- Letter
- Open Access
Spin splitting in the surface electronic structure of antiferromagnet NdBi
Phys. Rev. Research 7, L022005 – Published 3 April, 2025
DOI: https://doi.org/10.1103/PhysRevResearch.7.L022005
Abstract
Spin splitting in electronic band structures via antiferromagnetic orders is a new route to control spin-polarized carriers that is available for spintronics applications. Here, we investigated the spin degrees of freedom in the electronic band structures of the antiferromagnet NdBi using laser-based spin- and angle-resolved photoemission spectroscopy (laser-SARPES). Our laser-SARPES experiments revealed that the two surface bands that appear in the antiferromagnetic state are spin polarized in opposite directions as a counterpart of the spin splitting. Moreover, we observed that the spin polarization is antisymmetric to the time-reversal invariant momentum, indicating that spin degeneracy is lifted due to the breaking of inversion symmetry at the surface. These results are well reproduced by our density functional theory calculations with the single- magnetic structure, implying that the spin-split surface state is determined by the breaking of inversion symmetry in concert with the antiferromagnetic order.
Physics Subject Headings (PhySH)
Article Text
References (59)
- A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, New perspectives for Rashba spin–orbit coupling, Nature Mater. 14, 871 (2015).
- A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces, Nature (London) 539, 509 (2016).
- Q. L. He, T. L. Hughes, N. P. Armitage, Y. Tokura, and K. L. Wang, Topological spintronics and magnetoelectronics, Nature Mater. 21, 15 (2022).
- T. Okuda and A. Kimura, Spin- and angle-resolved photoemission of strongly spin-orbit coupled systems, J. Phys. Soc. Jpn. 82, 021002 (2013).
- D. Y. Petrovykh, K. N. Altmann, H. Höchst, M. Laubscher, S. Maat, G. J. Mankey, and F. J. Himpsel, Spin-dependent band structure, Fermi surface, and carrier lifetime of permalloy, Appl. Phys. Lett. 73, 3459 (1998).
- G. Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Phys. Rev. 100, 580 (1955).
- E. I. Rashba and V. I. Sheka, Symmetry of energy bands in crystals of wurtzite type: II. Symmetry of bands including spin-orbit interaction, Fiz. Tverd. Tela 1, 62 (1959).
- R. C. Casella, Toroidal energy surfaces in crystals with wurtzite symmetry, Phys. Rev. Lett. 5, 371 (1960).
- G. Bihlmayer, P. Noël, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nature Rev. Phys. 4, 642 (2022).
- T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nature Nanotechnol. 11, 231 (2016).
- V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018).
- 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).
- H. Watanabe and Y. Yanase, Group-theoretical classification of multipole order: Emergent responses and candidate materials, Phys. Rev. B 98, 245129 (2018).
- M. Yatsushiro, H. Kusunose, and S. Hayami, Multipole classification in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena, Phys. Rev. B 104, 054412 (2021).
- H. Kusunose and S. Hayami, Generalization of microscopic multipoles and cross-correlated phenomena by their orderings, J. Phys.: Condens. Matter 34, 464002 (2022).
- H. Kusunose, R. Oiwa, and S. Hayami, Symmetry-adapted modeling for molecules and crystals, Phys. Rev. B 107, 195118 (2023).
- L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
- P. A. McClarty and J. G. Rau, Landau theory of altermagnetism, Phys. Rev. Lett. 132, 176702 (2024).
- L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nature Rev. Mater. 7, 482 (2022).
- J. Železný, Y. Zhang, C. Felser, and B. Yan, Spin-polarized current in noncollinear antiferromagnets, Phys. Rev. Lett. 119, 187204 (2017).
- 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).
- 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).
- D. Kriegner, K. Výborný, K. Olejník, H. Reichlová, V. Novák, X. Marti, J. Gazquez, V. Saidl, P. Němec, V. V. Volobuev, G. Springholz, V. Holý, and T. Jungwirth, Multiple-stable anisotropic magnetoresistance memory in antiferromagnetic mnte, Nature Commun. 7, 11623 (2016).
