A Novel Spinel Ferrite-Hexagonal Ferrite Composite for Enhanced Magneto-Electric Coupling in a Bilayer with PZT

The magnetoelectric effect (ME) is an important strain mediated-phenomenon in a ferromagnetic-piezoelectric composite for a variety of sensors and signal processing devices. A bias magnetic field, in general, is essential to realize a strong ME coupling in most composites. Magnetic phases with (i) high magnetostriction for strong piezomagnetic coupling and (ii) large anisotropy field that acts as a built-in bias field are preferred so that miniature, ME composite-based devices can operate without the need for an external magnetic field. We are able to realize such a magnetic phase with a composite of (i) barium hexaferrite (BaM) with high magnetocrystalline anisotropy field and (ii) nickel ferrite (NFO) with high magnetostriction. The BNx composites, with (100 − x) wt.% of BaM and x wt.% NFO, for x = 0–100, were prepared. X-ray diffraction analysis shows that the composites did not contain any impurity phases. Scanning electron microscopy images revealed that, with an increase in NFO content, hexagonal BaM grains become prominent, leading to a large anisotropy field. The room temperature saturation magnetization showed a general increase with increasing BaM content in the composites. NFO rich composites with x ≥ 60 were found to have a large magnetostriction value of around −23 ppm, comparable to pure NFO. The anisotropy field HA of the composites, determined from magnetization and ferromagnetic resonance (FMR) measurements, increased with increasing NFO content and reached a maximum of 7.77 kOe for x = 75. The BNx composite was cut into rectangular platelets and bonded with PZT to form the bilayers. ME voltage coefficient (MEVC) measurements at low frequencies and at mechanical resonance showed strong coupling at zero bias for samples with x ≥ 33. This large in-plane HA acted as a built-in field for strong ME effects under zero external bias in the bilayers. The highest zero-bias MEVC of ~22 mV/cm Oe was obtained for BN75-PZT bilayers wherein BN75 also has the highest HA. The Bilayer of BN95-PZT showed a maximum MEVC ~992 mV/cm Oe at electromechanical resonance at 59 kHz. The use of hexaferrite–spinel ferrite composite to achieve strong zero-bias ME coupling in bilayers with PZT is significant for applications related to energy harvesting, sensors, and high frequency devices.


Introduction
Multiferroic materials exhibit more than one ferroic order, such as ferromagnetism, ferroelectricity, and ferroelasticity [1].They have recently attracted significant attention due to their potential for applications in spintronics, magneto-electrics, nonvolatile memories, sensors, and electrically tunable magnetic microwave devices [2,3].A ferromagneticferroelectric composite is a multiferroic that shows a variation of its ferroelectric order parameters when subjected to an external magnetic field, direct magnetoelectric (ME) effect, or changes in magnetic parameters in an applied electric field, converse ME effect [4].In ME materials, the induced electric polarization P is related to the applied external magnetic field H by P = αH, where α is a second order ME-susceptibility tensor.Another parameter of importance is the ME voltage coefficient (MEVC) α E = δE/δH, where δE is the induced electric field due to applied magnetic field δH, and is related to α by α = ε 0 ε r α E , where ε r is the relative permittivity of the material.According to models for the ME effects in single-phase materials, the upper bound α is limited to the relation α ≤ (µε) 1/2 , where µ and ε are the permeability and permittivity of the material, respectively [5].One known single-phase multiferroic with a large α at room temperature is BiFeO 3 [6].In composite ME materials, α can be enhanced by exploiting the strain mediated interactions between the two phases [4].
To obtain the maximum ME voltage coefficient (α E ) in a ferromagnetic-ferroelectric composite, an optimized magnitude of the DC magnetic bias field H is needed.A maximum in the α E occurs when the piezomagnetic coefficient q = dλ/dH (where λ is the magnetostriction) of ferro/ferrimagnetic component of the composite is also maximum.Hence, a bias magnetic field is generally essential to achieve a strong ME response.The need for a bias field, however, could be eliminated with a self-bias in the ferromagnetic.There are several avenues to accomplish the self-bias condition, such as a large magneto-crystalline anisotropy field or the use of a functionally graded ferromagnet [7][8][9].Other avenues include the use of a compositionally graded ferromagnetic phase [10].There are several experimental findings [11][12][13] and theoretical models [11][12][13] on graded ME composites.In laminated composites, changing the mechanical resonance modes through electrical connectivity evokes zero bias coupling when the bending strain activates a built-in bias [9].Thin films that rely on magnetic field dependence of resonant frequency and angular dependence of exchange bias field [14,15] can also show a zero-bias ME effect.It is also shown that a homogeneous magnetostrictive phase can also produce a zero bias ME effect [16].Cofired layered composites consisting of textured Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) and Cu and Zn doped NiFe 2 O 4 show a giant zero-bias ME coefficient ~1000 mV/cm Oe [17], wherein built in stress induces zero-bias effect.Very recently, Huang et.al. [18] have shown a very large self-bias ME effect with LiNbO 3 single crystal and Ni trilayers with residual stress engineering by using Ni as the electrode and the piezomagnetic layer simultaneously using RF sputtering.Wu et.al. [19] have shown that large sensitivity in PMN-PT-Metglass ME sensors by utilizing shear stress induced self-bias effect.Annapureddy et.al. [20] have obtained a large self-bias effect (~4200 mV/cm Oe) by utilizing the graded magnetization.To date, all the reported self-bias effects are sample specific.The role of the sample configuration and/or preparation is crucial to obtain the self-bias.
This work focuses on a novel, never-before-used approach for a self-biased ME composite with the use of a ferromagnetic layer consisting of both M-type barium ferrite hexagonal ferrite, BaO 6Fe 2 O 3 (BaM), with uniaxial anisotropy on the order of ~17.4 kOe, and nickel ferrite NiFe 2 O 4 with high magnetostriction and piezomagnetic coefficient q [21].Composites of BaM-NFO with (100 − x) wt.% of BaM and x wt.% of NFO, (BNx), were prepared by sintering powders of both ferrites.X-ray diffraction revealed the presence of both BaM and NFO and the absence of impurity phases.Scanning electron microscopy images showed crystallites of both ferrites.Magnetization measurements at room temperature for static fields up to 2 T showed an increase in 4πM with increasing BaM content in the composite.Magnetostriction λ measurements for BNx indicated an increase with increasing x, and for x > 65, reached values comparable that of pure NFO.High frequency measurements were carried out to determine the anisotropy field H A from dependence of the ferromagnetic resonance (FMR) frequency f r on static magnetic field H.The in-plane H A values in BNx were found to be well above the value of 500 Oe for pure NFO.These composites show a large piezomagnetic coefficient and large magnetocrystalline anisotropy simultaneously, which is somewhat unique to this spinel ferrite-hexaferrite composite.Platelets of sintered BNx were bonded to PZT to form bilayers for ME voltage coefficient (MEVC) measurements that showed a significant zero-field ME effects.Details on results of the studies are provided in the following sections.

