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The transverse and longitudinal magnetoelectric susceptibilities (MES) werequantitatively determined for (001) heteroepitaxialBiFeO$_{3}$-CoFe$_{2}$O$_{4}$ nanostructures. Both of these MES values weresharply enhanced at magnetic fields below 6 kOe and revealed asymmetriclineshapes with respect to the dc magnetic field, demonstrating thestrain-induced magnetoelectric effect. The maximum transverse MES, whichreached as high as $\sim$60 mV/cm Oe, was about five times larger than thelongitudinal MES. This observation signifies that transverse magnetostrictionof the CoFe$_{2}$O$_{4}$ nanopillars is enhanced more than the bulk value dueto preferred magnetic domain alignment along the [001] direction coming fromcompressive, heteroepitaxial strain.

Quantitative determination of anisotropic magnetoelectric coupling in BiFeO$_{3}$-CoFe$_{2}$O$_{4}$ nanostructures