Figure 1

Voltage tunable inductor (VTI). Schematic of (a) the structure of VTI. (b) The working principle of VTI. VTI operates on the principle of modulation of magnetic properties in the magnetostrictive layer through strain generated at the interface by applying voltage to the piezoelectric layer. The magnitude of change in the magnetic property in the magnetostrictive layer is dependent upon various anisotropic factors. (c) Pie diagram of the various types of anisotropy (magnetocrystalline anisotropy K _u , shape anisotropy K _d , stress induced anisotropy for magnetostrictive materials \({K}_{\sigma }\), and others including magnetic bias, exchange and random anisotropy) influencing the tunability of permeability and inductance. (d) State-of-the-art inductance tunability of VTIs. Under condition of stress induced anisotropy being dominant, small magnetocrystalline and shape anisotropy are essential requirements towards achieving large inductance tunability. The magnetic anisotropy factor K ₀ represents the summation of initial magnetocrystalline and shape anisotropy. By minimizing K ₀ this study was able to significantly advance the magnitude of tunability. Sphere shape data points represent this study, and square shape data points refer to prior studies (Ref. Lou⁵ and Ref. Liu⁶). (e) Magnetization M behavior under different magnitude of tuning voltage E or stress \(\sigma \): low field Regime I (blue) corresponds to rotation of in-plane magnetization and high-field Regime II (red) corresponds to rotation of out-of-plane magnetization.