Title: Electric field modulation of the non-linear areal magnetic anisotropy energy,
Abstract: 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.