Materials
The ferrite composites were prepared by the traditional ceramic synthesis techniques.Micrometer-sized polycrystalline NFO and BaM powders were first synthesized separately.High purity NiO, BaCO 3 , and Fe 2 O 3 were mixed and ball milled for 8 h.The powders were dried and pre-sintered at 900 • C for 6 h.The pre-sintered powders were ball milled again, and then sintered at 1200 • C for 6 h.Composites of (100 − x) wt.% BaM-x wt% NFO (BNx) (x = 5, 9, 13, 33, 38, 41, 44, 47, 60, 75, 85 and 95) were prepared by mixing the ferrite powders.A binder, 2% PVA, was added to the powder and pressed into disks (diameter ~18 mm and thickness ~2 mm) by applying uniaxial pressure of 250 MPa.The disks of BNx were finally sintered at 1250 • C for 6 h.

Characterizations
The crystal structure of the composites was characterized by a powder X-ray diffractometer (Miniflex, Rigaku, Japan) at room temperature.Morphological features of the samples were studied with an SEM (JSM-6510/GS, JEOL, Tokyo, Japan).Magnetostriction of the composite on rectangular platelets was measured using a strain gauge and a strain indicator/recorder (P3, Micro-Measurements, Wendell, NC, USA).The magnetic field was applied parallel to the sample plane and along the length (direction-1) of the gauge, and magnetostriction measured in this configuration is labeled λ 11 .Magnetization at room temperature as a function of H was measured with an Evercool Physical Property Measurement System (PPMS, Quantum Design Inc., San Diego, CA, USA).Ferromagnetic resonance (FMR) measurements were conducted on thin rectangular platelets of the composites with the sample placed on a coplanar waveguide and with the magnetic field H parallel to the sample plane and along its length.A vector network analyzer (E8361A, Agilent, Santa Clara, CA, USA) was used to record profiles of the scattering matrix S 21 vs. frequency f for a series of H. Measurements of ME coupling strengths were completed on a bilayer of BNx and vendor-supplied PZT that was bonded with a thin layer of epoxy.Composite platelets of dimensions 10 mm × 5 mm and 1 to 1.5 mm in thickness, and 0.3 mm thick PZT plates of similar lateral dimensions as the composite, were used.The ME voltage coefficient (MEVC) measurements were completed by subjecting the bilayer to an ac magnetic field H ac and a bias field H.Both H-and f-dependence of the MEVC were measured for both the magnetic fields parallel each other and either parallel or perpendicular to the sample plane.

Structural Characterization
Representative powder X-ray diffraction (XRD) patterns for the BNx samples are shown in Figure 1.XRD patterns of other BNx compositions are shown in the Figure S1 in the Supplementary Materials.The XRD patterns show diffraction peaks from NFO and BaM.With increasing x-values, the NFO lines become stronger and BaM lines get weaker, as expected.This is due to the reduced weight fraction of the BaM phase as we increase x.X-ray intensity corresponding to a particular phase is proportional to the weight fraction of the phase.We have deliberately varied the weight fraction of the NFO/BaM phases, and when the NFO weight fraction is increased, the line intensity corresponding to NFO becomes stronger; likewise, BaM intensity gets weaker.A small amount of an impurity phase, identified as antiferromagnetic Ba 5 Fe 2 O 8 , is present only in BN41, BN44, and BN75 [22].Usually, Ba 5 Fe 2 O 8 type impurities (5BaO + Fe 2 O 3 ) occur during the sintering of BaO and Fe 2 O 3 based ferrites, especially in BaFe 12 O 19 [22].However, since Ba 5 Fe 2 O 8 is antiferromagnetic, the overall ME character of the BNx-PZT bilayers is expected to be unaffected.
Representative SEM images for BNx (x = 5, 33, 60 and 95) are shown in Figure 2. The gradual increase in the grain size in the BN composites with increasing x (also in Supplementary Figure S2) may indicate that NFO aids in the growth of hexagonal BaM grains for x ≥ 9. Large grains are absent in BN5, but a closer examination of the surface morphology shows hexagonal-like features with grain size less than 2 µm.With increasing NFO content, grains larger than 5 µm are present.For x > 41, the number of large grains reduces again.For the highest content of NFO (BN95), we observe a similar grain distribution as pure NFO (Supplementary Figure S2).BN5 also shows a similar grain distribution as pure BaM.When the weight fraction of the BaM phase is high (x~5), the composite is more likely to behave as pure BaM.Hence, the corresponding morphological features of composites with high BaM content should also look like pure BaM.Similarly, when the weight fraction (x > 41) of NFO is increased, the composites tend to show a reduction in BaM grains.Barium ferrite itself tends to form hexagonal grains [23] and, with a tweak in the synthesis process, the particle shape can be made nearly spherical [24].In our case, the processing has a large impact on the grain growth on these composites.The stabilization of the typical hexagonal BaM grains amongst NFO particles is worth noting.and Fe2O3 based ferrites, especially in BaFe12O19 [22].However, since Ba5Fe2O8 is antiferromagnetic, the overall ME character of the BNx-PZT bilayers is expected to be unaffected.Representative SEM images for BNx (x = 5, 33, 60 and 95) are shown in Figure 2. The gradual increase in the grain size in the BN composites with increasing x (also in Supplementary Figure S2) may indicate that NFO aids in the growth of hexagonal BaM grains for x ≥ 9. Large grains are absent in BN5, but a closer examination of the surface morphology shows hexagonal-like features with grain size less than 2 µm.With increasing NFO content, grains larger than 5 µm are present.For x > 41, the number of large grains reduces again.For the highest content of NFO (BN95), we observe a similar grain distribution as pure NFO (Supplementary Figure S2).BN5 also shows a similar grain distribution as pure BaM.When the weight fraction of the BaM phase is high (x~5), the composite is more likely to behave as pure BaM.Hence, the corresponding morphological features of composites with high BaM content should also look like pure BaM.Similarly, when the weight fraction (x > 41) of NFO is increased, the composites tend to show a reduction in BaM grains.Barium ferrite itself tends to form hexagonal grains [23] and, with a tweak in the synthesis process, the particle shape can be made nearly spherical [24].In our case, the processing has a large impact on the grain growth on these composites.The stabilization of the typical hexagonal BaM grains amongst NFO particles is worth noting.
The XRD results in Figure 1 and the SEM images of Figure 2 are indicators of the absence of any significant amount of impurity phases of crystal structures apart from spinel and hexagonal phases.An in-depth investigation and analysis of the crystal and magnetic structures are in order.For example, possible migration of Ni-ion from the spinel The XRD results in Figure 1 and the SEM images of Figure 2 are indicators of the absence of any significant amount of impurity phases of crystal structures apart from spinel and hexagonal phases.An in-depth investigation and analysis of the crystal and magnetic structures are in order.For example, possible migration of Ni-ion from the spinel phase to the hexagonal phase has to be addressed since the M-type hexagonal phase also has the spinel blocks.Such an investigation, however, is not the primary focus of this particular study.

