1 Introduction

Multiferroic magnetoelectric (ME) composites consisting of piezoelectric (PE) and magnetostrictive (MS) materials pave new dimensions in various technologies including magnetic sensors, voltage tunable inductors, data storage elements, spintronic, energy harvesters, etc. [1,2,3]. The ME effect in ME composites is a product property of the PE and MS phases through their interfacial coupling [4, 5]. The transfer of mechanical strain between the two phases induces a change in electric polarization in the PE phase or magnetic flux in the MS phase, and the effect is known to be the largest in 2–2 laminate structures [1, 6,7,8]. Since the strain in the MS phase, which determines the overall performance of the ME device, follows a quadrative dependence of DC bias magnetic field (HDC), an external HDC is essential to elicit the best ME performance. The requirement of an external HDC imposes several concerns of the device including electromagnetic interference and system bulkiness as well [3].

In order to circumvent the limitations caused by the necessity of an external HDC, self-biased ME composites have been investigated extensively in recent years [9]. Self-biased magnetoelectric (SME) effect is defined as the ME coupling under an external AC magnetic field (HAC) when HDC = 0. There are five main types of SME composites that have been investigated both experimentally and theoretically: (a) functionally graded ferromagnetic (FM)-based SME; (b) exchange bias-mediated SME; (c) magnetostriction hysteresis-based SME; (d) built-in stress-mediated SME and (e) non-linear SME [4, 9]. Exchange biasing of MS layer is found to be one of the most promising way to achieve SME [4, 10]. Exchange bias (EB) refers to the shift of magnetic hysteresis (M‒H) loop along the field axis, and it is commonly observed in magnetic materials containing hard and soft magnetic phases when cooled through the Néel temperature of antiferromagnetic phase under a suitable magnetic field [4, 10,11,12]. The magnetization shift of the FM layer in laminate composites due to EB field yields corresponding shift in magnetostriction (λ) versus HDC curve of the FM layer, resulting in SME response [9]. Most of the previous studies of EB-mediated SME effects in ME composites have focused on the EB controlled by an external electric field (converse ME effect) [13, 14]. The magnetically controlled EB-mediated SME effect is very rarely reported, although it is important in direct ME devices such as sensors, tunable transformers and energy harvesters [10, 14]. The lack of progress in EB-mediated SME response is due to the difficulties in synthesizing heterogeneous FM materials, requirements of the special protocol including field-cooling, degradation of EB over time, reciprocal dependences on magnetostrictive layer thickness, etc.

Similar to the EB-mediated approach, but much simpler, a pre-applied magnetic field inside the MS layer can be implemented by employing permanent magnets to shift λ versus HDC curve. This approach is expected to be applied to any desired MS materials without complicated experimental procedures. More importantly, deterioration of device characteristics over time is not expected because “permanent” magnet is utilized. Nevertheless, no systematic studies have yet been conducted to verify this method and to understand underlying physical mechanism. Here, we report giant SME effects in MS/PE/MS laminate composite, clamped at its nodal point, with its free ends loaded with magnetic tip masses. Four different layouts of attaching the magnetic tip masses were explored to derive the optimal structure to secure high SME performance. A very high SME voltage coefficient of 52.35 V cm−1 Oe−1 was achieved from the simple laminate structure. To understand the mechanism behind the giant SME response, we discuss the correlation between tendencies of ME voltage versus HDC curve, distribution of pre-applied magnetic field and resultant magnetization of MS layer.

2 Results and Discussion

Figure 1a shows the design schematics of the laminate composite composed of a PE layer sandwiched between two MS layers. The laminate is clamped at its center (nodal point), and its free ends are loaded with a pair of NdFeB (Nd) permanent magnets as tip masses. The magnetic fields of the two Nd magnets can be combined to form a pre-applied magnetic field (HPA) in the MS layers along the longitudinal direction of the laminate. To induce the HPA collinear to HDC through the MS layers, we considered four layouts of attaching Nd magnets as shown in Fig. 1b: (i) the direction of magnetization of Nd magnets (\(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)) is perpendicular to the longitudinal direction of the laminate (\(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case) and Nd magnets are attached to only one MS layer; (ii) \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\) is perpendicular to the longitudinal direction of the laminate and Nd magnets are attached to both MS layers; (iii) \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\) is parallel to the longitudinal direction of the laminate (\(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case) and Nd magnets are attached to only one MS layer; (iv) \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\) is parallel to the longitudinal direction of the laminate and Nd magnets are attached to both MS layers. The four layouts in Fig. 1b are all intended to form HPA inside the MS layers by attractive magnetic force between two Nd magnets. Note that any repulsive configuration of Nd magnets was found to be ineffective for the SME response (i.e., for the shift of λ vs. HDC curve).

