Structural transformation and improved dielectric and magnetic properties in Ti-substituted Bi_0.8La_0.2FeO₃ multiferroics

Figure 1 shows the XRD patterns of Bi_0.8La_0.2Fe_1−xTi_xO₃ (x = 0.0, 0.05, 0.1, 0.15) samples. A very small amount of impurity phase Bi₂Fe₄O₉, as labelled by '•', was detected in the sample for x = 0.15. This could not be removed even by longer calcination times which could also lead to more volatization of Bi₂O₃. Minor impurity phases observed have also been reported to form during the synthesis of BFO; La-doped BFO and co-substituted BFO ceramics [13, 15]. The observed impurity phase is neither magnetic nor ferroelectric at RT. Therefore, its presence will not affect ferroelectric and ferromagnetic properties of the system. XRD peak intensity ratios observed in XRD pattern suggest polycrystalline behaviour with good crystallinity of these samples. The existence of splitting peaks around 31° and 52° for x = 0.0 suggests the distorted rhombohedral R3c structure which is consistent with those reported by Du et al [38]. For x = 0.0 ceramic the peaks (1 0 4) and (1 1 0) are clearly split, but with Ti substitution this peak splitting decreases. The observed disappearance of peak splitting (1 0 4)/(1 1 0) in the XRD pattern is a common feature for Ti substitution [39, 40]. The intensity of peaks observed around 2θ ≈ 39° and 52° for x = 0.0 ceramic gradually decreases and merges partially to form a broadened peak with the increase in Ti content which is also reported by Gu et al [39]. Splitting of peaks around 22° and 45° takes place with the increase in Ti content which suggests phase transition from rhombohedral to tetragonal. For detailed structure analysis, structural parameters obtained from XRD pattern were further refined using GSAS+EXPGUI program [41, 42]. It is known that the RT phase of BFO is a rhombohedrally distorted perovskite structure described by space group R3c. Rhombohedral cell is very close to the cubic one (angle α in the rhombohedral cell is about 89.4°). In this structure, cations are displaced from their centrosymmetric position along the pseudocubic [1 1 1]_C axes [21]. The unit cell can also be described in a hexagonal frame of reference with hexagonal c-axis parallel to the diagonals of the perovskite cube. Therefore, the miller indices (h k l) of diffraction peaks in figure 1 are referred to as hexagonal axes rather than rhombohedral axes. The lattice parameters 'a' and 'c' were calculated using (1) as given below

$$\begin{equation} {\rm Sin}^2\theta =\frac{\lambda ^2}{3a^2}(h^2+hk+k^2)+\frac{\lambda ^2l^2}{4c^2} \end{equation} \tag{ 1 }$$

where θ is Bragg's angle and λ is the wavelength of x-rays used. The strong peaks (0 1 2) and (1 1 0) were used for such calculations. Calculated values of lattice parameters 'a' and 'c' from (1) were used as the initial parameters during the refinement and these parameters were further refined. The Rietveld refinement requires that intensities as well as the shapes of diffraction peaks must be reproduced. To model a crystal structure with the Rietveld refinement, we must fit a large number of experimental parameters in addition to the crystallographic parameters. The Rietveld refinement of the XRD patterns for the x = 0.0 and 0.05 samples (figures 2(a) and (b), respectively) was performed using same space group, i.e. R3c and the structural model allowed us to reproduce all the observed peaks. The initial Rietveld refinement was carried out by zero point shift, the unit cell and background parameters. The background was modelled using cosine Fourier series and peak shapes were described by pseudo-Voigt functions. After a good match, the peak positions were achieved, the peak profile parameters including the peak symmetry were refined. The Rietveld refinement of the XRD pattern for the x = 0.1 sample (figure 2(c)) was performed using both space groups, i.e. R3c and P4mm separately. But none of these give satisfactory results. Then refinement was carried out by combining R3c and P4mm space groups. Fairly good values of reliable factors were obtained using this combination of two phases (i.e. R3c + P4mm). Refinement pattern for the x = 0.15 sample (figure 2(d)) was best fitted with space group P4mm. Therefore, with the increase in Ti content, there is a continual change in crystal structure from rhombohedral to tetragonal and phase boundary occurs at x = 0.1. Refined structural parameters along with profile R-factors are listed in table 1 and different bond lengths and bond angles are given in table 2. It is clear from table 1 that there is a continual decrease in lattice constants, and hence volume, with increase in Ti content. This volume contraction is due to small difference in ionic radius of Ti⁴⁺ (0.604 Å) and Fe³⁺ (0.645 Å). The change in the value of c/a with Ti substitution shows a change in crystal anisotropy.

