Electric field modulation of the non-linear areal magnetic anisotropy energy

We study the ferromagnetic layer thickness dependence of the voltage-controlled magnetic anisotropy (VCMA) in gated CoFeB/MgO heterostructures with heavy metal underlayers. When the effective CoFeB thickness is below ~1 nm, the VCMA efficiency of Ta/CoFeB/MgO heterostructures considerably decreases with decreasing CoFeB thickness. We find that a high order phenomenological term used to describe the thickness dependence of the areal magnetic anisotropy energy can also account for the change in the areal VCMA efficiency. In this structure, the higher order term competes against the common interfacial VCMA, thereby reducing the efficiency at lower CoFeB thickness. The areal VCMA efficiency does not saturate even when the effective CoFeB thickness exceeds ~1 nm. We consider the higher order term is related to the strain that develops at the CoFeB/MgO interface: as the average strain of the CoFeB layer changes with its thickness, the electronic structure of the CoFeB/MgO interface varies leading to changes in areal magnetic anisotropy energy and VCMA efficiency.