1 Introduction

Perovskite ceramic materials with multifunctional properties are successfully used in modern microelectronic and micromechatronic applications [1,2,3,4]. Multiferroic materials are often obtained as ceramic composites by combining materials with magnetic and piezoelectric properties [5,6,7,8,9,10]. The magnetoelectric effect ME of the multiferroic composite is a feature created from the interaction of the two-component phases of the composite [2, 11,12,13]. Neither the ferroelectric nor ferromagnetic phase exhibit ME, but combining the two phases can produce a high magnetoelectric effect [5]. Theoretical assumptions indicate that obtaining the most excellent ME coupling in multiferroics requires many requirements, including maintaining balanced ferroelectric and ferrimagnetic phases [5]. However, numerous studies indicate that a compromise should be sought between the high coupling and maintaining the favorable multifunctional, e.g., due to the high electrical conductivity of a magnetic material [14, 15]. Ferrite in multiferroic composites causes a significant deterioration of properties, and the sample polarization process is significantly hindered and limited. It forces the design of multiferroic composites with a significant predominance of the ferroelectric phase [16].

Generally, there are three main methods to measure the ME effect, i.e., static, quasi-static, and dynamic [17, 18]. The static method measures the ME signal as a function of increasing magnetic field using a high input impedance electrometer. A charge is generated during the experiment and may accumulate at the grain boundaries during the poling process and ME measuring. This charge moving towards the electrode and its excess may lead to erroneous measurement results [19]. In the case of the quasi-static method, the ME signal is measured as a function of time using a high input impedance electrometer. In contrast, the applied DC magnetic field varies with time [20]. The high charge accumulation, especially for polycrystalline samples, leads to a distortion of research results and is the main problem of this measurement method. Recently, the most popular method of measuring the ME effect is the dynamic method (the lock-in technique). A multiferroic sample is exposed to a sinusoidal, alternating current (AC) magnetic field with an additional direct current (DC) bias [18, 21, 22]. The superimposed fields lead to the electric polarization of the material via the magnetoelectric effect [18].

Various ferrites with different chemical compositions are used in designing multiferroic composites as magnetic phases, e.g., cobalt–zinc [9], nickel–zinc [10, 23], and nickel–cobalt [24]. Nickel–zinc ferrites exhibit good magnetic properties with relatively high resistance at room temperature [25]. Materials with high piezoelectric, dielectric, and ferroelectric parameters are used as the ferroelectric component. The solid solution Pb(Zr1–xTix)O3 (PZT) is a good candidate for this application. PZT is usually modified with appropriate admixtures [26, 27], and the admixtures introduced to the main composition fulfill specific tasks. The donor admixture increases bulk resistance due to the reduction of intrinsic oxygen vacancy. In contrast, the acceptor's admixture decreases the grain resistance and slows the domain motion due to increased oxygen vacancy [28]. The electro-physical properties of the PZT-type material depend on the Zr/Ti percentage content, which change allows for various functional properties [29,30,31,32,33,34,35]. PZT-type materials are applied in many microelectronic devices, e.g., piezoelectric transducers, capacitors, memories, filter elements, batteries, actuators, and sensors [36, 37]. In the technological process of multiferroic composites, many sintering methods are used, e.g., solid-state reaction [38, 39], microwave [40], spark plasma sintering [41], and hot pressing [39]. However, many are expensive, uneconomic, and require meeting special technological conditions. Also, obtaining the repeatability of multifunctional properties of multiferroic materials is still a significant technological problem, so in the technological process of multiferroic composites, the sintering at atmospheric pressure is still the most common and effective method.

The work aimed to obtain multiferroic composites exhibiting magnetic and electrical properties at RT with magnetoelectric coupling. An analysis and comparison of multifunctional properties for two types of ferroelectric composite matrix containing a hard and a soft admixture was carried out.

