Generation of Spin Currents by Magnetic Field in $\mathcal{T}$- and $\mathcal{P}$-Broken Materials

Pure spin currents carry information in quantum spintronics and could play an essential role in the next generation low-energy-consumption electronics. Here we theoretically predict that the magnetic field can induce a quantum spin current without a concomitant charge current in metals without time reversal symmetry $\mathcal{T}$ and inversion symmetry $\mathcal{P}$ but respect the combined $\mathcal{PT}$ symmetry. It is governed by the magnetic moment of the Bloch states on the Fermi surface, and can be regarded as a spinful generalization of the gyrotropic magnetic effect in $\mathcal{P}$-broken metals. The effect is explicitly studied for a minimal model of an antiferromagnetic Dirac semimetal, where the experimental signature is proposed. We further propose candidate materials, including topological antiferromagnetic Dirac semimetals, Weyl semimetals, and tenary Heusler compounds.