Room-temperature ferroelectricity, superparamagnetism and large magnetoelectricity of solid solution PbFe_1/2Ta_1/2O₃ with (PbMg_1/3Nb_2/3O₃)_0.7(PbTiO₃)_0.3

Abstract

We report the properties of first synthesized ceramic samples of a perovskite solid solution (PbFe_1/2Ta_1/2O₃)_x[(PbMg_1/3Nb_2/3O₃)_0.7(PbTiO₃)_0.3]_1−x, x = 0.4, 0.5. The solution is a single-phase material contrary to broadly studied multiphase (magnetic/ferroelectric) composites. Both compounds are ferroelectrics with a diffuse phase transition. An increase in x value results in a decrease in phase transition diffuseness, and an increase in the remnant polarization. ²⁰⁷Pb NMR shows that iron ions are nonuniformly distributed over octahedral sites and tend to random occupation of these sites in the perovskite structure. In particular, the NMR data indicate a tendency to form regions with a higher concentration of iron in the perovskite structure. Magnetic measurements show the coexistence of superparamagnetic and paramagnetic phases in the samples. The paramagnetoelectric (PME) coefficients determined by a dynamic method at room temperature have values β ≈ 0.15 × 10⁻¹⁵ s A⁻¹ (x = 0.4) and 0.54 × 10⁻¹⁵ s A⁻¹ (x = 0.5) at low magnetic fields (± 300 Oe), which are three thousands times larger than that in most single-phase magnetoelectric materials. Our measurements show that the main contribution to the PME response is caused by the superparamagnetic phase. Because the ME response is proportional to dM²/dH, it can be amplified by many orders of magnitude for the multiferroics with the superparamagnetic phase due to a sharp change of magnetization with the field.

Introduction

A strong magnetoelectric (ME) coupling existing at room temperature is especially vital for novel functional device fabrication [1,2,3,4,5,6]. A straightforward way of increasing the magnitude of the ME response is to choose the components with large magnetostrictive and piezoelectric coefficients. For a long time, mainly composite multiferroics on the base of PbZr_1−xTi_xO₃ (PZT) or (PbMg_1/3Nb_2/3O₃)_0.7(PbTiO₃)_0.3 (PMN–PT) has been used. The latter component produces the largest ME effect and has been often used (see, e.g., [3]) in the multilayer multiphase (ferroelectric/ferromagnetic) structures. The reason is the large piezoelectricity of PMN–PT in the morphotropic region with the coexistence of the relaxor and ferroelectric phases. For a single crystal, it is 7 times larger than the piezoelectricity of PZT [6]. For ceramic materials, the piezoelectricity in PMN–PT is 2 times larger than that in PZT [7].

In the last years, considerable attention of scientists and engineers was paid to ferroelectric antiferromagnets PbFe_1/2Ta_1/2O₃ (PFT), T_N ≈ 130–180 K, and PbFe_1/2Nb_1/2O₃ (PFN), T_N ≈ 140 K [8, 9] and their solid solutions with PbZr_0.53Ti_0.47O₃ [10,11,12,13,14,15,16,17]. Some of these solid solutions exhibit room-temperature multiferroism and large enough ME coupling, which includes a mixture of linear and biquadratic contributions. The ME coupling has been theoretically analyzed in Refs. [18, 19] and described by second and fourth rank tensors, namely, μ_ijP_iM_j and ξ_ijklP_iP_jM_kM_l (P is polarization and M is magnetization). The authors of Refs. [18, 19] have shown that large ME effect and the appearance of magnetization originate from the nanostructure of considered materials. Another mechanism of magnetization appearance in chemically disordered antiferromagnetic multiferroics was considered in Refs. [20, 21]. It was shown that antiferromagnetically interacting Fe³⁺ ions may form superstructures having a ferrimagnetic ground state. Such a structure has a different number of nonequivalent Fe positions in a unit cell. As a result, the ground state magnetization may reach several μB per Fe spin. Experimental indications on the ferrimagnetic superstructure formation were reported in Ref. [22] for PbFe_1/2Sb_1/2O₃. The F-center exchange mechanism was proposed in Ref. [23]. It provides an explanation for the existence of ferromagnetism in oxides due to the presence of oxygen vacancies.

Recently the attention of scientists and engineers was attracted to the paramagnetoelectric (PME) effect introduced by Hou and Blombergen [24] described by term λ_ijkP_iM_jM_k. The results of experimental and theoretical studies of this effect in PFN and its solid solution with PbTiO₃ were published in Refs. [25, 26].

It was not excluded that the replacement of PZT by PMN–PT in solid solution with PFT could lead to an essential increase in ME effect due to a larger piezoelectric coefficient in PMN–PT. Surprisingly, to the best of our knowledge, there is no information about the synthesis of the (PFT)_x(PMN–PT)_1−x solid solution. Perhaps the more complex characteristics of PMN–PT than PZT and thus the more complicated mechanism of ME effect were the main reason for the fact. On the other hand, both components of the (PFT)_x(PMN–PT)_1−x solid solution were broadly studied (see, e.g., [27,28,29,30,31,32,33]). In particular, it was shown that multiferroic PFT is antiferromagnetic–ferroelectric with ferroelectric phase transition at T_C ≈ 250 K [31]. Considered PMN–PT is nonmagnetic with a maximum of dielectric permittivity at T_m ≈ 410–420 K [32, 33].

The aim of this study is to describe briefly the synthesis methodology of the novel single-phase multiferroic, to characterize the obtained samples and to present results of experimental and theoretical investigation of its properties, namely, polar, magnetic and magnetoelectric characteristics.

