Abstract: Magnetism is the posterchild of how the interplay between electron-electron interactions and quantum physics promotes novel macroscopic phenomena. Historically, the evolution of our understanding of magnetism has been related to the discovery of new paradigms in condensed-matter physics, as exemplified by the connections between antiferromagnetism and Mott insulators, spin glasses and non-ergodic states, and spin liquids and fractionalized excitations. Recently, a new framework proposed to classify magnetic phases brought renewed interest in unconventional magnetic states, which are qualitatively distinct from ferromagnets and standard Néel antiferromagnets. Among those, altermagnetic phases have been met with enthusiasm by the scientific community, as they display properties found in both ferromagnets (like the splitting of electronic bands with opposite spins) and conventional antiferromagnets (like the absence of a net magnetization). Formally, what distinguishes these three different magnetic states are the crystalline symmetries that, when combined with time reversal, leave the system invariant. In the case of altermagnets, because these symmetries involve rotations, the system is endowed with unique properties such as nodal spin-splitting and piezomagnetism. In this talk, I will introduce the concept of altermagnetism and discuss its connection to long-standing problems in the field of quantum materials, such as multipolar magnetism and electronic liquid-crystalline phases. I will also present the predicted experimental signatures of altermagnetic order in thermodynamic and transport properties, and show that altermagnets provide a fertile ground to realize non-trivial topological and superconducting phenomena in quantum materials.
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