Intrinsic gyrotropic magnetic current from Zeeman quantum geometry

Quantum geometric tensor (QGT), which is usually obtained by evaluating the quantum distance between Bloch states parametrized by momentum, plays a key role in exploring the exotic responses of quantum materials. Herein, we revisit the concept of QGT by further taking into account the spin degree of freedom. Besides the conventional QGT relating to momentum translation, we uncover a new QGT (termed Zeeman QGT) relating to momentum translation as well as spin rotation, whose imaginary (real) part gives the Zeeman Berry curvature (quantum metric). Notably, we show that these novel quantum geometric quantities can drive an intrinsic gyrotropic magnetic current (IGMC) in spin-orbit coupled materials when the electron spin is steered by an oscillating magnetic field. With symmetry analysis, we show that a wide range of materials can support the IGMC, as illustrated by model calculations. Finally, we discuss the experimental aspects of detecting the IGMC driven by Zeeman QGT.