3.1. Magnetoimpedance Effect
As the structure of the FeGa/PZT bilayered composite is asymmetric, the asymmetrical stress distributions of the magnetostrictive and piezoelectric layers produce flexural deformation and result in the bending of the FeGa and PZT layers. Correspondingly, the bending vibration mode can be also observed for the FeGa/PZT composite in addition to the longitudinal vibration mode existing in the symmetrical trilayered composites. Here, the bending resonance frequency of the FeGa/PZT bilayered composite can be expressed by [
23].
where
and
n is the order of the bending vibration mode. When
n = 1, it is the first-order bending vibration mode.
d and
l are the thickness and length of the composite, respectively. The average density
and average Young’s modulus
of the FeGa/PZT laminated composite can be expressed as
where
m and 1 −
m are the volume fractions of the PZT and FeGa layers, respectively;
and
are the Young’s moduli of the PZT and FeGa layers, respectively; and
and
are the densities of the PZT and FeGa layers, respectively. The longitudinal resonance frequency is evaluated by [
23]
By using the typical material parameters of the bilayered composite listed in
Table 1, Equations (1) and (4), and the geometries of the laminate given above, the first bending resonance frequency (
n = 1) and longitudinal resonance frequency of the FeGa/PZT bilayered composite are predicted to be 28.9 kHz and 106.5 kHz, respectively. Here, the first bending resonance frequency is much lower than the first longitudinal resonance frequency.
The impedance and phase angle spectra of the FeGa/PZT composite are measured over a frequency range of 1 kHz < f < 120 kHz, as is shown in
Figure 3. Two minimum impedances of 9.5 and 2.3 kΩ can be observed at the electromechanical resonances of 28 kHz and 106 kHz, respectively. Here, the resonance peak at 28 kHz is ascribed to the first bending mode, while the resonance peak at 106 kHz is attributed to the first longitudinal resonance mode. Such experimental results agree with the predicted results well.
Next, the magnetoimpedance effects of the FeGa/PZT composites under both bending and longitudinal vibration modes were measured as a function of electrical excitation frequency at various dc magnetic fields (H
dc), as shown in
Figure 4 and
Figure 5. Firstly, the FeGa/PZT composite operates in the bending vibration mode due to the flexural deformation caused by asymmetric magnetostrictive stress in the bilayered composite. It can be seen in
Figure 4 that when H
dc = 3 Oe, the impedance reaches the minimum value (i.e., Z
n = 2.2 kΩ) at the bending resonance frequency
fr = 28.1 kHz and the maximum value (i.e., Z
m = 9.1 kΩ) at the bending antiresonance frequency
fa = 28.5 kHz. For comparison, the minimum impedance (i.e., Z
n = 0.55 kΩ) and maximum impedance (i.e., Z
m = 2.35 kΩ) of the FeGa/PZT composite under the same magnetic field of 3 Oe occur at the longitudinal resonance frequency
fr = 106.7 kHz and antiresonance frequency
fa = 107.9 kHz, respectively. It should be noted that the resonance and antiresonance frequencies of the FeGa/PZT composites under the bending and longitudinal vibration modes have great discrepancies due to the different vibration behaviors.
Furthermore, it is interesting to find that resonance frequency f
r and antiresonance frequency f
a of FeGa/PZT composites show obvious dependences on H
dc, as shown in
Figure 6. Specifically, f
r and f
a vary with the dc magnetic field in a similar trend for the ME composite operating at the same vibration mode; however, the trends of f
r and f
a as a function of H
dc are distinct between the bending mode and longitudinal mode. For the FeGa/PZT composite at the bending mode, f
r and f
a decrease to a minimum value with the increasing H
dc, and then gradually increase when H
dc further increases. For comparison, the f
r and f
a of the FeGa/PZT composite at the longitudinal mode increase with increased H
dc until reaching the maximum saturation value at H
dc = 800 Oe. The obvious nonmonotonic trend of the resonance frequency with H
dc is attributed to the varied Young’s modulus caused by magnetostriction (i.e., the
effect). Specifically, the Young’s modulus
Em of FeGa varies with H
dc due to different magnetic domain movements under various magnetic fields. According to Equations (1) and (4), the resonance frequency of the ME composite is proportional to the ME composite’s average Young’s modulus, which results in the dependence of H
dc on the resonance frequency. This study is expected to guide the design of magnetic field-tuned ultrasonic transducers.
