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Orbital-related gyrotropic responses in Cu2WSe4 and chirality indicator

Kazuki Nakazawa1, Terufumi Yamaguchi2,3, and Ai Yamakage4

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Phys. Rev. Materials 10, 064603 – Published 15 June, 2026

DOI: https://doi.org/10.1103/p5bw-w7mg

Abstract

In recent years, counterparts of phenomena studied in spintronics have been actively explored in the orbital sector. The relationship between orbital degrees of freedom and crystal chirality has also been intensively investigated, although the distinction from gyrotropic properties has not been fully clarified. In this work, we investigate spin and orbital Edelstein effects as well as the nonlinear responses in the ternary transition-metal chalcogenide Cu2WSe4, which has a gyrotropic but achiral crystal structure. We find that in the Edelstein effect, magnetization is dominated by the orbital contribution rather than the spin contribution. On the other hand, both the nonlinear chiral thermoelectric (NCTE) Hall effect—a response to the cross product of the electric field and the temperature gradient—and the nonlinear Hall effect—a conventional second-order response to the electric field—are found to be dominated by the Berry-curvature dipole. We further find that spin-orbit coupling plays only a minor role in these effects, whereas the orbital degrees of freedom are essential. Finally, we demonstrate that the orbital magnetic-moment contributions to both the Edelstein effect and the NCTE Hall effect are closely linked to chirality, and we discuss the possibility of using them as a chirality indicator.

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References (92)

  1. I. Žutić, J. Fabian, and S. D. Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76, 323 (2004).
  2. A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Diény, P. Pirro, and B. Hillebrands, Review on spintronics: Principles and device applications, J. Magn. Magn. Mater. 509, 166711 (2020).
  3. D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
  4. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys. 79, 1217 (2007).
  5. C. Kloeffel and D. Loss, Prospects for spin-based quantum computing in quantum dots, Annu. Rev. Condens. Matter Phys. 4, 51 (2013).
  6. M. I. Dyakonov and V. I. Perel, Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A 35, 459 (1971).
  7. M. I. Dyakonov and V. I. Perel, Possibility of orienting electron spins with current, JETP Lett. 13, 467 (1971).
  8. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Spintronics: A spin-based electronics vision for the future, Science 294, 1488 (2001).
  9. S. Murakami, N. Nagaosa, and S.-C. Zhang, Dissipationless quantum spin current at room temperature, Science 301, 1348 (2003).
  10. S. D. Ganichev and L. E. Golub, Interplay of Rashba/Dresselhaus spin splittings probed by photogalvanic spectroscopy–A review, physica status solidi (b) 251, 1801 (2014).
  11. D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y. Mokrousov, Orbitronics: Orbital currents in solids, Europhys. Lett. 135, 37001 (2021).
  12. D. Jo, D. Go, G.-M. Choi, and H.-W. Lee, Spintronics meets orbitronics: Emergence of orbital angular momentum in solids, npj Spintron. 2, 19 (2024).
  13. K. Ando, Orbitronics: Harnessing orbital currents in solid-state devices, J. Phys. Soc. Jpn. 94, 092001 (2025).
  14. M.-C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Phys. Rev. B 53, 7010 (1996).
  15. G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59, 14915 (1999).
  16. D. Xiao, J. Shi, and Q. Niu, Berry phase correction to electron density of states in solids, Phys. Rev. Lett. 95, 137204 (2005).
  17. T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Orbital magnetization in periodic insulators, Phys. Rev. Lett. 95, 137205 (2005).
  18. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Orbitronics: The intrinsic orbital current in p-doped silicon, Phys. Rev. Lett. 95, 066601 (2005).
  19. H. Kontani, T. Tanaka, D. S. Hirashima, K. Yamada, and J. Inoue, Giant intrinsic spin and orbital Hall effects in Sr2MO4 (M=Ru, Rh, Mo), Phys. Rev. Lett. 100, 096601 (2008).