Magnetic Characterization
We have carried out room-temperature measurements of the magnetization, 4πM, of the composites as a function of applied magnetic field H. Representative 4πM vs. H data are shown in Figure 3

Magnetic Characterization
We have carried out room-temperature measurements of the magnetization, 4πM, of the composites as a function of applied magnetic field H. Representative 4πM vs. H data are shown in Figures 3 and S3.The M vs. H loops show hysteresis and remanence as expected, and the saturation values of M increases with increasing BaM contents in the composites.The H-values for saturation of the magnetization is less than 3 kOe for NFO rich composites, and it increase as the amount of BaM increases.The magnetization 4πM at H = 20 kOe increases from 2.90 kG for BN95 to 4 kG for BN33.The highest value of remanent 4πM of 1.04 kG was measured for BN75.Since the magnetostriction λ is one of the key parameters that determine the strength ME interaction, we measured its value for the BNx composites.The measurements were completed with a strain gauge and a strain indicator and, for H, were was applied parallel to the sample plane and to the length of the strain gauge.Data on the magnetostriction λ11 vs. H are shown in Figure 4.The samples exhibit negative values for λ11 as expected since both NFO and BaM have negative λ11 values [25,26].None of the λ11 values for the composites in Figure 3 show saturation for the maximum H-values of ~3 kOe.With increases in

Magnetic Characterization
We have carried out room-temperature measurements of the magnetization, 4πM, of the composites as a function of applied magnetic field H. Representative 4πM vs. H data are shown in Figures 3 and S3.The M vs. H loops show hysteresis and remanence as expected, and the saturation values of M increases with increasing BaM contents in the composites.The H-values for saturation of the magnetization is less than 3 kOe for NFO rich composites, and it increase as the amount of BaM increases.The magnetization 4πM at H = 20 kOe increases from 2.90 kG for BN95 to 4 kG for BN33.The highest value of remanent 4πM of 1.04 kG was measured for BN75.Since the magnetostriction λ is one of the key parameters that determine the strength ME interaction, we measured its value for the BNx composites.The measurements were completed with a strain gauge and a strain indicator and, for H, were was applied parallel to the sample plane and to the length of the strain gauge.Data on the magnetostriction λ11 vs. H are shown in Figure 4.The samples exhibit negative values for λ11 as expected since both NFO and BaM have negative λ11 values [25,26].None of the λ11 values for the composites in Figure 3 show saturation for the maximum H-values of ~3 kOe.With increases in Since the magnetostriction λ is one of the key parameters that determine the strength ME interaction, we measured its value for the BNx composites.The measurements were completed with a strain gauge and a strain indicator and, for H, were was applied parallel to the sample plane and to the length of the strain gauge.Data on the magnetostriction λ 11 vs. H are shown in Figure 4.The samples exhibit negative values for λ 11 as expected since both NFO and BaM have negative λ 11 values [25,26].None of the λ 11 values for the composites in Figure 3 show saturation for the maximum H-values of ~3 kOe.With increases in the NFO content, λ 11 values at 3 kOe increase and tend to show similar behavior as pure NFO (shown in the inset of Figure 4).The highest value of λ 11 ~−23 ppm was measured for BN60, and similar values were obtained for x ≥ 60.Our measurements of pure BaM showed λ 11 = −1 ppm at 2.7 kOe.Hence, it is clear that the NFO phase is the major contributor to the net magnetostriction of BNx composites.
the NFO content, λ11 values at 3 kOe increase and tend to show similar behavior as pure NFO (shown in the inset of Figure 4).The highest value of λ11 ~−23 ppm was measured for BN60, and similar values were obtained for x ≥ 60.Our measurements of pure BaM showed λ11 = −1 ppm at 2.7 kOe.Hence, it is clear that the NFO phase is the major contributor to the net magnetostriction of BNx composites.

