Quantum geometric origin of orbital magnetization

The exploration of the Riemannian structure of the Hilbert space has given rise to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced our understanding of various electronic phenomena, its potential for elucidating magnetic phenomena has remained less explored. In this Perspective, we highlight how quantum geometry paves a new way for understanding magnetization within a single-particle framework. We first elucidate the geometric origin of equilibrium magnetization in the modern theory of magnetization, then discuss the role of quantum geometry in kinetic magnetization, and finally outline promising future directions at the frontier of quantum geometric magnetization.