  The transverse and longitudinal magnetoelectric susceptibilities (MES) were
quantitatively determined for (001) heteroepitaxial
BiFeO$_{3}$-CoFe$_{2}$O$_{4}$ nanostructures. Both of these MES values were
sharply enhanced at magnetic fields below 6 kOe and revealed asymmetric
lineshapes with respect to the dc magnetic field, demonstrating the
strain-induced magnetoelectric effect. The maximum transverse MES, which
reached as high as $\sim$60 mV/cm Oe, was about five times larger than the
longitudinal MES. This observation signifies that transverse magnetostriction
of the CoFe$_{2}$O$_{4}$ nanopillars is enhanced more than the bulk value due
to preferred magnetic domain alignment along the [001] direction coming from
compressive, heteroepitaxial strain.
