Magnetic quadrupole current generation and accumulation in noncentrosymmetric systems

Magnetization control via magnetic octupole injection has recently been proposed for a new class of centrosymmetric antiferromagnets, namely $d$-wave altermagnets, where the magnetic octupole is the lowest-rank magnetic multipole allowed by symmetry and serves as an alternative carrier to spin injection. In contrast, in noncentrosymmetric antiferromagnets, the magnetic quadrupole (MQ) constitutes the lowest-rank symmetry-allowed magnetic multipole, suggesting that MQ currents can provide an efficient route toward magnetization control through MQ injection. Here, we establish the symmetry conditions for MQ-current generation by constructing the multipole representation of the MQ conductivity tensor and show that MQ currents are generically allowed in noncentrosymmetric crystallographic point groups. As a representative example, we demonstrate MQ-current generation in the linear-response regime associated with symmetry lowering from the centrosymmetric point group ($mmm$) to its noncentrosymmetric subgroup ($mm2$). Furthermore, we reveal MQ accumulation near sample edges, analogous to spin accumulation induced by the spin Hall effect. This edge accumulation provides direct evidence of MQ-current generation and constitutes a key prerequisite for realizing MQ injection and MQ-based magnetization control in noncentrosymmetric antiferromagnets.