Influence of La doping on the structural, magnetic, and dielectric properties of sol-gel derived BiFeO₃ thin films

2.1 Materials

Bismuth nitrate (Bi(NO₃)₃.5H₂O) (99.9%, research grade (RG), 10022-31-8), iron nitrate (Fe(NO₃)₃.9H₂O) (99.9%, RG, 7782-61-8) and lanthanum nitrate (La(NO₃)₃.6H₂O) (99.9%, RG, 10277-43-7) were obtained from Sigma-Aldrich. Ethylene glycol (C₂H₆O₂) (RG, 107-21-1) were utilized as a solvent. To clean and etch the substrate, we employed a combination of diluted hydrochloric acid (HCl) (RG, 7647-01-0), acetone (RG, 67-64-0), and isopropyl alcohol (RG, 67-63-0).

2.2 Synthesis detail

The sol-gel process was utilized in order to produce thin films of bismuth iron oxide that were both undoped and doped with lanthanum. 0.1M solution of Bismuth nitrate (Bi(NO₃)₃.5H₂O) and iron nitrate (Fe(NO₃)₃.9H₂O) were employed as precursors, while ethylene glycol (C₂H₆O₂) was utilized as the solvent. Both of these substances were utilized. Before the final sol was synthesized, two solutions were produced. The preparation of Solution A was accomplished by dissolving bismuth nitrate in ethylene glycol at room temperature under constant stirring of 60 min. This was done in order to achieve the desired results. Through the process of dissolving iron nitrate in ethylene glycol, it was possible to successfully complete the creation of Solution B. To obtain bismuth iron oxide sol, solution A and solution B were combined, stirred for 2h, and then cooked on a hot plate at a temperature of 80^oC. The final sol maintained a pH of 2. Previous reports (Ahmed et al., 2013, Riaz et al., 2014) have provided information regarding the sol-gel synthesis. This was done in order to create Bi_1-xLa_xFeO₃ sol, where x = 0.1, 0.2, 0.3, 0.4, and 0.5. 0.1M solution of lanthanum nitrate (La(NO₃)₃.6H₂O) was dissolved in ethylene glycol and then added to the bismuth iron oxide sol.

The next step was to coat copper substrates with Bi_{1- x}La _xFeO₃ sols. The copper substrates were etched for 15 minutes with diluted HCl before deposition. Following multiple rinses with DI water, the substrates were subjected to an ultrasonic bath containing acetone and isopropyl alcohol for a duration of fifteen minutes in order to eradicate any remaining organic contaminants (Shah et al., 2014, Asghar et al., 2006). After that, the cleaned copper substrates were spin coated with sols at 3000 rpm for 20 seconds. The films were left to mature for 24 hours at room temperature before being annealed in a vacuum at 300˚C for 60 minutes using a 500Oe magnetic field. Detailed steps of synthesis can be seen in Fig. 1.

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Fig. 1.

Flow chart for the preparation of thin films.

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To examine the structural properties of Bi_{1- x}La _xFeO₃ thin films, the researchers utilized a Bruker D8 Advance X-Ray Diffractometer (XRD) equipped with a nickel filter and a copper target (Cukα = 1.5406Å). The 7407 Vibrating sample magnetometer (VSM) from Lakeshore was used to examine the magnetic characteristics. A parallel plate setup of the 6500B Precision impedance analyzer was utilized to ascertain the dielectric characteristics of Bi_{1- x}La _xFeO₃ thin films.

