Effect of polaron hoping on electrical properties of magneto electric composites

The Co0.7-xNixMn0.3Fe2O4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15, PbZr0.52Ti0.48O3 (PZT) ferroelectric and 30% CNMFO – 70% PZT magnetoelectric (ME) composites were synthesized by double sintering ceramic method. The XRD confirmed the pure phase formation of all compositions of ferrite, ferroelectric and ME composites. All compositions of ferrites, ferroelectric and ME composites show negative temperature coefficient of resistance (NTCR) confirming the semiconducting behavior, though the conduction mechanism is quite different than known semiconductors such as, silicon and germanium. The conduction, due to electron hoping in semiconductors against polaron hoping in ferrites is explained. The effect of cation distribution on resistivity of ferrite phase is also discussed. Thus, the effect of polaron hoping as well as cation distribution has been discussed on resistivity and dielectric constant of ferroelectric and ME composites. The effective resistance of ME composites due to combined resistance of the constituent phases has been studied.


Introduction
The development of two-phase Magnetoelectric (ME) composites consisting of magnetostrictive ferrite and piezoelectric ferroelectric has become a revolutionary trend for multiple state memory device in which data is stored both in electric and magnetic polarizations [1]. Apart from this, several other applications of ME composites have emerged including power harvesting, current transformer, phase shifters, waveguides, sensors and resonators [2]. According to Boomgard, higher ME coefficient necessary for device application is obtained by high and comparable resistivity of the constituent phases [3]. Ferroelectrics are insulating material with high resistivity being their inherent property. The ferrites show lower resistivity as compare to ferroelectrics. Now a day's research is being focused on higher resistivity of ferrite phase. Attempts are begin made to increase resistivity of ferrite phase, so that, the charges developed during ME coefficient measurement should not leak through the lower resistive ferrite phase [4]. Also, affects the resistivity of ferrite phase by change in cations distribution [5]. Whenever, increase or decrease in resistivity of ferrite phase which affects ME coefficient drastically.
The Co 0.7-x Ni x Mn 0.3 Fe 2 O 4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15 is selected as a ferrite phase. Due to highest magnetostriction Cobalt ferrite among all known cubic spinel ferrites; thus, it is selected as a parental ferrite [6]. The addition of Mn in small amount it enhances magnetostriction of cobalt ferrite. Hence, only the addition of 0.3 concentration of Mn shows highest magnetization and magnetostriction in Co-Mn series [7]. As we know that, nickel ferrite is well known for its higher resistivity [8], then attempt has been made to increase resistivity of Co-Mn ferrite by addition of nickel in step of 0.05. The amount of nickel has kept very low (x = 0.00, 0.05, 0.10 and 0.15) as magnetic moment of Ni 2? (2lB) is lower than Mn 2? (4lB) and Co 2? (3lB) and it may affect magnetic properties adversely [9]. The PbZr 0.52 Ti 0.48 O 3 (PZT) is selected as ferroelectric phase which shows highest value of dielectric and piezoelectric constant at morphotropic phase boundary (MPB) [10]. Also, it shows good coupling coefficient with cobalt ferrite [11]. The ME coefficient with 30% of ferrite phase and 70% of ferroelectric phase have been synthesized and characterized to understand effect of polaron hoping on resistivity.
Based on the recent literature survey, the change in resistivity of ferrite phase affects ME coefficient drastically. Ferroelectrics are naturally high resistive materials in comparison resistivity of ferrite phase is much small. High resistivity of ferrite phase enhanced ME coefficient. Charges produced during ME effect will not leak through less resistive ferrite phase. Thus, aim of the study is to attain high resistivity of ferrite phase and to study its effect on ME coefficient. Also, development and discharge of charges during ME effect is still unrevealed and also needs to understand conduction mechanism in ferrite, ferroelectric and ME composite.

