Magnetic-Field-Orientation Dependent Magnetoelectric Effect in FeBSiC / PZT / FeBSiC Composites

We investigate the magnetic-field-orientation dependent magnetoelectric (ME) effect in the FeBSiC/Pb(Zr,Ti)O 3 (PZT)/FeBSiC laminates. It is shown that, by only using the bias-magnetic-field dependent ME response measured with the magnetic-field parallel to the surface plane of PZT slab, the magnetic-field-orientation dependent ME coefficient upon magnetic-fields of various amplitudes can be obtained via computer simulations. The simulation results match well the experimental measurements, demonstrating the applicability of the ME laminates-based sensors in detecting magnetic-fields with uncertain amplitudes and/or orientations in environment.


Introduction
The magnetoelectric (ME) effect is a phenomenon in which the electric polarization can be modified by a magnetic-field or a voltage output can be produced by applying a magneticfield on the materials, that is, direct ME effect, or, conversely, the magnetism is modified by an electric field [1][2][3].It is well known that the ME effect in multiferroic ME composites is a product property of piezoelectricity and magnetostriction [4,5], which could provide greater flexibility for applications as multifunctional devices due to the strong ME coupling at room temperature.Giant ME coupling has been achieved in various composites.For example, Dong et al. [6] obtained a remarkable ME coefficient of 22 V/cmOe at a static magneticfield of 5 Oe with a collinear alternating magnetic-field of 6 Oe (1 kHz) in a composite composed by a piezofiber/epoxy layer laminated between two layers of FeBSiC alloy.And Robert et al. [7] made great breakthrough that gets the extremely high ME coefficients of up to 9.7 kV/cmOe in air and 19 kV/cmOe under vacuum in thin-film composites.
From the application perspective, highly sensitive magnetic-field sensors can be obtained using the ME composites with high ME coefficients.Several prototypes of novel room temperature magnetic-field sensors [8][9][10] have been developed.Though the sensitivity is not as high as that of the superconducting quantum interference device (SQUID), the ME sensors show significant superiority in simple preparation and low cost as compared to the SQUID, which is sophisticated, expensive, energy consumptive, and only operated at cryogenic temperature.For instance, in a laminate of Terfenol-D/PZT/Terfenol-D, Zhai et al. [11] developed a novel ME sensor that can detect magnetic-fields down to pico-Tesla (10 −12 T) at room temperature, quite close to the 10 −13 T in SQUID.Furthermore, the output bandwidth and frequency of the ME sensor can be improved by adding the number of ferromagnetic layers and/or using shapeengineered bimorph geometry [12,13].More recently, Wang et al. [14] demonstrated an extremely low equivalent magnetic noise ME sensor based on both the giant ME effects in the Metglas/piezofiber heterostructure and a careful control of each internal noise source.However, for the application of magnetic-field sensor, besides the sensitivity, the influence of magnetic-field-orientation on the direct ME effect and the corresponding sensor design are also critically important issues regarding the uncertain, complex orientation distributions of magnetic-fields during practical operations.Previous studies have demonstrated that the measured ME coefficient varies with the change in angle between the poling field and applied magnetic-fields [15,16].And it was also reported that ME response from a Metglas/PZT fiber laminates was strongly anisotropic, offering good sensitivity to magnetic-field variations only along its length direction, due to the giant permeability of Metglas [17].In this work, we investigate the magnetic-field-orientation dependence of direct ME effect in a laminated FeBSiC/PZT/FeBSiC trilayer.It is found that the certain angle where the laminate gets its peak ME output directly depends on the external magneticfields.It is further demonstrated that, by using the magneticfield-dependent ME coefficients at one certain angle as the input, the ME response at other angles can be numerically calculated and agree well with the experimental results.Thus it would offer a simple and effective approach to determine the orientation of the magnetic-field in the applications of ME magnetic-field sensors.