3.1 Structural analysis

Thin films of Bi_{1- x}La _xFeO₃ are shown in Fig. 2 by use of XRD patterns. According to JCPDS card number. 86-1518, the presence of diffraction peaks corresponding to planes (024), (116), and (128) suggests that BiFeO₃ has formed a phase pure rhombohedrally deformed perovskite structure. A bismuth-rich sillenite (Bi₂₄Fe₂O₃₉) or bismuth-deficient mullite (Bi₂Fe₄O₉) phase could not be identified. Obtaining phase-pure bismuth iron oxide thin films at a low temperature of 300˚C was previously shown to be influenced by the solvent choice and molar ratio Bi/Fe in sol-gel synthesis (Ahmed et al., 2013, Riaz et al., 2014. It should also be noted that diffraction peaks associated with non-perovskite phases, such as Bi₂O₃ and Fe₂O₃, do not exist. Further evidence that lanthanum has been effectively integrated into the host lattice is the absence of peaks associated with lanthanum oxide, even at a high dopant concentration of 0.5. On top of that, the peak position has moved somewhat toward the high diffraction angles that correspond to planes (024) and (122). Bi³⁺ (1.17 Å) has a wider ionic radius than La³⁺ (1.16 Å). As a result, the XRD peaks move to higher diffraction angles and the unit cell volume decreases. This causes the peak positions to move to higher diffraction angles, as predicted by Bragg’s law (Asghar et al., 2006). Furthermore, the La³⁺ to Bi³⁺ ionic radius ratio is 0.99 (∼1). As a result, it surpasses the threshold for synthesizing interstitial solid solutions, which is 0.59 (Asghar et al., 2006), Cullity, 1957). As a result, lanthanum ions usually end up replacing Bi³⁺ ions at substitutional sites rather than occupying interstitial sites. As the dopant concentration increased, the tolerance factor (Fig. 3) computed using Eq. (1) and (2) (Dhir et al., 2014) fell slightly from 0.8886 to 0.8869, indicating that the likelihood of La³⁺ cations occupying interstitial sites decreased (Riaz et al., 2015). As the concentration of dopants increases, the stiffness between the La³⁺/Bi³⁺-O bonds increases, and the tolerance factor decreases, suggesting that the angle between the Fe-O bonds decreases (Ding et al., 2011). To make it less rigid, an oxygen octahedron is rotated. As the relative angle between nearby octahedrons grows, the host lattice becomes more distorted (Dhir et al., 2014). The substitution of La³⁺ cations for Bi³⁺ cations does not occupy the entire available volume due to the fact that La³⁺ cations have a somewhat smaller ionic radius. The size of the interstices of the oxygen sublattice is reduced as a result of the oxygen octahedron rotating (Riaz et al., 2014). The host lattice becomes more distorted as a result of this.

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Fig. 2.

XRD patterns for Bi_1-xLa_xFeO₃ thin films with dopant concentration (x) as (a) 0.0 (b) 0.1 (c) 0.2 (d) 0.3 (e) 0.4, and (f) 0.5.

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Fig. 3.

Tolerance factor for Bi_1-xLa_xFeO₃ thin films calculated using Eq. (1-2).

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These are the ionic radii of the atoms at the A, B, and oxygen sites, denoted as r_A, r_B, and r_o, respectively. Eq. (2) is used to determine the effective radii of BiFeO₃ when the dopant concentration (x) in the host lattice is altered.

The variables shown in Fig. 4 are plotted as a function of dopant concentration and include crystallite size (D) (Asghar et al., 2006), crystallinity (Das et al., 2016), strain (Asghar et al., 2006), dislocation density (δ) (Reaney et al., 1994), and stacking fault probability (SFP) (Kumar et al., 2011). These values were determined using Eq. (3)-(8).

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Fig. 4.

Effect of La concentration (x) on (a) crystallite size and crystallinity, (b) strain and dislocation density, and (c) stacking fault probability for Bi_1-xLa_xFeO₃ thin films.

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The variables mentioned are the wavelength (1.5406Å), full breadth at half maximum (B), diffraction angle (θ), and change in d-spacing (Δd). As the dopant was introduced into the host lattice (x = 0.1), the size of the crystallites increased from 23.5 nm in undoped BiFeO₃ thin films to 25.8 nm, as shown in (Fig. 4a). The size of the crystallites rose to 28.3 nm when the dopant concentration was raised to 0.3. As the dopant concentration was increased to 0.4 and 0.5, the size of the crystallites decreased. A full dissolution of the dopant atoms in the host lattice is suggested by an increase in crystallite size at a low doping level (Reaney et al., 1994). At high dopant concentrations (x = 0.4, 0.5), however, the likelihood that dopant atoms reside on grain boundaries and/or occupy interstitial locations rises. Decreased crystallinity and, by extension, smaller crystallites, are symptoms of the atomic disorder that will eventually lead to their disintegration (Fig. 4a) (Chen et al., 2005). Furthermore, these atoms cause an increase in dislocation density at high dopant concentration Fig. (4b) and disrupt the stacking sequence in thin films (Fig. 4c). A decrease in dislocations and an increase in the diffusion of lanthanum atoms into the BiFeO₃ lattice are both predicted to occur at low dopant concentrations (Fig. 4b). As seen in Fig. 4(b), all of the lanthanum atoms settle on the film’s dislocations, which results in a decrease in strain (Akbar et al., 2014). Additionally, strain energy and neighboring grains with different energies owing to curvature of grain borders are the two main factors that determine grain formation in thin films (Jeetendra et al., 2014).