Samples preparation, structural characterization and experimental methods

Ceramic samples of (PFT)_x(PMN_0.7PT_0.3)_1−x were prepared by columbite precursor method [34] using the nanodispersed precursor powders of MgNb₂O₆ and TaFeO₄ synthesized by the organonitrate method from chemicals with purity better than 99%. The received powders of MgNb₂O₆ and TaFeO₄ were ground in an ethanol medium using a planetary mill with ZrO₂ balls. After that, they were annealed for 6 h in corundum crucibles at 1050° and ground again for 6 h. Obtained nanodispersed TaFeO₄ and MgNb₂O₆ were mixed in stoichiometric ratio with Ti(OH)₄·nH₂O and Pb(NO₃)₂, then ground in an ethanol medium for 6 h. A small amount of Li₂CO₃ (about 1 mol%) was added to the mixture. This addition promotes the formation of the perovskite modification of the solid solution and reduces its conductivity. The resulting powder was pressed into disks with a diameter of 13 mm and a height of 2.5 mm. The disks were calcined in corundum crucibles at temperatures from 950 to 1050 °C for 4 h.

Ceramic samples with x = 0.1, 0.2, 0.3, 0.4 and 0.5 were prepared for investigation. However, because the samples with x = 0.1, 0.2, 0.3 show only conventional paramagnetic behavior (see Fig. 10 in Appendix), only two compounds (x = 0.4 and 0.5) with multiferroic properties were chosen for detailed studies.

To confirm the perovskite structure of the synthesized samples, the X-ray diffraction patterns were obtained by using a DRON-UM1 diffractometer using monochromatic CuK_α radiation (Fig. 1). XRD diffraction patterns of both samples correspond to the perovskites structure with minor addition of pyrochlore phase (less than 2.5 wt%). No magnetic impurities like Fe₂O₃, Fe₃O₄ or PbFe₁₂O₁₉ were detected by the XRD measurements.

Figure 1

XRD diffraction pattern of (PFT)_0.4(PMN–PT)_0.6 sample with pyrochlore reflexes marked by the asterisks

Polished and additionally thermally etched cross sections of the dense samples were analyzed by field emission scanning electron microscopy (FE-SEM) (Ultra plus, Carl Zeiss), and elemental analysis of the identified phases was performed with energy-dispersive spectroscopy (EDS), using Inca detector (Oxford Instrument). The samples were carbon coated prior to SEM/EDS analysis to ensure good conductivity during the investigation.

The EDS spectra of both compounds show the presence of all elements and confirm the chemical composition of these samples. The spectra were measured in ten different regions of each sample and have shown average homogeneity of the chemical composition within the error bars of the method (about 1 at.%), which indicates a formation of a single-phase solid solution of PMN–PT and PFT. Figure 2 shows the EDS spectrum of (PFT)_0.4(PMN–PT)_0.6 sample. The scanning electron microscopy image of this material is presented in the inset to Fig. 2. It shows the presence of micro-grains (2 to 5 μm) uniformly distributed over the surface of the sample. However, the sizes of coherent scatter regions calculated on the base of X-ray data (by the broadening of the diffraction lines) appeared to be about 70–85 nm for these samples, which indicates that the ceramic micro-grains consist of nanoscale structural units.

Figure 2

EDS spectrum of (PFT)_0.4(PMN–PT)_0.6 sample and the SEM micrograph of this sample

Dielectric properties of both compounds were measured on samples prepared in the form of tablets. These tablets were polished and coated with a silver conductive layer used as electrodes. Dielectric measurements were conducted using E7-20 impedance analyzer. The dielectric permittivity was measured at frequencies 25 Hz–200 kHz in the temperature range 290–480 K.

Nuclear magnetic resonance (NMR) measurements were performed using a commercial Bruker (Avance II) 400 MHz NMR spectrometer at 9.41 T. Extremely broad ²⁰⁷Pb NMR spectra were accumulated by a frequency-stepped method by acquiring spin echoes every 100 kHz. Individual echoes were Fourier transformed and superimposed in the frequency domain. A four-phase “exorcycle” phase sequence (xx, xy, x–x, x–y) was used to form echoes with minimal distortions due to antiechoes, ill-refocused signals and piezoresonances [35]. The length of the π/2 pulse in the spin echo sequence was t_π/2 = 4.4 μs, the spin echo delay time τ was 15 μs and the repetition time was 0.1 s.

The magnetization measurements were performed on the magnetometer with vibrating sample LDJ-9500 that is equipped by the regulating temperature system on the liquid nitrogen base.

The paramagnetoelectric coefficients were determined by a dynamic method [36] as a function of bias magnetic field H_dc at a small ac field h_ac = 0.64 Oe and frequency 311 Hz by measuring the current across the sample utilizing a high-sensitive lock-in-amplifier. High homogenous ac and dc magnetic fields were provided by a conventional EPR spectrometer. Both fields were applied normal to the surface of the sample. Before the measurements, the samples were poled at room temperature by applying a dc electric field of 10–15 kV/cm for 30 min. In every experiment, more than two runs were repeated with a reversed direction of H_dc, which results in a change of a sign of the signal. In this way, a possible spurious electromagnetic induction signal was distinguished from a true ME one whose sign is dependent on the PH product.

Experimental results

Investigation of dielectric properties

In this section, the dielectric measurements of multiferroic (PFT)_x(PMN–PT)_1−x (x = 0.4 and 0.5) and a discussion of the results will be presented.

The dependence of polarization on the electric field P(E) was measured at room temperature and shown in Fig. 3. The well-saturated hysteresis loops of both samples indicate the presence of a ferroelectric phase in these materials. One can see that an increase in the PFT content from x = 0.4 (04PFT) to x = 0.5 (05PFT) leads to an increase in the residual polarization from ~ 3 to ~ 4.4 µC cm⁻² and to a decrease in the coercive field from ~ 3.5 to ~ 2.8 kV cm⁻¹.