- P. Wadley, B. Howells, J. Železný, C. Andrews, V. Hills, R. P. Campion, V. Novák, K. Olejník, F. Maccherozzi, S. S. Dhesi, S. Y. Martin, T. Wagner, J. Wunderlich, F. Freimuth, Y. Mokrousov, J. Kuneš, J. S. Chauhan, M. J. Grzybowski, A. W. Rushforth, K. W. Edmonds, B. L. Gallagher, and T. Jungwirth, Electrical switching of an antiferromagnet, Science 351, 587 (2016).
- N. L. Nair, E. Maniv, C. John, S. Doyle, J. Orenstein, and J. G. Analytis, Electrical switching in a magnetically intercalated transition metal dichalcogenide, Nature Mater. 19, 153 (2020).
- H. Tsai, T. Higo, K. Kondou, T. Nomoto, A. Sakai, A. Kobayashi, T. Nakano, K. Yakushiji, R. Arita, S. Miwa, Y. Otani, and S. Nakatsuji, Electrical manipulation of a topological antiferromagnetic state, Nature (London) 580, 608 (2020).
- Y.-P. Zhu, X. Chen, X.-R. Liu, Y. Liu, P. Liu, H. Zha, G. Qu, C. Hong, J. Li, Z. Jiang, X.-M. Ma, Y.-J. Hao, M.-Y. Zhu, W. Liu, M. Zeng, S. Jayaram, M. Lenger, J. Ding, S. Mo, K. Tanaka, M. Arita, Z. Liu, M. Ye, D. Shen, J. Wrachtrup, Y. Huang, R.-H. He, S. Qiao, Q. Liu, and C. Liu, Observation of plaid-like spin splitting in a noncoplanar antiferromagnet, Nature (London) 626, 523 (2024).
- J. Krempaský, L. Šmejkal, S. W. D'Souza, M. Hajlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. González-Hernández, A. Birk Hellenes, Z. Jansa, H. Reichlová, Z. Šobáň, R. D. Gonzalez Betancourt, P. Wadley, J. Sinova, D. Kriegner, J. Minár, J. H. Dil, and T. Jungwirth, Altermagnetic lifting of Kramers spin degeneracy, Nature (London) 626, 517 (2024).
- 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).
- C.-G. Duan, R. F. Sabirianov, W. N. Mei, P. A. Dowben, S. S. Jaswal, and E. Y. Tsymbal, Electronic, magnetic and transport properties of rare-earth monopnictides, J. Phys.: Condens. Matter 19, 315220 (2007).
- R. Settai, T. Goto, S. Sakatume, Y. S. Kwon, T. Suzuki, Y. Kaneta, and O. Sakai, Observation of heavy hole state in CeSb, J. Phys. Soc. Jpn. 63, 3026 (1994).
- H. Kumigashira, H.-D. Kim, A. Ashihara, A. Chainani, T. Yokoya, T. Takahashi, A. Uesawa, and T. Suzuki, Paramagnetic-to-antiferroparamagnetic phase transition of CeSb studied by high-resolution angle-resolved photoemission, Phys. Rev. B 56, 13654 (1997).
- A. Takayama, S. Souma, T. Sato, T. Arakane, and T. Takahashi, Magnetic phase transition of CeSb studied by low-energy angle-resolved photoemission spectroscopy, J. Phys. Soc. Jpn. 78, 073702 (2009).
- H. Oinuma, S. Souma, K. Nakayama, K. Horiba, H. Kumigashira, M. Yoshida, A. Ochiai, T. Takahashi, and T. Sato, Unusual change in the Dirac-cone energy band upon a two-step magnetic transition in CeBi, Phys. Rev. B 100, 125122 (2019).
- S. Jang, R. Kealhofer, C. John, S. Doyle, J.-S. Hong, J. H. Shim, Q. Si, O. Erten, J. D. Denlinger, and J. G. Analytis, Direct visualization of coexisting channels of interaction in CeSb, Sci. Adv. 5, eaat7158 (2019).