The “Powder Cell Software” was used to find and fine-tune the lattice parameters. Tables 1 and 2 show the refined data collected using the “Powder Cell Software” as well as the x-ray density and porosity of the Bi_{1- x}La _xFeO₃ thin films. Because lanthanum has a smaller ionic radius than bismuth, the unit cell volume and lattice parameters both decreased with increasing dopant concentration. The density of the films is enhanced as a result of a reduction in unit cell volume. Thick Bi_{1- x}La _xFeO₃ films have a compact structure, as seen by their high density. The XRD pattern in Fig. 2 shows that doping BiFeO₃ with La did not change its structure, but it does affect structural factors (see Fig. 4 and Table 2), which influence the material’s dielectric and magnetic characteristics.

3.2 Dielectric and impedance analysis

Under a parallel plate configuration, the 6500B Precision impedance analyzer was used to measure resistance and capacitance. After that, we used Eqs. (9 and 10) to find the dielectric constant and the tangent loss (Riaz et al., 2007).

The capacitance is represented by C, the film thickness by d, the area by A, the permittivity of free space by ε_o, and the resistivity by ρ. Fig. 5 shows the diagram of the Bi_{1- x}La _xFeO₃ thin films’ dielectric constant and tangent loss. As the frequency of the applied external field increases, the dielectric constant and tangent loss both drop until they reach a constant value at very high frequencies. Grain and grain boundary density is high in polycrystalline films. The conductivity of grains is higher than that of grain borders. Electrons travel through the grain and eventually reach its limits through a process known as hopping. Grain polarization occurs when electrons accumulate at grain borders, which have a higher resistance than grains themselves. When an external field’s frequency changes, the electrons’ velocity is flipped. The likelihood of electrons reaching the grain boundaries diminishes at high frequencies due to this reversal. At high frequencies, this causes the dielectric constant to drop because the polarization decreases (Zhang et al., 2016, Cullity, 1957, Pandey et al., 2019).

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Fig. 5.

(a) Dielectric constant, (b) tangent loss for Bi_1-xLa_xFeO₃ thin films.

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Fig. 6 shows the relationship between dopant concentration and the dielectric constant and tangent loss. Dopant concentrations ranging from 0.0 to 0.3 resulted in an increase of the dielectric constant from 36.8 to 287 (log f = 5.0). The dielectric constant dropped to 186 (log f = 5.0) as the dopant concentration was raised to 0.5. A thin film’s dielectric constant can be significantly altered by changes in crystallite/grain size, grain boundaries, and stress levels across the film (Ismail et al., 2012). Reductions in internal stresses and dislocations were seen as the size of the crystallites increased from 23.5 nm to 28.3 nm (Fig. 4a). The creation of 180˚ domains becomes more likely, leading to a rise in the dielectric constant. Partial clamping of domain wall motion occurs at high dopant concentration owing to large dislocations and strains Fig. 4(b), resulting in a drop in dielectric constant and an increase in tangent loss (Cullity, 1957, Ismail et al., 2012). More stable than Bi³⁺-O^2- bonds, La³⁺-O^2- bonds have also been found before. This lessens the amount of oxygen vacancies and helps decrease the volatile nature of Bi cations during annealing (Azam et al., 2015). Furthermore, as the dopant concentration increases, the oxygen vacancies decrease, leading to a rise in the dielectric constant and a decrease in the tangent loss (Yu et al., 2008). Nevertheless, it is anticipated that lanthanum substitution in the BiFeO₃ lattice reduces the lone pair activity of bismuth cations, which mostly causes ferroelectric deformation, at high dopant concentrations (x > 0.3). As a result, the dielectric constant drops because the contribution from dipolar polarization is reduced (Yu et al., 2008).

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Fig. 6.

