Magnetoelectric (1-x)AlFeO3-xBaTiO3 solid solutions with ferroelectric relaxor behavior near room temperature

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Magnetoelectric (1-x)AlFeO3-xBaTiO3 solid solutions with ferroelectric relaxor behavior near room temperature Y. Li, Y.G. Wang∗, N. Wang, F.L. Wang, Aditya Jain College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Multiferroic Ferroelectric relaxor Magnetoelectric Phase transition

The magnetoelectric ceramics with the composition (1-x)AlFeO3-xBaTiO3 ((1-x)AF-xBT, 0 ≤ x ≤ 0.2) have been synthesized by high energy ball milling method. The BaTiO3 substitution leads to a crystal structure transformation from orthorhombic Pna21 to rhombohedral R3c. Due to this structural transformation, variations are also induced in the a/b ratio and the phase fraction of the orthorhombic phase. Further, the substitution of AlFeO3 by BaTiO3 results in a chemical pressure which induces the ferromagnetic-like behavior and the ME effect in (1x)AF-xBT ceramics. All the ceramics have shown an unsaturated polarization behavior, and the maximum polarization is attained at x = 0.05. The ME coupling effect has been achieved in all the ceramics, and the optimal ME coefficient is obtained in the 0.95AF-0.05BT ceramic. Besides, it has also been confirmed that the 0.95AF0.05BT ceramic has shown the ferroelectric relaxor behavior near room temperature. The ME coupling in these ceramics is related to the ferroelectric relaxation, where the polarization of nanoregions is modified by the applied magnetic field.

1. Introduction

derived from Fe2O3 by the substitution of Fe3+ by Al3+, and its crystal structure shows an orthorhombic symmetry with the Pna21 space group at room temperature [16]. Furthermore, the AF based ceramics may exhibit a ferroelectric relaxor behavior near room temperature [17,18], which can broaden the application in energy storage for this material. However, the related reports are rather few, which hinders the comprehensive understanding of AF with peculiar multiferroic properties. These special properties originate from the octahedron composed of FeO and Al-O and the tetrahedron composed of Al-O, where cation sites are constituted by Fe1, Fe2, and Al1, Al2, respectively [19–21]. Furthermore, the study of the ME effect in AF based compounds mainly focuses on theoretical research due to their harsh preparation conditions. Up to now, AF with the desired structure can only be prepared by some inconvenient and expensive methods such as pulse laser deposition [22] and sintering followed by annealing at high temperature combined with high pressure in oxygen atmosphere [23]. This work aims to prepare the AF based ceramics with high-energy ball milling followed by the conventional sintering method and studied their dynamic ME coupling and ferroelectric relaxor behavior near room temperature. Herein, we report the evolution of the crystal structure in (1-x)AlFeO3-xBaTiO3 ((1-x)AF-xBT, 0 ≤ x ≤ 0.2) ceramics, which results in the optimization on multiferroic properties with BT substitution. The role of BT is to stabilize the crystal structure of AF and

Recently the multiferroic materials have drawn considerable attention due to their abundant physical properties and enormous potential applications in multi-functional devices [1–3]. Among them, it is an attractive topic to achieve the ME coupling effect in various materials. BiFeO3 is one of the most important ME material due to its flexible rhombohedral crystal structure, which favors in the realization of ME coupling by modulating the spin structure [4]. Other ME materials can be divided into various systems, such as the AMnO3 (A=Y, Bi), PbBO3 (B=Ni, Ti, V), TbMn2O5, Lu2CoMnO6, and LuFe2O4 [5–12]. Among the materials with ABO3 structure, the perovskite [13] structure stands out for its easy regulation of octahedral distortion, which is beneficial for generating the ME effect. In addition to this, the ilmenite and corundum structures are also found to have the potential to generate the ME effect due to the alternative configuration between A- and B-site cations and highly compacted oxygen layers [14,15]. Not all multiferroic materials are necessary to generate ME coupling due to the difficulty of the mutual interaction between magnetic and the electric orderings at the same temperature. However, the lead-free AlFeO3 (AF) is one of the multiferroic materials that potentially show ME coupling owing to the coexistence of ferroelectric- and a magneticstate transition at low temperatures. Generally, it is believed that AF is

∗

Corresponding author. E-mail address: [email protected] (Y.G. Wang).

https://doi.org/10.1016/j.ceramint.2019.12.013 Received 12 November 2019; Received in revised form 2 December 2019; Accepted 2 December 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Please cite this article as: Y. Li, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.12.013

