Abstract
Altermagnets host spin-split band structures while exhibiting vanishing equilibrium spin magnetization, making field-induced responses a direct probe of their quantum geometry. A central question, in this regard, is which quantum-geometric mechanism can generate a linear spin magnetization in centrosymmetric systems. Here we develop a unified framework based on a generalized quantum geometric tensor that incorporates both momentum translations and spin rotations of Bloch states, and decompose spin magnetization into equilibrium, electric-field-driven, and magnetic-field-driven contributions. We show that inversion symmetry forbids the linear electric-field response in centrosymmetric systems, while C_n T symmetry further suppresses the equilibrium contribution in altermagnets. Consequently, centrosymmetric altermagnets provide a particularly clean realization in which the magnetic-field-induced spin magnetization emerges as the only symmetry-allowed linear quantum-geometric response. We demonstrate that this contribution originates entirely from the spin-rotation quantum metric, establishing it as the sole linear quantum-geometric mechanism in such systems. Using representative centrosymmetric altermagnets, including the d-wave compound FeSb₂ and the g-wave compound CrSb, we show that the spin-rotation quantum metric directly controls this response. Crucially, we predict a giant linear spin magnetization of order 10⁻²μ_Bnm⁻³ at magnetic fields of ∼ 10mT, exceeding typical experimental values for conventional magnets by several orders of magnitude. Our results identify a universal quantum geometric mechanism of spin magnetization operative in centrosymmetric systems in general, and establish centrosymmetric altermagnets as an ideal platform for its experimental detection with potential applications in spintronics.