Voltage-Driven Nonlinearity in Magnetoelectric Heterostructures

Magnetoelectric (ME) heterostructures are widely studied to realize functional applications, such as magnetometers, ME random access memory (MERAM), ME antennas, energy harvesters, and voltage microwave devices. A good understanding of the nonlinearity of ME heterostructures can lead to potentially improved performance. Here, we present an investigation into the voltage-driven nonlinear phenomena of a ME heterostructure near its electromechanical resonance. The Stoner-Wohlfarth model and Duffing equation are used to study the ΔE effect in amorphous Metglas alloy and the nonlinear behavior of a ME heterostructure, respectively. Then, the dependence of the nonlinearity on bias field, driving voltage, mechanical quality factor, and the frequency sweeping direction are systematically studied and verified. Experimental results show that spring-hardening and -softening behavior is separately obtained at bias fields of 25 Oe and 50 Oe, respectively. In addition, hysteresis is observed when sweeping the frequency forward and then backward at a driving voltage of 5 V; this agrees well with qualitative analysis. This work provides a route to induce, control, and possibly exploit the nonlinear behavior of ME devices, such as magnetic-field energy harvesters and ME sensors and antennas.

Figure 1

(a) Schematic of the ME heterostructure incorporating Metglas as magnetostrictive phase and PMN-PZT crystals as piezoelectric phase. A sine voltage is used to drive the sample and a pick up is utilized to capture the induced signal. (b) The magnetic domain patter in the amorphous alloy Metglas is obtained by magneto-optic Kerr effect (MOKE) microscopy. The average width of the magnetic domain is 120 µm. (c) The calculated Young’s modulus of Metglas as a function of the applied magnetic field and stress along the long axis with K_⊥ = 100 J/m³, ${\mu }_0$M_s = 1.2 T, λ_s = 27 ppm, θ = 85° and E_s = 110 GPa.

Figure 2

(a) Exemplary frequency response of the displacement amplitude for a nonlinear system with k₃ = −100 × 10⁹, 0, and 100 × 10⁹ N/m³. The effective mass, m, and the linear spring constant are 22.62 mg and 1.6 × 10⁶ N/m, respectively. Q and driving force are kept as 100 and 1 N, respectively. The dependence of (b) the driving force, F (=0.5 N, 0.3 N, 0.1 N), and (c) Q_m (=100, 75, 50) on the nonlinearity.

Figure 3

(a) Measured frequency response of the induced voltage under different bias fields for the ME heterostructure. The x axis is the expressed as a frequency offset with respect to the center frequency, f₀. (b) Measured frequency response of the induced voltage under driving voltages from 1 V to 5 V at a fixed bias field of 20 Oe. The inset of Fig. 3 gives the corresponding −3 dB bandwidth values.

Figure 4

Measured frequency response of the induced voltage under different Q factors for the ME heterostructure.

Figure 5

(a) Measured frequency response of the induced voltage under different driving voltages at a fixed bias field of 20 Oe for the ME heterostructure. Here, the driving voltage is applied by forward and backward sweeping of the frequency. (b) Measured frequency response of the induced voltage under different bias fields, but at a fixed voltage of 5 V for the (1-1) ME sensor. The (1-1) ME sensor consists of a thickness-poled [011]-oriented PMN-PZT fiber with sizes of 30 × 1 × 0.2 mm³ and five-layered Metglas fibers with sizes of 100 × 1.5 × 0.125 mm³ bonded on the bottom and top sides of the piezoelectric phase.