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make the preparation of AF easier. 2. Experimental details The precursor powders were prepared by the ball-milled mixture of Al2O3 (99.9%), α-Fe2O3 (99.9%), TiO2 (99.95%), and BaCO3 (99.9%) reacted at 1300 °C for 2 h and followed by re-milling. The mixed powders were ball-milled at 350 rpm for 24 h in a cylindrical zirconia vial with 500 mL capacity. The milling medium is zirconia balls of 8 mm in diameter, and the ball to powder weight ratio was kept at 12:1 to get the desired powders. After re-milling, the prepared powders were fully mixed with the help of 3 wt% polyvinyl alcohol and then compacted into discs of 15 mm in diameter and 1 mm in thickness. The green discs were then sintered at 500 °C for 2 h to remove the polyvinyl alcohol and finally sintered at 1400 °C for 4 h and naturally cooled to obtain the ceramics with the desired composition. The phase structure of the synthetic (1-x)AF-xBT ceramics was studied by Smartlab9 X-ray diffractometer having Cu Kα radiation with a wavelength of 0.154056 nm. The X-ray diffraction (XRD) data were collected over a 2θ range of 20–70° and 0.02° in step size. The investigation of magnetic properties was performed by the HH-10 vibrating sample magnetometer in the magnetic field range of ± 8 kOe at 25 °C. Prior to the electric and ME measurement, silver electrodes were applied to both sides of the discs and kept at 550 °C for 30 min. The ferroelectric properties were examined using the RT Premier II Precision Materials Analyzer in the electric field range of ± 60 kV/cm at 10 Hz. The temperature dependence of dielectric permittivity and dielectric loss were obtained using an Agilent 4249A impedance analyzer at five frequency viz. 102, 103, 104, 105, and 106 Hz over a temperature range of −100 °C–130 °C. The discs were poled along the thickness direction in silicon oil under an electrical field of 20 kV/cm for 1 h at 120 °C for the dynamic ME measurement. The dynamic ME coupling coefficient was obtained using a ME measurement system with a frequency range of 1–200 kHz, a bias magnetic field range of 0–5000 Oe, and an ac magnetic field of 2.0 Oe.

Fig. 1. XRD patterns of (1-x)AF-xBT ceramics (a), and the local enlarged patterns around 2θ ≈ 43° (b), 55° (c) and 64°(d).

present work are solid solutions rather than composites. The Rietveld refinement was used to further analyze the above structural changes in the (1-x)AF-xBT ceramics. Fig. 2(a) depicts the fitting profiles after the Rietveld structure refinement for the 0.95AF0.05BT ceramic with the Pna21 and R3c space groups. The lattice parameters of the (1-x)AF-xBT ceramics are given in Table 1. As shown in Fig. 2(b), the a/b ratio of the orthorhombic phase increases with x increasing, which may be due to the unit cell expansion caused by large A-site ion substitution of Al3+ by Ba2+. The ceramics substituted by BT possess a biphasic structure composed of the orthorhombic Pna21 and the rhombohedral R3c structures. Furthermore, the R3c phase fraction reaches the maximum at x = 0.05, as shown in Fig. 2(c). It can be found that the BT substitution does not promote the increase in the phase fraction of the R3c phase. The structure transition caused by chemical pressure with BT substituting can be comparable to that for the perovskite ceramics with ionic substitutions [28–32]. The orthorhombic and the rhombohedral phases are both stable for the AF based ceramics at room temperature [24]. The transition from the Pna21 to R3c phases may be due to the mismatch of the host and substituted ions [33]. Further, the structural transition may also be caused by the polar-topolar ionic displacement along a certain direction [34]. Moreover, for the substituted ceramics, the decreased phase fraction of the R3c phase with the increase in BT contents may be due to the reduced stability of the R3c phase with the increase in chemical pressure caused by BT substituting [35,36]. Therefore, the chemical pressure caused by the substitution of BT induces the structure transition from the orthorhombic Pna21 to the rhombohedral R3c, and the 0.95AF-0.05BT ceramic possesses the maximum R3c phase fraction.