2 Materials and methods

2.1 Materials

Two composites with different ferroelectric hardness, i.e., Pb0.94Sr0.06(Zr0.46Ti0.54)0.99Cr0.01O3 (P1) and Pb0.84Ba0.16(Zr0.54Ti0.46)O.975Nb0.025O3 (P2) were obtained. Both PZT-type materials show structure from morphotropic region MR, i.e., the coexistence of tetragonal and rhombohedral phases. The P1 material (from the MR region closer to the tetragonal phase) has a ferroelectrically hard admixture (chromium). In contrast, the P2 material (from the MR region closer to the rhombohedral phase) has a ferroelectrically soft admixture (niobium). The magnetic component in multiferroic composite composition was Ni0.64Zn0.36Fe2O4 ferrite (F).

2.2 Technological process of the multiferroic composites

PZT powders were obtained by solid-state reaction technique. In the case of the P1 material, the following reagent was used: PbO (99.99%, POCH), SrCO3 (99.99%), Cr2O3 (99.99%), ZrO2 (99.5%), TiO2 (99.99%). In the case of the P2 material, the following reagent was used: BaCO3 (99.99%), PbO (99.99%), Nb2O5 (99.9%), ZrO2 (99.5%), TiO2 (99.99%). The particle size of the reagents used in the technology was as follows: PbO (< 10 μm), ZrO2 (5 μm), Cr2O3 (< 0.3 mm), Nb2O5 (– 325 mesh), TiO2 (– 325 mesh), BaCO3 (~ 2.2 μm), and SrCO3 (~ 3.2 μm). Because the powders had different particle sizes, they were subjected to long-term grinding in a planetary ball mill for 12 h in ethyl alcohol. Next, the powder mixture was compacted into pellets using a hydraulic press and synthesized in the solid-state reaction at 850 °C/2 h. The synthesis process of the P1 was described in detail in work [42] while for the P2 in work [43]. The Ni0.64Zn0.36Fe2O4 ferrite (F) was obtained as the result of the reaction of the simple oxides NiO (99.8%, < 50 nm), ZnO (99.99%, ~ 5 μm), and Fe2O3 (99.9%, < 5 μm). The powders were mixed in a planetary ball mill for 24 h and calcination was conducted at 1100 °C/4 h.

The ferroelectric and magnetic component was connected in composites in proportion 90/10. Powders were mixed in a planetary ball mill for 24 h, and next were calcined at 1050 °C/4 h. This composite powder was then pressed into compacts using a hydraulic press, and the composite disk-shaped samples were sintered in air at 1250 °C/2 h. After the technological process, the composite samples were sanded, polished, and annealed (to remove mechanical stresses), and next, the silver electrodes on both surfaces of the samples were placed. The composite samples were marked as P1-F and P2-F, respectively.

2.3 Characterizations

The X-ray study was performed at room temperature RT using a Philips X’Pert diffractometer (CuKα, a graphite monochromator, step 0.02°, and 4 s/step). Microstructure, EDS (energy dispersive spectrometry), and EPMA (electron probe microanalysis) tests of the multiferroic composite samples were carried out using a scanning microscope SEM JEOL JSM-7100F TTL LV. Two microscopic image capture techniques were used, i.e., BSE (detection of backscattered electrons) and BS (connection of signals with the secondary and backscattered electrons). The analysis of the chemical composition of the composite surface was carried out using spot, linear, and surface techniques. The average grain size was performed in the ImageJ program using SEM data. DC electric conductivity test was carried out using two multimeters (Keysight 34465A and Keithley 6517B) in a range from RT to 400 °C. Dielectric properties, i.e., the multiferroic composites’ permittivity and dielectric loss factor were measured using the QuadTech 1920 Precision LCR Meter at a range from RT to 450 °C and frequencies 20 Hz to 1 MHz. P–E hysteresis loops were examined at RT for a frequency of 5 Hz using a Sawyer–Tower circuit and the high-voltage Matsusada Inc. HEOPS-5B6 Precision amplifier. Electromechanical measurements were carried out using an optical displacement meter Philtec Inc. D63 and the high-voltage amplifier mentioned above. The data were stored using the transducer card NI USB-6002 (National Instrumental). Magnetic properties were investigated using the Quantum Design PPMS system (MPMS XL-7 Quantum Design) in the temperature range of − 271 °C to 30 °C and magnetic Faraday scale in the range of 27–700 °C.

