Anisotropy of the ΔE Effect in Ni-Based Magnetoelectric Cantilevers: A Finite Element Method Analysis

In recent investigations of magnetoelectric sensors based on microelectromechanical cantilevers made of TiN/AlN/Ni, a complex eigenfrequency behavior arising from the anisotropic ΔE effect was demonstrated. Within this work, a FEM simulation model based on this material system is presented to allow an investigation of the vibrational properties of cantilever-based sensors derived from magnetocrystalline anisotropy while avoiding other anisotropic contributions. Using the magnetocrystalline ΔE effect, a magnetic hardening of Nickel is demonstrated for the (110) as well as the (111) orientation. The sensitivity is extracted from the field-dependent eigenfrequency curves. It is found, that the transitions of the individual magnetic domain states in the magnetization process are the dominant influencing factor on the sensitivity for all crystal orientations. It is shown, that Nickel layers in the sensor aligned along the medium or hard axis yield a higher sensitivity than layers along the easy axis. The peak sensitivity was determined to 41.3 T^-1 for (110) in-plane-oriented Nickel at a magnetic bias flux of 1.78 mT. The results achieved by FEM simulations are compared to the results calculated by the Euler-Bernoulli theory.