Figure 3

P–E hysteresis loops of (PFT)_0.4(PMN–PT)_0.6 (solid curve) and (PFT)_0.5(PMN–PT)_0.5 (dashed-dotted curve) solid solutions

Figure 4 shows the temperature variation of the dielectric permittivity measured for studied samples. Both samples have a wide maximum of the dielectric permittivity at temperature T_m, which value does not depend on the frequency, and is typical for ferroelectrics with a diffuse phase transition [37]. The temperature T_m decreases with increasing PFT content from 378 K for the 04PFT compound to 371 K for 05PFT. These temperatures approximately correspond to the transition temperatures expected for the solid solutions of PMN–PT and PFT: T_m = (1 − x)T_PMN–PT + xT_PFT, where T_PMN–PT and T_PFT are the transition temperatures of the components (see dashed line in the inset of Fig. 4). Some deviation from this expression can be explained by variations in a degree of ordering of Mg, Nb, Fe, Ti and Ta cations over “B” positions in the perovskite structure, which depends on the sample preparation and affects the phase transition temperature [38]. It is important to underline that the absence of any additional peaks in ε’(T) confirms the single-phase nature of the studied compounds.

Figure 4

Dependence of dielectric permittivity ε of (PFT)_x(PMN–PT)_1−x (x = 0.4 and 0.5) solid solutions on temperature at different frequencies. The inset shows the phase transition temperature as a function of the PFT content; experimental data for (PMN)_0.7(PT)_0.3 and PFT are taken from [39,40,41], respectively

As shown in Fig. 5, the temperature dependence of the inverse dielectric permittivity, measured for both samples at 1 kHz, does not follow the linear behavior predicted by the Curie–Weiss law for a certain temperature range above T_m. In this case, the modified Curie–Weiss law can be used to describe the temperature dependence of the dielectric permittivity [42]:

Figure 5

Temperature dependences of the reciprocal dielectric permittivity of the (PFT)_x(PMN–PT)_1−x (x = 0.4, 0.5) compounds; the inset shows logarithmic dependence of 1/ε − 1/ε_m on T − T_m

$$ 1/\varepsilon = \, 1/\varepsilon_{\text{m}} + \left[ {\left( {T \, {-} \, T_{\text{m}} } \right)/C} \right]^{\gamma } ,(\varepsilon_{\text{m}} = \varepsilon^{{\prime }}_{ \hbox{max} } ). $$

Parameter γ characterizes the degree of phase transition diffuseness, and its values lay in the region from 1 (for ferroelectrics) to 2 (for relaxors). Fitting of the experimental data gives the γ values equal to ~ 1.85 for 04PFT and ~ 1.8 for 05PFT. As shown in Ref. [37], the diffuse phase transition could be considered as an intermediate state in which both ferroelectric and relaxor phases can be presented simultaneously. This allows us to suggest that both relaxor and normal ferroelectric phases coexist in the studied compounds, and an increase in the PFT content leads to an increase in the ferroelectric phase contribution, which is in agreement with the higher remnant polarization measured for 05PFT as shown in Fig. 3.

²⁰⁷Pb nuclear magnetic resonance

²⁰⁷Pb Nuclear Magnetic Resonance (NMR) spectra of PFT and the solid solutions (PFT)_x(PMN–PT)_1−x (x = 0.4, 0.5) are presented in Fig. 6. The spectra reflect magnetic interactions of Fe³⁺ ions responsible for magnetic properties of studied materials with the nuclei of Pb ions giving the main contribution to the polarization of these materials. Usually, ²⁰⁷Pb NMR spectra of perovskites comprising iron in their structure [43, 44] consist of a single featureless line (800 kHz–1 MHz wide) due to a distribution of superhyperfine interactions between ²⁰⁷Pb and Fe³⁺ presented in these samples. It is important that an analysis of spectra of studied solid solutions provides an opportunity to determine the distribution of Fe atoms over “B” sites in the perovskite structure. For better resolution of spectrum, the sample 04PFT was heated up to 450 K, to observe the narrowing of lines due to a motional averaging of the interactions, arising as a result of fast thermal reorientations of magnetic moments. This temperature is also much higher than the temperature of ferroelectric to paraelectric phase transition (~ 380 K, see Fig. 4), which reduces the effects associated with distribution of superhyperfine interactions due to a decrease in the spread of Fe–Pb distances, and well higher than the estimated temperature range of the superparamagnetic phase existence (T_c ≈ 400 K, see “Magnetization” section), which ensures that the entire sample is in a paramagnetic state and all Pb atoms are visible in the NMR spectrum.

Figure 6

²⁰⁷Pb NMR spectra of PFT, solid solutions (PFT)_x(PMN–PT)_1−x (x = 0.4, 0.5) at room temperature and (PFT)_0.4(PMN–PT)_0.6 at 450 K

The largest influence on the frequency shift of ²⁰⁷Pb NMR spectra has the Fermi contact interaction, which transferred a Fe³⁺ magnetization to Pb nucleus due to the chemical bond between these atoms. This interaction decreases quickly with the number of bonds involved and the main contribution to the spectra originates from nearest-neighbor Fe³⁺ ions. Thus, the spin-Hamiltonian for the sample being in the paramagnetic state can be presented in the form:

$$ {\mathbf{H}} = - \gamma_{\text{N}} \hbar {\mathbf{H}}_{0} {\mathbf{I}} + N{\mathbf{AI}}\left\langle S \right\rangle , $$

where μ₀H₀ ~ 9.4 T is the external magnetic field, γ_N is the gyromagnetic ratio of ²⁰⁷Pb nuclei, 〈S〉 is the thermally averaged spin of Fe³⁺, A is the Fermi contact interaction constant, and N is the number of nearest-neighbor Fe ions in Pb surroundings.

As shown in Fig. 6, ²⁰⁷Pb NMR spectra of 04PFT and 05PFT compounds can be represented as a convolution of two lines (spectral components), which indicates a nonuniform distribution of Fe atoms. This is quite obvious for (PFT)_0.5(PMN–PT)_0.5 with 25% of all “B” sites occupied by Fe. In the case of uniform distribution, each of the Pb atoms (surrounded by eight “B” sites) will have exactly two nearest-neighbor iron atoms (and four in the case of PFT), which should lead to a single line in the NMR spectrum of this compound.