Experimental
The simple ME trilayer made from two FeBSiC layers bonded on a PZT plate is schematically shown in Figure 1.The PZT ceramic slab with dimensions of 10 × 10 × 0.5 mm 3 (Sample 1) and 10 × 5 × 0.5 mm 3 (Sample 2) was prepared via conventional solid-state processing and then polarized along the thickness direction (denoted by 3-axis) under a poling field of 3 kV/mm, exhibiting a piezoelectric constant  33 of 458 pC/N measured by a standard  33 meter.The polarized PZT slab was bonded between two 30 m thick amorphous alloy FeBSiC layers (AT&M Co., Ltd., Beijing) by epoxy.The amorphous alloy FeBSiC layer has a relatively high permeability   ∼ 230 and saturation magnetostriction of  ∼ 20 ppm at  dc ∼ 100 Oe.The high   of FeBSiC results in a small demagnetization field in the surface plane, enabling a high effective piezomagnetic coefficient at low biases (∼ 70 Oe), which made the laminate exhibit a large ME response at quite low  dc .But contrastively the thickness direction was the hard axis because of its large demagnetization field.
Room-temperature ME measurements are carried out by superimposing an alternating current (AC) magnetic-field  provided by a pair of Helmholtz coils driven by an arbitrary waveform generator (Agilent 33220A) onto a static magnetic-field  dc . dc and  are parallel and fixed in the same direction, with the magnitude detected by a Gauss magnetometer (Lake Shore 455 DSP) in real time.During measurement, samples are rotated along axis 2, and  denotes the angle between the external magnetic-field and the electric polarization (Figure 1).