  20. T. Tanaka, H. Kontani, M. Naito, T. Naito, D. S. Hirashima, K. Yamada, and J. Inoue, Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals, Phys. Rev. B 77, 165117 (2008).
  21. Y.-G. Choi, D. Jo, K.-H. Ko, D. Go, K.-H. Kim, H. G. Park, C. Kim, B.-C. Min, G.-M. Choi, and H.-W. Lee, Observation of the orbital Hall effect in a light metal Ti, Nature (London) 619, 52 (2023).
  22. S. R. Park, C. H. Kim, J. Yu, J. H. Han, and C. Kim, Orbital-angular-momentum based origin of Rashba-type surface band splitting, Phys. Rev. Lett. 107, 156803 (2011).
  23. J.-H. Park, C. H. Kim, J.-W. Rhim, and J. H. Han, Orbital Rashba effect and its detection by circular dichroism angle-resolved photoemission spectroscopy, Phys. Rev. B 85, 195401 (2012).
  24. T. Yoda, T. Yokoyama, and S. Murakami, Current-induced orbital and spin magnetizations in crystals with helical structure, Sci. Rep. 5, 12024 (2015).
  25. S. Zhong, J. E. Moore, and I. Souza, Gyrotropic magnetic effect and the magnetic moment on the Fermi surface, Phys. Rev. Lett. 116, 077201 (2016).
  26. T. Yoda, T. Yokoyama, and S. Murakami, Orbital Edelstein effect as a condensed-matter analog of solenoids, Nano Lett. 18, 916 (2018).
  27. A. G. Aronov, Y. B. Lyanda-Geller, and G. E. Pikus, Spin polarization of electrons by an electric current, Sov. Phys. JETP 73, 537 (1991).
  28. V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun. 73, 233 (1990).
  29. J. C. R. Sánchez, L. Vila, G. Desfonds, S. Gambarelli, J. P. Attané, J. M. De Teresa, C. Magén, and A. Fert, Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials, Nat. Commun. 4, 2944 (2013).
  30. E. Lesne, Y. Fu, S. Oyarzun, J. C. Rojas-Sánchez, D. C. Vaz, H. Naganuma, G. Sicoli, J.-P. Attané, M. Jamet, E. Jacquet, J.-M. George, A. Barthélémy, H. Jaffrès, A. Fert, M. Bibes, and L. Vila, Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces, Nat. Mater. 15, 1261 (2016).
  31. T. Furukawa, Y. Shimokawa, K. Kobayashi, and T. Itou, Observation of current-induced bulk magnetization in elemental tellurium, Nat. Commun. 8, 954 (2017).
  32. 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).
  33. A. Johansson, Theory of spin and orbital Edelstein effects, J. Phys.: Condens. Matter 36, 423002 (2024).
  34. A. El Hamdi, J.-Y. Chauleau, M. Boselli, C. Thibault, C. Gorini, A. Smogunov, C. Barreteau, S. Gariglio, J.-M. Triscone, and M. Viret, Observation of the orbital inverse Rashba–Edelstein effect, Nat. Phys. 19, 1855 (2023).
  35. S. Krishnia, B. Bony, E. Rongione, L. M. Vicente-Arche, T. Denneulin, A. Pezo, Y. Lu, R. E. Dunin-Borkowski, S. Collin, A. Fert, J.-M. George, N. Reyren, V. Cros, and H. Jaffrès, Quantifying the large contribution from orbital Rashba–Edelstein effect to the effective damping-like torque on magnetization, APL Mater. 12, 051105 (2024).
  36. B. Göbel, I. Mertig, and S. Lounis, Chirality-induced selectivity of angular momentum by orbital Edelstein effect in carbon nanotubes, Commun. Phys. 8, 395 (2025).
  37. B. Göbel, L. Schimpf, and I. Mertig, Chirality-induced orbital edelstein effect in an analytically solvable model, Phys. Rev. Res. 7, 033180 (2025).