Ferromagnetic Resonance
A key objective of this work is to achieve large enough magneto-crystalline anisotropy field HA in BNx to realize a strong zero-bias ME effect in a composite with PZT.The magnetization data in Figures 3 and S3 indicate a large remnant magnetization, as high as 1 kG, which is clear evidence for a large HA.We utilized ferromagnetic resonance (FMR) studies in combination with the magnetization data to determine HA.Ferrite platelets, rectangular in shape, were placed in an S-shaped coplanar waveguide and excited with microwave power from a VNA.Profiles of the scattering matrix S21 as a function of frequency f were recorded.Figure 5 shows such profiles for a series of in-plane H along the sample length.For x values < 10, a single resonance mode was seen in the 50 GHz range (See Supplementary Figure S4).As NFO content increased, two resonance modes were seen as in Figure 5, one in the frequency range 3-20 GHz and another in the range 40-60 GHz.The S21 vs. f profiles in Figure 5 (and Figure S4) show clear asymmetry in the shape of the resonance absorption signals which can be attributed to the variations in the magnitudes of coupling between resonator and the transmission line at frequencies below and above the resonance.Such an asymmetry is not generally observed in cavity-type FMR measurements at a fixed frequency.Also, this effect is negligible for resonance modes with relatively narrow linewidth.However, in the case of transmission line broadband measurement systems and resonances with frequency-width of the order of a few GHz, asymmetry may manifest.Another possible factor is the frequency-dependent background absorption of the coplanar line, which superimposes on absorption through the resonator and leads to significant distortion of the resultant profile.Such asymmetry is most likely to occur at U-band frequencies, where any imperfections of the stripline, connectors, or shielding may unpredictably affect the shape of stripline transmission characteristics.The resonance frequency was estimated from frequency of maximum absorption in the profiles in Figure 5.As discussed, next, the resonance mode at the low frequency region in Figure 5 is due to FMR in NFO whereas the higher frequency resonance is a magneto-dielectric mode in the composite [27].

