  We discuss DC electric-field controls of superexchange interactions. We first
present generic results about antiferromagnetic and ferromagnetic superexchange
interactions valid in a broad class of Mott insulators, where we also estimate
typical field strength to observe DC electric-field effects: $\sim
1~\mathrm{MV/cm}$ for inorganic Mott insulators such as transition-metal oxides
and $\sim 0.1~\mathrm{MV/cm}$ for organic ones. Next, we apply these results to
geometrically frustrated quantum spin systems. Our theory widely applies to
(quasi-)two-dimensional and thin-film systems and one-dimensional quantum spin
systems on various lattices such as square, honeycomb, triangular, and kagome
ones. In this paper, we give our attention to those on the square lattice and
on the chain. For the square lattice, we show that DC electric fields can
control a ratio of the nearest-neighbor and next-nearest-neighbor exchange
interactions. In some realistic cases, DC electric fields make the two
next-nearest-neighbor interactions nonequivalent and eventually turns the
square-lattice quantum spin system into a deformed triangular-lattice one. For
the chain, DC electric fields can induce singlet-dimer and Haldane-dimer
orders. We show that the DC electric-field-induced spin gap $\propto
|\boldsymbol E|^{2/3}$ in the Heisenberg antiferromagnetic chain will reach
$\sim 10~\%$ of the dominant superexchange interaction in the case of a
spin-chain compound $\mathrm{KCuMoO_4(OH)}$ when the DC electric field of $\sim
1~\mathrm{MV/cm}$ is applied.
