Structural, electrical, dielectric and optical properties of PrCrO3 ortho-chromite

Journal of Alloys and Compounds 812 (2020) 152130

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Structural, electrical, dielectric and optical properties of PrCrO3 orthochromite R. Mguedla a, A. Ben Jazia Kharrat a, *, M. Saadi b, K. Khirouni b , N. Chniba-Boudjada a, c, W. Boujelben a Laboratoire de Physique des Mat eriaux, Facult e des Sciences de Sfax, Universit e de Sfax, B. P 1171, 3000, Sfax, Tunisia  l’Environnement, Facult Laboratoire de Physique des Mat eriaux et des Nanomat eriaux Appliqu ee a e des Sciences de Gab es, Universit e de Gab es, cit e Erriadh, 6079, Gab es, Tunisia c Institut N eel, B.P. 166, 38042, Grenoble Cedex 9, France a

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 July 2019 Received in revised form 29 August 2019 Accepted 1 September 2019 Available online 3 September 2019

The structural, optical, electrical and dielectric properties of PrCrO3 perovskite prepared through the solgel method were investigated in details. Our compound was characterized by X-ray powder diffraction (XRD) at room temperature. It has been demonstrated that it crystallizes in the orthorhombic system with Pnma space group. The infrared (IR) spectrum highlighted a set of absorption peaks that can be attributed to the OeCreO and CreO vibrations. The reflectance spectrum, determined by UVeVis absorption spectrometry, provides the direct optical band gap Eg ¼ 3.24eV of the studied structure. The electrical and dielectric study was carried out by impedance spectroscopy (IS) in a wide frequency (40 e106Hz) and at a temperature varying from 160 to 440 K. DC conductivity measurements indicate that PrCrO3 discloses a semiconductor behavior with a semiconductor to metal transition estimated at TMS ¼ 400 K. AC conductivity follows Jonscher's equation. Nyquist plots reveal the existence of two well separated relaxation contributions related to the grains at high frequencies and grain boundaries at low frequencies. Furthermore, colossal dielectric permittivities were detected, showing the importance of this compound in electronic devices. © 2019 Elsevier B.V. All rights reserved.

Keywords: PrCrO3 Ortho-chromites IR results Electrical properties Dielectric properties

1. Introduction Rare earth orthochromites with the general formula RCrO3 (where R ¼ Y or a trivalent rare earth ion) were proposed to build up a new family of multiferroic systems characterized by the presence of strong correlations between their structural, electric and magnetic properties owing to their 4f electrons. Indeed, it is very significant to have a variety of properties within the same material in order to fulfill multiple applications, which could be appropriate and feasible for electronic devices based on these materials [1e3]. Among the orthochromite specificities, we mention their large magnetocaloric effect MCE at low temperatures, which makes them potential candidates for magnetic refrigeration [4e6]. Orthochromites are semiconductors in nature at room temperature [7] and

* Corresponding author. Aida Ben Jazia Kharrat Laboratoire de Physique des riaux Faculte  des Sciences de Sfax, B. P. 1171, 3000, Sfax, Tunisia. Mate E-mail address: [email protected] (A. Ben Jazia Kharrat). https://doi.org/10.1016/j.jallcom.2019.152130 0925-8388/© 2019 Elsevier B.V. All rights reserved.

present a high conductivity at high temperature. From an optical point of view, new research avenues can be explored with these materials since they can be used for the selective and intense absorption of the UV radiation in the electromagnetic spectrum. As a matter of fact, these compounds can be used as basic materials for solid oxide fuel cells, solar blind UV photodetectors, UV photonic devices, gas sensors [8e11]. A literature survey highlights that there is no detailed work on the PrCrO3 compound that has been reported before. This compound has triggered our attention because of its specific properties such as electrical, dielectric and optical ones. Indeed, this material has drawn the attention and whetted the interest of multiple researchers in view of its effective giant permittivity evaluated at 3  104 near room temperature [12] in the frequency range 100e106 Hz and in the temperature range 80e300 K. The electronic properties, varying with temperature, are governed by Pr3þePr3þ, Cr3þePr3þ, and Cr3þeCr3þ interactions [13]. It is worth noticing that all rare-earth orthochromites are isostructural and, in addition, they crystallize in a distorted

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orthorhombic perovskite structure with Pnma or Pbnm space group [14,15]. Dielectric properties of these compounds are quite interesting. Some investigations of dielectric properties were carried out on the compounds such as SmCrO3 [16], SmFe0.5Cr0.5O3 [17] GdCrO3 [153] and HoCrO3 [18]. SmCrO3 and HoCrO3 proved to exhibit giant dielectric permittivity which may be assigned to the extrinsic grain boundary and sample-electrode interface effects. Similar dielectric properties were reported in GdFexCr1-xO3 systems [15]. In this paper, the dielectric and electrical responses of PrCrO3 were determined as a function of temperature and frequency using the admittance spectroscopy technique. The optical energy gap obtained from reflectance measurements was reported. This compound was prepared by the sol-gel method. We chose this technique in view of its low cost and simplicity. 2. Experimental details The polycrystalline PrCrO3 sample was prepared by the sol-gel method using pure powders (with purity higher than 99%) of Pr6O11 and Cr2O3 according to the following reaction:

Fig. 1. EDX analysis of the chemical elements of the studied PrCrO3 compound. The inset shows the scanning electron micrograph of the same material.

