Current-induced quasiparticle magnetic multipole moments

Magnetic ordering that goes beyond the standard dipolar order has attracted significant attention in recent years, but it remains an open question how to effectively manipulate such nontrivial order using external perturbations. In this context, we present a theory for Cartesian magnetic multipole moments carried by electric currents in either magnetic or non-magnetic conductors. We consider the magnetic multipole moments of quasiparticle wave packets, which can circumvent the conceptual difficulties in defining higher-order multipole moments in periodic crystals. As a prototypical example, we pointed out that the low-energy quasiparticles in multi-layer black phosphorous host magnetic octupole moments, which can result in a nonequilibrium magnetic octupole polarization in the presence of electric currents.