The composite samples were polarized in silicon oil using the high-voltage Matsusada Inc. HEOPS-5B6 Precision amplifier. The dynamic lock-in method tested the ME effect at RT [17, 18]. AC and DC magnetic fields were applied perpendicularly to the sample's surface. The bias magnetic field was modulated by a small sinusoidal magnetic field (HAC) produced by the Helmholtz-type coils. An SM102 Hall probe system (Asonik) was used to measure the DC and AC magnetic fields. The lock-in amplifier SR 830 (Stanford Research System) with a precisely defined frequency (input resistance of 100 MΩ and a capacitance of 25 pF) measured the voltage input signal while the αME magnetoelectric coefficient was calculated from formula (1):

$${\alpha }_{\mathrm{ME}}=\frac{dE}{dH}=\frac{1}{d}\frac{dV}{dH}=\frac{{V}_{\mathrm{out}}}{{h}_{0}d},$$
(1)

where d is the effective thickness of the piezoelectric phase, Vout – is the lock-in amplifier output voltage, H – magnetic field, V – voltage appears, h = h0sinωt AC field superimposed [17].

3 Results and discussion

3.1 X-ray study

Figure 1 presents the results of X-ray tests for P1-F (a) and P2-F (b) composite materials and their components (P1, P2, and F). The X-ray diffraction patterns of P-F composite materials show firm maxima derived from the ferroelectric phase (PZT-type material) and weak ones derived from the ferrite without a foreign phase. X-ray examinations confirmed the presence of mixed tetragonal and rhombohedral phases (MR morphotropic region) in the ferroelectric component for both multiferroic composite materials. In the case of the P1, the chemical composition is from the MR region (closer to the tetragonal phase), while in the case of the P2 (closer to the rhombohedral one). The correct fit of the experimental results was obtained for the JCPDS pattern card no. 01-073-2022 (space group R3m) for the rhombohedral phase and card no. 00-033-0784 (space group P4mm) for the tetragonal phase. Faint reflections have been recorded for Ni0.64Zn0.36Fe2O4 ferrite materials, and a good fit of the experimental results was obtained for pattern card no. 01-077-9718 with spinel phase and space group Fd − 3m [39, 44].

Fig. 1
figure 1

X-ray diffraction patterns for material tested: P1-F, P1, and F (a) and P2-F, F2 and F (b)

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The maximum peak from the XRD pattern (100) was considered for the calculation of crystallite size using Scherrer’s Formula (2):

$$D=\frac{K\lambda }{\beta \mathrm{cos}\theta },$$
(2)

where D is the crystallite size, K is a shape constant, λ is the X-ray wavelength (1.54056 Å), β is the full width at half maximum (FWHM) of the (110) peak, and θ is the angle of diffraction [45]. For the multiferroic composites, the calculated crystallite size value is 23.9 nm for P1-F sample and 24.9 nm for P2-F sample. Similar results were obtained for the PZT material in the work [46].