(1) The precursors were at first dried, then intimately mixed in stoichiometric quantities in appropriate quantities of nitric acid and distilled water. In a second step, the citric acid (C6H8O7) and the ethyl-glycol (C2H6O2) were added in order to homogenize the solution. After that, the obtained mixture was heated on a hot plate equipped with a magnetic stirrer at a moderate temperature (70  C) until the formation of a gel which was dried at temperatures up to 150  C. The obtained powder was at first well mixed and calcined at 500  C for 12 h. The same procedure was applied at 600  C. Then heating cycles up to 800  C (by step of 50  C) accompanied by grinding and pelletizing were essential to obtain a homogenous, pure and compact compound. In a previous study, P. S. Devi [19] has demonstrated that the minimum calcination temperature for obtaining phase pure PrCrO3 by citrate gel process is 873 K. The purity and the phase identification were confirmed by XRD measurements at room temperature using (CueKa) radiation (lKa ¼ 1.5406 Å) from 18 to 85 Bragg's angle range and the obtained data were analyzed with the standard Rietveld method. In addition, the morphology of the PrCrO3 compound was analyzed by scanning electron microscopy (SEM). On the other side, in order to provide electrical and dielectric measurements, a thin film of silver was deposited on both sides of the sample. Therefore, the configuration of a capacity with which the conductance can be measured and the complex impedance as well as the capacity were determined. These measurements were performed in a wide range of frequency [40e107 Hz] and temperature [80e440 K] using an Agilent 4294 A analyzer and Janis VPF800 cryostat. The optical measurements, giving the reflectance of the compound, were performed at room temperature with a UVeViseNIR 3101 PC Shimadzu scanning spectrophotometer from 200 to 2400 nm wavelength.

chemical element during the elaboration or the sintering of our sample. In addition, there is no trace of impurity peaks in the studied compound, which confirms the purity and the homogeneity (as the analysis was undertaken in different points of the sample) of the studied material. Moreover, the morphology of the studied sample was observed using a scanning electron microscope (SEM) as illustrated in the inset of the same figure. The estimated average grain size is DSEM ¼ 185 nm. In Fig. 2-a, we reported the X-ray diffraction pattern of the PrCrO3 compound recorded at room temperature. The refinement of X-ray spectrum, using the standard Rietved technique, shows that our compound crystallizes in the orthorhombic structure with the Pnma space group as obtained by Saha et al. [20]. Indeed, all orthochromite compounds crystallize in a distorted orthorhombic structure with space group Pnma [21] or Pbnm [22]. Detailed results of the refinement of our compound are summarized in Table 1. The quality of this refinement was determined by means of the goodness of the c2 factor. As can be noticed, a tilting of the CrO6 octahedrons may occur following the important distortion observed in the CreOeCr bond angles, which may be compensated by an increase of the average bond length. The distortion from the ideal cubic structure can be confirmed, theoretically, by calculating the tolerance factor introduced by Goldschmidt [23]:

3. Results and discussion 3.1. Structural analysis

< Pr  O > texp ¼ pffiffiffi 2 < Cr  O >

To check the presence of all the chemical elements used in the preparation procedure, we performed an energy dispersive X-Ray analysis (EDX). Results, presented in Fig. 1, confirm the presence of all elements (Pr, Cr and O), which means that there is no loss of any

The obtained value of texp is 0.851 which is not far from the theoretical value confirming the orthorhombic structure of our compound. The average crystallite size of our sample was, at first, estimated from the most intense diffraction peak (131) of the XRD data using

r þ rO tth ¼ pffiffiffi A 2ðrB þ rO Þ

(2)

where rA, rB are, respectively, the average ionic radii of the A and B sites and rO is the average ionic radius of oxygen [24]. The calculated value of tth is 0.905 proving that our sample crystallizes in the orthorhombic structure. On the other hand, the tolerance factor may be calculated experimentally using the determined average bond-lengths < Pr  O > (2.402 Å) and < Cr  O > with the relation:

(3)

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Table 1 Refinement results obtained for PrCrO3 structure. Crystallographic data

PrCrO3

a (Å) b (Å) c (Å) V (Å3)

5.472 7.710 5.444 229.723

Pr X Y Z

0.5357 0.2500 0.4946

Cr X Y Z

0.5000 0.0000 0.0000

O1 X Y Z

0.0184 0.2500 0.5945

O2 X Y Z

0.2891 0.0235 0.7207

Cr-OI (Å) Cr-OII(Å) (Å) Cr-OI-Cr ( ) Cr-OII-Cr ( ) ( ) (Å) ε(103)