Fig. 1
figure 1

a Design schematics of self-biased magnetoelectric laminate composed of two magnetostrictive layers, one piezoelectric layer and two Nd magnets. b Various layouts of attaching Nd magnets at the free ends of the laminate. c Photograph of equipment for measuring magnetoelectric voltage output from the laminate. d Phase angle spectra of Metglas/PZT/Ni laminates with the layouts represented in b. e Bending motion images of Metglas/PZT/Ni laminate with layout (i) in b measured under 2 V at 262 Hz. fαME versus HDC curve of Metglas/PZT/Ni laminate without Nd tip mass. (Color figure online)

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To fabricate the laminate composites, two different MS materials, FeSiB-based alloy (Metglas, stacked to 150 µm-thick, 2605SA1, Metglas Inc.) and nickel (Ni, 160 µm-thick, 99+%, Nilaco Corp.), were used as upper and lower MS layers. As a PE material, Pb(Zr,Ti)O3 (PZT)-based 31-mode piezoelectric ceramics (250 µm-thick, PSI-5H4E, Piezo Systems Inc.) poled along the thickness direction was used. The Metglas and Ni were attached to the top and bottom surfaces of the PZT layer by using epoxy adhesive (DP460, 3 M) and cured at 80 °C. Areal dimensions of all constitutive layers were fixed at 60 mm (l) × 5 mm (b). Then, two small Nd magnets (6 mm × 4 mm × 3 mm) were attached to end surfaces of the MS layers to complete the laminate structures in Fig. 1b. The phase angle spectra of the laminates was measured by using an impedance analyzer (IM3570, Hioki). The actuation shape of the laminate was visualized using a scanning laser vibrometer (Polytec, PSV 500). To characterize ME responses, the laminate was placed at the center of a Helmholtz coil located at the center of the electromagnet (Fig. 1c), and the voltage induced on the laminate was monitored using a lock-in amplifier (SR860, Stanford Research System).

Since the sign of piezomagnetic coefficient (q = dλ/dHDC) of Metglas is positive (+ q), opposite to that of Ni (− q), a bending actuation of the Metglas/PZT/Ni laminate beam can be promoted when exposed to HAC [15]. This approach was effective for achieving low frequency bending resonance of the laminate as shown in Fig. 1d. The Metglas/PZT/Ni laminate without Nd magnets exhibited a bending resonance peak at 483 Hz. The bending resonance peak was further reduced to around 260 Hz by attaching the Nd tip masses, regardless of the attachment layout. The structural bending characteristic is clearly identified by the actuation shape of the Metglas/PZT/Ni laminate in Fig. 1e.

Figure 2 shows the ME voltage coefficient (αME = EAC/HAC, EAC: output electric field) versus HDC curves of the Metglas/PZT/Ni laminate for the magnet attachment layouts (i) and (ii) shown in Fig. 1b. For the layout (i), we investigated two cases: Nd magnets on Metglas surface (case 1) and Nd magnets on Ni surface (case 2). As can be seen in Fig. 2a, the αME versus HDC curves in both cases deviate significantly from the symmetrical shape for both HDC and αME axes (unlike the symmetrical curve of the laminate without Nd magnets in Fig. 1f), exhibiting giant αME- values at HDC = 0 (αSME). The amount shifted on the HDC axis from the origin (ΔH) is determined by the HPA distribution inside the MS layers. The ΔH indicates the HDC required to zero the effective magnetization in the MS layers. In addition, the integral of αME over HDC reflects the effective λ (λeff) of the MS layer (Fig. 2b) since the αME is directly proportional to the q [16]. In case 1, the ΔH and resultant αSME were 20.42 Oe and 52.35 V cm−1 Oe−1, respectively. In case 2, the ΔH was 13.51 Oe and the observed αSME value (23.39 V cm−1 Oe−1) was less than half of case 1. Interestingly, in case 1, the amount of αME of increasing-field maximum (+ αMAX) (point a) was larger than that of decreasing-field maximum (− αMAX) (point b), whereas in case 2, + αMAX (point c) was smaller than − αMAX (point d). However, for the layout (ii), there was no significant difference between + αMAX and − αMAX values as shown in Fig. 2c. The ΔH and αSME for the layout (ii) were 20.97 Oe and 28.25 V cm−1 Oe−1, respectively.