The relative intensities of the abovementioned two lines indicate a close to a random distribution of Fe atoms over the “B” sites in the perovskite structure. Indeed, in the case of a random distribution of iron atoms, the probability of the simultaneous location of N iron atoms in the nearest environment of a lead can be expressed as:

$$ P(N_{Fe} ) = (1 - p)^{8 - N} p^{N} \frac{8!}{(8 - N)! \cdot N!}, $$

(1)

where p is a probability of finding an iron atom in the nearest environment of lead. For 04PFT (p = 0.2) this gives P(0) = 0.168, P(1) = 0.336, P(2) = 0.294, P(3) = 0.147 and P(4) = 0.046. Taking into account that due to the superhyperfine interaction, the shift of a particular spectrum ∆ν = –NA〈S〉/h depends on the number of nearest-neighbor Fe ions, the spectrum from all ²⁰⁷Pb nuclei should consist of five lines located at distances A〈S〉/h from each other, whose relative integral intensities equal to P(N) and whose width depends on the number of neighboring iron atoms. Analysis of the spectrum for this compound shows that the relative integral intensities of two lines obtained after fitting are close to P(0) + P(1) = 0.504 and P(2) + P(3) + P(4) = 0.487 (see Table 1). This allows us to suppose that the narrow line corresponds to lead atoms having from 0 to 1 nearest neighboring iron atoms, and the wide line to lead with a larger number of nearest neighboring iron atoms.

Table 1 Results of fitting of the experimental ²⁰⁷Pb NMR spectra of PFT, 05PFT and 04PFT compounds

The relative integral intensities obtained for 05PFT also fit the assumption of a close to a random distribution of iron atoms (see Table 1), but higher temperature range of the superparamagnetic phase existence (~ 490 K) does not allow to reliably overreach this temperature in order to obtain the paramagnetic state of the entire sample.

In a case of arbitrary distribution of Fe atoms in PFT, the probability of B sites occupation by Fe is 0.5. Thus, the probability of the location of 0 or 1 Fe atoms in the nearest environment of Pb is negligibly small [see Eq. (1)], and a much more essential contribution arises from Pb having from two to six nearest neighboring iron atoms. Overlapping of these lines (extremely broadened by the magnetic interactions between Pb and Fe atoms) would results in only one wide line in the ²⁰⁷Pb NMR spectrum of PFT. Thus, the ²⁰⁷Pb NMR spectra of PFT cannot be used for the determination of iron atoms distribution.

Thereby, ²⁰⁷Pb NMR shows that iron atoms tend to random occupation of the sites “B” in the perovskite structure. At the same time, the intensity of the line corresponding to Pb with a higher number of nearest-neighbor Fe ions is noticeably larger than it follows from Eq. (1) (see Table 1). This allows us to suppose the existence of some tendency to form areas with a higher concentration of iron.

Magnetic properties

The magnetic response of solid solutions (PFT)_x(PMN–PT)_1−x is due to the presence of octahedrally coordinated Fe³⁺ ions having 3d⁵ electronic d-shell configuration in S-state, spin S_Fe =5/2 and g-factor g ≈ 2. Their fraction in the formula unit is x/2. Figure 7 shows magnetization isotherms M(H) at T = 120, 193, 293 K for two samples. The M(H) isotherms have a qualitatively similar look for x = 0.4 and 0.5. For all considered temperatures, the curves are anhysteretic, i.e., reversible. We see that the measured magnetization may be presented as a sum of a paramagnetic contribution that is proportional to the field M_p(H, T) = χ_p(T)H and of superparamagnetic-like contribution M_s(H, T) that saturates at the field of the order of 1 kOe. The absence of noticeable hysteresis for observed curves allows considered nonparamagnetic contributions as superparamagnetic ones registered at T ≫ T_b, T_b being a blocking temperature [45, 46]. Therefore, the blocking temperature is T_b <120 K.

Fig. 7

Magnetization dependence on magnetic field for solid solution (PFT)_x(PMN–PT)_1−x for x = 0.4 (a) and x = 0.5 (b) at T = 120 K (open squares), 193 K (open circles) and 293 K (open triangles). The solid curves show the fit by Eq. (2). The values of fitting parameters are given in Table 2

The solid lines in Fig. 7 show the fit of M(H) curves by the sum of paramagnetic and superparamagnetic contributions

$$ \begin{aligned} M(H,T) &= M_{\text{s}} + M_{\text{p}} , \\ M_{\text{s}} (H,T) &= N_{\text{s}} \mu_{\text{s}} \left( T \right)L\left[ {\frac{{\mu_{\text{s}} \left( T \right)H}}{{k_{\text{B}} T}}} \right], \\ \end{aligned} $$

(2)

where N_s is the number of magnetic moments μ_s(T) in 1 g of the material; L(x) is the Langevin function $L(x) \equiv \coth(x) - 1/x$. The parameters of the fit are given in Table 2. The details of the fitting procedure are given in the Appendix [Eqs. (6, 7)].

Table 2 Fitting parameters for M(H) curves of Fig. 7

The susceptibility χ_p(T) is determined by the slope of the curve at large H and approximated by Curie–Weiss law (see Fig. 8)

Figure 8

Inverse magnetic susceptibility of the (PFT)_x(PMN–PT)_1−x solid solutions with x = 0.4 (squares) and x = 0.5 (triangles). The lines show the Curie–Weiss law fit by Eq. (2)

$$ \chi_{\text{p}} \left( T \right) = C_{\text{p}} /\left( {T \, {-}T_{\text{CW}} } \right), $$

(3)

where the paramagnetic Curie–Weiss temperature T_CW is the measure of average interaction between the spins [47,48,49]; C_p is the Curie constant. The negative sign of T_CW ≈ − 80 K means that the average interaction between spins in paramagnetic regions of our samples has AFM sign.

