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Direct and converse magnetoelectric effects in Metglas/LiNbO3/Metglas trilayers

Electromechanical and magnetoelectric properties of Metglas/LiNbO3/Metglas trilayers have been studied in the frequency range from 20 Hz to 0.4 MHz. A trilayer of Metglas/PMN-PT/Metglas prepared in the same way was used as a reference. Though PMN-PT has much larger charge piezocoefficients than LiNbO3 (LNO), the direct magnetoelectric voltage coefficient is found to be comparable in both trilayers due to the much lower dielectric permittivity of LNO. The magnitude of the direct magnetoelectric effect in the LNO trilayers is about 0.4 V/cm*Oe in the quasistatic regime and about 90 V/cm*Oe at electromechanical resonance. Calculations show that the magnetoelectric properties can be significantly improved (up to 500 V/cm*Oe) via controlling the cut angle of LNO, choosing the appropriate thickness ratio of the ferroelectric/ferromagnetic layers, and a better bonding between Metglas and LNO. Advantages of using LiNbO3-type ferroelectrics in magnetoelectric composites are discussed.


Introduction
Magnetoelectric properties of composite multiferroics are being intensively investigated today [ 1 ]. Though the underlying physics of the single-phase multiferroics is much deeper, the observed magnitudes of the magnetoelectric (ME) effect as well as typical temperatures of its experimental observation are by far too low for any reasonable practical application. In composite multiferroics [2][3][4], the required properties of the ferroelectric (FE) and ferromagnetic (FM) phases can be adjusted separately. As the estimated magnitude of the direct ME effect is proportional to the product [ 5 ] of the magnetostrictive and piezoelectric properties of the FM and FE phases, carefully designed composites have an extraordinary ME response by orders of magnitude higher than that in single-phase multiferroics [2][3][4]6 ]. The same tendency is observed for the converse ME effect [2][3][4][5][6].
Among different connectivity types of the FM and FE phases in ME composites [2][3][4], the 2-2 type laminate structures demonstrate the maximum efficiency due to low leakage currents and a strong mechanical coupling between the FE and FM phases. Additional improvements could be achieved by a proper choice of the FE and FM phases' properties. For example, the low saturation field of the FM phase, H s , is usually more important than the high magnetostriction constant, λ s .
Though the Terfenol-D and related magnetostrictive alloys [ 17 ] have two orders of magnitude higher λ s values than different types of metallic glasses [ 18,19 ], the magnetic fields needed to saturate these systems are typically above 1 kOe, which is by two or even three orders of magnitude higher than in abovementioned amorphous alloys. As a result, the magnetoelectric voltage coefficient, α E , in laminates based on metallic glasses can even be higher, which is extremely important for the ultralow magnetic field sensing applications.
The "L-T" operation mode, in which the FM layer is longitudinally magnetized and the FE layer is perpendicularly polarized, is often used in laminate structures [2][3][4]. Necessary requirements for the FE phase are a high d 31 piezocoefficient for the direct ME effect and the condition d 31 ≠ d 32 for the converse ME effect, in order to achieve an effective generation of the in-plane stress.
Though the frequently used Pb(Zr,Ti)O 3 (PZT) ceramics does not satisfy these requirements from a general point of view, the design of PZT-based ME composites and multilayers is still ongoing.
Remarkable progress has been achieved with a special geometry of electrodes, in the so-called "push-pull" mode [ 20,21 ], allowing the laminate to work effectively in the length extensional resonance. However, the question of miniaturization of such a complicated structure is still open.