Fig. 2
figure 2

aαME versus HDC curves of Metglas/PZT/Ni laminates with layout (i) measured under HAC of 1 Oe at bending resonance frequencies. b Integral values of αME with respect to HDC for layout (i). cαME versus HDC curve of Metglas/PZT/Ni laminate with layout (ii) measured under HAC of 1 Oe at bending resonance frequency. d Schematics of magnetic field formation by a pair of Nd magnets for layouts (i) and (ii). (Color figure online)

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To elucidate the differences between the αME versus HDC curves observed in layouts (i) and (ii), we considered the distribution of the magnetic field due to Nd magnets as shown in Fig. 2d. For the layout (i), the HPA is concentrated on the upper MS layer and relatively weak inside the lower MS layer when HDC = 0. Moreover, a non-negligible outside magnetic field (HOUT) exists above the laminate between two Nd magnets. In this situation, we first analyze the change in αME under the HDC applied in reverse direction (\(\overleftarrow {{{\text{ } - \text{ H}}_{{{\text{DC}}}} }}\)) for the case 1 (from point a to point b) and case 2 (from point c to point d) in Fig. 2a. In case 1, the + αMAX appears near HDC = 0 (point a), implying that the slope of λeff curve (i.e., q) of the MS layers is maximized by the HPA (point e). As the \(\left| {\overleftarrow {{{\text{ } - \text{ H}}_{{{\text{DC}}}} }} } \right|\) increases gradually by ΔH, the slope of λeff curve gradually decreases and becomes zero at point f. Here, the effective strain of Metglas and Ni layers is zero under HAC = 1 Oe, i.e., the direction of local magnetic dipoles in those MS layers is nominally random. After then, the local magnetic dipoles start to align in the direction of the \(\overleftarrow {{{\text{ } - \text{ H}}_{{{\text{DC}}}} }}\) with further increasing the field strength, and the second maximum of the slope of λeff curve appears at point g, resulting in the − αMAX (point b). Note that during the progression from point a to point b, the directions of HOUT and \(\overleftarrow {{{\text{ } - \text{ H}}_{{{\text{DC}}}} }}\) coincide with each other. Then, a significant amount of attraction force by the HOUT causes compressive stress on Metglas layer and tensile stress on Ni layer. Both of these stresses are contrary to the piezomagnetic nature of Metglas (+ q) and Ni (− q), therefore, the − αMAX should be smaller than the + αMAX.