Ferromagnetic Resonance
A key objective of this work is to achieve large enough magneto-crystalline anisotropy field H A in BNx to realize a strong zero-bias ME effect in a composite with PZT.The magnetization data in Figure 3 and Figure S3 indicate a large remnant magnetization, as high as 1 kG, which is clear evidence for a large H A .We utilized ferromagnetic resonance (FMR) studies in combination with the magnetization data to determine H A .Ferrite platelets, rectangular in shape, were placed in an S-shaped coplanar waveguide and excited with microwave power from a VNA.Profiles of the scattering matrix S 21 as a function of frequency f were recorded.Figure 5 shows such profiles for a series of in-plane H along the sample length.For x values < 10, a single resonance mode was seen in the 50 GHz range (See Supplementary Figure S4).As NFO content increased, two resonance modes were seen as in Figure 5, one in the frequency range 3-20 GHz and another in the range 40-60 GHz.The S 21 vs. f profiles in Figure 5 (and Figure S4) show clear asymmetry in the shape of the resonance absorption signals which can be attributed to the variations in the magnitudes of coupling between resonator and the transmission line at frequencies below and above the resonance.Such an asymmetry is not generally observed in cavity-type FMR measurements at a fixed frequency.Also, this effect is negligible for resonance modes with relatively narrow linewidth.However, in the case of transmission line broadband measurement systems and resonances with frequency-width of the order of a few GHz, asymmetry may manifest.Another possible factor is the frequency-dependent background absorption of the coplanar line, which superimposes on absorption through the resonator and leads to significant distortion of the resultant profile.Such asymmetry is most likely to occur at U-band frequencies, where any imperfections of the stripline, connectors, or shielding may unpredictably affect the shape of stripline transmission characteristics.The resonance frequency was estimated from frequency of maximum absorption in the profiles in Figure 5.As discussed, next, the resonance mode at the low frequency region in Figure 5 is due to FMR in NFO whereas the higher frequency resonance is a magneto-dielectric mode in the composite [27].
The H-dependence of the low-and high frequency mode frequencies f r are shown in Figure 6 (and in Supplementary Figure S5).Data on f r vs. H for the low-frequency mode are shown in Figure 6a for BN33 and BN60.With f r increasing from 8.6 GHz at H = 1 kOe to 15.9 GHz for H = 3.5 kOe for BN60, which amounts to an increase in f r at the rate 2.8 GHz/kOe.A similar rapid increase in f r with H is seen in Figure 6a for BN33.Based on the rate of change in f r with H, one may associate this mode with FMR in NFO. Figure 6b shows f r vs. H for the high frequency mode for BN33 and BN60.In Figure 5 and Figure S5, this mode shows a variation in f r with H that could be approximated to a linear increase ~1.3 GHz/kOe.This slow variation in f r with H is indicative of a magneto-dielectric mode in the composite platelet.This mode is not of importance for the current study and is not considered in further analysis [27].The H-dependence of the low-and high frequency mode frequencies fr are shown in Figure 6 (and in Supplementary Figure S5).Data on fr vs. H for the low-frequency mode are shown in Figure 6a for BN33 and BN60.With fr increasing from 8.6 GHz at H = 1 kOe to 15.9 GHz for H = 3.5 kOe for BN60, which amounts to an increase in fr at the rate 2.8 GHz/kOe.A similar rapid increase in fr with H is seen in Figure 6a for BN33.Based on the rate of change in fr with H, one may associate this mode with FMR in NFO. Figure 6b shows fr vs. H for the high frequency mode for BN33 and BN60.In Figures 5 and S5, this mode shows a variation in fr with H that could be approximated to a linear increase ~1.3 GHz/kOe.This slow variation in fr with H is indicative of a magneto-dielectric mode in the composite platelet.This mode is not of importance for the current study and is not considered in further analysis [27].The built-in bias due to magnetic anisotropy field H A in the composites is a key parameter that accounts for the zero-bias ME coupling in bilayers of the ferrite composites with PZT, as discussed later.There are several avenues for the determination of H A , such as direct measurements and from M vs. H data.We utilized FMR results in combination with magnetization values to estimate H A .Data on f r vs. H in Figure 7 (and Figure S5) were fitted to appropriate expression for f r to determine the effective magnetization 4πM eff = 4πM + H A , where 4πM is the magnetization and H A is the magnetocrystalline anisotropy field.It is essential to note that 4πM is not the saturation magnetization since the M vs. H in Figure 3 (and Figure S3) clearly indicate that there is no saturation of M with The built-in bias due to magnetic anisotropy field HA in the composites is a key parameter that accounts for the zero-bias ME coupling in bilayers of the ferrite composites with PZT, as discussed later.There are several avenues for the determination of HA, such as direct measurements and from M vs. H data.We utilized FMR results in combination with magnetization values to estimate HA.Data on fr vs. H in Figure 7 (and Figure S5) were fitted to appropriate expression for fr to determine the effective magnetization 4πMeff = 4πM + HA, where 4πM is the magnetization and HA is the magnetocrystalline anisotropy field.It is essential to note that 4πM is not the saturation magnetization since the M vs. H in Figure 3 (and Figure S3) clearly indicate that there is no saturation of M with H for several of the composites used in this study.We instead used the average value of 4πM for H-values for FMR profiles in Figure 5.The resonance frequency fr for FMR mode is given by the Kittel equation, where γ is the gyromagnetic ratio, H is the in-plane external magnetic field along the xdirection, Nx, Ny, and Nz are the demagnetization factors along the length, width, and thickness of the platelet, respectively.These values are shown in Table 1 for each of the composites in which FMR mode was observed.The data in Figure 7 (and Supplementary Figure S5) were fitted to Equation ( 1) to determine 4πMeff.The Kittel equation in the presented form is, strictly speaking, applicable to the ferromagnetic samples of ellipsoidal  The built-in bias due to magnetic anisotropy field HA in the composites is a key parameter that accounts for the zero-bias ME coupling in bilayers of the ferrite composites with PZT, as discussed later.There are several avenues for the determination of HA, such as direct measurements and from M vs. H data.We utilized FMR results in combination with magnetization values to estimate HA.Data on fr vs. H in Figure 7 (and Figure S5) were fitted to appropriate expression for fr to determine the effective magnetization 4πMeff = 4πM + HA, where 4πM is the magnetization and HA is the magnetocrystalline anisotropy field.It is essential to note that 4πM is not the saturation magnetization since the M vs. H in Figure 3 (and Figure S3) clearly indicate that there is no saturation of M with H for several of the composites used in this study.We instead used the average value of 4πM for H-values for FMR profiles in Figure 5.The resonance frequency fr for FMR mode is given by the Kittel equation, where γ is the gyromagnetic ratio, H is the in-plane external magnetic field along the xdirection, Nx, Ny, and Nz are the demagnetization factors along the length, width, and thickness of the platelet, respectively.These values are shown in Table 1 for each of the composites in which FMR mode was observed.The data in Figure 7 (and Supplementary Figure S5) were fitted to Equation ( 1) to determine 4πMeff.The Kittel equation in the presented form is, strictly speaking, applicable to the ferromagnetic samples of ellipsoidal The resonance frequency f r for FMR mode is given by the Kittel equation, where γ is the gyromagnetic ratio, H is the in-plane external magnetic field along the xdirection, N x , N y , and N z are the demagnetization factors along the length, width, and thickness of the platelet, respectively.These values are shown in Table 1 for each of the composites in which FMR mode was observed.The data in Figure 7 (and Supplementary Figure S5) were fitted to Equation (1) to determine 4πM eff .The Kittel equation in the presented form is, strictly speaking, applicable to the ferromagnetic samples of ellipsoidal shape, magnetized to saturation, and has uniform static and dynamic magnetization.However, the samples presented in this investigation had a parallelepiped shape rather than an ellipsoidal one.That means that, even after an external magnetic field H > N x 4πM was applied and domain structure was suppressed, the sample was still not in a uniformly magnetized state.There were regions of ferrite present (mostly around edges and corners [28]) where the magnetization deviates from the direction of bias magnetic field.Thus, an even larger H should be applied before the magnetic state of the sample becomes uniform and the Kittel equation becomes applicable.For these reasons, we took only the high-frequency (and high-field) portion of the dependencies shown in Figure 7 and fit them with the Kittel equation to obtain the most reliable fitting parameters.Estimated values of the gyromagnetic ratio γ and 4πM eff from the fits and the average values of 4πM for H = 1 kOe to 3.5 kOe (from M vs. H data) are given in Table 2.The values of γ range from 3.17 GHz/kOe for x = 33 to 2.61 GHz/kOe for x = 0.60, which are comparable to the 3.0 to 3.2 GHz/kOe value reported for pure NFO [29,30].The value of the anisotropy H A estimated from FMR data is also given in Table 2, and will have an error of at least 0.5 kOe.The anisotropy field H A is positive for x = 33-95, indicative of in-plane anisotropy for all the polycrystalline BNx composites with x = 33-95.The anisotropy increases from ~0.90 kOe for x = 33 to ~7.77 kOe for x = 75.A further increase in x results in a decrease in H A , but the in-plane character of the anisotropy remains.One may therefore infer from these H A -values that a majority of BaM crystallites in x = 33-95 have a unique in-plane orientation leading to positive values of magnetic anisotropy.With increasing value of NFO content in x ≥ 33, the higher concentration of NFO appears to promote the growth of BaM crystallites with in-plane orientation for the c-axis and a net in-plane anisotropy field that reaches a maximum value for x = 75.Several reported efforts in the past on polycrystalline BaM mainly dealt with textured thin and thick films and showed, depending on the degree of texture, an out-of-plane H A in the range 4.5 to 15 kOe [31,32].In this work, however, the BaM component in composites results in overall effective in-plane anisotropy field.
We have also calculated the Gilbert damping coefficient (GDC) [33,34] of the composites by analyzing the FMR spectra of the samples.GDC is a dimensionless quantity which can be used as a measure of the losses in a ferromagnetic material.GDCs of the composites were calculated using the equation, where α is the damping coefficient, f r is the resonance frequency, ∆H is the linewidth that was estimated from the FMR frequency-width for profiles in Figure 5, and γ is the gyromagnetic ratio.Estimated values are given in Table 2. Composites with x ≤ 47 show GDC ~0.024, and we get a smaller GDC of less than 0.02 for x ≥ 60, which is indicative of a decrease in the losses in the composites as the NFO increases.The composites seem to have a much larger damping coefficient compared to pure and doped NFO [34,35], but it is smaller than the GDC of BaM [36].