Magnetoelectric measurements

In our experiment, the ME effect is manifested as a polarization P_ac induced by a small ac magnetic field h_ac under application of dc field H_dc [24,25,26]. We use the standard notations for ME coefficients that are given by the expansion [see Eqs. (8)–(20) of the Appendix]

$$ P_{i} = - \frac{\partial F}{{\partial E_{i} }} = P_{i}^{0} + \varepsilon_{0} \varepsilon_{ij} E_{j} + \alpha_{ij} H_{j} + \frac{{\beta_{ijk} }}{2}H_{j} H_{k} + \cdots , $$

where P⁰ is the spontaneous polarization; α_ij is a linear coupling, which is absent in the paramagnetic phase, β_ijk is the PME coupling coefficient.

With using collinear dc and ac magnetic fields H = H_dc + h_ac sin ωt, the first harmonic of the ac polarization detected by lock-in detector is

$$ P_{\text{ac}} \left( T \right) = \beta \left( T \right) H_{\text{dc}} h_{\text{ac}} . $$

(4)

Here β(T) is the paramagnetoelectric susceptibility. In ceramics, β(T) represents an average of the different elements of the tensor

$$ \beta_{ijk} = - \frac{{\partial^{3} F}}{{\partial E_{i} \partial H_{j} \partial H_{k} }}, $$

where F(E,H) [6] is the free energy density.

The PME response is studied by measuring the current across the sample. More precisely, the PME current is determined from Eq. (4) as

$$ I_{\text{ME}} = \frac{{{\text{d}}(\beta \sigma H_{\text{dc}} h_{\text{ac}} \sin \omega t)}}{{{\text{d}}t}} = \beta \omega \sigma H_{\text{dc}} h_{\text{ac}} \cos \omega t $$

(5)

with the lock-in (phase) detection at the frequency ω. Here σ is the area of the sample.

Figure 9 shows ME current as a function of the applied dc magnetic field in a PFT–PMN–PT ceramics for two compositions x = 0.4 and 0.5.

Figure 9

ME current amplitude in (PFT)_x(PMN–PT)_1−x as a function of applied dc magnetic field for ax = 0.4 measured at 293 K and bx = 0.5 measured at 293 K and 120 K. Room temperature value of the paramagnetoelectric coefficient β is indicated. The dash line in (b) shows a “linear” part of the ME current from paramagnetic component. Inset: ME current amplitude for x = 0.4 superimposed with dM²/dH calculated from the data of Fig. 7a

One can see that in both samples, ME signal sharply increases with an increase in the dc magnetic field in the range of ± 300 Oe, then it saturates in value and decreases down to almost zero at fields larger ± 3000 Oe. Inset in Fig. 9a shows that ME response correlates well with the dM²/dH for the M(H) curves presented in Fig. 7 (see the derivation of Eq. (20) in Appendix for arguments in favor of this correlation). The ME current does not change too much with temperature lowering down to 120 K (Fig. 9b). Only the current peak position moves from ± 300 to ± 400 Oe at 120 K.

In the field range |H| < 300 Oe, the slope of the curves allows us to extract the coefficient β via the formula (5). This results in β ≈ 0.15 × 10⁻¹⁵ s A⁻¹ for x = 0.4 and β ≈ 0.54 × 10⁻¹⁵ s A⁻¹ for x = 0.5 in (PFT)_x(PMN–PT)_1−x, which are about three orders of magnitude larger than those measured in conventional magnetoelectric materials at room temperatures (see “Discussion” section).

Our measurements show that the main contribution to the ME current is caused by the superparamagnetic phase while the contribution of isolated Fe³⁺ spins from the paramagnetic phase is negligibly small due to their much lower magnetic moment. The “linear” part of the ME response from the paramagnetic phase is illustrated by the dashed line in Fig. 9b. For the sample with lower Fe concentration (x = 0.4), this contribution is practically invisible.

Discussion

Let us discuss in more detail the ME effect in the PFT–PMN–PT solid solution. It would be interesting to compare the measured PME coefficients with those obtained by the same method for other multiferroics. The authors of Refs. [25, 26] have investigated solid solution (PbFe_1/2Nb_1/2O₃)_x(PbTiO₃)_1−x (PFN–PT). The structure, properties and phase diagram of PFN are similar to those of PFT; however, the properties of the second components of solid solutions, namely (PMN)_0.7(PT)_0.3 and PT [25], are completely different. One can suppose that the difference in the ME effect is mainly induced by the second component of the solid solution. The ME coefficient measured by us at room temperature is equal to β ≈ 0.54 × 10⁻¹⁵ s A⁻¹ (x = 0.5) and is related to superparamagnetic component in the PFT–PMN–PT solid solution, while that coefficient obtained for PFN-PT [25, 26] appeared to be much smaller, β ~ 10⁻¹⁸ s A⁻¹ and is related to paramagnetic component which dominates over a superparamagnetic impurity. The superpaparamagnetic contribution is not even visible in magnetic measurements for PFN–PT (see Fig. 1d of Ref. [25]). The obtained values of the PME coefficient appeared to be also much larger than that determined in several other antiferromagnetic multiferroic materials (see Table I in Ref. [26]): BiFeO₃ (2.1 × 10⁻¹⁹ s A⁻¹) Gd₂(MoO₄)₃ (0.8 × 10⁻¹⁸ s A⁻¹) and NiSO₄·6H₂O (0.7 × 10⁻¹⁸ s A⁻¹).

Note that the strong scattering of ME effect values in PFT–PZT solid solutions (see, e.g., [10, 12,13,14] made it cumbersome to perform a direct comparison with our results obtained for PFT–PMN–PT solid solution.

In some works [50,51,52], the slim hysteresis loops in perovskite ceramic samples are ascribed to a small amount of ferro- or ferri- magnetic impurity phases. The presence of such impurities in our samples would imply that they are, in fact, 0–3 type two-phase composites (see, e.g., review paper [53]). However, a small undetectable by XRD fraction of the magnetic impurity phase (see estimates in Appendix) can not produce appreciable ME response for two-phase composite material as the ME signal sharply goes to zero at approaching zero fraction volume of the magnetic component [53].