Synthesis and characterization
AR graded chemicals are used as a starting material for synthesis of ferrite, ferroelectric and magnetoelectric composite (ME). Recently reported by A. Aubert et.al [12] the material like CoFe 2 O 4 and study their role in the synthesis of magnetoelectric composite and their applications has been studied by M. Bichurin et. al. [13]. Therefore, synthesized magneto electric composites with (30%) Co 0. 7 TiO 2 ) and (ZrO 2 ) zirconium oxide, acetone used as a mixing medium so that stoichiometry is maintained) and ground for three hours. Mixed powder is kept in crucible without lid and the crucible is kept in furnace with small amount of PbO in a boat aside. At higher temperature PbO in boat will evaporate and PbO content is dispersed inside the crucible. An attempt has been made to avoid Pb deficiency in most PZT synthesis. This mixed powder was pre-sintered at 1000 0 C for 6 h in PbO atmosphere. The calcinated powder were grinded for 1 h before the final sintering, which was carried out at 1100°C for 12 h again in PbO atmosphere. For the synthesis of Co 0.7-x Ni x-Mn 0.3 Fe 2 O 4 (CNMFO) with ''x'' varying from 0.00 to 0.15 with an increment of 0.05, equimolar amounts of CoO, NiO, Mn 2 O 3 , and Fe 2 O 3 . The obtained powder was then pre-sintered at 1000°C for 10 h and ferrites were obtained at final sintering temperature of 1100 0 C for 11 h. For both pre-sintering and final sintering of ferrites oxygen atmosphere was maintained. After preparing the individual components, for the preparation of the composites, obtained PZT and CNMFO powders were ground in molecular ratio of 70:30, respectively, in acetone medium. The mixed powders were hard-pressed into pellets and finally sintered at 900°C for 9 h. Samples were accordingly designated as K, L, M and N for x = 0.00, 0.05, 0.10 and 0.15 (representing the content of Ni in the CNMFO phase), respectively. The synthesized magnetoelectric composite (ME) was confirmed by FTIR, X-ray diffraction patterns were recorded on X1PHILIPS, Holland and Bruker D8 Advance X-ray diffractometer with CuKa radiation (k = 1.5407 Å ). Surface morphology of samples was recorded by scanning electron microscope (JEOL, Model JSM-6360A). Variation of dielectric constant with frequency was measured by using LCR meter, HP 4248A. Resistivity measurements were carried out from room temperature to 500°C.

Results and discussion
The synthesized material such as ME composite is confirmed by FTIR and its results show in FTIR spectrum. The FTIR spectrum was clearly observed J Mater Sci: Mater Electron (2022) 33:8566-8575 above the frequency range of 4000-500 cm -1 as shown in Fig. 1. In the FTIR spectrum clearly reflected that the decomposition of hydroxide to oxide phase for the formation of spinel ferrites. The reported IR bands of solids are usually attributed to the vibration of ions in the crystal lattice. The tetrahedral and octahedral modes of ferrite was well represented at the bands at 552 cm -1 and 464 cm -1 in the FTIR spectra. The suppressed band at 3500 cm -1 indicate less amount of water absorbed in the powder. The prominent peak at 600 cm -1 indicate formation of PZT with peaks in between the range of 1400 to 1600 cm -1 . The stretching vibrations of the metaloxygen of various composites show merged peak at 400 to 500 cm -1 .