3.2 Microstructure and EDS analysis

The microstructural analysis showed that the composite samples are characterized by a compact and dense microstructure (Fig. 2). The use of the BSE technique (detection of backscattered electrons) allowed visualizing the grain of the magnetic (dark areas) and ferroelectric (bright areas) components of the multiferroic composites (Fig. 2b, d). Ferrite grains are properly crystallized with clear and sharp edges (grain boundaries). Larger ferrite grains are present in the microstructure of the P2-F sample. In the case of a composite matrix (ferroelectric PZT-type material), a high degree of solidification is noticeable due to the high sintering temperature of the technological process. In the case of the P1-F, the grains of the PZT material grow unevenly, resulting in smaller and large grain clusters in the microstructure. Ferroelectric grains show a large grain size distribution. In the P2-F composite, grain size heterogeneity is also observed, but in a much smaller amount. Figure 3 shows the P-F multiferroic composite samples' grain size distribution (for dielectric phase and ferrite phase). The average ferroelectric grain size is 1.89 μm for P1-F sample and 2.24 μm for P2-F sample, while for ferrite grains, it 2.31 μm and 2.53 μm for P1-F and P2-F samples, respectively.

Fig. 2
figure 2

SEM microstructure of multiferroic ceramic composites: P1-F (a, b) and P2-F (c, d); the SEM images captured by the SB technique (a, c) and in the BSE technique (b, d)

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Fig. 3
figure 3

Surface EDS analysis (a, c) and grain size distribution (b, d) of multiferroic ceramic composites: P1-F (a, b) and P2-F (c, d)

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The dielectric and piezoelectric properties of PZT-type materials strongly depend on their microstructure and chemical composition [47]. The PZT material with a tetragonal structure has a complex microstructure with 180° and 90° domains [30]. Under the influence of applying an external electric field, the 180° reorientation of the domains does not cause the emergence of stresses. On the other hand, domain rotations of 90° result in the appearance of elastic deformations near domain boundaries, making it difficult to move them. The domain structure of the rhombohedral phase of PZT has domains of 180° and 71° (109°) and applying external field results in a more effective reorientation of the domains in the microstructure. In the morphotropic region of the PZT-type material, higher permittivity values occur for compositions closer to the tetragonal phase. In comparison, higher values of orientation polarization occur for compositions closer to the border of the rhombohedral phase [30].

In the case of multiferroic composites, their functional properties and potential applications mainly depend on the perfection and condition of the microstructure, e.g., density, homogeneity, and grain size. The microstructure is affected by the methods of synthesis and sintering, optimal conditions of the technological process, and the powder mixing method. The high homogeneity of the grains of the microstructure of ceramic materials ensures optimal and beneficial properties of ceramic materials. The grain size also affects the permittivity of ceramic materials, which can be used to select sintering conditions. Permittivity increases with grain size (i.e., is linearly proportional to the average grain size and inversely proportional to the grain boundary thickness) [48].

The surface EDS analysis (energy dispersive spectrometry) of the P-F multiferroic composites is depicted in Fig. 3a–c. The EDS analysis confirmed the assumed percentage composition of the particular ingredients and the presence of elements forming a chemical composition of the composite samples. At the same time, tests showed the absence of foreign elements. The experimental results of the percentage of elements in the composite samples are summarized in the tables attached to Fig. 3.

The visualization of the multiferroic composite microstructure was also confirmed by spot and linear EDS analysis (Fig. 4). Spot EDS analysis (for P1-F sample) was performed on light (001) and dark (002) grains of the composite microstructure (Fig. 4a). On the light grain, maxima from the ferroelectric phase were recorded (Fig. 4b), and on the dark grain, from ferrite one (Fig. 4c). Linear EDS analysis was performed along the red line marked in Fig. 4a, which passes through light and dark grains in the microstructure. Evident concentration changes are observed along the linear EDS analysis for the main components of the ferroelectric phase (Pb, Zr, Ti) and the magnetic phase (Fe). In the light areas, there are maximum concentrations of the elements Pb, Zr, and Ti (which corresponds to ferroelectric grains) while in the dark areas (ferrite grains) their concentration disappears. In registering the presence of iron (Fe), the opposite tendency occurs, i.e., in the dark areas, there is a maximum concentration of Fe, and in the light areas, the concentration of Fe disappears. Also, EPMA (electron probe microanalysis) studies revealed areas of microstructure with increased or decreased intensity of the magnetic and ferroelectric phase elements. Example maps (for the P1-F) of the distribution of representative Fe and Pb elements in the cross-sectional area of the sample are depicted in Fig. 4d.