It is also found that the maximum impedance (Z
m) corresponding to the antiresonance frequency f
a and the minimum impedance (Z
n) corresponding to the resonance frequency f
r vary nonmonotonically with H
dc, as shown in
Figure 2 and
Figure 3. When H
dc increases from 0 Oe to 1500 Oe, the maximum impedance Z
m of the bending-mode FeGa/PZT composite varies from 7.02 kΩ to 10.22 kΩ and the maximum impedance Z
m of the longitudinal-mode FeGa/PZT composite changes from 21.01 kΩ to 25.62 kΩ. This means that the impedance of the FeGa/PZT laminated composite can be magnetically tuned. The reason for this is that the impedance is inversely proportional to the relative effective permittivity. According to the constitutive equations of the piezoelectric and magnetostrictive phases and the interlayer elastic coupling [
24], the relative effective permittivity
can be given by
where
;
is the angular frequency;
kl/2 = π/2 is the resonant condition;
and
are the piezoelectric coefficient and relative effective permittivity of the piezoelectric material, respectively;
is the piezomagnetic coefficient of the magnetostrictive material;
and
are the compliance coefficient of the magnetostrictive and piezoelectric materials, respectively;
is the average mass density; and
n is the piezoelectric material volume fraction. Equation (5) shows that the
of the ME composite is closely relative to the piezomagnetic coefficient
, compliance coefficient
and the angular frequency. For the FeGa/PZT laminated composite, the applied dc magnetic field induces the magnetostriction of FeGa due to the varying piezomagnetic effect with the dc magnetic field H
dc. Such strains are transferred to the neighboring piezoelectric material PZT due to the interface coupling, which changes the dielectric polarization of the FeGa/PZT composite. Furthermore, the applied dc magnetic field produces the varied Young’s modulus of FeGa due to the
effect, which results in the variations of the resonance frequency and compliance coefficient
. Such magnetic field-induced changes of the piezomagnetic coefficient, the resonance frequency and the compliance coefficient cause the varied
of the FeGa/PZT composite with H
dc, which in turn leads to a change of impedance considering that the impedance of the ME composite is inversely proportional to the relative effective permittivity
.
To further investigate the magnetoimpedance (MI) ratio with H
dc, the MI ratios of the FeGa/PZT composite were measured at f
a and f
r of both the resonant and antiresonant frequencies (
Figure 7), respectively. Here, the MI ratio is defined as
where
and
are the impedance values at H
dc and the maximum field
of 1500 Oe, respectively. It was found that the maximum MI ratio ΔZ/Z of the bending-mode FeGa/PZT composite at the antiresonance frequency f
a = 28.78 kHz and resonance frequency f
r = 28.5 kHz is about 215% and 115.8%, respectively. For comparison, the maximum ΔZ/Z of the longitudinal-mode FeGa/PZT composite is about 85% and 11.67% at the antiresonance frequency f
a = 107.9 kHz and resonance frequency f
r = 106.6 kHz, respectively. Compared with the longitudinal-mode FeGa/PZT composite, the ΔZ/Z of the bending-mode FeGa/PZT composite is much higher at both the resonance and antiresonance frequencies, respectively. Specifically, the maximum ΔZ/Z of the bending-mode FeGa/PZT composite is 2.53 times as high as that of the longitudinal-mode FeGa/PZT at the antiresonance frequency. The reason is as follows: on the one hand, the longitudinal resonance frequency is about 4 times higher than the bending resonance frequency, and the compliance coefficient is inversely proportional to the resonance frequency. Hence, the compliance coefficient of the FeGa/PZT composite at the bending mode is much higher than that at the longitudinal mode. It is known that the ME composite’s impedance is determined by the compliance coefficient, since the obvious change of the compliance coefficient at the bending mode with the dc magnetic field causes the significant variations of the relative effective permittivity
and impedance with increased H
dc. On the other hand, the applied
along the length direction of FeGa induces the magnetostriction, and the magnetostrictive strain is transferred to the neighboring piezoelectric material PZT due to the interface coupling effect. When the FeGa elongates, the PZT shortens at first due to the bending strain caused by the modulus discrepancy of FeGa and PZT and the asymmetric structure of the bilayered FeGa/PZT composite. In this case, the bilayer FeGa/PZT laminated structure will be bent for the bending vibration mode. Due to the nonsymmetrical stress distribution in the bilayered FeGa/PZT composite, the bending strain varies more obviously under various H
dc compared to that at the longitudinal mode. Correspondingly, the bilayered ME composite operating at the bending vibration mode exhibits a lower resonance frequency and stronger magnetoimpedance effect compared with that at the longitudinal vibration mode. Hence, the bilayered bending-mode FeGa/PZT composite not only exhibits a giant ΔZ/Z effect, but also keeps its size small and decreased eddy current loss compared to the longitudinal-mode ME composite at the high frequency. This result facilities the optimization of ME composites with a giant magnetoimpedance effect. Furthermore, the magnetically modulated impedances of FeGa/PZT composites provide wide applications for tunable spin filters, memory devices, magnetic anomaly sensing, etc.
