Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries

Abstract

The search for novel magnetic quantum phases, phenomena and functional materials has been guided by relativistic magnetic-symmetry groups in coupled spin and real space from the dawn of the field in 1950s to the modern era of topological matter. However, the magnetic groups cannot disentangle non-relativistic phases and effects, such as the recently reported unconventional spin physics in collinear antiferromagnets, from the typically weak relativistic spin-orbit coupling phenomena. Here we discover that more general spin symmetries in decoupled spin and crystal space categorize non-relativistic collinear magnetism in three phases: conventional ferromagnets and antiferromangets, and a third distinct phase combining zero net magnetization with an alternating spin-momentum locking in energy bands, which we dub "altermagnetic". For this third basic magnetic phase, which is omitted by the relativistic magnetic groups, we develop a spin-group theory describing six characteristic types of the altermagnetic spin-momentum locking. We demonstrate an extraordinary spin-splitting mechanism in altermagnetic bands originating from a local electric crystal field, which contrasts with the conventional magnetic or relativistic splitting by global magnetization or inversion asymmetry. Based on first-principles calculations, we identify altermagnetic candidates ranging from insulators and metals to a parent crystal of cuprate superconductor. Our results underpin emerging research of quantum phases and spintronics in high-temperature magnets with light elements, vanishing net magnetization, and strong spin-coherence.

An anomalous Hall effect in altermagnetic ruthenium dioxide

“…The theoretically predicted large relativistic Berry-phase AHE in RuO 2 is linked 7,15 to a spin-splitting and T -symmetry breaking in the band structure 15,[24][25][26][27] . The spin splitting, whose strength is comparable to ferromagnets but whose sign alternates across the magnetically compensated Brillouin zone, and the T -symmetry breaking in the band structure have a leading strong non-relativistic origin 15,[24][25][26][27] . It has inspired a reclassification of collinear magnetic phases based on a non-relativistic spin-symmetry group formalism, and to the delimitation of a separate symmetry class, dubbed altermagnetism 26,27 .…”

“…The spin splitting, whose strength is comparable to ferromagnets but whose sign alternates across the magnetically compensated Brillouin zone, and the T -symmetry breaking in the band structure have a leading strong non-relativistic origin 15,[24][25][26][27] . It has inspired a reclassification of collinear magnetic phases based on a non-relativistic spin-symmetry group formalism, and to the delimitation of a separate symmetry class, dubbed altermagnetism 26,27 . This emerging phase has a characteristic alternating spin polarization in both real-space crystal structure and momentum-space band structure 26,27 .…”

“…It has inspired a reclassification of collinear magnetic phases based on a non-relativistic spin-symmetry group formalism, and to the delimitation of a separate symmetry class, dubbed altermagnetism 26,27 . This emerging phase has a characteristic alternating spin polarization in both real-space crystal structure and momentum-space band structure 26,27 . Apart from the AHE, altermagnets have been predicted to allow for robust non-relativistic spin-polarized currents that can facilitate counterparts of the GMR and other key non-relativistic phenomena employed for reading and writing information in ferromagnetic memories 18,22,23 .…”

“…As already pointed in the theory work on the AHE 15 , RuO 2 is a representative of a remarkable type of crystal structures. The broken PT -symmetry in the real-space crystal structure of rutiles, enabling the altermagnetic spin splitting and T -symmetry breaking in the electronic band structure, and the resulting AHE or GMR magneto-electronic responses 7,15,[18][19][20][21][22][23][24][25][26][27][28][29] , lies in the crystal field from the anisotropic arrangement of the non-magnetic atoms 15,26,27 . The mechanism was thus referred to as crystal PTsymmetry breaking 15 .…”

“…1a, instead of the real-space inversion, the two crystal sublattices with opposite magnetic moments are connected by a real-space rotation transformation when the non-magnetic atoms are brought into the picture. The real-space rotation connecting the opposite-spin sublattices is the defining symmetry that results in the magnetically compensated phase, while allowing for the alternating spin splitting and T -symmetry breaking in the band structure 26,27 .…”