Theoretical Modeling of ME effect at Low frequency and Resonance   Frequency for Magnetoelectric Laminates with Anisotropic Piezoelectric   Properties
  A new theory is developed for the magnetoelectric (ME) coupling in a symmetric 2-2 ME laminate having a representative piezoelectric crystal (PMN-PT) particularly with anisotropic piezoelectric properties. Considering the average field method, the theoretical expressions for the transverse ME voltage coefficients at low and resonance frequencies were derived. The theory takes into account the anisotropic properties of the piezoelectric materials providing two different expressions of transverse ME voltage coefficients for different in-plane magnetic fields both at low and resonance frequencies. The numerical simulations show multiple resonance frequencies and phase differences between transverse ME voltage coefficients showing good agreement with the experimental results. Our theory should be generally applicable to other ME laminates with any piezoelectric with anisotropic piezoelectric coefficients. 
Deepak Rajaram Patil, Yisheng Chai, Rahul C. Kambale, Byung-Gu Jeon,   Jungho Ryu, Woon-Ha Yoon, Dong-Soo Park, Dae-Yong Jeo...
cond-mat.mtrl-sci