We use spin‐density‐functional theory to study the magnetization of quantum rings. We study in this work two‐dimensional systems containing up to 24 electrons in a perpendicular magnetic field. Increasing the field leads to quasiperiodic Aharonov‐Bohm oscillations and to different magnetic regimes with characteristic spin properties. We find several phases reminiscent of both integer and fractional quantum‐Hall states. We discuss the properties of these states in quantum rings and suggest possible measurements to observe them experimentally.

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