  Manipulating spin currents in magnetic insulators is a key technology in
spintronics. We theoretically study a simple inversion-asymmetric model of
quantum antiferromagnets, where both the exchange interaction and the magnetic
field are staggered. We calculate spin currents generated by external electric
and magnetic fields by using a quantum master equation. We show that an ac
electric field with amplitude $E_0$ leads, through exchange-interaction
modulation, to the dc and second-harmonic spin currents proportional to
$E_0^2$. We also show that dc and ac staggered magnetic fields $B_0$ generate
the dc and ac spin currents proportional to $B_0$, respectively. We elucidate
the mechanism by an exactly solvable model, and thereby propose the ways of
spin current manipulation by electromagnetic fields.
