Strain-coupled magnetoelectric (ME) phenomena in piezoelectric / ferromagnetic thin-film bilayers are a promising paradigm for sensors and information storage devices, where strain is utilized to manipulate the magnetization of the ferromagnetic film. In-plane magnetization rotation with an electric field across the film thickness has been challenging due to the virtual elimination of in-plane piezoelectric strain by substrate clamping, and to the requirement of anisotropic in-plane strain in two-terminal devices. We have overcome both of these limitations by fabricating lithographically patterned devices with a piezoelectric membrane on a soft substrate platform, in which in-plane strain is freely generated, and a patterned edge constraint that transforms the nominally isotropic piezoelectric strain into the required uniaxial strain. We fabricated 500 nm thick, (001) oriented [Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$]$_{0.7}$-[PbTiO$_3$]$_{0.3}$ (PMN-PT) unclamped piezoelectric membranes with ferromagnetic Ni overlayers. Guided by analytical and numerical continuum elastic calculations, we designed and fabricated two-terminal devices exhibiting Ni magnetization rotation in response to an electric field across the PMN-PT. Similar membrane heterostructures could be used to apply designed strain patterns to many other materials systems to control properties such as superconductivity, band topology, conductivity, and optical response.
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