X-ray diffraction studies
The X-ray diffraction patterns of Co 0.7-x Ni x Mn 0.3 Fe 2-O 4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15, PbZr 0.52 Ti 0.48 O 3 (PZT) ferroelectric and 30% CNMFO -70% PZT magneto electric (ME) composites (The ferrites 30% and ferroelectric 70%, Because of the magnetoelectric composites show of two constituent phases as magneto strictive ferrite phase and piezoelectric ferroelectric phase. To attain high direct ME coefficient ferrite grains is an input phase whereas ferroelectric matrix phase is output. Ferrite grains apply strain on the ferroelectric matrix and it will generate charges due to piezoelectricity so as to give high ME coefficient. The Distribution of ferrite phase in ferroelectric matrix should be uniform and such that each ferrite grain is surrounded by ferroelectric matrix. This distribution is achieved if 30% ferrite and 70% ferroelectric phase is selected. Less amount of ferrite will supply less magnetostriction resulting into low ME coefficient and for higher amount of ferrite phase, there are chances of ferrite grain connectivity and charges produced during ME effect may leak through ferrite phase. Thus, it is necessary to have 30% ferrite and 70% ferroelectric phase to achieve high ME coefficient) are shown in Fig. 2 (a), (b), and (c) respectively. Figure 2 confirmed that pure phase formation without any impurity for all compositions of ferrite, ferroelectric and ME composites. From Fig. 2 (a), presence of particular characteristic peaks at certain 2h positions confirms cubic spinel structure for all four compositions of ferrites. With the addition of Ni content, lattice parameter decreases from 8.40 Å to 8.37 Å . This decrease in lattice parameter is due to the replacement of larger Co 2? (0.78 Å ) ions by smaller Ni 2? (0.74 Å ) ions. Lattice contraction obeys Veegards law, its states that, cell volume decreases with addition of smaller cation and vice-versa [14]. Figure 2(b) shows well defined peaks as well as splitting of peaks which confirms tetragonal perovskite structure for ferroelectric phase. Lattice parameters (c = 4.14 c and a = 4.03 Å ) are in good agreement with reported values [15].
The study of X-ray diffraction patterns of ME composites in Fig. 2(c) show characteristic peaks of both ferrite and ferroelectric phases. The absence of any unidentified peak confirms that, there is no any chemical reaction between two constituent phases. Two distinct phases are sustained as the final sintering temperature of ME composites is kept lower than that of final sintering temperature of pure phases. Because, sintering temperature plays an important role in manipulating and governing properties of ME composites. Slight change in sintering temperature enhances mechanical properties of constituent phases considerably. Mechanical properties like connectivity between two constituent phases is very sensitive to sintering temperature which in turn is responsible for high ME coefficient. Thus, it is necessary to choose accurate sintering temperature of final ME composite so as to get high ME coefficient. However, it is always necessary to keep sintering temperature of ME composites lower than final sintering temperature of ferrite and ferroelectric phase. If final sintering temperature is kept lower then there will be no chemical reaction between constituent phases. Constituent phases were retaining their properties of magnetostriction as well as piezoelectricity and ME composite will also show new connectivity properties.

Scanning electron microscopy
The Fig. 3 (a)  content, it is observed that due to the addition of Ni content grain size was decreased from 4.9 lm to 3.8 lm and also, the number of grain boundaries and pores was found to increase with addition of Ni content which may increase the resistivity of ferrite phase and may serve our purpose i.e., to increase the resistivity of ferrite phase. Figure 4 shows SEM of PbZr 0.52 Ti 0.48 O 3 (PZT) ferroelectric phase. The grains are grown and well connected with grain size of nearly 5.1 lm are observed. As observed from SEM grain size decreases with increase in Ni content in ferrite phase. As grain size decreases, number of grain boundaries increases. This increased number of grain boundaries increases pore in material. Increases number of grain boundaries and pores offers more opposition to flow of polarons. Thus, decrease in grain size, enhance resistivity. Two different regions of large size well grown grains and smaller size grains are observed in Fig. 5(a), (b), (c) and (d) confirming co-existence of two constituent phases in ME composites. The present investigation, ME composites are synthesized in ferroelectric rich (with 70%  PZT) region. Obviously, the grains of major component would grow rapidly and vice-versa, as a result, microstructure becomes heterogeneous. Variation of grain size with Ni content is random as ferrite and ferroelectric are mixed randomly.