(a) Dielectric constant (b) tangent loss for Bi_1-xLa_xFeO₃ thin films plotted as a function of dopant concentration (x).

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Fig. 6(a) adds to the picture by comparing the dielectric characteristics of Bi_{1- x}La _xFeO₃ thin films to those in the literature. Compared to what is described in the literature, the dielectric constant of Bi_{1- x}La _xFeO₃ thin films is high.

Fig. 7 illustrates the real impedance (Z’) and the imaginary impedance (Z’) for thin films composed of Bi_1-xLa_xFeO₃. Fig. 7(a) demonstrates that the value of Z’ does not change in the low frequency area, where the logarithm of f is less than 4.0 (log f < 4.0). This indicates that polarization effects are dominant and the resistive component is frequency-independent in this range (Kumar et al., 2015, Jiang et al., 2006). As the frequency of the applied field increases in the intermediate frequency zone (2.0 < log f < 6.0), Z’ falls. However, in the high frequency region (log f > 6.0), Z’ remains constant. The rise in conductivity gives birth to this frequency-independent zone of Z’. However, in the low frequency range (log f < 4.0), Z’’ grows with the applied field frequency, reaches its maximum value (Z’’max), and then declines in the high frequency range. As seen in Fig. 7(b) and Fig. 6(b), the tangent loss decreases and the relaxation time increases when the dopant concentration increases to 0.3. This is in accordance with previous observations (Singh et al., 2007) and the data

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Fig. 7.

(a) Real impedance (b) Imaginary impedance for Bi_1-xLa_xFeO₃ thin films plotted as a function of log f.

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A potent tool for understanding the heterogeneity of polycrystalline specimens is impedance spectroscopy. Cole-Cole plots (-Z’’ vs. Z’) are shown in Fig. 8 for the purpose of understanding the function of grain and grain boundaries. Thin films of Bi_1-xLa_xFeO₃ show an increase in resistance and a decrease in leakage current as the curvature of the Cole-Cole curves increases up to 0.3 dopant concentration. The Z-view program was then used to fit these Cole-Cole layouts. You can observe the comparable circuit model utilized for fitting in Fig. 8(b) for undoped BiFeO₃ thin films. The bulk response is clearly more prominent in the Cole-Cole plots of La-doped BiFeO₃ thin films than the grain boundary or electrode interface contribution, which is negligible. It is possible that a slight curvature will occur at low frequencies as a result of weak interfacial polarization. However, this curvature will continue to be greatly reduced in comparison to the counterpart that has not been doped, which is evidence that the insertion of La improves microstructural homogeneity and charge transport. Consequently, the thin films of doped BiFeO₃ were fitted with the equivalent circuit model shown in Fig. 8(c). In Table 3, you can see the Z-view fitting parameters. As the dopant concentration (x) was raised to 0.3, the grain boundary resistance rose from 53.11 kΩ to 179.23 kΩ. The buildup of space charge carriers at grain borders is caused by an increase in grain boundary resistance (Cullity, 1957). As shown in Figs. 5(a) and 6(a), the dielectric constant increases as a result of this accumulation.

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Fig. 8.

(a) Cole-Cole plots for Bi_1-xLa_xFeO₃ thin films. (b) Equivalent circuit model defined for undoped BiFeO₃ thin films fitting of Cole-Cole plots using Zview software (c) Equivalent circuit model for fitting La-doped BiFeO₃ thin films: R_g is grain resistance, R_gb and CPE_gb are grain boundary resistance and constant phase elements, C_gb is grain boundary capacitance, and R_i and C_i are interface region resistance and capacitance.

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The conductivity of BiFeO₃ thin films was determined using Eq. (11) (Behera et al., 2014) in order to study the effect of dopant on electronic conduction.

See fig. 9 for a plot of the conductivity of Bi_1-xLa_xFeO₃ thin films vs. log f. Fig. 9 shows two separate areas. The first, known as Region I, is direct current (d.c.) conductivity and is associated with free charge carriers; the second, known as Region II, is ac (alternating current) conductivity and is caused by bound charges (Patri et al., 2008). An increase in conductivity occurs at high frequencies as a result of charge carriers hopping between potential wells. Eq. (12) of Jonscher’s Power Law (Pandey et al., 2019) provides an explanation for the frequency-dependent conductivity.