Another important aspect is nonlinear magnetoelectric effect that can help avoid DC magnetic bias, yet giving high magnetoelectric response at second harmonics [ 22 ]. [ [33][34][35]. Even magnetically tuned surface acoustic wave devices were designed and tested in doped LiNbO 3 [ 15,[36][37][38][39] ]. However, as a functional layer in ME laminate structures, it has been considered and/or implemented only in a few studies [40][41][42]. Calculations of the ME response for a Terfenol/LNO/Terfenol structure were performed in Ref. [40]. An experimental study of such a structure was done in Ref. [42]. A noticeable tunability of the magnetic properties of a polycrystalline nickel film deposited atop a single-crystalline LNO substrate has been shown experimentally in Ref. [41]. Though the piezocoefficients of LNO are much lower than those of PMN-PT and PZN-PT, the dielectric constant is also much lower, which should yield a notable magnetoelectric voltage coefficient in direct ME effect measurements. Even in the weakly piezoelectric quartz [ 24 ] the magnetoelectric coefficient has been found to be very high In this work, we present a study of the direct and converse magnetoelectric effects for a trilayer structure of Metglas/LiNbO 3 /Metglas. As the thickness of the FM layer was not optimized and, besides, the FM/FE bonding method is believed to be far from optimum, another trilayer of Metglas/PMN-PT(011)/Metglas was prepared under the same conditions just to serve as a reference ME sample for comparison.

Experimental methods and samples
Several "2-2" connectivity type trilayer ME composites were fabricated by bonding foils of an amorphous ferromagnetic alloy to opposite sides of the square plates (10100. were poled by the supplier immediately after growth. After the poling procedure, the LNO crystals remain in the single-domain state, and repolarization/depolarization does not occur at room temperature (RT). The main physical properties of LNO can be found in Ref. [ 32 ]. The data presented there are valid for Z-cut substrates only. In our study we used Y-cut and 41ºY-cut crystals, whose physical properties (with respect to the sample geometry) are poorly represented in the literature. Thus, the piezocoefficients, dielectric permittivity and elastic compliances of the used LNO substrates will be calculated below. (011)-cut PMN-PT plates were chosen as a reference.
The prepared trilayer also operates in the L-T ME mode, i.e. with the transverse polarized piezoelectric phase (out-of-plane geometry) and longitudinal magnetized magnetostrictive phase (in-plane geometry). The PMN-PT crystals used in these measurements were poled beforehand along their thickness (i.e., parallel to the <011> direction), so that the mm2 multidomain symmetry was engineered [ 25 ] with the effective in-plane extensional piezocoefficients d 31 = -1700 pC/N and To study the electromechanical and ME properties of the trilayers, impedance spectroscopy, as well as direct and converse ME effect measurements were carried out. The impedance measurements were performed in the frequency range from 0 -10 MHz. A reference resistor was connected in series with a trilayer sample, and a frequency sweep with a constant voltage was performed by a function generator. The voltage amplitudes and phases on the reference resistor and sample were detected, and then, using a simple equivalent circuit model, the active and reactive parts of the sample impedance were obtained. This technique was used mainly to determine the quasi-static dielectric constant of the trilayers and to find the frequencies of the electromechanical resonances. ammeter (Agilent®, model 34401A), and its value was used to calibrate the generated magnetic AC field amplitude δH throughout a large frequency range (up to 500 kHz). A gaussmeter (DSP®, model 475) was used to measure the exact value of the bias field produced by the electromagnet.
The transverse voltage δV induced across the sample by the applied in-plane AC magnetic field δH was measured with a lock-in amplifier (Zurich Insruments®, model HF2LI). The measuring system as a whole is synchronized by a TTL output signal from the function generator and is driven by a custom-made data acquisition software.
The samples were magnetized in the x-y plane, while the induced AC voltage was measured along the z-direction. The RT measurements of the direct ME voltage coefficient α E3i = δV/(δH·t), (with i = 1,2; t being the thickness of the piezoelectric crystal) were performed for the trilayers as a function of the bias field H. The modulation amplitude of the AC field was fixed at δH = 1 Oe and its frequency was f = 5 kHz. The transverse ME voltage coefficients α E31 and α E32 were measured in two orthogonal in-plane orientations: α E31 was measured with H oriented along the <100> crystallographic direction (i.e. <100> || x axis), while for the α E32 coefficient measurements the sample was rotated in-plane counterclockwise by 90º (i.e. <100> || y axis). Beside the magnetic field dependences (α E31 (H) and α E32 (H)), the measurements of α E31 and α E32 were conducted also as a function of the AC magnetic field frequency, f, in the range from 20 Hz -400 kHz (with a fixed bias field H = 25 -30 Oe and the AC field amplitude δH = 1 Oe). In both type of measurements a Faraday induction voltage has been detected additionally to the direct ME response. It results from the use of an AC excitation magnetic field and is dependent on the concrete geometry of the experiment. It was established that the induction amplitude linearly increased with the frequency with a slope of 108 mV/(MHz·Oe) in all our measurements. For the most experimental data presented here, this parasitic effect is negligibly small; otherwise it was subtracted from the data during the post-processing procedure (in the latter case it will be noted in the text).