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The average particle size for all the samples was calculated from XRD peak broadening using the Debye Sherrer formula;

$$\begin{equation} D=K\lambda /\beta \,{\rm Cos}\,\theta \end{equation} \tag{ 2 }$$

where D is the crystallite size, K (constant) = 0.89, β is the full width at half maxima (in radian) and θ is Bragg's angle. Effects of strain, instruments and other defects were ignored in the calculations. The values are found to be 33 nm, 31 nm, 28 nm and 26 nm for the x = 0.0, 0.05, 0.1 and 0.15 samples, respectively. The particle size gradually decreases with increasing concentration of Ti. This variation is further supported by SEM results.

Figure 3 exhibits the SEM micrographs of the surface morphologies of all prepared samples. Ti⁴⁺ ion plays the role of donor in BFO and the addition of Ti⁴⁺ requires charge compensation by filling of oxygen vacancies. Therefore, reduction of particle size with Ti substitution may be related to the suppression of oxygen vacancies due to charge compensation mechanism [26].

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Figures 4(a)–(d) show the temperature dependence of real (ε') and imaginary (ε'') (inset) parts of dielectric constant at different frequencies for all the prepared samples. It clearly reflects an active role of Ti substitution in modifying dielectric behaviour of Bi_0.8La_0.2FeO₃ multiferroic. It is clear from the figures that at a particular temperature all the samples show decreasing trend in both ε' and ε'' values with increasing frequency and reaches a nearly constant value at higher frequencies. The large value of ε' at lower frequency is due to interfacial dislocations pile ups, oxygen vacancies, grain boundary effects etc, while the decrease in ε' at higher frequency is natural because of the fact that any species contributing to polarization is found to show lagging behind the applied field at higher and higher frequencies. According to the Maxwell–Wagner model [43, 44], the dielectric material with heterogeneous structure can be imagined as a structure consisting of well conducting grains separated by high resistive grain boundaries. In this case, the applied voltage on the sample drops mainly across the grain boundaries and a space charge polarization is build up at the grain boundaries. The space charge polarization is governed by the available free charges on the grain boundary and the conductivity of the sample. Koops [45] proposed that the effect of grain boundaries is predominant at lower frequencies (i.e. higher dielectric constant for thinner grain boundaries) and grains are effective at higher frequencies. Figure 4(a) shows that both ε' and ε'' increase with the increase in temperature but an anomaly at around 463 K is observed. At low temperatures, the electric dipoles cannot orient themselves with respect to the direction of the applied field and therefore contribute weakly to the polarization resulting in low value of ε'. As temperature increases most of the electric dipoles get enough exciting thermal energy to be able to follow up the changes in the external field. This enhances the contribution of the dipoles to the polarization mechanism leading to an increase in the value of ε'. At higher temperatures, due to an increase in the number of charge carriers and their mobilities, the enhanced conductivity causes an increase in ε'' associated with conduction losses. It is well known that in perovskites, the oxygen vacancies $({\rm V}_{\rm O}^{2+})$ could be formed in the process of sintering due to the escape of oxygen from the lattice [46]. ${\rm V}_{\rm O}^{2+}$ comes mainly from Bi volatility and the transition from Fe³⁺ to Fe²⁺ which can be described by equations (3) and (4):

