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This paper describes the magnetoelectric (ME) coupling behavior of the nano bi-layer L-T (longitudinal-transverse) mode bar structure through the ME coefficient mathematical model that is developed in high frequency regime. Terfenol-D and Lead Zirconate Titanate (PZT) are used as ferromagnetic (FM) and ferroelectric (FE) layers, respectively. The ME coefficients are determined at different layer thickness ratios and products of the operating frequency ( f ) and structure length ( l ). It is found that the ME coefficient and optimal thickness ratio increases and decreases exponentially respectively, with  fl . The minimum and maximum peak ME coefficients at  fl  values of 0.1 and 1,200 respectively, are around 1,756 and 5,617 mV/Oe   $$\cdot $$  · cm with the optimal thickness ratio of 0.43 and 0.19, respectively. The ME coupling behavior depends largely on the magnetostrictive effect in the FM layer that is altered by the applied magnetic field and  fl . The demonstration as the read sensor for the hard disk drive (HDD) with 2 Tbit/in 2  areal density and 190 Oe/bit applied magnetic field shows the output voltage across the FE layer of around 0.43 mV, which is more than sufficient for the raw signal readback.

Mathematical modeling of the magnetoelectric effect of the nano bi-layer L-T mode bar structure in high frequency regime