  In this work, the strain modulation of electronic structure and magnetic
interaction in monolayer nanoribbons of B$_2$S, a recently realized monolayer
system, is investigated. In the first part of our study, we focus on how the
electronic structure of monolayer nanoribbons of B$_2$S is modified under
uniaxial strains, then employing a tight-binding framework together with the
conventional theory of elasticity, we discuss how strain-induced local
deformations can be used as a means to affect Ruderman-Kittel-Kasuya-Yosida
(RKKY) interaction in zigzag nanoribbons of B$_2$S. We show that breaking
inversion symmetry in zigzag B$_2$S nanoribbons (ZBSNR), e.g., by introducing
staggered sublattice potentials, play a key role in the modulation of their
electronic properties. More interestingly, for the ZBSNRs belong to the group
$M=4p$, with $M$ the width of the ZBSNR and $p$ an integer number, one can see
that a band gap, in which a pair of near-midgap bands completely detached from
the bulk bands is always observed. As a key feature, the position of the midgap
bands in the energy diagram of ZBSNRs can be shifted by applying the in-plane
strains $\varepsilon_x$ and $\varepsilon_y$. Moreover, the near-midgap
bandwidth monotonically decreases with increasing strength of the strain and
increases with the width of the ZBSNR. The energy gap of the ZBSNRs decreased
with increasing the applied strain and ribbon width. The spatial and strain
dependency of the exchange interaction in various configurations of the
magnetic impurities are also evaluated. The magnetic interactions between
adsorbed magnetic impurities in B$_2$S nanoribbons can be manipulated by
careful strain engineering of such systems. Our results suggest that these
tunable electronic and magnetic properties of ZBSNRs mean they may find
applications in spintronics and pseudospin electronics based on monolayer
B$_2$S nanoribbons.