Resistivity
Temperature dependent variation of dc resistivity for Co 0.7-x Ni x Mn 0.3 Fe 2 O 4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15 is shown in Fig. 6(a) and ME composite with x = 0.1 shows higher value of room temperature resistivity. Resistivity of ME composite shows random variation of resistivity with Ni content in ferrite phase and it also shows that, random variation with percentage of ferrite and ferroelectric phase. This is because of non-uniform and random distribution of ferrite grains in ferroelectric matrix. Distribution of ferrite and ferroelectric grains is not controlled during sintering. Thus, resistivity of ME composites is result of multiple number of permutations and combinations of ferrite grains in ferroelectric matrix. Even if all experimental provisions and percentage of constituent phases is kept constant, room temperature resistivity and nature of graph may vary accordingly. All compositions of ferrites show semiconducting behavior but the conduction mechanism is quite different than that of known semiconductors such as silicon and germanium. In semiconductors, carrier concentration increases with increase in temperature and results into decrease of resistivity. Here, electron jumps from lower energy state to higher energy state of same ion and then it is available for conduction. Thus, conduction in semiconductors is due to electron hoping and DE in Arrhenius equation is the activation energy. In case of ferrites, carrier concentration is almost constant but, mobility of charge carriers increases with increasing temperature. In ferrites electron jumps from one ion to another ion set at different crystallographic sites, thus DE is migration energy. As ferrites are resistive materials, electrons apply strain on the lattice while moving through it. Thus, electron coupled with strain field is called as polaron. If this strain field extends beyond the lattice parameter, polaron is called as large polaron and if the strain field is smaller than lattice parameter, polaron is called as small polaron. Many reports are available on conduction in ferrites due to small polaron [7]. Spatial extent of polaron will be the appropriate term to show size of polaron rather than ''polaron radius''. The term polaron radius is quite unclear and confusing, as strain field is not having exactly round shape. The conduction mechanism in ferrites is explained on the basis of Vervy de Bhor theory, which involves electron exchange between ions of the same element present in more than one valance state and randomly distributed over equivalent crystallographic sites. In cubic spinel ferrites iron ions are present in Fe 2? and Fe 3? states. This cubic spinel structure has 64 tetrahedral (A) and 32 octahedral (B) sites out of which iron ions have strong preference for B site. The distance between cation in B site (0.292) is much smaller than the distance between cation at A site (0.357). Thus, polaron hoping between Fe 2? and Fe 3? ions present at B site controls conduction in ferrites. This polaron hoping is thermally activated and with increase in temperature, conductivity increases showing NTCR. Careful observation of Fig. 4(a) shows increases in resistivity with addition of Ni content. This is obviously due to the fact that, Ni 2? ions have strong preference for B site [16]. This will displace Fe 2? or Fe 3? ions from B site reducing conduction at B site. Thus, it has been said that, inverse spinel structures have higher resistivity than normal spinel structures. As observed from SEM grain size decreases with Ni content. Increased number of grain boundaries and pores was act as opposing walls for conduction and will cause resistivity increase. Spatial extent of polaron can roughly calculated by the formula where, N is number of sites per unit volume = 64 (A) ? 32 (B)/ (a) 3 = 96/a 3 , where 'a' is lattice parameter.
Values of polaron field extent (Table 1) are smaller than lattice parameter. Thus, conduction due to small polaron hoping is confirmed. At certain higher temperature there is change in slope of graphs indicating phase transition from ferromagnetic to paramagnetic state. In the Fig. 6(b) shows variation of dc resistivity with temperature for PbZr 0.52 Ti 0.48 O 3 (PZT) ferroelectric phase. In resemblance with the ferrites conduction in ferroelectric can also be explained with the help of Vervy de Bhor mechanism. With increase in temperature polaron hoping between Zr 3? -Zr 4? , Pb 2? -Pb 3? and Ti 3? -Ti 4? . Polaron extent is calculated by using Eq. 1.
Where, N = number of sites per unit volume = (1 B ? 8 A)/a 3 = 9/ a 3 from the Table 1 it can be seen that for PZT also charge carriers are small polaron. But polaron extent is much bigger than ferrites as ferroelectrics are more resistive.
Variation of dc resistivity with temperature for ME composites with 30% CNMFO and 70% PZT is shown in Fig. 6(c). All compositions of ME composites show semiconducting behavior due to polaron hoping between Zr 3? -Zr 4? , Pb 2? -Pb 3? and Ti 3? -Ti 4? and Fe 2? -Fe 3? . As the resistivity increases with Ni content in ferrite phase dielectric constant decreases. Increase in resistivity is due to increased number of grain boundaries and pores. High dielectric constant is due to accumulation of charges at grain boundaries. As resistivity increases number of charges reaching to grain boundaries decreases. Thus, increase in resistivity then decrease dielectric constant. Resistivity of ME composites is randomly varying with Ni content as ferrite and ferroelectric grains are mixed randomly in ME composites.

