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We have fabricated a series of composition spreads consisting of ferroelectric BaTiO3 and piezomagnetic CoFe2O4 layers of varying thicknesses modulated at nanometer level in order to explore artificial magnetoelectricthin-film heterostructures. Scanning microwavemicroscopy and scanning superconducting quantum interference device microscopy were used to map the dielectric and magnetic properties as a function of continuously changing average composition across the spreads, respectively. Compositions in the middle of the spreads were found to exhibit ferromagnetism while displaying a dielectric constant as high as ≈120.