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Krempaský J, Šmejkal L, D'Souza SW, Hajlaoui M, Springholz G, Uhlířová K, Alarab F, Constantinou PC, Strocov V, Usanov D, Pudelko WR, González-Hernández R, Birk Hellenes A, Jansa Z, Reichlová H, Šobáň Z, Gonzalez Betancourt RD, Wadley P, Sinova J, Kriegner D, Minár J, Dil JH, Jungwirth T. Altermagnetic lifting of Kramers spin degeneracy. Nature 2024; 626:517-522. [PMID: 38356066 PMCID: PMC10866710 DOI: 10.1038/s41586-023-06907-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2023] [Accepted: 11/28/2023] [Indexed: 02/16/2024]
Abstract
Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3-7 to topological quantum matter8-14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin15. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin-orbit coupling (SOC)16-19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic20,21, that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization20-23. Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25.
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Affiliation(s)
- J Krempaský
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland.
| | - L Šmejkal
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
| | - S W D'Souza
- New Technologies Research Center, University of West Bohemia, Plzeň, Czech Republic
| | - M Hajlaoui
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University of Linz, Linz, Austria
| | - G Springholz
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University of Linz, Linz, Austria
| | - K Uhlířová
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
| | - F Alarab
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland
| | - P C Constantinou
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland
| | - V Strocov
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland
| | - D Usanov
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland
| | - W R Pudelko
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland
- Physik-Institut, Universität Zürich, Zürich, Switzerland
| | - R González-Hernández
- Grupo de Investigación en Física Aplicada, Departamento de Física, Universidad del Norte, Barranquilla, Colombia
| | - A Birk Hellenes
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Z Jansa
- New Technologies Research Center, University of West Bohemia, Plzeň, Czech Republic
| | - H Reichlová
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
| | - Z Šobáň
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
| | | | - P Wadley
- School of Physics and Astronomy, University of Nottingham, Nottingham, United Kingdom
| | - J Sinova
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
| | - D Kriegner
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
| | - J Minár
- New Technologies Research Center, University of West Bohemia, Plzeň, Czech Republic.
| | - J H Dil
- Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland
- Institut de Physique, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - T Jungwirth
- Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic.
- School of Physics and Astronomy, University of Nottingham, Nottingham, United Kingdom.
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Gonzalez Betancourt RD, Zubáč J, Gonzalez-Hernandez R, Geishendorf K, Šobáň Z, Springholz G, Olejník K, Šmejkal L, Sinova J, Jungwirth T, Goennenwein STB, Thomas A, Reichlová H, Železný J, Kriegner D. Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor. Phys Rev Lett 2023; 130:036702. [PMID: 36763381 DOI: 10.1103/physrevlett.130.036702] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 10/10/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
The anomalous Hall effect, commonly observed in metallic magnets, has been established to originate from the time-reversal symmetry breaking by an internal macroscopic magnetization in ferromagnets or by a noncollinear magnetic order. Here we observe a spontaneous anomalous Hall signal in the absence of an external magnetic field in an epitaxial film of MnTe, which is a semiconductor with a collinear antiparallel magnetic ordering of Mn moments and a vanishing net magnetization. The anomalous Hall effect arises from an unconventional phase with strong time-reversal symmetry breaking and alternating spin polarization in real-space crystal structure and momentum-space electronic structure. The anisotropic crystal environment of magnetic Mn atoms due to the nonmagnetic Te atoms is essential for establishing the unconventional phase and generating the anomalous Hall effect.
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Affiliation(s)
- R D Gonzalez Betancourt
- Institute of Solid State and Materials Physics, Technical University Dresden, 01062 Dresden, Germany
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
- Leibniz Institute of Solid State and Materials Research (IFW Dresden), Helmholtzstr. 20, 01069 Dresden, Germany
| | - J Zubáč
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
- Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Czech Republic
| | - R Gonzalez-Hernandez
- Departamento de Fisica y Geociencias, Universidad del Norte, Barranquilla 080020, Colombia
| | - K Geishendorf
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
| | - Z Šobáň
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
| | - G Springholz
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040 Linz, Austria
| | - K Olejník
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
| | - L Šmejkal
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55128 Mainz, Germany
| | - J Sinova
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55128 Mainz, Germany
| | - T Jungwirth
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - S T B Goennenwein
- Institute of Solid State and Materials Physics, Technical University Dresden, 01062 Dresden, Germany
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany
| | - A Thomas
- Institute of Solid State and Materials Physics, Technical University Dresden, 01062 Dresden, Germany
- Leibniz Institute of Solid State and Materials Research (IFW Dresden), Helmholtzstr. 20, 01069 Dresden, Germany
| | - H Reichlová
- Institute of Solid State and Materials Physics, Technical University Dresden, 01062 Dresden, Germany
| | - J Železný
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
| | - D Kriegner
- Institute of Solid State and Materials Physics, Technical University Dresden, 01062 Dresden, Germany
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
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