For the case 2, the + αMAX appears at point c (maximum slope of λeff curve at point h), implying that the HPA is slightly larger than the amount needed to obtain the maximum αSME. Moreover, the ΔH, the amount of \(\overleftarrow {{{\text{ } - \text{ H}}_{{{\text{DC}}}} }}\) required to zero the slope of λeff curve (point i), is smaller than that of case 1. These are possibly owing to the difference in λ versus HDC characteristics between Metglas and Ni. For the layout (i), since the HPA is concentrated in the MS layer with Nd magnets, it is natural to consider that the upper MS layer dominates the initial ME response. For the case 1 of layout (i), the concentrated HPA is appropriate to obtain the highest slope of λ versus HDC curve of Metglas, thus, the αSME is almost identical to the + αMAX. Meanwhile, for Ni, the maximum q value and the HDC value required for the maximum q are all smaller than those of Metglas [17]. Therefore, for the case 2, the ΔH should be smaller than that of case 1, and the αSME is smaller than the + αMAX. The difference in + αMAX value between cases 1 and 2 demonstrates well that the upper MS layer dominates the ME response for the layout (i). Next, we again invoke the presence of HOUT for the larger − αMAX (point d) than the + αMAX (point c) in case 2. For the case 2, the upper Ni layer experiences compressive stress by the HOUT while the lower Metglas layer is under tensile stress during the reverse biasing (\(\overleftarrow {{{\text{ } - \text{ H}}_{{{\text{DC}}}} }}\)). In this case, these stresses correspond to the bending motion of the laminate due to the piezomagnetic nature of Metglas (+ q) and Ni (− q), resulting in the highest slope of λeff curve at point j. However, for the layout (ii) in Fig. 2d, the HPA is evenly distributed in the upper and lower MS layers and the HOUT between two Nd magnets is negligible. Therefore, the magnitude of + αMAX is very similar with that of − αMAX due to the absence of stresses causing bending motions as shown in Fig. 2c. Furthermore, both + αMAX and αSME values of the laminate with layout (ii) were found to be smaller than those of case 1 and larger than those of case 2 of layout (i), demonstrating the concurrent contribution of Metglas and Ni layers to the initial ME response for the layout (ii). From the above results, one can find that the laminate structure in which the HPA is concentrated in Metglas layer is effective in obtaining a high αSME.

Figure 3a shows the αME versus HDC curves of the Metglas/PZT/Ni laminate for the magnet attachment layouts (iii) and (iv) in Fig. 1b. For the layout (iii), although the HPA is expected to be concentrated in the Metglas layer as shown in Fig. 3b, its + αMAX (18.04 V cm−1 Oe−1) was much smaller than that of the case 1 of layout (i). Moreover, the ΔH was 35.63 Oe, which is almost 70% larger than that of the case 1 of layout (i), and resultant αSME was also relatively low (14.11 V cm−1 Oe−1). In the case of layout (iv), both + αMAX and αSME values were found to be slightly larger than those of the layout (iii), implying that the Metglas layer with concentrated HPA did not dominate the ME response in layout (iii). For both layout (iii) and layout (iv), the magnitude of + αMAX was similar to that of − αMAX due to the absence of an influenceable HOUT (Fig. 3b). The αME versus HDC curve of the laminate with layout (iv) looks very similar to that of the laminate with layout (ii) in Fig. 2c, however, the ΔH and αSME of layout (iv) are quite different from those of layout (ii) despite their similar structures.

Fig. 3
figure 3

aαME versus HDC curves of Metglas/PZT/Ni laminates with layouts (iii) and (iv) measured under HAC of 1 Oe at bending resonance frequencies. b Schematics of magnetic field formation by a pair of Nd magnets for layouts (iii) and (iv). (Color figure online)

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The αSME values of layouts (iii) and (iv) are smaller than those of layouts (i) (case 1) and (ii), therefore, it can be recognized that the change in λ of the MS layer (Δλ) under a HAC at HDC = 0 is larger in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case rather than in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case. To understand the underlying mechanism of the phenomena found, we considered in more detail the distribution of HPA by Nd magnets and the resultant magnetization distributions inside the MS layer for both cases as shown in Fig. 4. The HPA by Nd magnets aligns the local magnetizations (or magnetic dipole moments in local domains) in MS layer (\(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\)). Schematics of the expected distribution of HPA and \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) are shown in Fig. 4a, b for the \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) and \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) cases, respectively. Due to the difference in layout of attaching Nd magnets, the HPA and resultant \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) distribution shows a difference between \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) and \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) cases. Based on the expected HPA distribution, we figured out two different magnetization regions in the MS layer (regions I and II) as shown in Fig. 4. In region I, all magnetic domains are parallel to the longitudinal direction, whereas in region II, the direction of the magnetic domains is not parallel to the longitudinal direction. In both \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) and \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) cases, the strength of HPA is high enough to saturate the \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) magnitude adjacent to the Nd magnet and lowest at the center of the laminate, resulting in a gradient of \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) magnitude across the MS layer. For the \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case, region I consists of magnetic domains with small \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) magnitudes parallel to the longitudinal direction, and region II consists of magnetic domains with various angles (θi) to the longitudinal direction and almost saturated \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) magnitude. However, for \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case, region I is wider than that of \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case and consists of magnetic domains with various \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) magnitudes ranging from a small value to a saturation value. The region II of \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case is much narrower than that of \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case, and magnetic domains with θi = 90° and 180° are expected to dominate in this region.

