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Pure spin currents carry information in quantum spintronics and could play anessential role in the next generation low-energy-consumption electronics. Herewe theoretically predict that the magnetic field can induce a quantum spincurrent without a concomitant charge current in metals without time reversalsymmetry $\mathcal{T}$ and inversion symmetry $\mathcal{P}$ but respect thecombined $\mathcal{PT}$ symmetry. It is governed by the magnetic moment of theBloch states on the Fermi surface, and can be regarded as a spinfulgeneralization of the gyrotropic magnetic effect in $\mathcal{P}$-brokenmetals. The effect is explicitly studied for a minimal model of anantiferromagnetic Dirac semimetal, where the experimental signature isproposed. We further propose candidate materials, including topologicalantiferromagnetic Dirac semimetals, Weyl semimetals, and tenary Heuslercompounds.

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