3. Results and discussion 3.1. Structural analysis The XRD patterns of (1-x)AF-xBT ceramics are shown in Fig. 1(a). The perovskite structures can be seen in all the ceramics, and there is no impurity peak observed for all the compositions. For the pure AF sample, the diffraction peaks show the characteristics of orthorhombic structure (Pna21), which is identical to the structure in the reported AF phase [24]. However, for the samples with BT substitution, an additional diffraction peak appears at 2θ ≈ 24°, and the peaks at 2θ ≈ 32.8°, 47.7°, and 64° tend to split as shown in partially enlarged patterns in Fig. 1(b), 1(c) and 1(d). The emerging diffraction peaks at 2θ ≈ 24° can be assigned to the rhombohedral structure (R3c), which is often observed in the pure AF samples synthesized by the sol-gel method with ethanolamine, acetic acid, or citric acid [25–27]. According to related research [24], the transformation from the Pna21 phase to the R3c phase can be facilitated under pressure. Apparently, the substitution by BT will induce chemical pressure in the AF matrix due to the large ionic radius differences. Therefore, it can be concluded that the BT substituting contributes to the transformation from the orthorhombic phase to the rhombohedral phase, which indicates a morphotropic phase transition in these compounds. It can also be found that the peaks at 2θ ≈ 32.8° and 47.7° shift to low angle side, and the peak at 2θ ≈ 64° almost remains at the same position for the ceramics within the BT content range of 0.5–1.5. The peak shift may be due to the unit cell volume expansion, which indicates the successful substitution of A-site Al3+ ion by Ba2+ ion. It should be noted that the XRD patterns of (1-x)AF-xBT ceramics confirm the formation of AF phase without traces of BT phase. Therefore, the (1-x)AF-xBT ceramics in the

3.2. Ferroelectric properties The room temperature polarization-electric field hysteresis (P–E) loops are shown in Fig. 3(a) for all the (1-x)AF-xBT ceramics. It can be observed that all the loops are slim and do not show a hysteresis 2

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Fig. 3. (a) Room-temperature P-E loops of the (1-x)AF-xBT ceramics, (b) the maximum polarization in an electric field up to 60 kV/cm as functions of x.

of Pmax agrees with the change in phase fraction of the rhombohedral phase in the (1-x)AF-xBT ceramics. The variation of Pmax may be due to the fact that the rhombohedral structure is beneficial for the polarization of the AF based ceramics. 3.3. Magnetic properties For the pure AF ceramic, the super-exchange between magnetic ions determines its paramagnetism at room temperature [23]. Fig. 4(a) shows the room temperature magnetic hysteresis (M–H) loops of the (1x)AF-xBT ceramics. Notably, all the loops exhibit no apparent magnetic hysteresis behavior, and a weak ferromagnetic-like feature is observed with the substitution of BT. In order to distinguish the contributions of various magnetism, the M–H loops were fitted by the following equation [38–40]:

Fig. 2. (a)Rietveld refinement of the XRD pattern of the (1-x)AF-xBT ceramic with x = 0.05, (b) the a/b ratio as functions of x (c) and the phase fraction as functions of x.

characteristic, which indicates that the (1-x)AF-xBT ceramics may be ferroelectric relaxors. Meanwhile, the unclosed loops may suggest the presence of leakage current. It has been reported that the AF nanoparticles can show a typical ferroelectric behavior at room temperature [37]. Those nanoparticles are synthesized by the sol-gel method and possess a rhombohedral structure. The different characteristics of P–E loops between the (1-x)AF-xBT ceramics and the AF nanoparticles may be due to the different phase structure induced by the different preparing methods. Fig. 3(b) shows the BT content dependence of the maximum polarization (Pmax) at 60 kV/cm. The Pmax increases with x increasing from 0 to 0.05 and decreases with the further increase in x, and the largest Pmax ~5.8 μC/cm2 is attained at x = 0.05. The variation

S R ⎧ M ⎛ H ± Hci ⎞ tan ⎜⎛ πMFM ⎟⎞ ⎤ ⎫ + χH M = 2 FM tan−1 ⎡ S ⎢ ⎥ ⎨ π H 2 M ci ⎠ ⎝ FM ⎠ ⎦ ⎬ ⎣⎝ ⎩ ⎭ ⎜

S MFM

⎟

(1)

R MFM

where and are the saturated and the remnant magnetization of the ferromagnetic (FM) part, respectively, Hci is the intrinsic coercivity, χ is the magnetic susceptibility of paramagnetic (PM) part, M is the observed magnetization, and H is the applied magnetic field. In Eq. (1), the first term represents the FM contribution, and the second term denotes the PM contribution. The fitted loops for the 0.95AF-0.05BT ceramic are shown in Fig. 4(b), and the extracted parameters for all the

Table 1 Results of Rietveld refinements of XRD patterns of the (1-x)AF-xBT ceramics. x

a(Å)

b(Å)

c(Å)

a(Å)