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Fig. 9.

Conductivity for Bi_1-xLa_xFeO₃ thin films as a function of log f.

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In this context, _d.c. is the direct current conductivity, n is the frequency exponent proportional to the interaction between the lattice and mobile ions, ϋ denotes the frequency, and A is the constant proportional to the specimen’s strength of polarizability. Fig. 9 was fitted using Jonscher’s Power Law (Eq. 12). The contribution from direct current (d.c.) conductivity is indicated by a value of zero for “n,” while a value smaller than one is used to refer to a.c. conductivity (Jamal et al., 2011). The fact that “n” is less than 1 for Bi_1-xLa_xFeO₃ thin films suggests that the charge carriers are moving in a translational fashion and that there is hopping happening at the grain boundaries (Sharif et al., 2016).

From these findings, a temperature-dependent impedance analysis was performed within the 30˚C-210˚C temperature range to further assess the impact of the dopant on electrical properties. Fig. 10 shows the relationship between temperature and the dielectric constant and tangent loss. As the temperature is raised from 30˚C to 210˚C, the dielectric constant Fig. 10(a) increases. The dielectric constant increases at low temperatures (between 30˚C and 90˚C) at a very slow rate as the temperature increases. At low temperatures, dipoles contribute less to polarization, which causes this phenomenon to occur (Pattanayak et al., 2013). The amount of free dipoles that contribute to polarization is increased in the high temperature area (>90˚C) by the thermal energy. Applying an electric field at high temperatures causes the dipoles to better align with the field, which in turn increases the dielectric constant. Also, as temperature rises, charge carriers are more mobile. As a consequence, the dielectric constant rises as more charges build up near grain boundaries. As the temperature rises, the tangent loss increases Fig. 10(b) due to a rise in space charge polarization, which in turn increases conductivity (El-Desoky et al., 2016).

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Fig. 10.

(a) Dielectric constant, (b) Tangent loss as a function of temperature for Bi_1-xLa_xFeO₃ thin films.

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Fig. 11(a) shows the temperature effect on Z’, while Fig. 11(b) shows the same thing for Z’’. Z’ becomes frequency independent in the high frequency zone (log f > 6.5), however, it decreases as the frequency increases (log f < 6.5). The emission of space charge carriers causes Z’ to merge at high frequencies within the temperature range that was examined (Benali et al., 2015). Contrarily, Z’’ grows at low frequencies, peaks at Z’’_max, and then drops off sharply at high ones. As a result of the buildup of space charge carriers, Z’ merges at all temperatures at high frequencies (Benali et al., 2015). Fig. 11(b) shows that as the temperature is raised from 30˚C to 210˚C, the thermally induced relaxation process in thin films is indicated by a shift to higher frequencies and a broadening of the peak. Due to immobile charges at low temperatures and the existence of vacancies and flaws at high temperatures, the relaxation process is believed to occur (Benali et al., 2015). As shown in Fig. 10(b) for the resistive property of La doped BiFeO₃ thin films, there is a drop in both Z’ and Z’’, which indicates negative temperature coefficient behavior (Benali et al., 2015).

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Fig. 11.

(a) Real impedance (b) Imaginary impedance for Bi_1-xLa_xFeO₃ thin films in the temperature range of 30˚C-210˚C.

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Fig. 12 displays the temperature dependence of Cole-Cole plots for La doped BiFeO₃ thin films with a dopant concentration (x) of 0.3. The temperature-dependent Cole–Cole plots and AC conductivity measurements were carefully investigated for the x = 0.3 composition. This particular sample demonstrated the most stable impedance response with clear semicircular arcs, which made it possible to accurately fit and evaluate the data. Other doped compositions, on the other hand, exhibited overlapping arcs, unstable fitting parameters, and high noise in the low-frequency domain, all of which contributed to the limited accuracy of thermal relaxation analysis. This led to the selection of x = 0.3 as the optimal composition for the purpose of representing the intrinsic conduction and relaxation mechanisms of La-doped BiFeO₃ thin films. As the temperature is raised from 30˚C to 210˚C, the diameter of the semicircle in a Cole-Cole plot decreases, suggesting that the films’ resistance lowers and their conductivity increases with temperature. Fig. 8(c) shows the analogous circuit model that was used to fit these curves in Z-view software. Table 4 displays the results of the Z-view fitting. Thin films of La-doped BiFeO₃ exhibit negative temperature coefficient behavior, as seen by the reduction in resistance at the grain and grain border (Benali et al., 2015).