  38. J. E. Sipe and A. I. Shkrebtii, Second-order optical response in semiconductors, Phys. Rev. B 61, 5337 (2000).
  39. Y. Gao, S. A. Yang, and Q. Niu, Field induced positional shift of bloch electrons and its dynamical implications, Phys. Rev. Lett. 112, 166601 (2014).
  40. I. Sodemann and L. Fu, Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials, Phys. Rev. Lett. 115, 216806 (2015).
  41. R. Takashima, Y. Shiomi, and Y. Motome, Nonreciprocal spin Seebeck effect in antiferromagnets, Phys. Rev. B 98, 020401 (2018).
  42. Y. Hidaka, S. Pu, and D.-L. Yang, Nonlinear responses of chiral fluids from kinetic theory, Phys. Rev. D 97, 016004 (2018).
  43. R. Nakai and N. Nagaosa, Nonreciprocal thermal and thermoelectric transport of electrons in noncentrosymmetric crystals, Phys. Rev. B 99, 115201 (2019).
  44. R. Toshio, K. Takasan, and N. Kawakami, Anomalous hydrodynamic transport in interacting noncentrosymmetric metals, Phys. Rev. Res. 2, 032021 (2020).
  45. D. E. Parker, T. Morimoto, J. Orenstein, and J. E. Moore, Diagrammatic approach to nonlinear optical response with application to weyl semimetals, Phys. Rev. B 99, 045121 (2019).
  46. S. M. João and J. M. Viana Parente Lopes, Basis-independent spectral methods for non-linear optical response in arbitrary tight-binding models, J. Phys.: Condens. Matter 32, 125901 (2020).
  47. Y. Michishita and R. Peters, Effects of renormalization and non-hermiticity on nonlinear responses in strongly correlated electron systems, Phys. Rev. B 103, 195133 (2021).
  48. Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nat. Rev. Phys. 3, 744 (2021).
  49. Y. Li, Y. Li, P. Li, B. Fang, X. Yang, Y. Wen, D.-X. Zheng, C.-H. Zhang, X. He, A. Manchon, Z.-H. Cheng, and X.-X. Zhang, Nonreciprocal charge transport up to room temperature in bulk Rashba semiconductor α-GeTe, Nat. Commun. 12, 540 (2021).
  50. K. Nakazawa, Y. Kato, and Y. Motome, Asymmetric modulation of Majorana excitation spectra and nonreciprocal thermal transport in the Kitaev spin liquid under a staggered magnetic field, Phys. Rev. B 105, 165152 (2022).
  51. H. F. Legg, M. Rößler, F. Münning, D. Fan, O. Breunig, A. Bliesener, G. Lippertz, A. Uday, A. A. Taskin, D. Loss, J. Klinovaja, and Y. Ando, Giant magnetochiral anisotropy from quantum-confined surface states of topological insulator nanowires, Nat. Nanotechnol. 17, 696 (2022).
  52. R. Oiwa and H. Kusunose, Systematic analysis method for nonlinear response tensors, J. Phys. Soc. Jpn. 91, 014701 (2022).
  53. R. M. A. Dantas, H. F. Legg, S. Bosco, D. Loss, and J. Klinovaja, Determination of spin-orbit interaction in semiconductor nanostructures via nonlinear transport, Phys. Rev. B 107, L241202 (2023).
  54. S. Gholizadeh, J. H. Cullen, and D. Culcer, Nonlinear Hall effect of magnetized two-dimensional spin-32 heavy holes, Phys. Rev. B 107, L041301 (2023).
  55. R. B. Atencia, D. Xiao, and D. Culcer, Disorder in the nonlinear anomalous Hall effect of PT-symmetric Dirac fermions, Phys. Rev. B 108, L201115 (2023).
  56. K. Das, S. Lahiri, R. B. Atencia, D. Culcer, and A. Agarwal, Intrinsic nonlinear conductivities induced by the quantum metric, Phys. Rev. B 108, L201405 (2023).