Pna21 0.00 0.05 0.10 0.15 0.20

5.47942(0) 5.47977(3) 5.48073(2) 5.49743(4) 5.49333(4)

c(Å)

Rwp, Rp, χ2 (%)

13.30267(9) 13.37867(5) 13.63567(2) 13.38009(0)

9.56,8.75,3.65 10.13,9.31,4.78 9.24,7.32,4.02 10.07,7.56,2.88 10.93,9.12,3.27

R3c 8.47589(8) 8.47641(9) 8.47868(7) 8.49638(1) 8.48632(5)

9.17086(2) 9.17305(9) 9.25142(2) 9.31541(6) 9.30601(4)

3.52401(7) 3.51054(1) 3.50450(6) 3.50617(2)

3

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symmetry. For the pure AF ceramic, the orthorhombic structure consists of octahedron and tetrahedron. This kind of structure affects the arrangement of spins at different ionic sites, which finally forms a stable antiferromagnetic order and thus leads to the paramagnetism of the orthorhombic AF ceramic at room temperature. The magnetism of orthorhombic AF ceramic originates from super-exchange interactions of Fe–O–Fe and Fe–O–Al, and the strength of the interaction depends on the bond angles and bond lengths. It has been reported that the strength of super-exchange interaction is proportional to bond angles and inversely proportional to the bond length [41]. The BT substituting results in a structural transition from the orthorhombic Pna21 to rhombohedral R3c. For the rhombohedral AF, the Fe–O–Fe interaction is stronger than that of Fe–O–Al and dominates the magnetism of AF. The small unit cell volume of the R3c phase contributes to the decrease in the bond lengths of Fe–Fe and the increase in the Fe–O–Fe exchange angles, similar to that in doped BiFeO3 ceramics [42]. Therefore, it is possible to induce weak ferromagnetism by the phase transition resulted from the substitution of BT. With further BT substitution, the amount of R3c phase decreases, which may cause the recovery of the deformed magnetic structure, and thus a deterioration of ferromagnetic properties. In order to better understand the BT content dependence of the magnetic properties for the (1-x)AF-xBT ceramics, a comparative analysis has been carried out. Table 2 lists the structural and magnetic characteristics of various magneto-dielectric materials. The comprehensive literature survey indicates that the elemental substitution and/ or formation of composites still remain the most popular way to improve the magnetic characteristics of multiferroic oxides. The isostructural compounds such as AF and Ga0.6Fe1.4O3 (GF) both exhibit orthorhombic crystal structure. However, AF is paramagnetic, whereas GF is ferrimagnetic at room temperature. For GaFeO3 based ceramics, the ionic occupancy of Ga3+ and Fe3+ is the same as that of Al3+ and Fe3+ in AF, respectively [43]. Ga1 is at the center of the oxygen tetrahedron, whereas Ga2, Fe1, and Fe2 are at the center of the oxygen octahedron. The non-equivalent magnetic moments between Ga1-O4 tetrahedron and Ga2(Fe1/Fe2)-O6 octahedron leads to the magnetic crystalline anisotropy in GF [52], which gives a possibility for net magnetization. Moreover, it has been reported that the cationic site disorder is induced by the substitution of Ga2 by the transition metal cation Fe [53]. Fe at the Ga2 site tends to couple with 4 Fe1 via oxygen, which may generate a ferromagnetic order. Therefore, the GF exhibits a ferrimagnetic feature. However, the different magnetization induced by different cations on octahedral sites determines the macro magnetization of AF. The anti-ferromagnetic super-exchange interaction of Fe–O–Fe and Fe–O–Al contributes to the paramagnetic order of AF. Besides, the cationic site disorder is much weaker in AF than that in GF due to the worse matching of ionic radii of Fe and Al compared to Fe and Ga, which can hardly generate a strong magnetic interaction [41].

Fig. 4. (a) Room-temperature M-H loops of the (1-x)AF-xBT ceramics, (b) the fitted M-H loops of the 0.95AF-0.05BT sample, the comparison of (c) saturated magnetization (Ms), (d) remnant magnetization (Mr) and (e) coercive magnetic field (Hc) between the fitted data of FM part and the experimental data.

samples are shown in Fig. 4(c), 4(d), and 4(e). It can be deduced from these figures that extremely weak ferromagnetism is induced in the paramagnetic AF ceramic by BT substituting. With the substitution of BT, the symmetry of crystal structure of the (1-x)AF-xBT ceramics changes from the orthorhombic symmetry to the rhombohedral

Table 2 Comparisons of magnetic properties and ME coupling coefficient α of magneto-dielectric materials. Material system

