The rise of unconventional magnetism

Unconventional magnetism represents a paradigm shift in condensed matter physics, effectively bridging the fast, high-density advantages of antiferromagnets with the facile read-write capability of ferromagnets. Recent developments in spin space group theory have established a systematic methodology to decouple magnetic geometry from relativistic spin-orbit coupling, driving the exploration of unconventional magnets that exhibit compensated magnetization with time-reversal-odd responses. Here, we review unconventional magnetism across three pivotal facets in momentum space: spin textures, quantum geometry, and emergent quasiparticles. From the perspective of symmetry analysis, we elucidate the mechanisms underlying time-reversal-odd physical responses, including non-relativistic spin splitting, anomalous and nonlinear Hall effects, and exotic electronic and magnonic topological phases. Finally, we provide a forward-looking perspective on coupling unconventional magnetism with ferroelectricity, superconductivity, and moir\'e engineering. By exploiting symmetry-driven insights, this review highlights the functional potential of unconventional magnets in developing next-generation, high-speed, and energy-efficient spintronic devices.