  In order to establish the correlation between the magnetoelectric coupling
and magnetic instability, we have studied the structural, magnetic, and
ferroelectric properties of \textit{x}BaTiO${_3}$-(1-\textit{x})BiCoO${_3}$ as
a function of BaTiO$_3$ concentration ($x$) and volume.The $G-$type
antiferromagnetic ordering is found to be energetically favorable for $x<$ 0.45
and higher concentrations stabilize with nonmagnetic states. We observe
metamagnetic spin state transitions associated with paraelectric to
ferrolectric transitions as a function of volume and $x$ using synchrotron
diffraction and computational studies, indicating a strong magnetoelectric
coupling. Specifically for $x=$ 0.33 composition, a pressure induced high spin
(HS) to low spin (LS) transition occurs when the volume is compressed below
5\%. Our orbital$-$projected density of states show a HS state for Co$^{3+}$ in
the ferroelectric ground state for $x<$ 0.45 and the corresponding paraelectric
phase is stable in the nonmagnetic state due to the stabilization of LS state
as evident from our fixed$-$spin$-$moment calculations and magnetic
measurements. High values of spontaneous ferroelectric polarizations are
predicted for lower $x$ values which inversely vary with $x$ because of the
reduction of tetragonality ($c/a$) with increase in $x$. Moreover, we find that
the HS$-$LS transition point and magnetoelectric coupling strength can be
varied by $x$.