Results and Discussion
The dependence of the ME voltage coefficient   of Sample 1 on the static magnetic-field  dc is present in Figure 2(a), with  being fixed at 0 ∘ or 90 ∘ ; that is, the magnetic-field is perpendicular (out-of-plane) or parallel (in-plane) to the surface plane.It can be seen that, at  = 90 ∘ ,   (=  31 herein; see Figure 1) increases almost linearly before one certain  dc-optimal , where  31 reaches a maximum of 138 mV/cmOe (Point B) and then decreases nonlinearly as  dc further increases.Such a variation trend should essentially be determined by the bias-dependent piezomagnetic coefficient / 1 of the FeBSiC ribbon as reported in similar CoFe 2 O 4 /PZT composites [18], clearly demonstrating a strain-mediated direct ME effect.However, at  = 0 ∘ , the magnetostrictive deformation under  dc along the 3-axis is negligible because of the strongly magnetic anisotropy of the Metglas FeBSiC.As a result, the   (=  33 ) is insignificant and shows little dependence on  dc (Figure 2(a)).Such distinct angular anisotropy of the ME response can be used as an important criterion to determine the orientation of the external magnetic-field.However, in practical terms, we cannot simply identify the azimuth angle  with the maximal ME output as the field-orientation parallel to the PZT surface.
For illustration, we further measure the   as a function of  under various  dc ; representatively, Points A, B, and C in Figure 2(a) are selected.Point B respects the certain  dc-optimal (73.2 Oe for Sample 1) where  31 reaches its maximum value, while Points A and C denote the magneticfield less and larger than  dc-optimal .As seen in Figure 2(b), when  dc is fixed at 36.6 Oe (Point A in Figure 2(a)) and 73.2 Oe, the orientation dependence of ME coefficient shows a well-defined twofold symmetry in the corresponding polar plots, with the   reaching its maximal at  = 90 ∘ and 270 ∘ (i.e., the magnetic-field parallel to the surface plane) and almost vanishing at  = 0 ∘ and 180 ∘ (i.e., the magneticfield perpendicular to the surface plane).And the magnitude of the maximal   also increases with increasing  dc from 36.6 Oe (Point A) to 73.2 Oe (Point B), following the trend in Figure 2 at  max ≈ 30 ∘ /210 ∘ and 150 ∘ /330 ∘ when  dc reaches 146.4 Oe (Point C in Figure 2(a)), showing a fourfold symmetry in its polar plot accordingly.Since only the magnetic-field parallel to the PZT surface would induce an obvious ME output and the ME coefficient exhibits magnetic-field dependence as shown in Figure 2(a), the effective magnetic-field  dc-eff of an arbitrary  dc that induces a ME output can be expressed by Consequently, the azimuth angles with maximum   upon an arbitrary  dc , denoted by  max , can be straightforwardly calculated by  dc-optimal =  dc |sin( max )|.
In this case,  dc reaches 146.4 Oe (Point C) and  dc-optimal is 73.2 Oe for this sample, so | sin( max )| =  dc-optimal / dc = 0.5, and  max can be 30 ∘ , 210 ∘ , 150 ∘ , and 330 ∘ , exhibiting a fourfold symmetry in its polar plot.Thus, for the potential ME sensor applications, by simply presetting the  dc bias-dependent ME voltage coefficient   at  = 90 ∘ as the standard ME response, the ME outputs upon magnetic-fields with arbitrary amplitudes and orientations can in principle be obtained via computer simulations.When the ME sensor rotated in the magnetic-field, the magnetic-field can be decomposed along two directions: parallel and perpendicular to the surface plane.As the perpendicular direction almost has no contribution to the ME output, the ME output caused by the parallel direction can be obtained by the presetting standard ME response.By further comparing the magnetic-field-orientation dependent   measured in practical environment to the simulation results, both the direction and amplitude of the external magnetic-field can be conveniently identified.Following this procedure, we design a virtual ME sensor prototype using the Labview software based on the FeBSiC/PZT/FeBSiC trilayer, and the magnetic-field-orientation dependent   measured upon magnetic-fields of various amplitudes is numerically calculated as shown in Figure 2(c).As seen, the good match between experiments and simulations demonstrates the applicability of such ME sensors in detecting magneticfield with uncertain amplitudes and/or orientations.
Moreover, similar dependency of the magnetic-fieldorientation on the ME voltage coefficient   is obtained in the FeBSiC/PZT/FeBSiC trilayer with a dimension of 10 × 5 × 0.5 mm 3 for the PZT slab (i.e., Sample 2), as shown in Figures 3(a)-3(c).The larger in-plane aspect ratio and the smaller volume of Sample 2 should be helpful in designing rod-shaped probe for practical sensor applications [19].Moreover, the large ME voltage coefficient   in Sample 2 (∼150 mV/cmOe) guarantees a high magnetic-field sensitivity similar to that in Sample 1 with   ∼ 138 mV/cmOe.

Conclusions
In summary, the dependence of magnetic-field-orientation on the ME voltage coefficient   has been studied for FeBSiC/PZT/FeBSiC trilayers.Based on the experimentally measured magnetic-field dependent   with  dc parallel to the surface of the PZT slab, the magnetic-field-orientation dependent ME voltage output upon magnetic-fields of various amplitudes can be obtained via computer simulations.The simulation results agree well with corresponding experimental measurements, demonstrating the applicability of such ME sensors in detecting magnetic-fields with uncertain amplitudes and/or orientations in environment.

Figure 1 :
Figure 1: Schematic illustration of the FeBSiC/PZT/FeBSiC trilayer.The  denotes the angle between the directions of magnetic-field and the electric polarization.

Figure 2 :
Figure 2: (a) Magnetic-field dependence of ME coefficient   in the FeBSiC/PZT/FeBSiC trilayer with a dimension of 10 × 10 × 0.5 mm 3 for the PZT slab (Sample 1).(b) Experimentally measured polar plots of the angular dependent ME coefficient   in Sample 1 and (c) the computer simulation.

Figure 3 :
Figure 3: (a) Magnetic-field dependence of ME coefficient   in the FeBSiC/PZT/FeBSiC trilayer with a dimension of 10 × 5 × 0.5 mm 3 for the PZT slab (Sample 2).(b) Experimentally measured polar plots of the angular dependent ME coefficient   in Sample 2 and (c) the computer simulation.