Measurements of the converse ME effect were performed by applying an AC voltage from the function generator to the sample and using the Helmholtz coil to detect the magnetic flux variation due to the changing magnetic permeability of the sample. The ME voltage amplitude and phase as a function of either the driving frequency at a constant DC magnetic field or the swept magnetic field at a constant excitation frequency were detected by the lock-in. The resulting ME effect was represented as a ratio of the AC voltage detected on the Helmoltz coils to the voltage applied to the sample. The accessible frequency range for this type of measurements spans from a few Hz up to several tens of MHz.

Experimental results and discussion
The prepared trilayers were first measured using the impedance spectroscopy setup in order to find and to identify the electromechanical resonance modes. The results are shown in Figure 2.
The sound velocity for the longitudinal waves in LiNbO 3 propagating along the principal axes is: for the Z-direction, 7.27110 5 cm/s; for the Y-direction, 6.54910 5 cm/s; and for the X-direction, 6. (ii) The samples demonstrate anisotropy of the in-plane ME properties. The trilayer prepared from the Y-cut LiNbO 3 crystal exhibits a difference between α E31 (H || <100>) and α E32 (H || <001>) by more than an order of magnitude. The obtained values are: α E31 = +0.46 V/(cm·Oe) and α E32 = -0.024 V/(cm·Oe). For the <001> direction, the ME response is comparable to the parasitic Faraday induction voltage, so that the corresponding correction has been applied to the measured data. In contrast, for the 41ºY-cut LNO crystal an isotropic in-plane behavior has been observed: for both in-plane directions, α E31 and α E32 are approximately the same: α E31 ≈ α E32 ≈+0. 42  To achieve a deeper understanding of the observed effects, one needs to calculate the effective piezoconstants for these two LNO substrates. Using the data for the Z-cut crystal [ 43 ] we applied a standard method [ 40,43,44 ] for the determination of the piezoelectric and other properties in the rotated (i.e. cut) crystal. The obtained physical quantities were put into the model presented in Ref. [ 40 ] to calculate the magnetoelectric response of the trilayers. Figure 4a shows the results of the calculations of the α E31 and α E32 coefficients as a function of the crystal cut angle. As it can be seen, Also the 129ºY-cut is of great importance as it has the maximal ME voltage coefficient α E32 = 27 V/(cm·Oe). Figure 4b demonstrates the calculated ME voltage coefficients as a function of the ferroelectric/ferromagnetic relative thickness ratio using the same formalism as in Ref. [ 40 ]. The calculation was done for the most interesting LNO crystal cuts. The smaller is the thickness of the ferroelectric layer, the more strain is transferred to it from the ferromagnet. However, even if these calculations are absolutely correct quantitatively, the detected voltage is proportional to the ferroelectric layer thickness. Thus, the thinner the layer is, the lower is the output signal. Taking into account that any measuring circuit has its own input noise, the maximal signal-to-noise ratio will be observed at a finite ferroelectric film thickness.
Another important conclusion is that the magnitudes of the observed ME voltage coefficients measured on the LNO trilayers are only three times lower than those for the PMN-PT trilayer. The maximal off-resonance ME voltage coefficient for the PMN-PT trilayer is 1.16 V/(cm·Oe), while it is 0.47 V/(cm·Oe) and 0.421 V/(cm·Oe) for the LNO trilayers produced from Y-cut and 41ºY-cut crystals, respectively. Comparable magnitudes are mainly explained by the fact that the dielectric constant of PMN-PT is more than 60 times higher. Thus, the same amount of generated charge will give a 60 times lower voltage, so that the effectiveness of the huge PMN-PT piezocoefficients is fully masked by the much higher dielectric permittivity.