Fig. 4
figure 4

The line (a) and spot (b, c) EDS analyses (001 – P1, 002 – F) and EPMA maps of iron and lead (d) for the P1-F composite sample

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3.3 DC conductivity

At RT, the P-F multiferroic composite samples show high resistivity, namely, 1.1 × 109 Ωm (for the P1-F) and 6.4 × 1010 Ωm (for the P2-F). Electrical conductivity studies (Fig. 5) have shown that P-F composite materials have a similar trend in electrical conductivity behavior, and the P1-F sample shows higher electric conductivity values. From RT, with increasing temperature, the DC electrical conductivity increases gradually. Increasing temperature causes the localized defects to gain sufficient energy to cross the potential barrier contributing to conductivity increment [49]. Above 90 °C, the increase in conductivity is higher. Based on the Arrhenius equation [44], the activation energy Ea was calculated from rectilinear sections of the lnσDC(1000/T) graph. At a lower temperature, the Ea activation energies are 0.26 and 0.24 eV; at a higher temperature, there are 0.89, and 0.98 eV, for P1-F and P2-F, respectively. In perovskite materials, electrical conductivity depends on the presence of ceramic samples' oxygen vacancies and is associated with defect dipolar effects [50, 51]. In the case of magnetic materials (including ferrites), the nature of the conductivity is different, and here, the hopping of charge carriers between the iron ions occurring in various valence states has a decisive influence on the conductivity [52]. Calculated activation energy values indicate that the influence of oxygen vacancies on the nature of conductivity is the dominant factor in the case of the P-F multiferroic composites [53]. At lower temperatures, ionization processes mainly govern conductivity, and holes or electrons dominate charge carriers. The higher temperatures activate the extrinsic defects, and the mobility of those defects is responsible for higher conductivity [49]. Above mentioned defects usually form in ceramic materials at high temperatures during grain growth, and densification can be avoided with a slow cooling rate [31, 53].

Fig. 5
figure 5

The lnσDC(1000/T) plot for multiferroic composites

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3.4 Dielectric properties

The dielectric properties of the ferroelectrics depend on individual internal physical characteristics of the ceramic materials, e.g., porosity, grain size, admixtures, and composition stoichiometry, however also depend on many external factors such as temperature, humidity, frequency of an electrical field or applied loading force [54]. Temperature dielectric tests for multiferroic composite materials are presented in Fig. 6. The multiferroic materials have high permittivity values and correspondingly low dielectric loss factor and show diffused phase transition from ferroelectric to paraelectric phase. In ferroelectric materials, the blurring of the phase transition is influenced by many factors, e.g., deviations from the chemical composition, doping, heterogeneity of defects distribution, and mechanical strains [55]. For 10 kHz, at RT, the permittivity values are 630 for the P1-F and 1120 for P2-F, while at the phase transition temperature Tm is 8385 for the P1-F and 5356 for the P2-F. Low values of dielectric loss factor (tanδ < 0.2) of multiferroic composite materials are maintained up to high temperatures, i.e., for the frequency of 10 kHz up to 150 °C for the P1-F composite sample and 210 °C for the P2-F composite sample.

Fig. 6
figure 6

Temperature dependences of permittivity (a, c) and dielectric loss factor (b, d) for the P1-F (a, b), P2-F (c, d) multiferroic composites

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At low frequencies, the dielectric constant is high because of space charge polarization at the grain boundaries, creating a potential barrier. An increase in charge accumulation at the grain boundary causes growth permittivity values. The dielectric dispersion can be explained by the increased effect of grain boundaries' effect compared to the weaker effect of the grains [56]. At high temperatures, the dielectric dispersion is related to the conductivity mechanism, precisely with the space charge mechanisms of relaxation phenomena (oxygen vacancies and related defects are mainly responsible for them). For example, at high sintering temperatures, lead shows high volatility, which results in the formation of vacancies that generate conduction electrons in the ionization process [10]. Furthermore, ferrite's presence in multiferroic composites also causes a blurring of the phase transition (lack of a clear maximum permittivity εm in Tm), which is particularly visible at lower frequencies. The maximum permittivity εm at the phase transition temperature Tm is preserved at higher frequencies for the multiferroic composites.