Magneto-Electric Effects in the BNx-PZT Bilayers
The strength of ME coupling was measured in bilayers of the composites and vendorsupplied PZT (PZT850, American Piezo Ceramics, Mackeyville, PA, USA).Ferrite platelets of approximate lateral dimensions 5 mm × 10 mm and thickness t = 0.3-0.5 mm were bonded to PZT with 20 µm thick layer of a fast-dry epoxy.The ME voltage coefficient (MEVC) was measured for two different orientations of the applied magnetic fields: (i) α 31 for the DC filed H and ac field H ac were parallel to each other and along the length of the sample (direction-1), and the induced voltage was measured across the thickness of PZT (direction-3) and (ii) α 33 for the magnetic fields was applied perpendicular to the sample plane (direction-3) and induced voltage was measured across PZT thickness.The MEVC is given by α = V 3 /(H ac t), where V 3 is the strain-induced ac voltage measured across PZT.The ME coefficients were measured at low frequencies, as well as at the mechanical resonances in the bilayers.
Figure 8 (and Figure S6 in the Supplementary Materials) shows the H dependence of α 31 for ac field at 100 Hz.The MEVC is directly proportional to the piezomagnetic coupling q = dλ/dH.The value of α 31 increases when H is increased to the maximum.The maximum value of MEVC for BN5 is rather small due to low q-value for this BaM rich composite.With further increases in the NFO content in the composites, α 31 increases to a maximum value of ~152 mV/cm Oe for BN95.Upon further increase in H, α 31 in general decreases to a minimum for composites with x > 5. Bias field H dependence of α 31 in Figure 8 essentially tracks the variation in q with H, reaches a maximum at the maximum in the slope of λ 11 vs. H, and drops to near zero when the magnetostriction (Figure 3) shows near saturation.Other significant features in the results from Figure 8  vs. H, and drops to near zero when the magnetostriction (Figure 3) shows near saturation.Other significant features in the results from Figure 8   Figure 9 shows results of MEVC measurements for the magnetic fields applied perpendicular to the bilayers of BNx-PZT (also shown in Figure S6).The variation in MEVC has similar hysteresis and remanence as the in-plane magnetic fields.However, the following features in α33 vs. H differ from the dependence of MEVC for in-plane magnetic fields.(i) Overall MEVC values are smaller in Figure 9 since demagnetization factors reduce both the dc and ac magnetic fields.(ii) The decrease in MEVC for H > 1.5 kOe is relatively small compared to α31 vs. H.(iii) Data in Figure 9 for BN95-PZT bilayers show a reversal in the sign of for H > 0.75 kOe for both positive and negative H. Figure 9 shows results of MEVC measurements for the magnetic fields applied perpendicular to the bilayers of BNx-PZT (also shown in Figure S6).The variation in MEVC has similar hysteresis and remanence as the in-plane magnetic fields.However, the following features in α 33 vs. H differ from the dependence of MEVC for in-plane magnetic fields.(i) Overall MEVC values are smaller in Figure 9 since demagnetization factors reduce both the dc and ac magnetic fields.(ii) The decrease in MEVC for H > 1.5 kOe is relatively small compared to α 31 vs. H.(iii) Data in Figure 9 for BN95-PZT bilayers show a reversal in the sign of for H > 0.75 kOe for both positive and negative H.
The strength of ME coupling in the bilayers was also characterized by measuring the ac magnetic field frequency f dependence of the MEVC at mechanical resonance modes.Prior to these measurements, we obtained the electromechanical resonance (EMR) frequencies (f r ) for the composites by measuring the frequency dependence of the impedance with an LCR meter.Mode frequencies could not be obtained for BNx for x ≤ 19, but we were able to determine the frequency of longitudinal resonance modes for higher x-values.MEVC α 31 vs f under a bias field H = 100-200 Oe for the bilayers is shown in Figure 10.One observes an increase in α 31 with increasing f and a sharp peak in its value at f r ~55-75 kHz.We were able to identify f r with the longitudinal EMR mode from the known composite dimensions.For x = 33, the figure shows a fine structure with a double peak in the α 31 vs f profile with values of 147 mV/cm Oe at 72.9 kHz and 132 mV/cm Oe at 73.2 kHz.Bilayers of BNx-PZT with x > 33 have a single peak in the profiles and BN95-PZT shows the highest value of α 31 = 992 mVcm −1 Oe −1 at 59 kHz.One observes a significant enhancement in the ME coefficients at f r compared to values at 100 Hz (Figure 8), and for example, by a factor 36 for x = 41.The highest Q-factor obtained from this data is found to be 130.4 for BN44.BN41 also has a large Q-factor of 118.After BN44, the Q-factor reduced to 75 at BN60.We discuss the results of these ME measurements in the following section.The strength of ME coupling in the bilayers was also characterized by measuring the ac magnetic field frequency f dependence of the MEVC at mechanical resonance modes.Prior to these measurements, we obtained the electromechanical resonance (EMR) frequencies (fr) for the composites by measuring the frequency dependence of the impedance with an LCR meter.Mode frequencies could not be obtained for BNx for x ≤ 19, but we were able to determine the frequency of longitudinal resonance modes for higher x-values.MEVC α31vs f under a bias field H = 100-200 Oe for the bilayers is shown in Figure 10.One observes an increase in α31 with increasing f and a sharp peak in its value at fr ~ 55-75 kHz.We were able to identify fr with the longitudinal EMR mode from the known composite dimensions.For x = 33, the figure shows a fine structure with a double peak in the α31vs f profile with values of 147 mV/cm Oe at 72.9 kHz and 132 mV/cm Oe at 73.2 kHz.Bilayers of BNx-PZT with x > 33 have a single peak in the profiles and BN95-PZT shows the highest value of α31 = 992 mVcm −1 Oe −1 at 59 kHz.One observes a significant enhancement in the ME coefficients at fr compared to values at 100 Hz (Figure 8), and for example, by a factor 36 for x = 41.The highest Q-factor obtained from this data is found to be 130.4 for BN44.BN41 also has a large Q-factor of 118.After BN44, the Q-factor reduced to 75 at BN60.We discuss the results of these ME measurements in the following section.

