matter analog of solenoids, Nano Lett. 18, 916 (2018).
- D. Go, J.-P. Hanke, P. M. Buhl, F. Freimuth, G. Bihlmayer, H.-W. Lee, Y. Mokrousov, and S. Blügel, Toward surface orbitronics: Giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals, Sci. Rep. 7, 46742 (2017).
- L. Salemi, M. Berritta, A. K. Nandy, and P. M. Oppeneer, Orbitally dominated Rashba-Edelstein effect in noncentrosymmetric antiferromagnets, Nat. Commun. 10, 5381 (2019).
- S. A. Nikolaev, M. Chshiev, F. Ibrahim, S. Krishnia, N. Sebe, J.-M. George, V. Cros, H. Jaffrès, and A. Fert, Large chiral orbital texture and orbital Edelstein effect in Co/Al heterostructure, Nano Lett. 24, 13465 (2024).
- M. G. Lopez, D. Vanderbilt, T. Thonhauser, and I. Souza, Wannier-based calculation of the orbital magnetization in crystals, Phys. Rev. B 85, 014435 (2012).
- A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 185, 2309 (2014).
- S. S. Tsirkin, High performance Wannier interpolation of Berry curvature and related quantities with WannierBerri code, npj Comput. Mater. 7, 33 (2021).
- J. Krempaský, S. Muff, F. Bisti, M. Fanciulli, H. Volfová, A. P. Weber, N. Pilet, P. Warnicke, H. Ebert, J. Braun, F. Bertran, V. V. Volobuev, J. Minár, G. Springholz, J. H. Dil, and V. N. Strocov, Entanglement and manipulation of the magnetic and spin–orbit order in multiferroic Rashba semiconductors, Nat. Commun. 7, 13071 (2016).
- J. Krempaský, H. Volfová, S. Muff, N. Pilet, G. Landolt, M. Radović, M. Shi, D. Kriegner, V. Holý, J. Braun, H. Ebert, F. Bisti, V. A. Rogalev, V. N. Strocov, G. Springholz, J. Minár, and J. H. Dil, Disentangling bulk and surface Rashba effects in ferroelectric α-GeTe, Phys. Rev. B 94, 205111 (2016).
- J. Krempaský, M. Fanciulli, L. Nicolaï, J. Minár, H. Volfová, O. Caha, V. V. Volobuev, J. Sánchez-Barriga, M. Gmitra, K. Yaji, K. Kuroda, S. Shin, F. Komori, G. Springholz, and J. H. Dil, Fully spin-polarized bulk states in ferroelectric GeTe, Phys. Rev. Res. 2, 013107 (2020).
- L. Ponet and S. Artyukhin, First-principles theory of giant Rashba-like spin splitting in bulk GeTe, Phys. Rev. B 98, 174102 (2018).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
- S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
- N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
- N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012).
- L. Vojáček, J. Medina Dueñas, J. Li, F. Ibrahim, A. Manchon, S. Roche, M. Chshiev, and J. H. García, Field-free spin–orbit torque switching in Janus chromium dichalcogenides, Nano Lett. 24, 11889 (2024).
- L. Vojáček, Multiscale modeling of spin-orbitronic phenomena at metal, oxide, and 2D material interfaces for spintronic devices, Ph.D. thesis, Université Grenoble Alpes, 2024.
- L. Fu, Hexagonal warping effects in the surface states of the topological insulator , Phys. Rev. Lett. 103, 266801 (2009).
- C. R. Ast, J. Henk, A. Ernst, L. Moreschini, M. C. Falub, D. Pacilé, P. Bruno, K. Kern, and M. Grioni, Giant spin splitting through surface alloying, Phys. Rev. Lett. 98, 186807 (2007).
- S. Vajna, E. Simon, A. Szilva, K. Palotas, B. Ujfalussy, and L. Szunyogh, Higher-order contributions to the Rashba-Bychkov effect with application to the Bi/Ag(111) surface alloy, Phys. Rev. B 85, 075404 (2012).
- T. P. Cysne, W. J. M. Kort-Kamp, and T. G. Rappoport, Controlling the orbital Hall effect in gapped bilayer graphene in the terahertz regime, Phys. Rev. Res. 6, 023271 (2024).
- T. Hakioglu, W.-C. Chiu, R. S. Markiewicz, B. Singh, and A. Bansil, Nonorthogonal spin-momentum locking, Phys. Rev. B 108, 155103 (2023).
- F. Kadlec, C. Kadlec, P. Kužel, and J. Petzelt, Study of the ferroelectric phase transition in germanium telluride using time-domain terahertz spectroscopy, Phys. Rev. B 84, 205209 (2011).
- J. E. Boschker, X. Lü, V. Bragaglia, R. Wang, H. T. Grahn, and R. Calarco, Electrical and optical properties of epitaxial binary and ternary GeTe- alloys, Sci. Rep. 8, 5889 (2018).
- D. Guo, C. Li, K. Qiu, Q. Yang, K. Li, B. Shao, D. Chen, Y. Ma, J. Sun, X. Cao, W. Zeng, Z. Wang, and R. Xie, The - and -type thermoelectricity property of GeTe by first-principles study, J. Alloys Compd. 810, 151838 (2019).
- X. Yang, X.-M. Li, Y. Li, Y. Li, R. Sun, J.-N. Liu, X. Bai, N. Li, Z.-K. Xie, L. Su, Z.-Z. Gong, X.-Q. Zhang, W. He, and Z. Cheng, Three-dimensional limit of bulk Rashba effect in ferroelectric semiconductor GeTe, Nano Lett. 21, 77 (2021).
- V.L. Deringer, M. Lumeij, and R. Dronskowski, Ab initio modeling of α-GeTe(111) surfaces, J. Phys. Chem. C 116, 15801 (2012).
- J. Krempaský, S. Muff, J. Minár, N. Pilet, M. Fanciulli, A. P. Weber, E. B. Guedes, M. Caputo, E. Müller, V. V. Volobuev, M. Gmitra, C. A. F. Vaz, V. Scagnoli, G. Springholz, and J. H. Dil, Operando imaging of all-electric spin texture manipulation in ferroelectric and multiferroic Rashba semiconductors, Phys. Rev. X 8, 021067 (2018).
- H. Jafari, A. Roy, and J. Sławińska, Ferroelectric control of charge-to-spin conversion in , Phys. Rev. Mater. 6, L091404 (2022).
- E. C. Souza, J. E. Abrão, M. A. Correa, F. Bohn, M. Gamino, and S. M. Rezende, Unveiling the mechanism of spin to charge conversion in the ferroelectric topological crystalline insulator SnTe, Phys. Rev. B 110, 014444 (2024).
- D. Go, D. Jo, C. Kim, and H.-W. Lee, Intrinsic spin and orbital Hall effects from orbital texture, Phys. Rev. Lett. 121, 086602 (2018).
- S. Leiva, L. Vojacek, J. Li, M. Chshiev, L. Vila, I. Mertig, and A. Johansson, Supporting data for “Current-induced spin and orbital polarization in the ferroelectric Rashba semiconductor GeTe” [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.15536123.
- G. Kremer, T. Jaouen, B. Salzmann, L. Nicolaï, M. Rumo, C.W. Nicholson, B. Hildebrand, J. H. Dil, J. Minár, G. Springholz, J. Krempaský, and C. Monney, Unveiling the complete dispersion of the giant Rashba split surface states of ferroelectric by alkali doping, Phys. Rev. Res. 2, 033115 (2020).