1.990 2.000 1.997 154.30 161.10 158.83 1.170 6.7 2.33

c2

Fig. 2. (a) X-ray diffraction pattern of the PrCrO3 compound and Rietveld refinement results at room temperature and (b) the plot of bcosq vs. 4sinq to determine the crystallite size by the Williamson-Hall method.

the Scherrer formula [25]:

DSC ¼

0:9 l b cos q

(4)

where l is the X-ray wavelength (l ¼ 1.5406 Å), b and q are the fullwidth at half maximum and the Bragg angle of the most intense peak respectively. The calculated value of DSC is 18 nm. The obtained nanometric crystallite size supports the choice of the sol-gel method for the preparation of our compound. The agglomeration rate DSEM/DSC ¼ 10.3, demonstrates that the average grain size estimated by the SEM is larger compared to that calculated from DRX measurements. On another side, the crystallite size can be evaluated through the Williamson-Hall method. Indeed, this technique has the merit of separating the size and the distortion effects [26]. In this study, only the prominent peaks in the XRD pattern (where b is the full width at half maximum of each peak) are taken into account. Then, the crystallite size DCR and the microstrain ε parameters can be determined using the relation:

0:9 l bcosq ¼ þ 4ε sinq DCR

(5)

It is important to clarify that the instrumental corrected

broadening b, corresponding to each diffraction peak, can be estimated by the relation:

h

b ¼ b2measured  b2instrumental

i1=2

(6)

In fact, the Bragg peaks in the XRD pattern consist of a combination of instrument and sample dependent effects. Using the silicon as standard material to determine the instrumental broadening, the two contributions can be decoupled. Fig. 2-b corresponds to the evolution of cosq versus 4sinq. The crystallite size value DCR can be obtained from the intercept of the plot with vertical axis (at sinq ¼ 0) and the strain is calculated from the slope of this curve. We obtained DCR ¼ 26 nm and ε ¼ 1.8 103. We notice that the grain size observed by SEM is much larger than crystallite size calculated by Williamson- Hall and Scherrer's methods. This can be explained by the fact that each grain observed by SEM is made up of an agglomeration of many crystallites. In addition, we can remark that the crystallite size evaluated by the Williamson-Hall model is larger than that obtained by Scherrer's formula. Indeed, the broadening effect, resulting from the presence of strains, is completely neglected in Scherrer's method [27]. 3.2. Optical properties The IR spectrum of the PrCrO3 compound performed in the range of 4000e400 cm1 is illustrated in Fig. 3. The transmittance curve shows the two strong metal oxygen absorption bands, which confirms the presence of the perovskite structure [28]. As depicted in the spectrum, the absorption bands located at 423 cm1,

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R. Mguedla et al. / Journal of Alloys and Compounds 812 (2020) 152130

Fig. 3. IR Spectrum of the PrCrO3 ceramic compound.

curve in the high-energy side [32]. Indeed, according to Marotti et al., the reflectance's first derivative turns to zero for a compound with an indirect gap or for an amorphous semiconductor. But, for a direct bandgap semiconductor, dR/dl shows a peak near Eg. The inset of Fig. 4 demonstrates that the optical band gap of our sample is direct and it is evaluated at 3.24eV characterizing PrCrO3 as a wide band-gap material. This value is comparable to that obtained in YCrO3 (3.721 eV) but higher than that estimated in SmCrO3 compound (2.66 eV) [33,34]. For La0.6Ga0.4Fe1-xMnxO3 (x ¼ 0; 0.1; 0.2 and 0.3) compounds, the optical band gap increases from 2.72 to 3.25 eV with the increase of the Mn content [35]. In Cu-doped ZnO nanoparticles, a decreased band gap value from 3.34 eV to 3.27 eV with an increasing Cu doping content is found [36]. Consequently, the band-gap of the PrCrO3 compound is of the same order of magnitude of those of the compounds mentioned. So we can get good optical characteristics with good electrical and dielectric results for technological applications with our compound which is easier to prepare. We notice that the obtained larger value of Eg indicates that our compound may be a good candidate for opto-electronic devices.