3.5 Ferroelectric properties and strain response

It is well known that ferrite weakens the dielectric and ferroelectric properties of multiferroic composites [14]. Figure 7 shows P–E hysteresis loops for multiferroic composites with an increasing electric field. The P–E hysteresis loops in RT do not reach full saturation, even with an applied field of 4 kV/mm. However, the high polarization values are retained in the P2-F sample (with soft admixture—Fig. 7b). For 4 kV/mm the Pr residual polarization is 6.65 µC/cm2 while the maximum polarization Pm is 16.25 µC/cm2. In contrast, for the P1-F sample (with hard admixture), the values of Pr and Pm are 1.04 and 4.88 µC/cm2, respectively.

Fig. 7
figure 7

Hysteresis P–E loops for P1-F (a) and P2-F (b) multiferroic composites

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The bipolar strain curves tested of the multiferroic ceramic composites at RT and with an increasing electric field are presented in Fig. 8. The addition of ferrite explicitly degrades the piezoelectric properties. The P1-F composite sample shows a negligible deformation effect, while the P2-F sample shows butterfly shape S–E loops. The S–E deformation loop is typical for ferro-soft ferroelectric materials, i.e., with low coercive and small internal field values. In the case of the P1-F composite sample, the low-strain hysteresis results from the small mobility of the domain wall in the microstructure of the ferroelectrically hard PZT materials.

Fig. 8
figure 8

Bipolar strain S–E curves for P1-F (a) and P2-F (b) multiferroic composites

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3.6 Magnetic properties

Temperature dependencies of magnetization M(T) are similar for both multiferroic composites (Fig. 9a, b). As the temperature increases, the magnetization decreases. At − 270 °C, M is 5 emu/g for the P1-F and 5.23 emu/g for the P2-F composite sample. On the M(T) curves, there are some temperature ranges with different magnetic behaviors, i.e., below − 180 °C behavior is typical for a para/super-paramagnetic material. In contrast, at a higher temperature range, the trend is characteristic of ferro/ferrimagnetic materials. At 25 °C, M magnetization is 4.63 emu/g for the P1-F and 4.74 emu/g for the P2-F, while above 400 °C, the multiferroic composite materials show paramagnetic properties. Decreasing magnetization with increasing temperature is associated with the increased thermal motion of magnetic moments and is typical for magnetic materials in which the signal from the ferrimagnetic component dominates [57, 58].

Fig. 9
figure 9

Temperature dependencies of the M(T) for multiferroic composite samples: P1-F (a), and b) P2-F (b). Inset graphs: on the left—magnetic hysteresis loops at − 270 °C, − 173 °C, and 25 °C; on the right—area enlargement of the M(H) loop

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For multiferroic composites also, the same behavior is shown by magnetic hysteresis M(H) loops made at three temperatures, i.e., − 270 °C, − 173 °C, and 25 °C (Fig. 9a, b inset, of the left). It indicates that the magnetic properties depend mainly on the amount of ferrite in the composite compositions. The M(H) curves are typical for soft ferromagnetic materials (narrow hysteresis loop, with small values of the Hc coercive field). At 25 °C, the saturation magnetization Ms is 6.16 emu/g for the P1-F and 6.38 emu/g for the P2-F. The coercivity Hr decreases with increasing temperature (Fig. 9a, b inset, of the right) and at 25 °C is 12.6 Oe for the P1-F sample and 12.2 Oe for the P2-F sample.

