Altermagnets and beyond: Nodal magnetically-ordered phases

TL;DR

This paper reviews the recent discovery and properties of altermagnets, a new class of magnetic materials with complex orderings, highlighting their electronic signatures, emergent phenomena, and potential for spintronics applications.

Contribution

It provides a comprehensive overview of altermagnetism, including symmetry identification, material realizations, electronic signatures, and extensions to non-collinear spin structures.

Findings

Altermagnets exhibit unique symmetry-based electronic signatures.

They host relativistic and topological phenomena in their band structures.

Potential realization of p-wave magnetic phases in crystals.

Abstract

The recent discovery of altermagnets has opened new perspectives in the field of ordered phases in condensed matter. In strongly-correlated superfluids, the nodal p-wave and d-wave ordered phases of $^{3}$He and cuprates play a prominent role in physics for their rich phenomenology of the symmetry-breaking order parameters. While the p-wave and d-wave superfluids have been extensively studied over the past half a century, material realizations of their magnetic counterparts have remained elusive for many decades. This is resolved in altermagnets, whose recent discovery was driven by research in the field of spintronics towards highly scalable information technologies. Altermagnets feature d, g or i-wave magnetic ordering, with a characteristic alternation of spin polarization and spin-degenerate nodes. Here we review how altermagnetism can be identified from symmetries of collinear spin densities in crystal lattices, and can be realized at normal conditions in a broad family of insulating and conducting materials. We highlight salient electronic-structure signatures of the altermagnetic ordering, discuss extraordinary relativistic and topological phenomena that emerge in their band structures, and comment on strong-correlation effects. We then extend the discussion to non-collinear spin densities in crystals, including the prediction of p-wave magnets, and conclude with a brief summary of the reviewed physical properties of the nodal magnetically-ordered phases.