The observation and theory of a large remanent magnetoelectric (ME) coefficient and coercivity in the static field $H$ dependence of the low-frequency ME effects are reported for bilayers of lead zirconate titanate (PZT) and a functionally graded ferromagnetic layer. The grading involves magnetization with the use of nickel zinc ferrite of composition Ni${}_{0.7}$Zn${}_{0.3}$Fe${}_2$O${}_4$ (NZFO) and pure Ni. In homogeneous bilayers of PZT-Ni or PZT-NZFO, the ME voltage coefficient (MEVC) vs $H$ data do not show any hysteresis or remanence. Upon grading the ferromagnetic layer, significant changes including hysteresis and remanece are observed. In PZT-Ni-NZFO, MEVC vs $H$ data show a positive remnant MEVC and a negative coercive field. When the grading is reversed, in samples of PZT-NZFO-Ni, the remnant MEVC is negative and the coercive field is positive. A theory is proposed for the low-frequency ME effects in the graded composites. According to the model, the grading in the magnetization leads to a built-in magnetic field in the ferromagnetic layer, and this field depends on the sequence of grading and the thickness of the NZFO and Ni layers. As a result, the total torque moment and flexural deformations in the composite and the bias field dependence of ME voltage coefficient becomes strongly hysteretic. Calculated MEVC vs $H$, remnant MEVC, and coercive field are in good agreement with the data.

• Received 31 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.104404