3.7 Magnetoelectric effect

The samples were polarized in silicon oil under the following conditions (Ep/Tp/tp): 3.5 kV/mm/80 °C/2 h for the P2-F and 2.5 kV/mm/80 °C/1 h for the P1-F. In the case of the P1-F composite sample, a smaller field and polarization time were used due to the higher electric conductivity, which effectively hindered the polarization process. Nevertheless, the possibility of applying such high external electric fields (as for the PZT-type material) proves the microstructure's high quality and strength of the composite samples. It confirms the properly conducted technological process of multiferroic composites. Piezoelectric parameters were calculated by the resonance-antiresonance method after the polling process. The electrical coupling coefficient kp is 0.29 for the P1-F, and 0.44 for the P2-F, while the piezoelectric coefficient d31 is 41 pC/N and 202 pC/N for the P1-F and the P2-F, respectively. Higher values of piezoelectric parameters for the P2-F composite sample result from the physical characteristics of the P2 material (the ferroelectric composite component). The soft admixture (niobium) in PZT allows for effective (facilitated) polarization of the P2-F composite sample. Weakly attached domains easily align themselves to the direction of the external electric field. The more easily a material be polarized, the greater the amount of charge can be stored in the multiferroics. In the case of the P1-F, a hard admixture (chromium) increases the stability of piezoelectric parameters but hinders the sample polarization process (polarization is less effective). More strongly fixed domains require a more effective influence of external factors in the form of higher temperature and high electric field for more effective rotation of the domains on the direction of the field.

It is well-known that the ME effect in multiferroic materials depends on the ferroelectric phase's piezoelectricity and the ferrite phase's magnetostriction. The stresses generated in the piezoelectric subsystem depend on its mechanical properties and result from the mechanical coupling between the magnetostrictive and piezoelectric subsystems. These stresses cause an increase in the polarization of the domains in the direction of stretching and a decrease in the direction of compression, and the change in polarization results from the change in the density of electric charges near the domain walls [5]. The magnetoelectric ME effect of the multiferroic composites was tested at RT by the dynamic lock-in method. The test results of magnetoelectric coefficient αME were presented as a function of the HDC magnetic field (HAC = 5 Oe, v = 1 kHz, Fig. 10a) and as a function of the HAC magnetic field frequency (HAC = 5 Oe, HDC = 1200 Oe, Fig. 10b). AC and DC magnetic fields were applied perpendicularly to the sample's surface. For both composites, αME(HDC) dependencies show similar tendencies (Fig. 10a). With the increase of the HDC, αME increased and reached a maximum at the HDC magnetic field and is 1.95 mVcm−1Oe−1 for 1160 Oe (for P1-F composite sample) and 3.25 mVcm−1Oe−1 for 1136 Oe (for P2-F composite sample). Above this maximum, with a further increase in the magnetic field, αME decreases. This phenomenon is common in ferrites with a spinel structure, where at a specific magnetic field value, αME reaches its maximum state [59]. The DC bias field Hmax, where maximum αME occurs, corresponds to the field where maximum linear magnetostriction occurs [60]. Further increase of the HDC magnetic field decreases the magnetostriction of the material, and above 3000 Oe, the decrease in αME is slight. Compared to the P2-F, the αME values of the P1-F composite sample are lower, and additionally, at higher HDC magnetic fields (2000–4000 Oe), the αME shows a visible hysteresis. The wide-range scattering of the αME visible on the graphs may result from the difference in the composition structure of the composite materials [17]. Similar results of ME effect studies for multiferroic composite materials were obtained in [59, 61, 62], but with weaker amplitudes.