Dielectric constant
Dielectric constant decreases with increase in frequency showing regular dielectric dispersion behavior for all compositions of ferrites, ferroelectrics and ME composites as shown in Fig. 7 (a), (b), and (c) respectively. High values of dielectric constants at lower frequencies are sum of four types of polarizations; electronic, ionic, orientational and space charge polarization. Each polarization has different dimensions e. g. electronic polarization is smallest and its dimensions are nearly 10 19 Å . Ionic polarization is slightly sluggish and has dimensions of nearly 10 15 Å . whereas dimensions of orientational polarization are approximately 10 9 Å and so on. Due to   [17]. Thus, all compositions show dielectric dispersion behavior. With the present instrument we can measure dielectric constant up to 10 7 Hz. Thus, only space charge and orientational polarizations are reduced and observed [18] due to limitations of instrument. Resultant value due to sum of electronic and ionic polarization is called as static value of dielectric constant [19]. In the Fig. 7 (a) shows variation of dielectric constant with frequency for all compositions of ferrites. According to Maxwell Wanger theory and Koops phenomenological theory in homogeneous dielectric is made up of conducting grains, less conducting grain boundaries and non-conducting cracks, pores and defects [20]. Polarization in ferrites is similar process to the conduction. Conduction of polaron in Fe 2? -Fe 3? ions present at B site leads to local displacement of charges responsible for polarization. Due to higher resistivity of grain boundaries these charges pile up at grain boundaries and contribute for higher dielectric constant. Resistivity increases with addition of Ni content in ferrites are already discussed in the resistivity section. Due to increased resistivity of grains, charges reaching the grain boundaries are reduced and as a result dielectric constant decrease. Thus, with increase in resistivity dielectric constant decreases and it can be said that, resistivity and dielectric have inverse proportion [21]. Variation of dielectric constant with frequency for PZT is shown in Fig. 7(b). PZT shows much higher dielectric constant as compared to ferrites. Fig 7(c) shows variation of dielectric constant with frequency for all compositions of ME composites. Random variation of dielectric constant with Ni content was observed as ferrite and ferroelectric grains are randomly mixed. Variation of tand with frequency for Co 0.7-x Ni x Mn 0.3 Fe 2 O 4 (CNMFO) ferrites, 30% CNMFO-70% PZT magnetoelectric (ME) composites with x = 0.00, 0.05, 0.10 and 0.15 and PbZr 0.52 Ti 0.48 O 3 (PZT) and is shown in Fig. 8 (a, b and  c). All samples show dispersion behavior that is decrease in tand with increase in frequency. It is reported that tand of ME composites decreases with increasing percentage of ferrite phase. This increase in dielectric loss tand is due to increased conductive path provided by ferrite phase. At lower frequencies tand varies in random fashion but at higher  frequencies minimum tand is observed. Thus, it is expected to get higher ME coefficient at higher frequencies.

Conclusion
The synthesized Co 0.7-x Ni x Mn 0.3 Fe 2 O 4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15, PbZr 0.52 Ti 0.48 O 3 (PZT) ferroelectric and 30% CNMFO -70% PZT magneto electric (ME) composites by double sintering ceramic method. Presence of both phases in ME composites without any chemical reaction was achieved by keeping final sintering temperature of ME composites lower than that of final sintering temperature of constituent phases. Due to addition of smaller cation decreased lattice parameter and grain size in ferrites. In ferrites conduction is due to polaron hoping between Fe 2? and Fe 3? ions situated at B site whereas polaron hoping between Zr 3? -Zr 4? , Pb 2? -Pb 3? and Ti 3? -Ti 4? is responsible for conduction in PZT and Mixed type of conduction was observed in ME composites. Change in cation distribution changes resistivity. Thus, inverse spinel structures have higher resistivity than normal spinel structures, similar results were reported by A. Aubert et. al [12]. Resistivity affects dielectric constant adversely. Further it is interesting to observe that the effect of change in resistivity and dielectric constant on ME coefficient.