450 cm1 and 490 cm1 can be attributed to the deformation vibration of OeCreO as proposed by Zhang et al. [29]. In the cited work, the absorption bands are around 421 and 456 cm1. The strong absorption obtained at 570 cm1 shows the existence of BO6 Octahedron stretching vibration and consequently, it can be attributed to the stretching vibration of CreO [19,30]. According to Boudad et al. [31], in the SmFe0.5Cr0.5O3 compound, the absorption peak detected at 441 cm1 is attributed to the OeCreO vibration, while the peaks located at 499, 930 and 991 cm1 are attributed to the stretching and bending vibrations of CreO. While studying the effect of Fe substitution on GdCr1-xFexO3 compounds, Shanker et al. have obtained two absorption bands: the first one where the wave number is between 570 and 700 cm1 is attributed to the Cr/FeeO stretching vibration and the second one from 400 to 500 cm1 which is due to the OeCr/FeeO bending vibration [15]. It is worth noticing that the IR results confirm also the purity of the PrCrO3 prepared sample. The estimation of the energy band gap value Eg is determined through UVeVisible-Near Infra Red measurements using numerous methods. Fig. 4 portrays the UVevis reflectance spectrum R(l) of the PrCrO3 sample at room temperature. Many methods can be used to evaluate this parameter such as the minimum of the dR/dl

3.3.1. DC conductivity study The temperature evolution of the DC conductivity data sDC for PrCrO3 compound determined experimentally at low frequencies (40 Hz) is plotted in Fig. 5. As illustrated, our sample exhibits a semiconductor behavior from 80 to 400 K followed by a metallic regime when the temperature increases up to 440 K. The transition temperature is estimated at 400 K. This transition is not observed in other orthochromites [37]. As explained and demonstrated by many studies in the literature, there is no exact explanation of the transition mechanism from the semiconductor to the metallic regime, although this effect has been observed in several ceramic materials [38e40]. But we can suggest that the semiconductor character observed at temperatures lower than 400 K proves that the conductivity sDC(T) is governed by the hopping of localized short-range charge carriers. Otherwise, at high temperatures, the observed transition from semiconductor to the metallic regime may due to the additional thermal energy and electron scattering effects [41]. As will be seen in the AC conductivity study, this transition is not consistent with the frequency

Fig. 4. UV-VIS- NIR reflectance spectrum R(l) (and its derivative in the inset) of the PrCrO3 sample at room temperature.

Fig. 5. Temperature evolution of the DC conductivity for the PrCrO3 compound. The inset illustrates the evolution of Ln(sDCT) vs (1000/T).

3.3. Electrical results

R. Mguedla et al. / Journal of Alloys and Compounds 812 (2020) 152130

5

evolution of AC conductivity measurements sAC(u), which confirms that this transition does not induce a true metallic state [38] where the conductivity sAC(u) follows the Drude model [41,42]. In the inset of Fig. 5, we have plotted the variation of Ln(sDC TÞ vs. 1000/T. At high temperatures, the obtained curve obeys the Arrhenius relation expressed by: Ea

sDC T ¼ s0 e kB T

(7)

where s0 is a constant, kB is the Boltzmann constant and Ea represents the activation energy. The obtained linear plot confirms that the conduction mechanism is ensured by the thermally activated small polaron hopping model (SPH) [43]. The activation energy relative to the PrCrO3 compound is 263 meV, which is close to the value of other orthochromite compounds (GdCrO3 ¼ 0.30 eV [15], EuCrO3 ¼ 0.322eV [44] and SmCrO3 ¼ 0.33eV [45]). It is interesting to state that these activation energies are larger than those reported for manganites [40,46] indicating that the hoping of eg electrons is harder in orthochromite materials than manganites. 3.3.2. AC conductivity and conduction mechanism analysis The frequency evolution of AC conductivity sAC for PrCrO3 compound, determined by IS at various temperatures, is outlined in Fig. 6-a. As illustrated, two regions are distinguished. At low frequencies (f < 105 Hz), sAC ðuÞ (where u ¼ 2pf) displays a plateau, which can be attributed to the DC contribution. In the second region (at high frequencies f > 105 Hz), the conductivity dispersion can be described using the equation of Jonscher [47]:

sAC ðuÞ ¼

ss s∞ t2 u2 þ þ BðTÞus 2 2 1þt u 1 þ t2 u2

(8)

where t represents the characteristic relaxation time, ss is the conductivity at low frequencies, s∞ is an estimation of the AC conductivity at high frequencies, B depends only on temperature and s is an exponent ranging between 0 and 1 which reflects the degree of interaction between the charge carriers and their environment. Basically, the classical equation of Jonscher is used to describe the AC conductivity data. The related expression is given by:

sAC ðuÞ ¼ sDC ðTÞ þ Au

s

(9)

where A describes the strength of polarizability in the structure. We tried to fit the AC conductivity data using relations (8) and (9). The best fit is obtained using relation (8) as illustrated in Fig. 6a. The first term in sAC(u) intervenes at low frequencies (u/0) and is attributed to thermal activated transition of charge carriers from valence band to conduction band. The second term of the conductivity arises due to short range hopping of charge carriers at the grain boundaries and the term BðTÞus describes the conductivity evolution at high frequencies and is attributed to localized hopping of charge carriers within the grains [48]. Using the obtained results, we plotted in Fig. 6-b the temperature evolution of the exponent s(T) in order to determine the conduction mechanism model in the studied structure. The charge carriers, responsible of this conduction mechanism may be electrons, polarons, or ions. In this context, four models were proposed in literature to describe the conduction mechanism in disordered materials [49], which are the non-overlapping small polaron tunneling (NSPT), the correlated barrier hopping (CBH), the quantum mechanical tunneling (QMT), and the overlapping large polaron tunneling (OLPT) models.