Fig. 10
figure 10

Magnetoelectric coefficient αME as a function of applied DC magnetic bias field HDC (c) and frequency dependent on αME coefficient (d) for multiferroic composites P1-F and P2-F

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Measurements of the αME coefficient as a function of the frequency of the HAC magnetic field show a different tendency of changes in the ME effect of the tested composites (Fig. 10b). In the case of the P1-F composite (up to about 1 kHz), the αME values increase rapidly with the change in the frequency of the HAC field, and above 1 kHz, αME retains an almost constant value. At the same time, no clear maximum of the αME coefficient is observed. In the case of the P2-F composite sample, the magnetoelectric coupling between the magnetostrictive and ferroelectric phases increases with the frequency of the magnetic field. It reaches its maximum value (approx. 210 Hz), corresponding to the resonant magnetoelectric effect. With a further increase in the frequency, there is a systematic decrease in the αME value. This coupling behavior between the magnetostrictive and ferroelectric phases is typical for most magnetoelectric materials. In work [17], a similar optimal frequency (approx. 200 Hz) was obtained for the CoFe2O4–BaTiO3 material but with a lower amplitude of the αME(f) waveform. The observed behavior for the P1-F composite sample with the lack of a clear maximum may indicate that at low frequencies, the magnetoelectric effect is also affected the factors such as the composition of the composite, microstructure, and conductivity of the ferrite magnetic phase [63, 64]. The size of the ME effect is correlated with the microstructure of the multiferroic ceramic composites. It is because the coupling between the ferroelectric and ferromagnetic subsystems occurs through elastic interaction at the interface [65]. In the case of the tested composites, the P2-F sample with larger ferrite grains and greater homogeneity of the ferroelectric phase has a higher ME effect. In the case of the P1-F, fine and large grains of the ferroelectric component is present in the microstructure, which may additionally hinder the coupling of the magnetic and electrical subsystems and reduce the ME effect. In addition, the higher values of the αME coefficient obtained for the P2-F material (with a soft admixture) result mainly from higher piezoelectric parameters of the composite sample, i.e., more effective polarization.

The ME effect in multiferroic composite materials results from mutual interaction between piezoelectricity and magnetostriction, ferroelectric and ferrite phases. The αME values of the obtained composites are higher than in the works [62, 66, 67] but smaller than in the works [68, 69]. In the case of ferroelectric-ferromagnetic materials, obtaining very high αME values is limited due to the different types of structures that make up the composite (perovskite/spinel) and the mutual diffusion of ions from the ferroelectric to the magnetic phase (and vice versa) [69]. Also, in the measurement lock-in method used may occur the discharging process. For low frequencies, the discharge may happen through the resistance of the sample, while at high ones, the discharge will occur through the capacitance of the sample [17]. It typically results in lower ME effect values compared to other measurement methods.

4 Conclusion

Two multiferroic composite materials with magnetoelectric properties were obtained via solid-state reaction. A comparison of test results using hard and soft doping in a composite matrix was presented. The tests showed that composite materials made of nickel-zinc ferrite and PZT-type material exhibit properties suitable for applications as sensors or magnetoelectric transducers. This is ensured, among others, by the appropriate microstructure of composite samples. The ferroelectric PZT material P2 (from the morphotropic region with a soft admixture) ensures the preservation of the beneficial functional properties of the multiferroic composite and a significant magnetoelectric effect. Compared to the hard-doped PZT material (P1), P2 is a more attractive candidate for the matrix of the multiferroic composites for the applications mentioned above. At room temperature P2-F multiferroic composite show advantageous parameters: ρDC = 6.4 × 1010 Ωm, ε = 1120, Pm = 16.25 μC/cm2, Pr = 6.65 μC/cm2, M = 5.23 emu/g, kp = 0.44, d31 = 202 pC/N and the magnetoelectric coupling coefficient αME = 3.25 mVcm−1Oe−1. The more effective polarization of the P2-F multiferroic composite provides a higher ability to store energy. A hard admixture in PZT material ensures higher stability of parameters, but it makes it difficult to obtain high piezoelectric parameters and, consequently, a high magnetoelectric effect (for P1-F αME = 1.95 mVcm−1Oe−1). The choice of this type of material in multiferroic composite constructions is justified when the dominant criterion is the stability of functional parameters.