Type of material

Structure

Magnetism

Ga0.6Fe1.4O3 0.6BiFeO3-0.4Ba0.1Sr0.9TiO3 0.8Pb(Fe0.5Nb0.5)O3/0.2Co0.65Zn0.35Fe2O4 0.5SrTiO3-0.5Co0.7Fe2.3O4 0.6(0.7BiFeO3-0.3Bi0.5Na0.5TiO3)-0.4CoFe2O4 Ba0.5Sr0.5Nb2O6/CoCr0.4Fe1.6O4 0.75(Bi0.99La0.01)FeO3-0.25BaTiO3 Bi1.35(1)Fe0.64(1)Nb1.26(1)Mn0.75(1)O6.39(5) Ba4Sm2Fe2Nb8O30 0.95AlFeO3-0.05BaTiO3

SS SS Cp Cp SS Cp SS SS SS SS

O T+R C+M

FIM AFM FM+PM FM FM FM AFM+FM PM FM PM+FM

T+C R+C C T O+R

SS: solid solution, Cp: composite. O: orthorhombic, T: tetragonal, R: rhombohedral, C: cubic M: monoclinic. FIM: ferrimagnetism, AFM: antiferromagnetism, FM: ferromagnetism, PM: paramagnetism. All the parameters in Table 2 are measured at room temperature. 4

Mr (emu/g)

0.06 0.3 16 11 70 0.05

0.002

α (mv/(cm∙Oe))

Ref.

9.1 1.541 12.04 7.5 5.54 0.0274 10.9

[43] [44] [45] [46] [47] [48] [49] [50] [51] This work

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frequency of 200 kHz. Table 2 shows a comparative analysis of ME coupling coefficient in various magneto-dielectric materials. The obtained α of 10.9 mV/(cm·Oe) is comparable to that of the composite Ba0.5Sr0.5Nb2O6/CoCr0.4Fe1.6O4 and 0.5SrTiO3-0.5Co0.7Fe2.3O4, and much higher than that of the perovskite BiFeO3, pyrochlore Bi1.35(1)Fe0.64(1)Nb1.26(1)Mn0.75(1)O6.39(5) or tungsten bronze Ba4Sm2Fe2Nb8O30 based materials. It is well known that the composites always possess a relatively high ME coefficient due to their excellent magnetostrictive performance. For solid solutions, the coupling between the adjacent crystal lattices is known to be one of the effective ways to generate the ME effect. However, the obtained value of α is still relatively low. Moreover, the previously reported ceramic compositions with improved magneto-dielectric properties generally contain a ferroor ferri-magnetic part in order to generate a strong response to the magnetic field. However, the AF based ceramics show a paramagnetic feature at room temperature. The BT substitution in AF results in the deterioration of magnetic characteristics. However, due to higher super-exchange interaction of Fe-O-Fe and Fe-O-Al, there is an improvement in magnetoelectric properties of the (1-x)AF-xBT solid solution. The results suggest that the obtained value of α is comparable to that of some layered ceramics, which may be useful in the design of multi-functional devices. The measurement of the frequency-dependent ME coefficient is attempted to find out the resonant frequencies in the (1-x)AF-xBT solid solution [54]. However, in the measured frequency range, the ME coefficient does not show a resonant value. Due to the correlations among the frequency, the dielectric permittivity, the electromechanical coupling factor, and the ME coefficient, the relationship between ME coefficient and frequency can be clarified from the perspective of dielectric permittivity. According to the Debye equation, the dielectric permittivity is inversely related to the frequency. It is widely accepted that the square root of dielectric permittivity is inversely proportional to the electromechanical coupling factor, which is positively related to the ME coefficient [55]. Therefore, the ME coefficient is positively correlated to the frequency. Fig. 5(c) shows the BT content dependence of the maximum α derived from Fig. 5(a) to understand the effect of BT substitution on the ME coupling. It can be observed that the maximum α increases with x increasing from 0 to 0.05 and decreases with the further increase in x, and the largest α = 4.9 mV/(cm·Oe) is attained at x = 0.05. The nonlinear ME effect in (1-x)AF-xBT ceramics agrees well with previous theoretical investigations [56], and the relationship between the polarization of a polar nanoregion and the external magnetic field in a ferroelectric relaxor can be expressed as follows:

Fig. 5. ME coefficient α of the (1-x)AF-xBT ceramics as functions of Hbias at 40 kHz (a) and f at 500 Oe (b), and the maximum α at 500 Oe and 40 kHz versus x (c).