Our study demonstrates that multiferroics with superparamagnetic and ferroelectric phases can be considered as promising materials for applications along with composite multiphase (ferroelectric/ferromagnetic) structures. Because the ME response in multiferroics with the superparamagnetic phase is proportional to dM²/dH, its value can be amplified by many orders due to a sharp change of magnetization with the field.

Conclusions

The solid solutions (PbFe_1/2Ta_1/2O₃)_x[(PbMg_1/3Nb_2/3O₃)_0.7(PbTiO₃)_0.3]_(1−x) = (PFT)_x(PMN–PT)_(1−x), x = 0.4, 0.5 have been synthesized. XRD diffraction patterns of investigated samples correspond to the perovskite structure with minor addition of pyrochlore phase (less than 2.5 wt%). The EDS analysis reveals the homogeneity of the chemical composition and indicates the formation of a single-phase solid solution. Dielectric measurements show that both materials are ferroelectrics with a diffuse phase transition with the spontaneous polarization of about 5 µC cm⁻². An increase in the PFT content leads to an increase in the relative volume of the ferroelectric phase. Temperature dependence of the dielectric permittivity also confirms that both studied compounds are single-phase solid solutions (PFT)_x(PMN–PT)_1−x. ²⁰⁷Pb NMR shows that iron atoms tend to random occupation of the sites “B” in the perovskite structure. Analysis of ²⁰⁷Pb NMR data reveals a tendency to form areas with a higher concentration of iron.

Magnetic properties measurements manifest a superparamagnetic behavior of the samples.

The magnetoelectric coefficients are determined by the dynamic method. Their low-field values at room temperature β ≈ 0.15 × 10⁻¹⁵ s A⁻¹ and 0.54 × 10⁻¹⁵ s A⁻¹, respectively, for samples with x = 0.4 and x = 0.5 are three orders of magnitude larger than that in conventional antiferromagnetic multiferroics. Our measurements and theoretical analysis show that the main contribution to the ME current is caused by the superparamagnetic phase.

Appendix

Magnetization analysis

The solid solutions are materials with perovskite structure ABO₃. We may rewrite the chemical formula as (PFT)_x(PMN–PT)_1−x = PbFe_x/2Ta_x/2Mg_0.7(1−x)/3Nb_1.4(1−x)/3Ti_0.3(1−x)O₃. Magnetic ions Fe and nonmagnetic M = Ta, Mg, Nb, Ti occupy the sites of cubic sublattice B with the percentage given by the corresponding subscript in the formula. The Fe ions may be distributed randomly or form some kind of short- or long-range chemical order. Evidence for partial chemical ordering in the B sublattice of complex perovskites comes from experiments [54,55,56,57] and theory [20,21,22, 58, 59]. Our NMR studies (see above) confirm the nonuniform distribution of Fe in the B sublattice.

Magnetic measurements for (PFT)_x(PMN–PT)_1−x with x = 0.1, 0.2, 0.3 (Fig. 10) show that these samples are in the paramagnetic state in the studied temperature range. Thus, we omitted any additional investigations of these samples and focused our attention on samples with x = 0.4 and 0.5.

Figure 10

Magnetization dependence on magnetic field for solid solution (PFT)_x(PMN–PT)_1−x for x = 0.1 (a), 0.2 (b) and 0.3 (c) at different temperatures

We assume that a part of Fe³⁺ ions x_Fe < x/2 contribute to the paramagnetic response χ_p(T), another part, x_s= x/2 − x_Fe, participates in superparamagnetic response. The Curie constant

$$ C_{p} = N_{p} \frac{{\left( {g\mu_{B} } \right)^{2} S_{Fe} \left( {S_{Fe} + 1} \right)}}{{3k_{B} }} $$

gives the number N_p of Fe spins (per 1 g of the material) in the paramagnetic state; μ_B is Bohr magneton. Figure 8 shows that these numbers are very close for both samples N_p ≈ 2.8 × 10²⁰. Using the molar mass of the solid solution m_M(x), we find x_Fe = m_M(x)N_p/N_A ≈ 0.16 for both samples, N_A is the Avogadro number.

After that, we fit M(H) curves by the sum of paramagnetic and superparamagnetic contributions (cf. Eq.~(3) from Ref. [45]) given by Eq. (2).

We assume that the distribution of superspin moments is sharply peaked at the value μ_s(T) (i.e., all superspins are equal). Noting that L(x) → 1, for x → ∞, and $\left. {\frac{\partial L(x)}{\partial x}} \right|_{x = 0} = \frac{1}{3}$, we may obtain the superspin moment value, and the number of superspins

$$ \begin{aligned} \mu_{\text{s}} \left( T \right) & = \frac{{3k_{\text{B}} T}}{{M_{\text{s}} \left( {\infty ,T} \right)}}\left. {\frac{{\partial M_{\text{s}} \left( {H,T} \right)}}{\partial H}} \right|_{H = 0} \\ N_{\text{s}} & = \frac{{M_{\text{s}} \left( {\infty ,T} \right)}}{{\mu_{s} \left( T \right)}}, \\ \end{aligned} $$

(6)

from the slope of the superparamagnetic contribution to the isotherm curve at the origin $\left. {\frac{{\partial M_{s} \left( {H,T} \right)}}{\partial H}} \right|_{H = 0}$ = (7.5 ± 0.6) × 10⁻⁴ emu (g Oe)⁻¹ and saturated value of the superparamagnetic magnetization at large field M_s(∞,T) = 0.240 ± 0.003 emu g⁻¹, for T = 293 K. For the other isotherms, we find (assuming that N_s does not change with T)

$$ \mu_{\text{s}} \left( T \right) = \frac{{M_{\text{s}} \left( {\infty ,T} \right)}}{{N_{\text{s}} }}, $$

(7)

where M_s(∞,T) = 0.323 ± 0.003, 0.385 ± 0.003 emu g⁻¹, for T = 193 K, 120 K.

