Strain gradient mediated magnetoelectricity in Fe-Ga/P(VDF-TrFE) multiferroic bilayers integrated on silicon

The primary advantage of magnetoelectric heterostructures exhibiting direct magnetoelectric effect is the possibility to induce and modulate the electrical response of the ferroelectric phase directly with an external magnetic field (i.e., wirelessly, without applying electric field). Nevertheless, the magnetoelectric coupling in such heterostructures is commonly limited by substrate clamping which hinders effective strain propagation. In this work, 1 μm thick ferromagnetic Fe-Ga layers were electrodeposited onto rigid Si/Cu substrates and subsequently coated with ferroelectric P(VDF-TrFE). Under magnetic field, the (110) textured Fe-Ga alloy is compressed along the z-direction by 0.033%, as demonstrated by X-ray diffraction. The experimental results suggest that while the bottom of the Fe-Ga layer is clamped, its air side exhibits a pronounced tetragonal deformation thanks to the residual nanoporosity existing between the columnar grains, that is, a strain gradient develops across the thickness of the Fe-Ga film. This strain gradient in Fe-Ga induces a change in the piezoresponse of the adjacent ferroelectric P(VDF-TrFE) layer. These results pave the way to the design of high-performance microelectromechanical systems (MEMS) with magnetoelectric response integrated on rigid substrates