However, this concurrent influence on the trilayers' performance observed for the direct ME effect is not anymore favorable for the case of the converse ME effect measurements. In this regime, the huge difference in piezoconstants between PMN-PT and LiNbO 3 becomes crucial, and the PMN-PT trilayer shows a much stronger converse ME response. Figure 5 shows the converse magnetoelectric measurements represented as a ratio of the voltage generated on the sensing coil (due to the Faraday induction) to the voltage applied to the trilayer. The effect is linked to changes of the effective permeability of the Metglas film under the strain transferred from the piezoelectric substrate. Though this type of measurements is not calibrated yet to the traditionally used (G·cm)/V units, it is still possible to conduct a comparative study, as all our samples are of the same shape, size, and are measured under the same conditions. The dependences of the converse ME effect versus the external magnetic field ( Figure 5) are qualitatively similar to those observed in the direct ME effect measurements ( Figure 3). Thus, only the high-response direction for each trilayer will be discussed below. The relative amplitudes of the converse ME effect have been found to be noticeably differing: the 41ºY-cut LNO trilayer demonstrates a two orders of magnitude lower amplitude in comparison with the PMN-PT trilayer. Undoubtedly, for the converse ME effect the difference between the piezocoefficients in the trilayers becomes crucial. However, a noticeable difference is observed even between different LNO crystals. The Y-cut trilayer has a six times larger response, pointing to a stronger electromechanical coupling (k 31 ) in it. Naturally, under the electromechanical resonance conditions each trilayer will show several orders of magnitude higher converse ME effect. However, the benefits of using PMN-PT crystal with its superb piezoelectric performance for the converse ME effect in such a structure remain indisputable.
Regarding the direct ME effect measurements, the benefits of PMN-PT look not so convincing. Only three times greater ME voltage coefficient in trilayers hardly justifies an order of magnitude higher price and considerably lower Curie temperature (and associated with this instabilities) of the PMN-PT crystal. It has been found that at the electromechanical resonance, the ME performance of the LNO crystals can be even better (see Figure 6). Surprisingly, the 41ºY-cut LNO-based trilayer has exhibited the maximal ME effect of about 90 V/(cm·Oe), while in the PMN-PT trilayer it was only of 70 V/(cm·Oe). In principle, the same trend has been observed while comparing direct ME effect in ferromagnetic/piezoelectric trilayers (Fig. 7 of Ref. [24]) in different materials based on their d/ε ratio.
It is also worth noting that the electromechanical resonance occurs in a very suitable frequency range. From the point of view of possible sensor applications, this means that the LNObased magnetic sensor can be built using standard low-cost electronic components. As compared to low-temperature ferroelectrics using LNO-based sensors is of utmost importance for hightemperature applications. And, finally, the observed values of the direct ME effect were measured for a non-optimized thickness ratio of the ferroelectric/ferromagnetic components. Optimization of this ratio, as well as a better bonding, should improve the direct ME response by at least one order of magnitude, with the theoretically calculated limit of 490 V/(cm·Oe) in the quasi-static regime.
Interesting possibilities are expected while combiningthe strong magnetoelectric effect observed in LNO-based composites with the unique electrooptic and photorefractive properties of this material.

Conclusions
In conclusion, we have conducted a study of the electromechanical and magnetoelectric properties of 2-2 type metglass/LiNbO 3 /metglas trilayers using single-crystalline substrates of different cuts. Metglas foils were bonded to the 10100.5 mm 3 ferroelectric substrates using a commercial cyanoacrylate-based glue.
Due to the simplified preparation method and non-optimal ferroelectric/ferromagnetic thickness ratio, the observed ME effect was rather modest. To avoid this problem, an additional an optimized trilayer would theoretically yield a magnitude of the direct ME effect of up to 490 V/(cm Oe) in the quasi-static regime. The use of different cuts will in principle allow obtaining the desired in-plane anisotropy of the magnetoelectric response, which could be very useful in vector magnetic field sensors.
Finally, the lithium niobate-based magnetoelectric 2-2 composites, featuring an excellent stability of the chemical and physical properties at high temperatures and a relatively low price, have a great potential to be used in the magnetic field sensing applications in a wide temperature range.