- Y. Kushnirenko, B. Schrunk, B. Kuthanazhi, L.-L. Wang, J. Ahn, E. O'Leary, A. Eaton, S. L. Bud'ko, R.-J. Slager, P. C. Canfield, and A. Kaminski, Rare-earth monopnictides: Family of antiferromagnets hosting magnetic Fermi arcs, Phys. Rev. B 106, 115112 (2022).
- A. P. Sakhya, B. Wang, F. Kabir, C.-Y. Huang, M. M. Hosen, B. Singh, S. Regmi, G. Dhakal, K. Dimitri, M. Sprague, R. Smith, E. D. Bauer, F. Ronning, A. Bansil, and M. Neupane, Complex electronic structure evolution of NdSb across the magnetic transition, Phys. Rev. B 106, 235119 (2022).
- P. Li, T. Li, S. Liao, Z. Cao, R. Xu, Y. Wang, J. Yao, S. Cui, Z. Sun, Y. Wang, X. Wan, J. Jiang, and D. Feng, Origin of the exotic electronic states in antiferromagnetic NdSb, npj Quantum Mater. 8, 22 (2023).
- K. Kuroda, Y. Arai, N. Rezaei, S. Kunisada, S. Sakuragi, M. Alaei, Y. Kinoshita, C. Bareille, R. Noguchi, M. Nakayama, S. Akebi, M. Sakano, K. Kawaguchi, M. Arita, S. Ideta, K. Tanaka, H. Kitazawa, K. Okazaki, M. Tokunaga, Y. Haga, S. Shin, H. S. Suzuki, R. Arita, and T. Kondo, Devil's staircase transition of the electronic structures in CeSb, Nature Commun. 11, 2888 (2020).
- Y. Arai, K. Kuroda, T. Nomoto, Z. H. Tin, S. Sakuragi, C. Bareille, S. Akebi, K. Kurokawa, Y. Kinoshita, W.-L. Zhang, S. Shin, M. Tokunaga, H. Kitazawa, Y. Haga, H. S. Suzuki, S. Miyasaka, S. Tajima, K. Iwasa, R. Arita, and T. Kondo, Multipole polaron in the devil's staircase of CeSb, Nature Mater. 21, 410 (2022).
- T. Tsuchida and W. E. Wallace, Magnetic characteristics of lanthanide—bismuth compounds, J. Chem. Phys. 43, 2087 (1965).
- B. Schrunk, Y. Kushnirenko, B. Kuthanazhi, J. Ahn, L.-L. Wang, E. O'Leary, K. Lee, A. Eaton, A. Fedorov, R. Lou, V. Voroshnin, O. J. Clark, J. Sánchez-Barriga, S. L. Bud'ko, R.-J. Slager, P. C. Canfield, and A. Kaminski, Emergence of fermi arcs due to magnetic splitting in an antiferromagnet, Nature (London) 603, 610 (2022).
- A. Honma, D. Takane, S. Souma, K. Yamauchi, Y. Wang, K. Nakayama, K. Sugawara, M. Kitamura, K. Horiba, H. Kumigashira, K. Tanaka, T. K. Kim, C. Cacho, T. Oguchi, T. Takahashi, Y. Ando, and T. Sato, Antiferromagnetic topological insulator with selectively gapped Dirac cones, Nature Commun. 14, 7396 (2023).
- L.-L. Wang, J. Ahn, R.-J. Slager, Y. Kushnirenko, B. G. Ueland, A. Sapkota, B. Schrunk, B. Kuthanazhi, R. J. McQueeney, P. C. Canfield, and A. Kaminski, Unconventional surface state pairs in a high-symmetry lattice with anti-ferromagnetic band-folding, Commun. Phys. 6, 78 (2023).
- S. R. Park, J. Han, C. Kim, Y. Y. Koh, C. Kim, H. Lee, H. J. Choi, J. H. Han, K. D. Lee, N. J. Hur, M. Arita, K. Shimada, H. Namatame, and M. Taniguchi, Chiral orbital-angular momentum in the surface states of , Phys. Rev. Lett. 108, 046805 (2012).
