We find the realization of large converse magnetoelectric (ME) effects at room temperature in a multiferroic hexaferrite Ba$_{0.52}$Sr$_{2.48}$Co$_{2}$Fe$_{24}$O$_{41}$ single crystal, in which rapid change of electric polarization in low magnetic fi
elds (about 5 mT) is coined to a large ME susceptibility of 3200 ps/m. The modulation of magnetization then reaches up to 0.62 $mu$$_{B}$/f.u. in an electric field of 1.14 MV/m. We find further that four ME states induced by different ME poling exhibit unique, nonvolatile magnetization versus electric field curves, which can be approximately described by an effective free energy with a distinct set of ME coefficients.
Comparative studies of magnetoelectric susceptibility ($alpha$), magnetization ($M$), and magnetostriction ($u$) in TbMn$_{2}$O$_{5}$ reveal that the increment of $M$ owing to the field-induced Tb$^{3+}$ spin alignment coins a field-asymmetric line s
hape in the $alpha(H)$ curve, being conspicuous in a low temperature incommensurate phase but persistently subsisting in the entire ferroelectric phase. Correlations among electric polarization, $u$, and $M^{2}$ variation represent linear relationships, unambiguously showing the significant role of Tb magnetoelastic effects on the low field magnetoelectric phenomena of TbMn$_{2}$O$_{5}$. An effective free energy capturing the observed experimental features is also suggested.