Discussion
It is evident from the results of this study that (i) it is possible to synthesize composites of spinel and M-type hexagonal ferrites free of ferromagnetic impurity phases, (ii) the composites, depending on the amount of BaM, have a moderately high induced planar anisotropy in all compositions, and (iii) the magnetostriction is quite small for BaM rich composites but increases significantly with increasing NFO content; however, the piezomagnetic coefficient q is rather small in all of the composites due to a slow increase in λ with H compared to pure NFO.
It is interesting to note that the coercive field estimated from M vs. H data for the BNx composites remains well under 0.3 kOe for all compositions from x = 33-95.The co-

Discussion
It is evident from the results of this study that (i) it is possible to synthesize composites of spinel and M-type hexagonal ferrites free of ferromagnetic impurity phases, (ii) the composites, depending on the amount of BaM, have a moderately high induced planar anisotropy in all compositions, and (iii) the magnetostriction is quite small for BaM rich composites but increases significantly with increasing NFO content; however, the piezo-magnetic coefficient q is rather small in all of the composites due to a slow increase in λ with H compared to pure NFO.
It is interesting to note that the coercive field estimated from M vs. H data for the BNx composites remains well under 0.3 kOe for all compositions from x = 33-95.The coercive field gradually increases from 35 Oe for BN33 to 256 Oe for BN95.BN75, the material that has highest anisotropy field of 7.77 kOe, has a coercive field of ~45 Oe.It is also important to note that the highest remanent magnetization obtained for BN75 also has the highest anisotropy.The anisotropy acts as a driving force that gives rise to a remanent magnetization for all BNx samples and a zero-bias MEVC in bilayers with PZT.All the BNx samples remain soft magnetic material with a coercive field less than 300 Oe with no significant hysteresis loss for x = 33-95.The value of this coercive field is well below the coercive field of pure polycrystalline BaM which possesses a large coercive field ~5 kOe.In the composites, the stabilization of the BaM grains (Figure 2) does not seem to increase the coercive field.
It is also clear from the results of ME measurements in Figures 8-10 that the bilayers of BNx and PZT show MEVCs that are much higher than the values reported for M-type hexaferrite-PZT bilayers [37], but smaller than those reported for NFO-PZT [38].Under the optimum value of H, the highest MEVCs are α 31 = 152 mV/cm Oe and α 33 = 90 mV/cm Oe, both for BN95-PZT.These values, however, are relatively small due to the weak piezomagnetic coupling strengths in BNx compared to nickel ferrite or nickel zinc ferritebased layered composites with PZT [34,39].
A key and primary objective of this work was to synthesize a ferromagnetic oxide with a moderately large H A and high magnetostriction and piezomagnetic coupling for use with PZT to achieve ME coupling in the absence of an external bias magnetic field.It is worth noting that this goal was indeed accomplished.Bilayers of BNx-PZT used in this study do show a zero-bias MEVC (Figure S7 in the Supplementary Materials).Bilayer of BN75-PZT shows the highest α 31 = 22 mV/cm Oe at zero-bias, and the BN85-PZT bilayer shows the highest α 33 = 9 mV/cm Oe at zero-bias.It is noteworthy that the remanent magnetization of 1.04 kG for BN75 is the highest for the composites (Table 2).Strategies employed in the past to realize zero-bias ME effects included the use of an external stimuli or functionally graded composites, either in magnetization or in composition, etc. [7][8][9][10][11][12][13][14][15][16][17].The use of an easy to synthesize composite of a spinel ferrite and hexaferrite in this work for zero-bias ME effect makes this method more viable than others.There are reports wherein composites consisting of NFO and PZT show a large ME coefficient of 460 mV/cm Oe for bilayers and ~1200 mV/cm Oe for multilayers [40].The MEVC at resonance in these systems was as high as ~1 V/cm Oe [41].Modified NFO and PZT multilayers even showed a higher ME coefficient [42].However, there is hardly any evidence for ME coupling zero-bias effect in these composites [37][38][39][40][41][42][43].
Due to very low magnetostriction, BaM is not suitable for strong direct ME coupling, but the very high uniaxial anisotropic field in the system was utilized in this work.Even though BaM grains in our BNx composites are expected to be completely randomized, leading to a net zero the anisotropic field, the increase in the NFO content in BNx seems to promote the growth BaM grains with in-plane c-axis and a net in-plane anisotropy field.
Finally, we compared the zero-bias MEVC values with results reported in the past.Use of a nickel zinc ferrite graded either in magnetization or composition in a bilayer with PZT resulted in a zero-bias MEVC of 37 mV/cm Oe.Electric field-induced bending vibration mode generated zero-bias ME effect in lead free system, shows an MEVC ~30 mV/cm Oe [9].The low field hysteresis-based zero-bias effect also showed a value of ~60 mV/cm Oe [16].In our work, we have obtained a zero-bias ME coefficient ~22 mV/cm Oe for BN75-PZT bilayer, which is comparable to the earlier report [10].The zero-bias ME response in our study could be improved with the use of composites of NFO and M-type strontium ferrite (SrM) or Al substituted SrM or BaM with higher λ than pure BaM.Substituted BaM or SrM may be good choices as they also have anisotropic fields as high as ~30 kG [43].

Figure 1 .
Figure 1.Representative X-ray diffraction data for BNx composites.All the composites bear the signatures of NFO and BaM.The stick patterns for NFO and BaM are shown in the bottom pane to visualize the one-to-one correspondence of the Braggs positions of each phase to the respective NFO and BaM lines.BN75 contains a small amount of an impurity phase, Ba5Fe2O8, and is denoted by a star.