$$\begin{equation} 2{\rm Fe}^{3+}+{\rm O}^{2-}\to 2{\rm Fe}^{2+}+{\rm V}_{\rm O}^{2+} +0.5{\rm O}_2 \end{equation} \tag{ 3 }$$

$$\begin{equation} 2{\rm Bi}^{3+}+3{\rm O}^{2-}\to 2{\rm V}_{{\rm Bi}}^{3-} +3{\rm V}_{\rm O}^{2+} +{\rm Bi}_2 {\rm O}_3. \end{equation} \tag{ 4 }$$

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Oxygen vacancies formed during sintering could interact with Fe³⁺/Fe²⁺ giving rise to hopping conduction between Fe³⁺ and Fe²⁺ ions, which give rise to an anomaly as shown in figure 4(a). This type of anomaly has also been reported by Catalan and Scott [8] and they have observed that this anomaly is not intrinsic type but due to charge defects. This can be interpreted as if this anomaly was not due to charge defects then it should also appear for Ti-substituted samples. But no such anomaly was observed for samples with x = 0.10 and 0.15. Therefore, this anomaly may be attributed to transient interaction between oxygen ion vacancies and Fe²⁺/Fe³⁺ redox couple. A similar type of peak is also reported in yttrium-doped BFO [47]. The absence of such an anomaly in Ti-substituted samples may be due to suppression of charge defects by the charge compensation mechanism due to higher valence of Ti⁴⁺ than Fe³⁺. At higher temperatures a remarkable increase in ε' manifests the occurrence of the Maxwell–Wagner effect in Bi_0.8La_0.2FeO₃ sample [40]. However, in Ti-substituted samples (x = 0.1, 0.15) such behaviour is not so remarkable. Therefore, stability of dielectric constant with temperature is considerably improved with the increase in Ti content. A decrease in the values of ε'' with Ti substitution indicates reduced conductivity and hence enhanced resistivity in doped samples.

The phenomenon of conductivity dispersion in solids is generally analysed using Jonsher's power law,

$$\begin{equation} \sigma (\omega )=\sigma _{{\rm dc}} +A\omega ^s \end{equation} \tag{ 5 }$$

where σ_dc is the dc conductivity due to excitation of electron from a localized state to the conduction bands, 'A' is pre-exponential factor and 's' is the fractional component (0 ⩽ s ⩽ 1); both 'A' and 's' are temperature and material dependent. The exponent 's' represents the degree of interaction between mobile ions with the lattice and coefficient 'A' determines the strength of polarizability. For random hopping of carriers 's' is equal to zero (frequency-independent conductivity) and tends to approach one as the correlation increases. Figure 5 depicts the frequency dependence of conductivity at various temperatures for all the samples. It is observed that the conductivity remains almost constant at lower frequencies but exhibits dispersion for higher frequencies which is well in accordance with equation (5). The experimental σ(ω) has been fitted by equation (5). A good overlap of the theoretical fitted values with experimental data is observed (figure 5). The values of 'A' and 's' obtained by fitting are listed in table 3. For the sample with x = 0.0 (figure 5(a)), σ(ω) shows temperature- and frequency-dependent behaviour in the whole frequency range. This temperature dependence decreases with an increase in Ti doping. For the sample with x = 0.15 (figure 5(d)), σ(ω) is almost independent of temperature in the whole studied frequency range. From table 3 and figure 5 it is clearly observed that stability of both 'A' and 's' parameters against temperature increase with the increase in Ti doping.