Equations (6), (7) allow to find the number N_s and the value μ_s(T) for our samples. The M(H) curves for 04PFT sample are well fitted by Eq. (2) with the parameter values, N_s = 6.3 × 10¹⁴, μ_s(T)/μ_B = 6.6 × 10⁴, 5.5 × 10⁴, 4.1 × 10⁴ for T = 120, 193, 293 K, respectively.

Assuming that the superspin moments display a mean-field like temperature dependence $\mu_{\text{s}} (T) = \mu_{\text{s}} (0)\sqrt {1 - T/T_{\text{c}} }$, we obtain μ_s(0)/μ_B ≈ 7.9 × 10⁴, T_c ≈ 400 K.

For x = 0.5, $\left. {\frac{{\partial M_{s} \left( {H,293} \right)}}{\partial H}} \right|_{H = 0}$ = 1.5 × 10⁻⁴ emu (g Oe)⁻¹, M_s(∞,T) = 0.089, 0.072, 0.058 emu g⁻¹ for T = 120, 193, 293 K, respectively. It gives N_s= 1.8 · 10¹⁴, μ_s(T)/μ_B= 4.8 × 10⁴, 4.3 × 10⁴, 3.5 × 10⁴ for T = 120, 193, 293 K, μ_s(0)/μ_B≈ 5.5 × 10⁴, T_c ≈ 490 K.

Let us consider the possibility to explain the superparamagnetism of our samples by magnetic impurity phases. In Refs. [50, 51], the hysteresis loops in PFT and solid solutions PFT–PbTiO₃ were supposed to be due to the presence of lead hexaferrite (magnetoplumbite) PbFe₁₂O₁₉. At room temperature, the saturation magnetization of the hexaferrite is ~ 50 emu g⁻¹ [60, 61], or 0.88μ_B per Fe spin. Thus, n_s12 = 4.7 × 10⁴ of Fe spins in a particle of PbFe₁₂O₁₉ would have a magnetic moment μ_s(T)/μ_B = 4.1 × 10⁴ at T = 293 K that would explain the superparamagnetism of 04PFT sample (see fourth row of Table 2). The size of the particle would be ~ 110 Å, because the volume of PbFe₁₂O₁₉ unit cell is 695 Å³ [62] and it contains 2 formula units, i.e., 24 Fe ions. Then the volume fraction of PbFe₁₂O₁₉ in our sample would be 0.7% and the mass fraction—0.48%; it can not be detected by XRD. But, as we have mentioned in the “Discussion” section, such a small fraction of the magnetic impurity phase can not produce appreciable ME response for two-phase composite material [53]. Also, against the presence of this impurity in our samples is the fact that the Curie temperature of bulk PbFe₁₂O₁₉ is 720 K [60, 63], which can be reduced in nanoparticles, but seems to be still much larger than T_c= 400–490 K found by us. If nonmagnetic ions substitute for Fe in the hexaferrite, the Curie temperature and the saturation magnetization are reduced dramatically [64,65,66,67]. In order to explain the superparamagnetism in our samples by such a diluted magnetoplumbite impurity, we would have to assume a larger fraction of the impurity phase, which is not observed by XRD.

In Ref. [52], the pyrochlore Pb₃FeTaO₇ impurity was supposed to be responsible for room-temperature hysteresis in PFT–PT solid solutions. Pb₃FeTaO₇ has 8 formula units in the cubic unit cell with a = 10.5 Å. The saturation magnetization at room temperature is ~ 2.7 emu g⁻¹. We obtain n_s,pyr = 8.8 · 10⁴ of Fe spins in a particle. The particle size is 233 Å, the volume fraction is ~ 7%, and the mass fraction is 9%. But our samples have no more than 2.4% of the pyrochlore admixture.

Therefore, neither PbFe₁₂O₁₉ nor Pb₃FeTaO₇ can be responsible for the magnetism and magnetoelectricity of the considered materials.

Magnetoelectric coupling

Within a phenomenological Landau–Ginzburg–Devonshire approach, linear and biquadratic ME couplings contribution to the system free energy are described by the terms μ_ijP_iM_j and ξ_ijklP_iP_jM_kM_l, respectively (P is polarization and M is magnetization, and μ_ij and ξ_ijkl are corresponding tensors of linear and biquadratic ME effects, respectively) [10, 19, 68]. In ceramics, the elements of the tensors are averaged and we are dealing with scalar LGD equations. If we start the description from the symmetric paraelectric paramagnetic phase, we should retain only biquadratic ME coupling

$$ F = F_{\text{P}} + F_{\text{M}} + F_{\text{ME}} , $$

(8)

$$ F_{\text{ME}} = \frac{{\xi_{\text{MP}} }}{2}M^{2} P^{2} , $$

(9)

where ξ_MP is the coupling parameter that is assumed to weakly depend on temperature. The terms F_P and F_M depend only on polarization and magnetization, respectively. For the second-order phase transitions they have the usual form in SI units system

$$ F_{\text{P}} = \frac{{\alpha_{\text{P}} }}{2}P^{2} + \frac{{\beta_{\text{P}} }}{4}P^{4} - {\text{PE}}, $$

(10)

$$ F_{\text{M}} = \frac{{\alpha_{\text{M}} }}{2}M^{2} + \frac{{\beta_{\text{M}} }}{4}M^{4} - \mu_{0} MH, $$

(11)

where only α_P,M have strong temperature dependence α ~ (T – T_C). For small external fields, we may write the solutions of Eq. (8) in the form

$$ P = P_{\text{s}} + \varepsilon_{0} \chi_{\text{E}} E, $$

(12)

$$ M = M_{\text{s}} + \chi_{\text{M}} H, $$

(13)

where P_s, M_s are spontaneous polarization and magnetization that become nonzero in the ordered phases; χ_E,M are dielectric and magnetic susceptibilities. Then ME coupling has the form

$$ F_{\text{ME}} = \frac{{\xi_{\text{MP}} }}{2}\left( {M_{\text{s}} + \chi_{\text{M}} H} \right)^{2} \left( {P_{\text{s}} + \varepsilon_{0} \chi_{E} E} \right)^{2} , $$