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Fig. 12.

Cole-Cole plots for Bi_1-xLa_xFeO₃ thin films with dopant concentration (x) as 0.3.

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Fig. 13(a) shows the conductivity of Bi_0.7La_0.3FeO₃ thin films from 30˚C to 210˚C. Conductivity is independent of frequency at low frequencies (log f < 4.5), suggesting that free charge carriers, or d.c. conductivity, are involved. The presence of tiny polarons that hop from one potential well to another is indicated by an increase in conductivity at high frequencies (log f > 4.5) (Rout et al., 2015, Kumar et al., 2014). Fig. 13(a) displays the parameters that were fitted to the conductivity data using Jonscher’s Power Law (Eq. 12). Quantum mechanical tunneling (QMT), correlated barrier hopping (CBH), and overlapping large polaron tunneling (OLPT) are three models that explain how “n” changes with temperature. For the QMT model, “n” is temperature independent. In the OLPT model, “n” reaches a minimum as temperature increases, whereas in the CBH model, “n” decreases as temperature increases (Sharma et al., 2014). According to the CBH model and previous research (Da Silva et al., 2011), as shown in Fig. 13(a), the value of “n” drops as the temperature rises from 30˚C to 210˚C. Fig. 13(b) displays the Arrhenius plot for conductivity. In Fig. 13(b), we may observe an Arrhenius plot with a straight line representing the activation energy (E_a). Activation energies vary in frequency from 1.82 eV to 2.38 eV. When compared to the usual ionization energy of around 1 eV, which is involved in the movement of doubly ionized oxygen vacancies, these values are significantly higher (Kolte et al., 2015). The activation energy for perovskite structures (ABO₃) that do not contain oxygen vacancies is approximately 2.0 eV, as stated in references (Shah et al., 2014, Chybczyńska et al., 2016). As demonstrated in reference (Shah et al., 2014), the activation energies of ABO_2.95, ABO_2.9, and ABO_2.8 perovskite structures are reduced to 1.0 eV, 0.5 eV, and 0 eV, respectively. The successful suppression of oxygen vacancies by lanthanum doping, as shown by the high activation energy in our instance (Fig. 13(b)), will result in a significant reduction in the leakage behavior of BiFeO₃ thin films.

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Fig. 13.

(a) Conductivity for Bi_0.7La_0.3FeO₃ thin films in the temperature range 30˚C-210˚C (b) Arrhenius plot for conductivity at various frequencies.

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3.3 Magnetic analysis of Bi_1–xBa_xFeO₃ thin films

The magnetic characteristics of Bi_1-xLa_xFeO₃ thin films were tested at room temperature following a thorough impedance study. Thin films of Bi_1-xLa_xFeO₃ are shown in Fig. 14(a) by means of M-H curves. Thick films of BiFeO₃ that have been doped with La or not exhibit ferromagnetic properties. The relationship between saturation magnetization and coercivity and dopant concentration (x) is seen in Fig. 14(b). As the dopant concentration was raised from x= 0.0 to 0.3, the saturation magnetization rose from 58.5 emu/cm³ to 136.75 emu/cm³. The magnetization dropped to 24.75 emu/cm³ as the dopant concentration was raised to 0.5. In bulk BiFeO₃, the magnetic moments of iron cations are said to be coupled ferromagnetically within the same planes, but they interact antiferromagnetically with the spins of neighboring planes, a phenomenon known as G-type antiferromagnetic behavior. When the spiral spin structure is suppressed, ferromagnetic behavior can emerge in BiFeO₃, which would normally exhibit antiferromagnetic behavior (Majid et al., 2015, Riaz et al., 2015, Yu et al., 2008). Undoped BiFeO₃ exhibits ferromagnetic activity with a high saturation magnetization of 58.5 emu/cm³ because its crystallite size is less than that of BiFeO₃’s cycloidal spin structure, which is 62 nm (Fig. 4(a). Saturation magnetization grows when the La concentration (x) approaches 0.3 because: 1) The substitution of La³⁺ cations for Bi³⁺ cations causes lattice deformation. A change in canting angle due to Fe-O-Fe bonding occurs as a result of this (Tamilselvan et al., 2014). 2) Magnetic sublattice: The structure develops magnetic sublattices connected with La^- and Fe^- as Bi³⁺ cations are replaced by La³⁺ cations. The enhanced magnetization is a result of the ferromagnetically connected La- and Fe-sublattices (Tamilselvan et al., 2014); 3) The suppression of the cycloidal spin structure by the substitution of La releases the net magnetic moment that was locked within the structure, resulting to enhanced magnetization (Yu et al., 2008).