3.2. Magnetocapacitance Effect
The capacitance with two plain plates is
, where
A is the area of a plate and
d is the thickness of the piezoelectric material. For the ME composite, the expression of the capacitance can be written as [
24]
From Equations (5) and (6), the capacitance
C depends on the relative effective permittivity
εr. The magnetic field-induced change of piezomagnetic coefficient
and compliance coefficient
in the magnetostrictive material leads to the variations of the relative effective permittivity
εr. Correspondingly, this leads to the change of capacitance with the dc magnetic field, namely the magnetocapacitance (MC) effect. Castel et al. have reported BaTiO
3/Ni nanocomposites which show a giant magnetodielectric effect or magnetocapacitance effect [
17,
18].
At electromechanical resonance frequency, a dramatic variation of
is induced by the enhancement of the stress. Due to the dependence of the MC effect on
, it is expected to show a giant MC effect at electromechanical resonance. This means that capacitance is a function of applied bias magnetic field intensity, as shown in
Figure 8. The capacitance
C values first decrease and then increase at the bending and longitudinal vibration modes’ resonant frequency with the increase of the magnetic field, then capacitance decreases again with further increased H
dc. Moreover, capacitance values have a smaller change at the dual-mode antiresonance frequency with the increasing H
dc. However, the impedance Z and capacitance C exhibit opposite trends as a function of the dc magnetic field. This is because the impedance is inversely proportional to the relative effective permittivity
or corresponding capacitance, while it is directly proportional to the relative permeability
μr and corresponding inductance of the ME composite. At the resonance frequency, the capacitance achieves the maximum value while the inductance reaches the minimum value, which leads to the minimum impedance, and vice versa [
25]. This also indicates that the MC effect of the ME composite caused by strain induces magnetic and ferroelectric domain interactions.
The magnetocapacitance ratio (MC) is defined as follows [
16]:
where
and
are the sample capacitance values at the dc bias magnetic fields and the maximum field
of 1500 Oe, respectively. To precisely observe the magnetic field-dependent magnetocapacitance at different frequencies, magnetocapacitance versus magnetic fields curves under different frequencies are shown in
Figure 9.
At the resonant frequency of 28.5 kHz, the magnetocapacitance ratio ΔC/C of the bending-mode FeGa/PZT composite reaches the maximum value of 406% at the magnetic field of 0.8 kOe. Compared with the previously reported room-temperature MC of 45% at the frequency of 1.0 kHz and saturated magnetic field of 6.0 kOe in Co
2+ doped SnO
2 dielectric films [
14] as well as the maximum MC of 200% for the piezoelectric–magnetostrictive resonator at the anti-resonance frequency [
11], the room-temperature MC achieved by this study is improved significantly. In the same case, the maximum MC of the longitudinal-mode FeGa/PZT composite reaches 115% at the resonant frequency of 106.6 kHz. Such strong abilities of tuning capacitance with the magnetic field make the FeGa/PZT composite an ideal candidate for tunable impedance device applications. Additionally, both in the longitudinal-mode and bending-mode condition, the maximum ΔC/C of the FeGa/PZT composite at resonance is larger than that of the FeGa/PZT composite at antiresonance. As previously mentioned, the change trend of impedance and capacitance with the magnetic field is opposite. At resonance, the FeGa/PZT composite is considered to act as a capacitor, where its capacitance reaches a maximum value and its impedance exhibits a minimum value.