Fig. 6. (a) Frequency dependence of the AC conductivity sAC at various temperatures for the PrCrO3 compound and (b) Temperature evolution of s and (1-s) parameters.

As reported in Fig. 6-b, two regions can be distinguished:  For 160  T  220 K, s decreases with the increase in temperature indicating that the correlated barrier hopping (CBH) is the most suitable model which describes the conductivity in this region. If we note t0 the characteristic relaxation time and Wm the binding energy required to move a charge carrier from one site to another, then s is indicated by the relation [50]:

sðTÞ ¼ 1 

6kB T WM þ kB Tlnðut0 Þ

(10)

In the case of WM [kB Tlnðut0 Þ, this relation can be written as:

sðTÞ ¼ 1 

6kB T WM

(11)

 For 220 K  T  440 K, s increases with increasing temperatures up to 440 K. Therefore, the conduction mechanism can be described by the NSPT model where the s parameter is expressed by Ref. [39]:

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sðT; uÞ ¼ 1 þ W

H

kB T

4

(12)

 Lnðut0 Þ

In this expression, WH is the polaron hopping energy. For larger values of WH/kBT, s can be simplified as:

sðTÞ ¼ 1 þ

4 kB T WH

(13)

The temperature evolution of (1-s) gives WM ¼ 0.240 eV and WH ¼ 0.229 eV. The same evolution of the s parameter (from CBH model to NSPT one) was observed in La0.57Eu0.1Ba0.33Mn0.85Fe0.15O3 and Pr0.5-xGdxSr0.5MnO3 (0  x  0.3) perovskites [39,46]. It can be noted also that the values of s don't exceed 1 suggesting that the conduction mechanism occurs with sudden hopping according to Funke [51]. 3.3.3. Complex impedance results The complex impedance of a dielectric material is provided by the following expression: 0

00

Z * ðuÞ ¼ Z ðuÞ  jZ ðuÞ

(14)

where Z’ is the real part and Z00 is the imaginary part of the complex impedance. Fig. 7-a shows the evolution of Z’(u) of the complex impedance with frequency at different temperatures. We can notice that the impedance Z’ is almost constant at low frequencies, which implies that the conductivity sAC for our compound is constant in this frequency range. At high frequencies, Z’ values decrease and converge to a constant value that may be assigned to the release of space charge polarization [52]. We plotted in Fig. 7-b the frequency dependence of (-Z00 ) at different temperatures. As shown, the spectrum of (-Z00 ) reaches two maximums at fmax1 and fmax2 reflecting the presence of two relaxation frequencies that correspond to the grain boundaries (at low frequencies) and the bulk at high frequencies respectively. The relaxation times associated with grain boundaries and grains can be determined with the relation t ¼ 1/(2 pfmax1,2). In both cases, the relaxation time decreases with the increase of temperature indicating that the dielectric relaxation phenomenon on the material is thermally activated. The plots of Ln(t) against 1000/T are reported in Fig. 7-c and the activation energies associated with grains Eag and grain boundaries Eagb can be determined using an Arrhenius model. The obtained values are Eagb ¼ 231 and Eag ¼ 215 meV. It is worth noticing that Eagb is higher than Eag, which refers, probably, to the existence of Maxwell-Wagner effect [40]. In addition, these values are close to those obtained by DC analysis, which suggests that the charge carriers need to overcome approximately the same energy barrier during conduction and relaxation processes. At a fixed temperature, 220 K for example, the frequency dependence of the imaginary part (-Z00 ) and the real part Z0 of the impedance for the PrCrO3 studied compound are illustrated in Fig. 8-a. These plots exhibit, on the one hand a deviation from the typical Debye's model and, on the other hand, confirm the presence of the two relaxation times associated with grains and grain boundaries. In order to verify if the relaxation frequencies of Z0 and (-Z00 )   d

have exactly the same value, we calculated

Z

0 Z 0 max

du

and we plotted

its evolution with frequency together with Z"=Z "max in Fig. 8-b. It is evident from these curves that the relaxation frequencies of Z0 and (-Z00 ) are far away confirming the deviation from the Debye's model. It is worth noting that the relaxation process confirmed in our

Fig. 7. Frequency evolution of (a) Z0 ,(b) -Z00 and (c) evolution of Ln(t) with 1000/T to determine activation energies.

material refers generally to the presence of charge carriers at low temperatures and defects at higher temperatures [53]. The Nyquist diagrams (-Z00 vs Z’) for our PrCrO3 compound, recorded at different temperatures, are illustrated in Fig. 9-a. These spectra are characterized by the existence of two semicircular arcs. The first is associated with grains, while the second is related to the grain boundaries. These semicircular arcs are centred below the real axis suggesting the presence of a distribution of relaxation times that indicates a non-Debye type relaxation in the studied structure [54]. Fig. 9-b presents the simulated Nyquist plot determined at

