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.

表现出直接磁电效应的磁电异质结构的主要优点是可以直接利用外部磁场（即，无线地，不施加电场）来感应和调制铁电相的电响应。然而，在这种异质结构中的磁电耦合通常受到衬底夹持的限制，这阻碍了有效的应变传播。在这项工作中，将1μm厚的铁磁Fe-Ga层电沉积到刚性Si / Cu衬底上，然后涂上铁电P（VDF-TrFE）。在磁场下，（110）织构的Fe-Ga合金沿z方向压缩如X射线衍射所证实的，方向为0.033％。实验结果表明，当Fe-Ga层的底部被夹持时，由于柱状晶粒之间存在残留的纳米多孔性，其空气侧呈现出明显的四方形变形，即在Fe-Ga的整个厚度上形成了应变梯度。嘎片。Fe-Ga中的这种应变梯度会引起相邻铁电P（VDF-TrFE）层的压电响应发生变化。这些结果为在硬质基板上集成磁电响应的高性能微机电系统（MEMS）铺平了道路。