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Figure 6(a) shows the RT M–H hysteresis loops of Bi_0.8La_0.2Fe_1−xTi_xO₃ (x = 0.0, 0.05, 0.1, 0.15) ceramics. It is obvious that non-zero remanent magnetization (M_r) and coercive field (H_c) are observed for all the samples. Magnetization curves were not saturated with the field up to 20 kOe. However, an enhancement in magnetization with the increase in Ti content is observed. Figure 6(b) shows the variation of measured remanent magnetization (M_r) as a function of Ti concentration. M_r is found to increase with the increase in Ti concentration and the corresponding values for x = 0.0, 0.05, 0.1 and 0.15 samples are 0.0048 emu g⁻¹, 0.0119 emu g⁻¹, 0.1373 emu g⁻¹ and 0.1487 emu g⁻¹, respectively. The value of M_r observed in x = 0.0 sample is consistent with the reported value for the same composition of La-modified BFO sample [48]. The appearance of remanent magnetization in Bi_0.8La_0.2FeO₃ (x = 0.0) sample is attributed to the suppression of the spiral spin structure with 20% La doping. However, the spiral spin structure is not completely destroyed with 20% La doping. With 5% Ti doping (x = 0.05), remanent magnetization increases slowly and may be attributed to the collapse of space-modulated spiral spin structure. It is observed from structural analysis that with Ti substitution, FeO₆ octahedron gets distorted and Bi–O, Fe–O bond distances and Bi–O–Fe angles get altered (table 2). The change in the bond lengths and bond angles is known to influence the magnetic properties of oxide systems, having indirect exchange interactions. Sometimes, structural distortion may associate with structural transformation (change in space group) or partial modification or change in bond length between oxygen with A (Bi) and B (Fe) site metal ions. Currently in Bi_0.8La_0.2FeO₃ ceramic, Ti substitution (up to 5%) does not promote any major structural transformations and space group. Only partial change in unit cell volume (R3c symmetry) is observed (table 1). This partial change (reduction) in unit cell volume with Ti substitution may cause internal structure distortion relating to the change in bond lengths between the Bi–O, Fe–O and bond angle of Bi–O–Fe within the defined unit cell volume. With further increase in Ti concentration (x = 0.1), there is a sharp increase in M_r value (figure 6(b)). Structural analysis suggests that for x = 0.1 there is coexistence of rhombohedral and tetragonal phases. Both the bond length and bond angles change drastically from one cell to another in the vicinity of phase boundaries. This drastic structure change may result in a modification on the short range canted G-type antiferromagnetic order of the nearest neighbour Fe³⁺ spins in the rhombohedral structure. This may give a net magnetization (figure 6(a)). For the x = 0.15 sample, the crystal structure transforms from rhombohedral to tetragonal which results in a further increase in M_r. Therefore, Ti substitution (x = 0.1, 0.15) results in structural phase transition wherein the spin cycloid might be destructed and homogeneous spin structure is formed, so that the latent magnetization locked within the cycloid might be released and significant increase in M_r value is observed. The corresponding values of coercive field (H_c) are 1.805 kOe, 2.161 kOe, 4.856 kOe and 5.904 kOe for the x = 0.0, 0.05, 0.10 and 0.15 samples, respectively. The strong coercive force should mainly result from the magnetic anisotropy. The possibility of M_r and H_c values in the present samples whether from destruction of spin cycloid by phase transformation or caused by other factors such as Fe₂O₃ and/or Bi₂Fe₄O₉ impurity phase cannot be ignored. The clarification is as follows: the samples have larger values of coercivities compared with Fe₂O₃ [<100 Oe] [49]. Therefore, it is quite unlikely that magnetization observed is a result of small Fe₂O₃ impurity phase. Also the impurity phase Bi₂Fe₄O₉ observed in the sample with x = 0.15 (figure 1) is paramagnetic at RT with Curie temperature (T_c = 264 K) well below RT, contributes nothing to magnetic properties in the samples at RT. Therefore, an increase in M_r with Ti substitution results from continuous collapse of space-modulated spin structure due to phase transformation of Bi_0.8La_0.2FeO₃ sample from rhombohedral to tetragonal.

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