R. Mguedla et al. / Journal of Alloys and Compounds 812 (2020) 152130

 d

Fig. 8. Frequency evolution of (a)

Z0

and

T ¼ 220 K as an example with its associated equivalent circuit. As observed, the calculated and the experimental data are in good agreement, indicating that the proposed equivalent circuit describes well the electrical properties of our PrCrO3 compound. The equivalent circuit, introduced in the inset of Fig. 9-b involves two parallel circuits associated in serial. The first one, which models the transport through the grains, is composed by a resistor Rg and a constant phase element CPEg. The second circuit describes the conduction mechanism through grain boundaries. It is composed of a resistor Rgb and a constant phase element CPEgb. The CPE impedance is given by Ref. [55]:

ZCPE ¼

1 where  1  a  1 Q ðjuÞa

(15)

In this expression, Q is the capacitance value of the CPE impedance and a describes the degree of deviation from the Debey's model. As a result, the real and the imaginary parts of the impedance Z(u) will be provided by the following expressions:

 i Rg 1 þ Rg Q1 ua1 cos a21 p 0 Z ¼  2   2 þ Rg Q1 ua1 sin a21 p 1 þ Rg Q1 ua1 cos a21 p h  i Rgb 1 þ Rjg Q2 ua2 cos a22 p þ  2   2 þ Rgb Q2 ua2 sin a22 p 1 þ Rgb Q2 ua2 cos a22 p

(b),

Z"=Z "max

and

(16)

Z

0 Z 0 max

du

 at T ¼ 220 K.

  R2g Q1 ua1 sin a21 p Z ¼  2   2 þ Rg Q1 ua1 sin a21 p 1 þ Rg Q1 ua1 cos a21 p   R2gb Q2 ua2 sin a22 p þ  2   2 þ Rgb Q2 ua2 sin a22 p 1 þ Rgb Q2 ua2 cos a22 p "

(17)

In these expressions, (Q1,Q2) and (a1,a2) refer to grains and grain boundaries respectively. Fig. 8-a highlights also a good agreement between the experimental data of Z0 (u) and Z"(u), which confirms that the suggested equivalent circuit is the most appropriate to describe the conduction mechanism through the studied compound. With a view to determine directly the different contributions to the conduction process, we have calculated the frequency evolution of the phase q of the complex impedance at different temperatures using the relation:

qðuÞ ¼ tan1

h

and

(-Z00 ),

7

 00  Z 0 Z

(18)

The results are gathered in Fig. 10. As illustrated, at low temperatures, two peaks in q spectrum can be identified. The peak, which appears at high frequencies, is associated with the grains response and the second peak positioned at the low frequency side is related to the grain boundary response. With the increase in temperature, charge carriers can easily overcome the potential barrier owing to the presence of defects in the grain boundaries and, therefore, the conduction will be mainly provided by the grains.

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0

00

M* ðuÞ ¼ M ðuÞ þ iM ðuÞ ¼ iu0 C0 Z * ðuÞ

(19)

where M’ and M00 denote the real and imaginary parts of the complex modulus and C0 is the vacuum capacitance of the cell under investigation. Fig. 11-a identifies the frequency evolution of M"(u) at various temperatures for our compound. The analysis of these curves characterizes the existence of two asymmetric relaxation peaks for each temperature and over the entire frequency range of analysis. The first peak, located at low frequency, is associated with the grain boundary effects and the second peak, observed at high frequency, is associated with grains. The maxima of these relaxation peaks move upwards frequencies when the temperature increases indicating the decrease of the relaxation time. The use of the modulus formalism has as a target the minimization of electrode polarization if it exists. In our case, the low values of the modulus may indicate the low contribution of the electrodes in the conduction mechanism. A comparative study illustrated in Fig. 11-b portrays that the maximums of Z00 and M00 curves coincide both in the low frequency region and in the high frequency region for the PrCrO3 sample. This result shows that conduction and the relaxation processes are governed by the same defects in this material.

3.4. Dielectric study The dielectric response of a semiconductor material can be described by the complex permittivity given by Ref. [56]:

Fig. 9. (a) Nyquist plots of the PrCrO3 compound at different temperatures and (b) simulated Nyquist plot with the electrical equivalent circuit determined at 220 K. The inset shows the equivalent circuit.

Fig. 10. Bode plots of the phase q of the complex impedance versus frequency at various temperatures for PrCrO3 compound.

3.3.4. Complex modulus analysis The electrical response as a function of frequency and at a fixed temperature of the PrCrO3 compound, can be investigated also using the complex electric modulus M* defined by Ref. [38]:

Fig. 11. (a) Complex modulus spectrum as a function of frequency at several temperatures and (b) frequency evolution of Z00 and M00 at T ¼ 220 K.

