Zeeman Quantum Geometry as a Probe of Unconventional Magnetism

Unconventional magnets with momentum-dependent spin-splitting but zero net magnetization form a recently identified class of collinear magnets that are challenging to probe via conventional means. We show that these systems can be distinguished through their intrinsic gyrotropic magnetic (IGM) currents, enabled by the Zeeman quantum geometry, which captures the coupled response of electronic states to momentum translation and spin rotation. Examining two prototypical two-dimensional unconventional magnets with Rashba spin-orbit coupling, a time-reversal-broken $d$-wave altermagnet and a time-reversal-symmetric $p$-wave magnet, we uncover a direct link between crystalline symmetry, spin-split band structures, and transport signatures. The $d_{x^2-y^2}$-wave altermagnet exhibits both transverse conduction and longitudinal displacement IGM currents, whereas the $p$-wave magnet supports only a transverse conduction IGM current. Remarkably, the mixed $d$-wave altermagnet supports all four types of IGM currents, including a longitudinal conduction current enabled by symmetric (Zeeman) Berry curvature that is forbidden in conventional quantum geometry. These responses, measurable via Hall transport and optical probes, persist even when conventional quantum geometry-driven linear responses vanish, offering unique access to hidden spin-split band structures. Our results establish Zeeman quantum geometry as both a diagnostic tool and a design principle for novel magnetic materials.