Therefore, the AF shows a paramagnetic characteristic at room temperature. The BT substitution in AF induces a magnetic transition from paramagnetism to weak ferromagnetism. However, for the BiFeO3 based oxides with BT substitution, 0.6BiFeO3-0.4Ba0.1Sr0.9TiO3 and 0.75(Bi0.99La0.01)FeO3-0.25BaTiO3, the appearance of magnetic transition depends on the concentration of BT. Furthermore, it is widely accepted that the variation in magnetism is closely related to the ME coefficient, although a high magnetization is not correlated to a large ME coefficient. The detailed comparison of ME effect will be discussed in the following ME part.

1 F = − λij Pi2 Mj2 2

(2)

λij = 2Ckl Qe, i Qm, j

(3)

Qe, ijkl = −

−1 −1 μ0 ⎡ ∂ (χm )kl ⎤ 1 ⎡ ∂ (χe )kl ⎤ = − ; Q m , ijkl 2ε0 ⎢ ∂Xij ⎥ 2 ⎢ ∂Xij ⎥ ⎦T ⎣ ⎦T ⎣

where F represents the Gibbs free energy, λ represents the fourth-order ME coupling constant, P and M represent the polarization and magnetization, Ckl represents the bulk modulus, Qe,i and Qm,j correspond to the macroscopic electro- and magneto-striction coefficients, respectively. On the condition of the assumption that the electro- and magnetostrictive deformations affect the magnetoelectric terms, Eqs. (2) and (3) indicate that the external magnetic field is responsible for the variation of polarization inside the polar nanoregion. The (1-x)AF-xBT ceramics have very weak ferromagnetic properties at room temperature, but it still exhibits a ME coupling effect. The inverse Dzyaloshinskii–Moriya (DM) interaction [57] gives another possible reason for the existence of ME effect in these samples:

3.4. ME coupling effect To further investigate the multiferroicity of (1-x)AF-xBT ceramics, it is significant to focus on the ME effect, which directly connects the magnetic order and electric order. The ME coefficient α as a function of the bias magnetic field is shown in Fig. 5(a). For all the (1-x)AF-xBT samples, a non-linear ME coupling effect can be observed, and the maximum α appears at an Hbias of about 500 Oe. The ME coupling coefficient α for (1-x)AF-xBT ceramics as a function of the frequency is shown in Fig. 5(b). It can be observed that all the α are positively proportional to the frequency, and the maximum value of α = 10.9 mV/(cm·Oe) is attained for the sample 0.95AF-0.05BT with the

→ → → P = β∑ → eij × ( Si × Sj ) ij

5

(4)

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where Si and Sj are the adjacent spins connected by the unit vector eij, and β is determined by the spin-orbit and spin-exchange interactions. The presence of a weak uncompensated magnetic moment was confirmed by the M-H loops, which can generate polarization under the application of an external magnetic field according to Eq. (4). The small unit cell volume of the R3c phase induces the decrease in the bond lengths of Fe–Fe and Fe–Al and the increase of the Fe–O–Fe and Fe–O–Al exchange angles, which contribute to the strong interactions of Fe–O–Fe and Fe–O–Al and thus lead to a large value of α. With the increase in BT content, the phase fraction of the R3c phase decreases, which may result in a weakening of the interactions of Fe–O–Fe and Fe–O–Al. Therefore, the value of α decreases with a further increase in BT content. It is observed in Fig. 5(c) that the variation of α with x agrees well with the variation of ferromagnetic properties in Fig. 4(c) 4(d) and 4(e). The variation of α and ferromagnetic properties is also consistent with that of Fe-O-Fe and Fe-O-Al spin structure caused by the structural transition from the orthorhombic Pna21 to rhombohedral R3c phase with BT substitution. Therefore, the sample with x = 0.05 possesses the maximum value of α = 10.9 mV/(cm·Oe).

Table 3 The maximum dielectric permittivity εm, the temperature of the maximum dielectric permittivity Tm, and the critical parameter γ for 0.95AF-0.05BT ceramic at different frequencies. f (Hz) 2

10 103 104 105 106

Tm(°C)