R. Mguedla et al. / Journal of Alloys and Compounds 812 (2020) 152130

0

00

ε* ¼ ε  jε ¼

1 juε0Z *

(20)

where ε0 and ε" denote, as known, the real and the imaginary parts of the dielectric permittivity describing respectively the storage and the loss of energy in the material. These parameters can be expressed as follows: 0

ε ð uÞ ¼

00

ε ð uÞ ¼

00



Z



Z

uC0 Z 0 2 þ Z 00 2



(21)



(22)

00

uC0 Z 0 2 þ Z 00 2

Fig. 12-a represents the frequency evolution of the real part ε0 of the dielectric constant for the PrCrO3 compound. We can notice that, at low frequencies and at a fixed temperature, ε0 has large values, then they decrease to a constant value at higher frequencies. At low frequency, colossal dielectric values that can be attributed especially to interfacial polarization were determined. The contribution of oxygen vacancies was not excluded. Similar behavior was obtained in Ho0.9(RE)0.1CrO3 (where RE ¼ Gd and Yb) [57] and Pr0.75Bi0.05Sr0.1Ba0.1Mn0.98TixO3 (x ¼ 0,0.04) [58] compounds.

In addition, at low frequencies, the dipoles can easily follow the applied electric field and ε0 reach its quasi static value. As the frequency increases, the dipoles existing in the material begin to lag behind this field until they can no longer follow it at very high frequency. Thus, giving rise to a constant value of the dielectric permittivity [59,60]. Similar behavior was observed by Bhowmik et al. [38]. Indeed, the frequency evolution of ε’ showed the predominance of the Maxwell-Wagner type interfacial polarization at low frequencies and high temperatures. Moreover, the ε0 (u) curves are almost stabilized over a wide frequency range where the dipolar contribution dominates. Relatively low values of ε’ which not exceed 100 is, usually, obtained if intrinsic electronic and ionic polarization mechanisms governs the studied structure [12]. Recent studies show that the extrinsic Maxwell-Wagner type polarization can be at the origin of giant permittivity values observed in many ceramic materials [46,58,61]. Consequently, the high values of permittivity observed in our PrCrO3 compound is not an intrinsic property related to the studied material. Fig. 12-b depicts the variation of the relative permittivity ε0 at several temperatures and at different excitation frequencies: 102, 103, 104 and 105 Hz. As detected, with the increase of temperature, ε0 increases to a constant value (z104 F.m1) around the room temperature and then increases further. This finding suggests that our sample may be proposed as a potential candidate for technology applications at room temperature. The inset of Fig. 12-b illustrates the temperature evolution of loss tangent (tgd) at the same frequencies for our studied sample. As seen, this curve shows high values of tgd at room temperature and above which will restrict any electrical use of this compound. In order to overcome this problem, some substitutions in A or B-sites can be proposed. Another solution is to elaborate a composite material formed by PrCrO3 and another ceramic compound having low losses even with a lower permittivity. By modifying the percentage of each compound, it is possible to select a composite having good performances, namely low losses and high dielectric permittivities as it can provide device miniaturization. We can notice that the presence of a maximum in the tgd plot (at TC ¼ 360 K) may indicate a transition from a ferroelectric to paraelectric transition. This temperature was evaluated at 530 and 490 K at 1 kHz for Ho0.9Gd0.1CrO3 and Ho0.9Yb0.1CrO3 respectively [57]. The frequency dependence of ε00 (u) at various for the PrCrO3 compound is illustrated in Fig. 13-a. The obtained curves display straight lines with very similar slopes (z1), which confirms that for our compound, the sDC conduction mechanism dominates. With the rise in temperature, the ε" values exhibit a significant increase. Moreover, the frequency evolution of ε00 at several temperatures can be analyzed using Giuntini law [62] as obtained with manganite perovskites [39,46,53]. The Giuntini expression can be simplified as:

ε" ðuÞ ¼ CðTÞ um

Fig. 12. (a) Frequency evolution of the real part ε0 of the dielectric constant for the PrCrO3 compound at several temperatures and (b) temperature evolution of ε0 at some selective frequencies. The inset shows the temperature evolution of tg d at the same frequencies.

9

(23)

where C(T) is a constant that depends only on temperature and m, which is given by m ¼  4kB T=WG, denotes an exponent describing the interaction between electric dipoles. WG is the energy necessary for charge carriers to jump above the potential barrier. In order to determine the WG values, we illustrated in Fig. 13-b the fit of Ln(ε00 ) ¼ f(Ln u) curves with relation (25) for our studied sample. The calculated values of WG as a function of temperature are gathered in the inset of Fig. 13-b. As depicted, WG presents higher values which confirms that the conduction mechanism is not ensured only by electron transport, but through a coexistence of

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R. Mguedla et al. / Journal of Alloys and Compounds 812 (2020) 152130

Fig. 14. Frequency evolution of ε"eff at several temperatures for PrCrO3 ceramic compound.