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Fig. 14.

(a) M-H curves for Bi_1-xLa_xFeO₃ thin films. (b) Saturation magnetization and coercivity plotted as a function of dopant concentration (x).

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As the thickness of BiFeO₃ thin films reaches 200 nm, ferromagnetism becomes apparent (Kim et al., 2013, Martin et al., 2008), but the films typically display antiferromagnetic or ferromagnetic characteristics. In accordance with what was anticipated, the ferromagnetic characteristics of thin films composed of BiFeO₃ improve as the concentration of La increases (Son et al., 2025, Lazenka et al., 2012, Fan et al., 2014). It is important to note that the remanent magnetization and saturation magnetization of BiFeO₃ thin films greatly improved once the concentration of La doping was increased. This enhancement in ferromagnetic properties can be attributed to two primary factors: first, the alteration of the out-of-plane oriented lattice constant, which is caused by La doping, which disrupts the antiferromagnetic spin spiral structure; and second, the formation of Fe³⁺ ions, which is also caused by La doping, which further aids in enhancing ferromagnetism (Son et al., 2025, Lazenka et al., 2012, Fan et al., 2014). As a result of the creation of Fe³⁺ ions brought about by La doping, the remaining portion is brought about by the rupture of the spin spiral structure. To put it another way, La doping boosts ferromagnetism by causing the spin spiral structure to be disrupted. This is accomplished through the production of Fe³⁺ ions and an increase in the out-of-plane lattice constant (Son et al., 2025, Lazenka et al., 2012, Fan et al., 2014).

Recent research have thoroughly investigated the magnetic strengthening of BiFeO₃ by diverse doping techniques; nonetheless, many have specific limits in attaining robust and stable magnetic properties appropriate for device applications. Using the sol–gel process, Sharma et al. (2025) were able to synthesize Co-doped BiFeO₃ powders and found increased magnetic moments as a result of lattice distortion. However, the materials suffered from non-uniform magnetic domains, high leakage, and instability at rising temperatures, which limited their practical application. Furthermore, Xu et al. (2023) published a report on thin films of BiFeO₃ that were co-doped with Gd and Co. These films displayed a considerable magnetic enhancement (M_s = 62 emu/cm³), but they also exhibited phase defects and restricted remanent magnetization. This indicates that it was challenging to achieve uniform spin ordering and sustained magnetoelectric coupling. According to Hu et al. (2016), the magnetic characteristics of BiFeO₃ thin films were significantly improved with La inclusion (x = 0.3) by enhancing crystallinity and suppressing the spin cycloid. Partial stabilization of ferromagnetism was confirmed by the greater remanent and saturation magnetization shown by the doped samples compared to the undoped films. The films still showed weak magnetic switching capabilities and relatively low coercive forces, hence the improvement was scale limited. Furthermore, because structural flaws and oxygen vacancies were not completely eliminated, dielectric losses and leakage current continued that impeded the proper operation of ferroelectric and magnetic materials. Alternatively, this study uses a sol-gel derived thin film method with controlled La doping (x = 0.0-0.5). This method stabilizes the perovskite structure, suppresses oxygen vacancies, and significantly increases the saturation magnetization (up to ≈136.75 emu/cm³) without bringing dielectric integrity into compromise. This comprehensive study provides a more stable and adjustable route for creating multifunctional thin film devices based on BiFeO₃ by establishing a stronger relationship between dopant concentration, structural distortion, and magnetic enhancement. The current study improves magnetic homogeneity and decreases leakage, showing that BiFeO₃ thin films’ multiferroic performance is enhanced by optimal La inclusion.