  57. T. Yamaguchi, K. Nakazawa, and A. Yamakage, Microscopic theory of nonlinear Hall effect induced by electric field and temperature gradient, Phys. Rev. B 109, 205117 (2024).
  58. K. Nakazawa, T. Yamaguchi, and A. Yamakage, Nonlinear charge transport properties in chiral tellurium, Phys. Rev. Mater. 8, L091601 (2024).
  59. T. Yamaguchi, K. Nakazawa, and A. Yamakage, Theory of nonlinear Hall effect induced by electric field and temperature gradient in 3D chiral magnetic textures, arXiv:2410.00563.
  60. H. Arisawa, Y. Fujimoto, T. Kikkawa, and E. Saitoh, Observation of nonlinear thermoelectric effect in MoGe/Y3Fe5O12, Nat. Commun. 15, 6912 (2024).
  61. K. Nakazawa, T. Yamaguchi, and A. Yamakage, Nonlinear charge and thermal transport properties induced by orbital magnetic moment in chiral crystalline cobalt monosilicide, Phys. Rev. B 111, 045161 (2025).
  62. K. Nakazawa, H. F. Legg, J. Klinovaja, and D. Loss, Interband contributions to nonlinear transport in semiconductor nanostructures, Phys. Rev. B 111, 125305 (2025).
  63. H. Arisawa, Y. Fujimoto, T. Kikkawa, S. Okamoto, M. Umeda, H. Chudo, and E. Saitoh, Cross-nonlinear generation induced by electric current and temperature gradient in MoGe/Y3Fe5O12, Phys. Rev. B 111, 214519 (2025).
  64. T. Nomoto, A. Kikkawa, K. Nakazawa, T. Yamaguchi, and F. Kagawa, Observation of the nonlinear chiral thermoelectric Hall effect in tellurium, Nat. Phys. 21, 1920 (2025).
  65. W.-Y. He and K. T. Law, Magnetoelectric effects in gyrotropic superconductors, Phys. Rev. Res. 2, 012073 (2020).
  66. G. Soavi and J. Wilhelm, The role of Berry curvature derivatives in the optical activity of time-invariant crystals, arXiv:2501.03684.
  67. S. Hayami, M. Yatsushiro, Y. Yanagi, and H. Kusunose, Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors, Phys. Rev. B 98, 165110 (2018).
  68. T. Miki, H. Ikeda, M.-T. Suzuki, and S. Hoshino, Quantification of electronic asymmetry: Chirality and axiality in solids, Phys. Rev. Lett. 134, 226401 (2025).
  69. R. Oiwa and H. Kusunose, Predominant electronic order parameter for structural chirality: Role of spinless electronic toroidal multipoles in Te and Se, Phys. Rev. Res. 7, 033250 (2025).
  70. K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr 44, 1272 (2011).
  71. E. A. Pruss, B. S. Snyder, and A. M. Stacy, A new layered ternary sulfide: Formation of Cu2WS4 by reaction of WS and Cu+ ions, Angew. Chem. Int. Ed. Engl. 32, 256 (1993).
  72. C. J. Crossland, P. J. Hickey, and J. S. O. Evans, The synthesis and characterisation of Cu2MX4 (M = W or Mo; X = S, Se or S/Se) materials prepared by a solvothermal method, J. Mater. Chem. 15, 3452 (2005).
  73. L.-Y. Gan and U. Schwingenschlögl, Two-dimensional square ternary Cu2MX4 (M = Mo, W; X = S, Se) monolayers and nanoribbons predicted from density functional theory, Phys. Rev. B 89, 125423 (2014).
  74. H. Chen, K. Zhang, W. Chen, I. Ali, P. Wu, D. Liu, and L. Song, Raman scattering of single crystal Cu2MoS4 nanosheet, AIP Adv. 5, 037141 (2015).
  75. M. Yıldırım, A. Sarılmaz, and F. Özel, Investigation of optical and device parameters of colloidal copper tungsten selenide ternary nanosheets, J. Mater. Sci.: Mater. Electron. 29, 762 (2018).