Fig. 13. (a) Frequency evolution of the imaginary part of dielectric constant and (b) Evolution of Ln(ε00 ) versus Ln (u) at several temperatures for PrCrO3 compound. The inset shows the temperature evolution of WG.

electronic and polaronic conduction. In addition, the increase of WG with temperature may be attributed to the disorder introduced to the system [46]. On the other side, the relaxation phenomenon which is generally obscured by the DC-conductivity process, can be extracted using the formula [63]:

 p dε0 ε"eff ðf Þ ¼  : 2 dðlogf Þ

(24)

The obtained spectra, illustrated in Fig. 14, confirms clearly that this method is suitable for investigating the dielectric relaxation in our compound, though this phenomenon is hided by hopping of charge carriers. Finally, we can notice that according to Zhang et al. [29], under el temperature TN, estimated at 232 K, the PrCrO3 compound the Ne exhibits a canted antiferromagnetic transition with weak ferromagnetic ordering due to the exchange interaction between Cr3þ spins. As a consequence, the ferromagnetic Cr3þ moments will be polarized oppositely to the paramagnetic Pr3þ moments. A possible coupling between canted spin structure and electronic states can affect the dielectric properties of our compound [38]. The magnetoelectric coupling in the PrCrO3 material may be evidenced [64]. 4. Conclusion The basic objective in this paper is to investigate, the structural, optical, electrical and dielectric properties of the multiferroic

PrCrO3 ceramic sample prepared by the sol-gel route. Our compound crystallizes in the orthorhombic system with Pnma space group. The IR spectrum displays a set of absorption peaks that can be attributed to the OeCreO and CreO vibrations. The optical band gap, determined by reflectance spectrum, is evaluated at 3.24eV. The electrical and dielectric properties are characterized by IS in a wide range of temperature and frequency. The PrCrO3 presents a semiconductor behavior with a semiconductor to metal transition estimated at the temperature TMS ¼ 400 K. The electrical conductivity measurements follow Jonscher's equation. The temperature variation of the exponent “s" proves that the CBH model dominates the conductivity at low temperatures and NSPT at higher ones. Dielectric results exhibit colossal dielectric permittivities that prove to the useful in technological applications. The relaxation process, which is hidden by the DC-conductivity in the dielectric spectra, can be extracted. In conclusion, we would assert that our research is a step that may be taken further. It offers different prospects and opens new horizons for future works to explore further this promising compound and investigate its practical use in multiple fields. Acknowledgements This work has been supported by the Tunisian Ministry of Higher Education and Scientific Research. References [1] K. Sardar, M.R. Lees, R.J. Kashtiban, J. Sloan, R.I. Walton, Direct hydrothermal synthesis and physical properties of rare-earth and yttrium orthochromite perovskites, Chem. Mater. 23 (2011) 48e56. [2] J.R. Sahu, C.R. Serrao, N. Ray, U.V. Waghmare, C.N.R. Rao, Rare earth chromites: a new family of multiferroics, J. Mater. Chem. 17 (2007) 42. [3] Z.X. Cheng, X.L. Wang, S.X. Dou, H. Kimura, K. Ozawa, A novel multiferroic system: rare earth chromates, J. Appl. Phys. 107 (2010), 09D905. [4] S. Yin, T. Sauyet, C. Guild, S.L. Suib, Jain, Effect of Gd substitution on the structural, magnetic, and magnetocaloric properties of HoCrO3, J. Magn. Magn. Mater. 428 (2017) 313. [5] L.H. Yin, J. Yang, R.R. Zhang, J.M. Dai, W.H. Song, Y.P. Sun, Multiferroicity and magnetoelectric coupling enhanced large magnetocaloric effect in DyFe0.5Cr0.5O3, Appl. Phys. Lett. 104 (2014), 032904. [6] S. Yin, T. Sauyet, M.S. Seehra, M. Jain, Particle size dependence of the magnetic and magneto-caloric properties of HoCrO3, J. Appl. Phys. 121 (2017), 063902. [7] B. Tiwari, M.K. Surendra, M.S.R. Rao, HoCrO3 and YCrO3: a comparative study, J. Phys. Condens. Matter 25 (2013) 216004. [8] J. Sfeir, LaCrO3-based anodes: stability considerations, J. Power Sources 118 (2003) 276e285. [9] G. Kotnana, S.N. Jammalamadaka, Band gap tuning and orbital mediated electron-phonon coupling, J. Appl. Phys. 118 (2015) 1e7. [10] N. Soltani, S.M. Hosseini, A. Kompany, Nanoscale ab-initio calculations of optical and electronic properties of LaCrO3 in cubic and rhombohedral phases, Phys. B Condens. Matter 404 (2009) 4007e4014.

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