- H. Ryu, I. Song, B. Kim, S. Cho, S. Soltani, T. Kim, M. Hoesch, C. H. Kim, and C. Kim, Photon energy dependent circular dichroism in angle-resolved photoemission from Au(111) surface states, Phys. Rev. B 95, 115144 (2017).
- V. Sunko, H. Rosner, P. Kushwaha, S. Khim, F. Mazzola, L. Bawden, O. J. Clark, J. M. Riley, D. Kasinathan, M. W. Haverkort, T. K. Kim, M. Hoesch, J. Fujii, I. Vobornik, A. P. Mackenzie, and P. D. C. King, Maximal Rashba-like spin splitting via kinetic-energy-coupled inversion-symmetry breaking, Nature (London) 549, 492 (2017).
- T. Iwata, T. Kousa, Y. Nishioka, K. Ohwada, K. Sumida, E. Annese, M. Kakoki, K. Kuroda, H. Iwasawa, M. Arita, S. Kumar, A. Kimura, K. Miyamoto, and T. Okuda, Laser-based angle-resolved photoemission spectroscopy with micrometer spatial resolution and detection of three-dimensional spin vector, Sci. Rep. 14, 127 (2024).
- P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. H. Madsen, and L. D. Marks, WIEN2k: An APW+lo program for calculating the properties of solids, J. Chem. Phys. 152, 074101 (2020).
- V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T. Czyżyk, and G. A. Sawatzky, Density-functional theory and nio photoemission spectra, Phys. Rev. B 48, 16929 (1993).
- G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Poncé, T. Ponweiser, J. Qiao, F. Thöle, S. S. Tsirkin, M. Wierzbowska, N. Marzari, D. Vanderbilt, I. Souza, A. A. Mostofi, and J. R. Yates, Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
- Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Wanniertools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2018).
- Y. Kushnirenko, B. Kuthanazhi, L.-L. Wang, B. Schrunk, E. O'Leary, A. Eaton, P. C. Canfield, and A. Kaminski, Directional effects of antiferromagnetic ordering on the electronic structure in NdSb, Phys. Rev. B 108, 115102 (2023).
- A. Honma, D. Takane, S. Souma, Y. Wang, K. Nakayama, M. Kitamura, K. Horiba, H. Kumigashira, T. Takahashi, Y. Ando, and T. Sato, Unusual surface states associated with -symmetry breaking and antiferromagnetic band folding in NdSb, Phys. Rev. B 108, 115118 (2023).
- K. Kuroda, K. Yaji, M. Nakayama, A. Harasawa, Y. Ishida, S. Watanabe, C.-T. Chen, T. Kondo, F. Komori, and S. Shin, Coherent control over three-dimensional spin polarization for the spin-orbit coupled surface state of , Phys. Rev. B 94, 165162 (2016).
- K. Yaji, K. Kuroda, S. Toyohisa, A. Harasawa, Y. Ishida, S. Watanabe, C. Chen, K. Kobayashi, F. Komori, and S. Shin, Spin-dependent quantum interference in photoemission process from spin-orbit coupled states, Nature Commun. 8, 14588 (2017).
- H. Bentmann, H. Maaß, E. E. Krasovskii, T. R. F. Peixoto, C. Seibel, M. Leandersson, T. Balasubramanian, and F. Reinert, Strong linear dichroism in spin-polarized photoemission from spin-orbit-coupled surface states, Phys. Rev. Lett. 119, 106401 (2017).
- C. Tusche, A. Krasyuk, and J. Kirschner, Spin resolved bandstructure imaging with a high resolution momentum microscope, Ultramicroscopy 159, 520 (2015), special Issue: LEEM-PEEM 9.
- C. Jozwiak, Y. L. Chen, A. V. Fedorov, J. G. Analytis, C. R. Rotundu, A. K. Schmid, J. D. Denlinger, Y.-D. Chuang, D.-H. Lee, I. R. Fisher, R. J. Birgeneau, Z.-X. Shen, Z. Hussain, and A. Lanzara, Widespread spin polarization effects in photoemission from topological insulators, Phys. Rev. B 84, 165113 (2011).