  76. M. Nadeem, M. U. Din, H. T. Naeem, Q. Ain, and J. Munir, Exploring the physical properties of Cu2WSe4 for optoelectronic and thermoelectric applications: A DFT study, ECS J. Solid State Sci. Technol. 11, 033009 (2022).
  77. O. Nbeg, M. Bouchenafa, A. Benmakhlouf, M.A. Fadla, Y. Bourourou, S. Maabed, M. Halit, and B. Saidat, Theoretical investigation of the structural, electronic, elastic and optical properties of the new layered ternary chalcogenide tetragonal compounds Cu2MX4 (M = W and Mo; X=S and Se), J. Solid State Chem. 321, 123880 (2023).
  78. A. Kocyigit, M. Yıldırım, A. Sarılmaz, and F. Ozel, The Au/Cu2WSe4/p-Si photodiode: Electrical and morphological characterization, J. Alloys Compd. 780, 186 (2019).
  79. OpenMX website, https://www.openmx-square.org/.
  80. T. Ozaki, Variationally optimized atomic orbitals for large-scale electronic structures, Phys. Rev. B 67, 155108 (2003).
  81. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  82. H. Weng, T. Ozaki, and K. Terakura, Revisiting magnetic coupling in transition-metal-benzene complexes with maximally localized Wannier functions, Phys. Rev. B 79, 235118 (2009).
  83. C. Stamm, C. Murer, M. Berritta, J. Feng, M. Gabureac, P. M. Oppeneer, and P. Gambardella, Magneto-optical detection of the spin Hall effect in Pt and W thin films, Phys. Rev. Lett. 119, 087203 (2017).
  84. Y. Marui, M. Kawaguchi, and M. Hayashi, Optical detection of spin–orbit torque and current-induced heating, Appl. Phys. Express 11, 093001 (2018).
  85. Y. Michishita and N. Nagaosa, Dissipation and geometry in nonlinear quantum transports of multiband electronic systems, Phys. Rev. B 106, 125114 (2022).
  86. G. Chang, B. J. Wieder, F. Schindler, D. S. Sanchez, I. Belopolski, S.-M. Huang, B. Singh, Di Wu, T.-R. Chang, T. Neupert, S.-Y. Xu, H. Lin, and M. Z. Hasan, Topological quantum properties of chiral crystals, Nat. Mater. 17, 978 (2018).
  87. A. N. Tamanna, A. Lakra, X. Ding, E. Buzi, K. Park, K. Sobczak, H. Deng, G. Sharma, S. Tewari, and L. Krusin-Elbaum, Transport chirality generated by a tunable tilt of weyl nodes in a van der Waals topological magnet, Nat. Commun. 15, 9830 (2024).
  88. M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, and T. Miyake, Weyl node and spin texture in trigonal tellurium and selenium, Phys. Rev. Lett. 114, 206401 (2015).
  89. P. Tang, Q. Zhou, and S.-C. Zhang, Multiple types of topological fermions in transition metal silicides, Phys. Rev. Lett. 119, 206402 (2017).
  90. G. P. Maruggi, J. Ferreira, E. Baggio-Saitovitch, C. Enderlein, and M. B. Silva Neto, Hedgehog orbital texture in p-type tellurium and the antisymmetric nonreciprocal Hall response, Phys. Rev. Mater. 7, 014204 (2023).
  91. Q. Yang, J. Xiao, I. Robredo, M. G. Vergniory, B. Yan, and C. Felser, Monopole-like orbital-momentum locking and the induced orbital transport in topological chiral semimetals, Proc. Natl. Acad. Sci. USA 120, e2305541120 (2023).
  92. K. Nakazawa, T. Yamaguchi, and A. Yamakage, Dataset for “Orbital-related gyrotropic responses in Cu2WSe4 and chirality indicator” [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.20131063.

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Phys. Rev. Materials 10, 064603– Published 15 June, 2026
  • Received 18 December 2025
  • Accepted 1 May 2026
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