Figure 1 .
Figure 1.Representative X-ray diffraction data for BNx composites.All the composites bear the signatures of NFO and BaM.The stick patterns for NFO and BaM are shown in the bottom pane to visualize the one-to-one correspondence of the Braggs positions of each phase to the respective NFO and BaM lines.BN75 contains a small amount of an impurity phase, Ba 5 Fe 2 O 8 , and is denoted by a star.

16 Figure 2 .
Figure 2. SEM images for BN5, BN33, BN60, and BN95 composites.There are no notable features in the image for BN5.Well-defined hexagonal grains corresponding to the BaM phase are seen in BN33 and BN60.BN95 does not show any hexagonal grain.

Figure 3 .
Figure 3. Room-temperature magnetization 4πM vs. magnetic field H data for (a) BN95 and (b) BN33 samples.The insets for low H-values clearly show the expected hysteresis and remanence in the M vs. H data.The arrows in the inset indicate which way the magnetic field increases or decreases.

Figure 2 .
Figure 2. SEM images for BN5, BN33, BN60, and BN95 composites.There are no notable features in the image for BN5.Well-defined hexagonal grains corresponding to the BaM phase are seen in BN33 and BN60.BN95 does not show any hexagonal grain.

Figure 2 .
Figure 2. SEM images for BN5, BN33, BN60, and BN95 composites.There are no notable features in the image for BN5.Well-defined hexagonal grains corresponding to the BaM phase are seen in BN33 and BN60.BN95 does not show any hexagonal grain.

Figure 3 .
Figure 3. Room-temperature magnetization 4πM vs. magnetic field H data for (a) BN95 and (b) BN33 samples.The insets for low H-values clearly show the expected hysteresis and remanence in the M vs. H data.The arrows in the inset indicate which way the magnetic field increases or decreases.

Figure 3 .
Figure 3. Room-temperature magnetization 4πM vs. magnetic field H data for (a) BN95 and (b) BN33 samples.The insets for low H-values clearly show the expected hysteresis and remanence in the M vs. H data.The arrows in the inset indicate which way the magnetic field increases or decreases.

Figure 4 .
Figure 4. Magnetostriction, λ11 vs. H data measured parallel to the in-plane H for BNx composites.The magnetic field was applied parallel to the length of the sample and the strain gauge.λ11 for pure NFO is shown in the inset.

Figure 4 .
Figure 4. Magnetostriction, λ 11 vs. H data measured parallel to the in-plane H for BNx composites.The magnetic field was applied parallel to the length of the sample and the strain gauge.λ 11 for pure NFO is shown in the inset.

Sensors 2023 , 16 Figure 5 .
Figure 5. Profiles of S21 vs. f showing resonances in BN33, BN47, and BN60 composites for in-plane static magnetic fields.The absorption in the profiles in (a,c,e) for 5-20 GHz is due to ferromagnetic resonance in the NFO contents of BNx.Profiles in (b,d,f) show absorption due to a magneto-dielectric mode in the composites.

Figure 5 .
Figure 5. Profiles of S 21 vs. f showing resonances in BN33, BN47, and BN60 composites for in-plane static magnetic fields.The absorption in the profiles in (a,c,e) for 5-20 GHz is due to ferromagnetic resonance in the NFO contents of BNx.Profiles in (b,d,f) show absorption due to a magneto-dielectric mode in the composites.

Figure 6 .
Figure 6.Ferromagnetic resonance frequency fr as a function of H for (a) FMR observed in the low frequency region in Figure 5 and (b) magneto-dielectric mode frequency vs. H for BNx composites.

Figure 7 .
Figure 7. Fitting of the FMR data on fr vs. H to Equation (1).

Figure 6 .
Figure 6.Ferromagnetic resonance frequency f r as a function of H for (a) FMR observed in the low frequency region in Figure 5 and (b) magneto-dielectric mode frequency vs. H for BNx composites.

Figure 6 .
Figure 6.Ferromagnetic resonance frequency fr as a function of H for (a) FMR observed in the low frequency region in Figure 5 and (b) magneto-dielectric mode frequency vs. H for BNx composites.

Figure 7 .
Figure 7. Fitting of the FMR data on fr vs. H to Equation (1).

Figure 7 .
Figure 7. Fitting of the FMR data on f r vs. H to Equation (1).
are as follows.(i) When H is decreased from ~3 kOe back to zero a hysteresis in α 31 vs. H is evident for all the BNx-PZT bilayers.(ii) Upon reversing the field H, a 180 deg phase shift (indicated by negative values for α 31 ) is observed in the ME voltage except for x = 5. (iii) The bilayers show a finite remnant value for α 31 at zero-bias that is, as discussed later, attributed to the built-in bias in BNx provided by the anisotropy field H A .
are as follows.(i) When H is decreased from ~3 kOe back to zero a hysteresis in α31 vs. H is evident for all the BNx-PZT bilayers.(ii) Upon reversing the field H, a 180 deg phase shift (indicated by negative values for α31) is observed in the ME voltage except for x = 5. (iii) The bilayers show a finite remnant value for α31 at zero-bias that is, as discussed later, attributed to the built-in bias in BNx provided by the anisotropy field HA.

Figure 8 .
Figure 8. Variation of the ME voltage coefficient MEVC α31 with the magnetic field H for both ac field h and DC magnetic field H applied parallel to the ferrite-PZT bilayer for (a) BN5-PZT, (b) BN33-PZT, (c) BN75-PZT and (d) BN95-PZT.

Figure 8 .
Figure 8. Variation of the ME voltage coefficient MEVC α 31 with the magnetic field H for both ac field h and DC magnetic field H applied parallel to the ferrite-PZT bilayer for (a) BN5-PZT, (b) BN33-PZT, (c) BN75-PZT and (d) BN95-PZT.

Figure 10 .
Figure 10.(a) Frequency dependence of ME coefficient α 31 for bilayer of BNx-PZT.The peak values of MEVC occur at longitudinal mechanical resonance frequency in the samples.(b) Q-factor as a function of NFO weight fraction of BNx composites from the resonance response.

Table 1 .
Demagnetization factors for BN composites.

Table 2 .
Fitting parameters for FMR and magnetic parameters for BNx composites.Gilbert damping constants are also given.