Altermagnetic lifting of Kramers spin degeneracy

Abstract Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids 1,2 . It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology 3–7 to topological quantum matter 8–14 . 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 origin 15 . 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 altermagnetic 20,21 , 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 magnetization 20–23 . 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 superconductors 20,21 , that have been either identified recently or perceived for many decades as conventional antiferromagnets 21,24,25 .

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