Magnetoelectric coupling is of interest for a variety of applications, but is weak in monolithic materials. Strain-coupled bilayers or multilayers of piezoelectric and magnetostrictive material are an attractive way of obtaining enhanced effective magnetoelectricity. This paper studies the optimization of magnetoelectricity with respect to the crystallographic orientations and the relative thickness of the two materials. We show that the effective transverse (α_(E,31)) and longitudinal (α_(E,33)) coupling constants can be enhanced many-fold at the optimal orientation compared to those at normal orientation. For example, we show that the constants are 17 and 7 times larger for the optimal orientation of a lithium niobate/Terfenol-D bilayer of equal thickness compared to the normal orientation. The coupling also increases as the piezoelectric phase gets thinner.
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