(14)

that allows us to express various magnetoelectric coefficients via ξ_MP

$$ \begin{aligned} \alpha \equiv - \frac{{\partial^{2} F}}{\partial E\partial H} = - 2\xi_{\text{MP}} M_{\text{s}} \chi_{\text{M}} P_{\text{s}} \varepsilon_{0} \chi_{\text{E}} , \\ \beta \equiv - \frac{{\partial^{3} F}}{{\partial E\left( {\partial H} \right)^{2} }} = - 2\xi_{\text{MP}} \left( {\chi_{\text{M}} } \right)^{2} P_{\text{s}} \varepsilon_{0} \chi_{\text{E}} , \\ \gamma \equiv - \frac{{\partial^{3} F}}{{\left( {\partial E} \right)^{2} \partial H}} = - 2\xi_{\text{MP}} M_{\text{s}} \chi_{\text{M}} \left( {\varepsilon_{0} \chi_{\text{E}} } \right)^{2} . \\ \end{aligned} $$

(15)

Due to the superparamagnetic contribution, the value of β will increase with temperature lowering according to the temperature dependence of magnetic susceptibility as [χ_M(T)]² ~ 1/T².

Using the value of β(T) obtained from experiments, we can estimate the biquadratic ME coefficient ξ_MP from the equation

$$ \xi_{MP} = - \frac{\beta \left( T \right)}{{2P_{s} \left( T \right)\varepsilon_{0} \chi_{E} \left( T \right)\left[ {\chi_{M} \left( T \right)} \right]^{2} }}. $$

(16)

We got ξ_MP ≈ –2.9 × 10⁻⁵ J m³ A⁻² C⁻² for the solid solution with x = 0.4 by substituting the room temperature values of parameters: β ≈ 0.15 × 10⁻¹⁵ s A⁻¹, the spontaneous electric polarization P_s≈3.0 μC cm⁻², susceptibilities dielectric χ_FE ≈2000, and magnetic (mass) χ_M ≈0.63 emu (g kOe)⁻¹. For x = 0.5, we have obtained ξ_MP≈ − 0.0014 J m³ A⁻² C⁻², using β ≈ 0.54 × 10⁻¹⁵ s A⁻¹, P_s≈ 4.4 μC cm⁻², χ_FE ≈2000, χ_M ≈0.142 emu (g kOe)⁻¹. All parameters were determined from the data of our experiments reported in previous sections.

Let us note that Eq. (11) is appropriate for the description of the paramagnetic phase in small fields where magnetization is proportional to H. For the description of the superparamagnetic phase at higher fields, we should consider another expression for the free energy part F_M

$$ F_{\text{M}} = - N_{\text{s}} T\ln Z, $$

(17)

where $Z = {{\sinh \left[ {\frac{{2\left( {S + 1} \right)\mu_{\text{s}} \left( T \right)H}}{{2Sk_{\text{B}} T}}} \right]} \mathord{\left/ {\vphantom {{\sinh \left[ {\frac{{2\left( {S + 1} \right)\mu_{\text{s}} \left( T \right)H}}{{2Sk_{\text{B}} T}}} \right]} {\sinh \left[ {\frac{{\mu_{\text{s}} \left( T \right)H}}{{2Sk_{\text{B}} T}}} \right]}}} \right. \kern-0pt} {\sinh \left[ {\frac{{\mu_{\text{s}} \left( T \right)H}}{{2Sk_{\text{B}} T}}} \right]}}$ is the partition function for an isolated spin S in the magnetic field H. For S ≫ 1 this gives $M_{\text{s}} \left( {H,T} \right) = - {{\partial F_{\text{M}} } \mathord{\left/ {\vphantom {{\partial F_{\text{M}} } {\partial H}}} \right. \kern-0pt} {\partial H}}$, Eq. (2). We will neglect the contribution from paramagnetic phase. Then instead of Eq. (14) we have

$$ F_{\text{ME}} = \frac{{\xi_{\text{MP}} }}{2}\left( {P_{\text{s}} + \varepsilon_{0} \chi_{\text{E}} E} \right)^{2} \left[ {M_{\text{s}} \left( H \right)} \right]^{2} $$

(18)

and

$$ \begin{aligned} P = - \frac{\partial F}{\partial E} = P_{\text{P}} + \Delta P_{\text{ME}} , \hfill \\ \Delta P_{\text{ME}} = - \xi_{\text{MP}} P_{\text{s}} \varepsilon_{0} \chi_{\text{E}} \left[ {M\left( H \right)} \right]^{2} \hfill \\ \end{aligned} $$

(19)

In the experiment, the ME effect is manifested as a polarization P_ac induced by a small ac magnetic field h_ac under application of dc field H_dc. With using collinear dc and ac magnetic fields H = H_dc + h_ac sin ωt, we obtain a generalization of Eq. (4)

$$ \begin{aligned} \Delta P_{ME} &= - \xi_{MP} P_{s} \varepsilon_{0} \chi_{E} \left[ {M\left( {H_{0} + h_{0} \sin\omega t} \right)} \right]^{2} \\ & = - \xi_{MP} P_{s} \varepsilon_{0} \chi_{E} \left[ {M\left( {H_{0} } \right)^{2} + 2M\left( {H_{0} } \right)\left. {\frac{\partial M\left( H \right)}{\partial H}} \right|_{{H = H_{0} }} h_{0} \sin\omega t} \right] \\ P_{ac} &= - \xi_{MP} P_{s} \varepsilon_{0} \chi_{E} 2M\left( {H_{0} } \right)\left. {\frac{\partial M\left( H \right)}{\partial H}} \right|_{{H = H_{0} }} h_{0} \sin\omega t. \\ \end{aligned} $$

(20)

Hence, the generalization of Eq. (5) shows that the amplitude of magnetoelectric current I_ME is proportional to dM²/dH (see inset in Fig. 9a).

The above consideration can only provide a qualitative agreement with the experiment. A more realistic theory should take into account at least a distribution of moment values.