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In order to establish the correlation between the magnetoelectric couplingand magnetic instability, we have studied the structural, magnetic, andferroelectric properties of \textit{x}BaTiO${_3}$-(1-\textit{x})BiCoO${_3}$ asa function of BaTiO$_3$ concentration ($x$) and volume.The $G-$typeantiferromagnetic ordering is found to be energetically favorable for $x<$ 0.45and higher concentrations stabilize with nonmagnetic states. We observemetamagnetic spin state transitions associated with paraelectric toferrolectric transitions as a function of volume and $x$ using synchrotrondiffraction and computational studies, indicating a strong magnetoelectriccoupling. Specifically for $x=$ 0.33 composition, a pressure induced high spin(HS) to low spin (LS) transition occurs when the volume is compressed below5\%. Our orbital$-$projected density of states show a HS state for Co$^{3+}$ inthe ferroelectric ground state for $x<$ 0.45 and the corresponding paraelectricphase is stable in the nonmagnetic state due to the stabilization of LS stateas evident from our fixed$-$spin$-$moment calculations and magneticmeasurements. High values of spontaneous ferroelectric polarizations arepredicted for lower $x$ values which inversely vary with $x$ because of thereduction of tetragonality ($c/a$) with increase in $x$. Moreover, we find thatthe HS$-$LS transition point and magnetoelectric coupling strength can bevaried by $x$.

Metamagnetism stabilized giant magnetoelectric coupling in ferroelectric \textit{x}BaTiO${_3}$-(1-\textit{x})BiCoO${_3}$ solid solution