  The study investigates the manipulation of the magnetic anisotropy in a thick
(1 $\mu$m) Ni$_{90}$Fe$_{10}$ layer electrodeposited on a ferroelectric
BaTiO$_3$(001) substrate, using a combination of Magneto-optical Kerr Effect,
Photoemission Electron Microscopy with X-ray circular magnetic dichroism and
X-ray diffraction. In the as-grown state, the system shows weak perpendicular
magnetic anisotropy and characteristic stripe domains. Upon out-of-plane
electrical poling of the BaTiO$_3$ substrate, the magnetic anisotropy switches
to in-plane with a strong uniaxial behavior. This change is ascribed to the
magnetoelastic effect due to the switching of the BaTiO$_3$ ferroelectric [001]
axis into the sample plane, as evidenced by XRD. The strong mechanical
interaction with the thick Ni$_{90}$Fe$_{10}$ overlayer prevents the full
inversion of the substrate. The perpendicular magnetic anisotropy can be
recovered by a mild thermal annealing above the BaTiO$_3$ tetrahedral to cubic
phase transition and can be cycled by repeated electrical poling/thermal
annealing. This method opens the path to a reversible control of the magnetic
anisotropy in Ni$_{90}$Fe$_{10}$/BaTiO$_3$ heterostructures from perpendicular
to in-plane.
