  The $J_1$-$J_2$ quantum spin sawtooth chain is a paradigmatic one-dimensional
frustrated quantum spin system exhibiting unconventional ground-state and
finite-temperature properties. In particular, it exhibits a flat energy band of
one-magnon excitations accompanied by an enhanced magnetocaloric effect for two
singular ratios of the basal interactions $J_1$ and the zigzag interactions
$J_2$. In our paper, we demonstrate that one can drive the spin system into a
flat-band scenario by applying an appropriate electric field, thus overcoming
the restriction of fine-tuned exchange couplings $J_1$ and $J_2$ and allowing
one to tune more materials towards flat-band physics, that is to show a
macroscopic magnetization jump when crossing the magnetic saturation field, a
residual entropy at zero temperature as well as an enhanced magnetocaloric
effect. While the magnetic field acts on the spin system via the ordinary
Zeeman term, the coupling of an applied electric field with the spins is given
by the sophisticated Katsura-Nagaosa-Balatsky (KNB) mechanism, where the
electric field effectively acts as a Dzyaloshinskii-Moriya spin-spin
interaction. The resulting novel features are corresponding reciprocal effects:
We find a magnetization jump driven by the electric field as well as a jump of
the electric polarization driven by the magnetic field, i.e.\ the system
exhibits an extraordinarily strong magnetoelectric effect. Moreover, in analogy
to the enhanced magnetocaloric effect the system shows an enhanced
electrocaloric effect.
