A Unified Review of Altermagnetism: Momentum-Space Spin Polarization and Emerging Applications.

Altermagnetism has recently emerged as a distinct class of collinear magnetic order that extends the conventional classification of ferromagnets and antiferromagnets. Unlike ferromagnets with finite net magnetization and conventional antiferromagnets with symmetry-protected spin degeneracy, altermagnets exhibit symmetry-enforced, momentum-dependent spin splitting despite possessing zero net magnetization. This unique behavior originates from crystal and spin-group symmetries, including proper and improper rotations, mirror reflections, and roto-inversions, which relate opposite-spin sublattices and generate anisotropic spin polarization throughout the Brillouin zone. In this review, we present a comprehensive and concept-driven overview of the fundamental principles, materials, and emerging functionalities of altermagnetism. We discuss the theoretical framework based on spin-space-group symmetry, its relationship to conventional magnetic space groups, and the role of symmetry in determining electronic, magnetic, and transport properties. We further review key experimental techniques for identifying altermagnetic states, including spin-resolved and soft-x-ray ARPES, x-ray magnetic dichroism, neutron scattering, and transport measurements, together with current challenges such as the ongoing RuO2 debate. Representative three-dimensional, two-dimensional, Janus, topological, superconducting and strain-engineered altermagnetic materials are surveyed alongside first-principles and multiscale computational approaches for materials discovery. Finally, we highlight emerging transport phenomena and potential applications in spintronics, superconducting heterostructures, valleytronics, magnonics, orbitronics, and quantum technologies.