Fig. 4
figure 4

Schematics of distribution of HPA (white lines) and \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) (yellow arrows) in MS layer when HDC = 0: a\(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\) is perpendicular, and b\(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\) is parallel to the longitudinal direction of the laminate. The size of arrow head on white line reflects the strength of HPA. The length of yellow arrows indicates the magnitude of \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\). c Schematics of Δλ(M) and Δλ(θ) contribution to total Δλ when HDC ≠ 0. dαME versus HDC curves of Metglas/PZT/Ni laminates with layouts (i) and (iii) measured under HAC of 1 Oe at bending resonance frequencies. (Color figure online)

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For detailed analysis of the Δλ due to the redistribution of \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) under small fluctuations of HDC (δHDC: amplitude of HAC) in regions I and II, we considered the contribution of Δλ owing to the change in the magnitude of \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) (Δλ(M)) and the contribution of Δλ owing to the rotation of \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\)(Δλ(θ)) as shown in Fig. 4c. The Δλ(M) is determined by the following relation [18]:

$$\lambda = \frac{{3\lambda_{S} }}{{2M_{S}^{2} }}M^{2} ,$$
(1)

where λS is a saturated magnetostriction and MS is a saturated magnetization. The Δλ(θ) is expressed by [18]:

$$\Delta \lambda \left( \theta \right) = \frac{{3\lambda_{S} }}{2}\left[ {\langle \cos^{2} \theta_{f}\rangle - \langle\cos^{2} \theta_{i} }\rangle \right],$$
(2)

where the angular brackets represent an average of cos2θ over all orientations in the initial state (θi) and the final state (θf). In region I, the Δλ(θ) is negligible (θi\(\approx\)θf) and the Δλ(M) can be regarded similar for both \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) and \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) cases because only unsaturated \(\overrightarrow {{{\delta M}_{{{\text{MS}}}} }}\) in region I contribute to the Δλ(M). However, the Δλ(θ) in region II of \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case is non-negligible and effectively contribute to total Δλ. Although the Δλ(θ) in region II of \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case is not zero, its contribution to total Δλ is very small due to the narrow region having magnetic domains with θi = 90°. The magnetic domains with θi = 180° in region II of \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case are hardly believed to contribute to total Δλ because the sign of Δλ(M) in this case is opposite. Therefore, a larger Δλ and a higher αSME can be obtained in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case rather than in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case under the same δHDC (or HAC). Furthermore, comparing Fig. 4a, b, it is clear that the magnitude of the magnetization parallel to the longitudinal direction of the laminate (i.e. parallel to the HDC) in region I is much smaller in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\bot\)) case than in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case. This implies that the HPA parallel to the HDC is larger in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case, therefore, the ΔH should also be larger in \(\overrightarrow {{{\text{M}}_{{{\text{Nd}}}} }}\)(\(\parallel\)) case as shown in Fig. 4d.

Finally, we note that the αSME value (or SME voltage output) can be easily adjusted in our device structures, by simply changing the direction of magnetic tip masses. We believe this advantage will impose ease on the fabrication of tunable SME devices.

3 Conclusions

In conclusion, strong SME responses were experimentally verified for the Metglas/PZT/Ni laminate structures with magnetic tip masses. Based on detailed analysis of ME characteristics of the laminates with four different layouts of attaching two permanent magnets, we demonstrated that the highest SME effect could be obtained when both magnetic tip masses are loaded on Metglas layer (high + q material) and their magnetization direction is normal to the Metglas surface. Identifying the cause of the observed ME responses, we proposed that non-parallel ferromagnetic dipoles contribute to the total magnetostriction effectively without affecting the amount of ΔH. The pre-biased Metglas/PZT/Ni laminate exhibited giant SME voltage coefficients ranging from 14.11 to 52.35 V cm−1 Oe−1 at around 260 Hz under 1 Oe, demonstrating its implementation potential for precision field sensors, magnetic energy harvesters, and field-tunable SME devices as well.