In order to delve deeper into the impact of La doping on the magnetic characteristics of the BiFeO₃ lattice, particularly coercivity, it is essential to consider magneto crystalline anisotropy. Eq. (13) (Lin et al., 2014, Peng et al., 2015) models the magneto crystalline anisotropy field (H_k) as a function of the first-order magneto crystalline anisotropy constant (K_u1).

The saturation magnetization is denoted by Ms. Eq. (13) shows that the anisotropy field and, by extension, the coercivity, are determined by K_u1/Ms. The coercivity is also significantly impacted by grain size, which is proportional to the size of the individual domain. Coercivity is inversely proportional to grain size when the grain is multi-domain. On the other hand, if the grain only has one domain, the coercivity drops with smaller grains. The precise calculation of M_s was accomplished by using the Law of Approach to Saturation (Eq. (14)) (Lin et al., 2014, Peng et al., 2015) to the process of determining K_u1 for Bi_1-xLa_xFeO₃ thin films.

A and B are constants that are connected to the contributions of micro-stresses and magneto crystalline anisotropy, respectively, whereas χH represents the forced magnetization that is caused by the applied field. Eq. (15) gives the magneto crystalline anisotropy for a system of hexagonal crystals (Lin et al., 2014, Peng et al., 2015).

Fig. 15 shows a straight line for high fields when plotting magnetization and 1/H². This means that the contributions of micro-stresses and the magnetization terms in Eq. (14) are very small. K_u1 is the slope of the straight line that yields saturation magnetization, which is obtained by extrapolating it from 1/H²∼0. To have a better understanding, we used Eqs. (16 and 17) to find the size of a single domain (d) (Lin et al., 2014).

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Fig. 15.

Magnetization plotted against 1/H².

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The domain wall energy density is denoted by γ, and the exchange stiffness is governed by the constant A, which has a value of 4.1×10^-7 erg/cm. Table 5 lists K_u1 and the size of a single domain. As the dopant concentration increased to 0.3 and the coercivity of the Bi_1-xLa_xFeO₃ thin films increased, it is observed that M_s increases as the contribution from magneto crystalline anisotropy (K_u1) decreases.

Table 6 shows the results of comparing the saturation magnetization of Bi_1-xLa_xFeO₃ thin films with the literature. Compared to what is reported in the literature, our saturation magnetization is clearly higher.

3.4 SPV measurements

Surface work function (WF) is able to accurately describe the condition of the surface in a very effective manner because of the mobility of electrons. WF is connected to the movement of charge carriers at the interface and surface; this connection is interconnected (Tahir et al., 2019). The WF has an effect on the defects, surface states, and combination of the material. We are now in a stage where we are able to explore the electrical structure of surfaces in a variety of ways, such as adhesion, photovoltaic response of surface, and surface corrosion, all of which can be described with the assistance of kelvin probe surface photovoltage spectroscopy (Tahir et al., 2019, Lin et al., 2023). The Kelvin probe is a straightforward method that can be utilized to ascertain the WF of the materials. WF is calculated using the vibrating tip method, and the equation for defining the contact potential difference (V) is found in Eq. (18).

where the WFs of the probing tip are represented by ${\phi }_t$ and the sample by ${\phi }_s$. The formula for calculating the voltage of a parallel plate capacitor is V = $\frac{e}{C}$ and C = $\frac{{}_{o}A}{d}$. Here, C, ε, A, and “d” represent capacitance, dielectric constant, area of the plate capacitor, and the distance between the sample and the tip, separately (Tahir et al., 2019). Therefore, the WF of the sample can be determined by applying Eq. (19).

The application of an external voltage, which is referred to as the backup potential (V_b), is what determines the difference in WF. For thin films of Bi_{1– x}Ba _xFeO₃, scanning Kelvin measurements showing WF are shown in Fig. 16. Increases in barium concentration from 0.1 to 0.3 result in an increase in the average WF of thin films composed of Bi_{1– x}Ba _xFeO₃, which goes from 4.65 eV to 5.80 eV. The premise that higher dielectric strength and lower conductivity are the result of reduced carrier concentration is unquestionably strengthened by this convincing evidence.

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Fig. 16.

Work function analysis for Bi_1-xLa_xFeO₃ thin films with dopant concentration (x) as (a) 0.1, (b) 0.2, (c) 0.3, (d) 0.4, (e) 0.5.

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