εm

γ

25 30 41 55 60

3520 3288 2958 2647 2412

2.0 2.2 2.0 2.1 2.0

(T − Tm) γ 1 1 − = ε εm C

(5)

where ε and εm represent the dielectric permittivity at temperature T and the maximum value of dielectric permittivity, respectively, Tm means the temperature at the maximum dielectric permittivity, C is the Curie constant, and γ indicates the degree of diffuseness. Generally, γ = 1 indicates a normal ferroelectric, and γ ≥ 2 suggests a complete diffuse phase transition (DPT) [59]. In order to determine the γ value, the plot of ln(1/ε-1/εm) versus ln(T-Tm) is fitted by Eq. (5), and the representative fitting at 10 kHz is shown in Fig. 6(b). Table 3 lists the γ values at various frequencies, and all the γ value is larger than 2.0, indicating the relaxor characteristic of the 0.95AF-0.05BT ceramic with complete DPT. The relaxation behavior can also be expressed by an empirical Vogel–Fulcher (VF) law [60]:

3.5. Dielectric study The ferroelectric relaxor behavior of ceramic material is related to the polar nano regions [58]. As discussed above, the ME effect of the (1x)AF-xBT ceramics correlates to its ferroelectric relaxor state. For understanding the relaxor behavior, the temperature dependence of dielectric permittivity (ε) for 0.95AF-0.05BT ceramic is shown in Fig. 6(a). The broad dielectric maximum shows a shift toward a higher temperature with the increase in frequency, which indicates a representative dielectric relaxor behavior. The relationship between the dielectric permittivity and temperature follows the Uchino and Nomura function [59]:

Ea ⎤ f = f0 exp ⎡− ⎢ k (Tm − Tf ) ⎥ ⎦ ⎣

(6)

where f0 represents the attempt frequency, Ea denotes the activation energy, k is the Boltzmann constant, and Tf indicates the static freezing

Fig. 6. (a) The temperature dependences of ε, (b) ln(1/ε-1/εm) as a function of ln(T-Tm) at 10 kHz, (c) Tm as a function of frequency, and (d) the temperature dependence of dielectric loss tan δ and the fitted lines based on Eq. (7) for the 0.95AF-0.05BT ceramic. 6

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Table 4 Comparison of activation energy (Ea), attempt frequency (f0), and static freezing temperature (Tf) obtained from Vogel-Fulcher law for various magneto-dielectric materials. Material system

Structure

Ea(eV)

f0(Hz)

Tf(°C)

Ref.

Ba(Zr0.1Ti0.9)O3 + 3 wt % Ho2O3 Ba0.97Bi0.02Ti0.9Zr0.05Nb0.04O3 Bi0.5(Na0.8K0.2)0.5TiO3 0.85(K0.5Na0.5)NbO3-0.15SrZrO3 0.35Bi(Ni1/2Ti1/2)O3-0.65Pb(Zr1/2Ti1/2)O3 0.95AlFeO3-0.05BaTiO3

T C R+T C R+T O+R

0.037 0.033 0.016 0.0187 0.0196 0.011

4.649 × 1013 1.03 × 1010 2.882 × 1012 9.02 × 1010 7.99 × 107 1.499 × 1010

−14.328 395.85 300 193.46 197.2 30.2

[61] [62] [63] [64] [65] This work

transition, defects, oxygen vacancies, and scattering of thermally activated charge carriers, which influences the resistivity of the ceramics. The reason for this high dielectric loss may be the conductivity effects of AF at room temperature, which induces large leakage current and subsequently increase the dielectric loss in the material.

Table 5 Comparison of dielectric loss in various dielectric ceramics. Material system

T (°C)

f(Hz)

tanδ

Ref.

0.9Ba0.9Sr0.1TiO3-0.1Bi(Zn0.5Zr0.5)O3 0.9Bi0.5Na0.5TiO3–0.1K0.5Na0.5NbO3+ 1 wt% Gd2O3 0.88NaNbO3–0.12Bi(Zn0.5Ti0.5)O3 Ba4Nd2Fe1Ni1Nb8O30 Al(Fe0.98Mn0.02)O3 0.95AlFeO3-0.05BaTiO3

39 300

106 104

0.7 0.1

[68] [69]

−25 −123 67 30

104 105 104 104

0.004 0.04 1.52 1.4

[70] [71] [72] This work

4. Conclusions The (1-x)AF-xBT ceramics were prepared by high energy milling method. With the help of the XRD patterns and the Rietveld structure refinement, it is confirmed that the crystal structure changes from the orthorhombic Pna21 to the rhombohedral R3c with the increase in BT content, and forms a morphotropic region for (1-x)AF-xBT ceramics with x ≥ 0.05. The introduction of BT induces a variation in a/b ratio as well as the fraction of Pna21 phase and R3c phase. All the ceramics show an unsaturated polarization behavior similar to that of the ferroelectric relaxor, and the maximum polarization is attained at x = 0.05 in an electric field of 60 kV/cm. Furthermore, the BT substitution results in a chemical pressure which induces the ferromagnetic like behavior and ME effect in (1-x)AF-xBT ceramics. The 0.95AF0.05BT ceramic possesses the maximum ME coefficient α ≈ 10.9 mV/ (cm·Oe) at 200 kHz with an optimum bias magnetic field of 500 Oe at an ac field of 2.0 Oe. Moreover, the quantitative fitting of the temperature-dependent dielectric permittivity confirms the relaxor behavior of 0.95AF-0.05BT ceramic with frequency dispersion and DPT. The experimental Tm data match well with the Vogel-Fulcher law, which indicates the spin-glass like behavior for the present system. The fitted small value of υ from the Cole-Cole relation agrees with the low value of Ea. It is believed that the ME coupling in (1-x)AF-xBT ceramics correlates to the ferroelectric relaxation, where the polarization of nanoregions is modified by the applied magnetic field.

temperature. Fig. 6(c) shows the temperature Tm dependence of frequency f, plotted as ln f versus Tm. The qualitative fit of Eq. (6) reveals that the 0.95AF-0.05BT ceramic is a relaxor and may behave like the spin-glass features in a magnetic system. The activation energy correlates to the difficulty for the dipoles to overcome the energy barrier during the polarization process. Table 4 lists the parameters obtained from Vogel-Fulcher law for various magneto-dielectric materials. It is found that the value of Ea in the present work is much lower than that of the (Ba, Bi, Na, K)(Ti, Nb)O3 based materials, which indicates an easier polarization orientation for the dipoles in the 0.95AF-0.05BT ceramic [65]. Meanwhile, the low value of Ea reflects a small size of the polar nano regions, which is responsible for the ME coupling effect for the magneto-dielectric materials, as discussed in Eqs. (2) and (3). Further, the Debye frequency f0 is related to the lattice vibration in the clusters with coordinate motion [66]. The low f0 (105–107 Hz) reflects the relaxation of the domain wall displacement, and the high f0 (108–1012 Hz) reflects the relaxation of dipoles induced by defects [67]. The fitted f0 is in the range of 108–1012 Hz, which also suggests the weak interactions between the small-sized nanoregions. Fig. 6(d) shows the dielectric loss (tanδ) as a function of the temperature dependence for the 0.95AF-0.05BT ceramic. To further understand its relaxation behavior, the dielectric loss was fitted by ColeCole relation [66,67]:

tan δ =

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

(ϖτ ) υ

sin(απ /2) ε0 − ε∞ ⎡ ⎤ 2υ υ ⎢ T ⎦ ⎣ 1 + (ϖτ ) + 2(ϖτ ) cos(απ /2) ⎥

(7)

Acknowledgments

where ϖ = ω ε∞/ ε0 , ω = 2πf is the angular frequency, ε0 denotes the static dielectric permittivity, ε∞ represents the dielectric permittivity at the infinite frequency, τ indicates the mean relaxation time, υ is the distribution parameter in the range of 0–1. Fig. 6(d) shows the bestfitted patterns at the temperature range of −50 °C - 100 °C. The obtained υ is larger than 0, indicating a non-Debye relaxation in the 0.95AF-0.5BT ceramic. The small value of υ indicates a strong interaction between various relaxation parameters, due to that an overall lower energy is required for the movement of oxygen vacancies [66]. Moreover, the small values υ agrees well with the Ea. Table 5 collects the dielectric loss of various dielectric ceramics. It can be found that the dielectric loss in the 0.95AF-0.05BT ceramic is higher than that of BaTiO3, Bi0.5Na0.5TiO3, NaNbO3, and Ba4Nd2Fe1Ni1Nb8O30 based dielectric ceramics. However, the values of tanδ in the 0.95AF-0.05BT ceramic is at the same level compared to other AF based ceramics. The dielectric loss is correlated to grain size, stability of elements, phase

This work is supported by a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors are grateful to Prof. Yang Ying and Prof. Zhu Kongjun (College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, P. R. China) for the electrical experiments. References [1] L. Zhang, Y.P. Pu, M. Chen, T.C. Wei, W. Keipper, R.K. Shi, et al., High energystorage density under low electric fields and improved optical transparency in novel sodium bismuth titanate-based lead-free ceramics, J. Eur. Ceram. Soc. 40 (2020) 71–77. [2] C.M. Fernández-Posada, A. Castro, J.M. Kiat, F. Porcher, O. Peña, M. Algueró, et al., A novel perovskite oxide chemically designed to show multiferroic phase boundary

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