Tunable multifunctionality in BaTiO₃–La_0.835Na_0.165MnO₃ composites: from UV-to-visible light absorption and nonmagnetism to room-temperature ferromagnetism

Abstract

The composites of ferroelectric BaTiO₃ and ferromagnetic La_0.835Na_0.165MnO₃, denoted as (1−x)BaTiO₃:(x)La_0.835Na_0.165MnO₃ (x = 0, 10, 20, 30, 50, 100 wt%), were prepared using the conventional solid-state reaction method. This work investigates the effect of magnetic inclusion in a nonmagnetic matrix. The synthesized nonmagnetic BaTiO₃ majorly crystallized in a ferroelectric tetragonal structure belonging to the P4mm space group, while the magnetic inclusion La_0.835Na_0.165MnO₃ exhibited phase segregation into a rhombohedral lattice belonging to the R3̄c space group and a monoclinic lattice belonging to a La_0.9MnO₃-like deficient structure of the I12/a1 space group. The resulting composites were immiscible solid solutions composed of Ti-deficient BaTiO₃ and A-site-deficient La_0.835Na_0.165MnO₃. BaTiO₃ and La_0.835Na_0.165MnO₃ were morphologically distinct, with contrasting grain sizes and distributions. Composites showed a loosely bound immiscible grain distribution. The mixing of a nonmagnetic insulator and a ferromagnetic metal/semiconductor endowed the composites with unique optical properties. The band gap was effectively tuned from the ultraviolet to the visible region of the electromagnetic spectra. The composites exhibited a large Urbach energy. BaTiO₃ in its non-stoichiometric form was found to be a weak ferromagnet at room temperature and exhibited spin-glass-like frustration at low temperatures. La_0.835Na_0.165MnO₃ showed a double magnetic transition due to structural phase segregation. The composites showed robust ferromagnetism at room temperature, inheriting it from the magnetic component La_0.835Na_0.165MnO₃. The salient ferroelectricity of BaTiO₃ disappeared in the composites due to large leakage currents. However, at low bias voltages, a leaky ferroelectric nature with ferromagnetism existed at room temperature for the x = 10% specimen, making it a photosensitive, multiferroic, magnetoelectric composite oxide suitable for room-temperature applications.

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1. Introduction

Multiferroic materials are a class of condensed-matter systems with two or more switchable ferroic ground states, such as ferromagnetic (FM), ferroelectric and (FE) ferroelastic (FEL).¹ Recently, there has been increased attention towards multiferroic materials, especially for magnetoelectric (ME) materials, in which an electric field controls the magnetic polarization and vice versa.² The escalation in the attempts to obtain such materials is rooted in a developing new area called versatile memory devices due to their unparalleled efficiency while reading and writing of data.³ The current-driven magnetization switching needs charge mobilization, which comes at the cost of Joule heating, energy dissipation and excessive power consumption. In contrast, the energy dissipation in electric field switching is very low, (reduced by an order) due to charging/discharging process. Ideally, the control of magnetism by the electric field can significantly enhance the non-volatile functionality of memory devices and reduce switching power. In ME materials, the electric field is coupled to magnetization or the magnetic field is coupled to electric polarization. Therefore, they can achieve low-power, high-density data storage with swift electrical writing and magnetic reading. Other than these next-generation memory devices, many other applications exploit ME coupling as their working principle, namely, AC and DC magnetic-field sensors, gyrators for voltage gain, ME transformers, and current sensors. The ME effect can also be employed in microwave devices like resonators, phase shifters and filters.⁴

It is very rare to have a single material that exhibits ME at room temperature (RT). This rarity is arises from the intrinsic nature of materials, where the coexistence of FE and FM can vanish when magnetic order is developed and vice versa. This lies at the core of the matter where the former requires filled orbitals in atoms, and the latter requires unfilled orbitals.⁵ Thus, to enhance the availability of new ME materials, several fabrication alternatives have been explored. This includes the substitution of different magnetic or nonmagnetic ions at an appropriate site in FE and FM materials or the fabrication of a ferromagnetic/ferroelectric superlattices and heterostructures. The disadvantage of superlattices or heterostructures is that they show substrate clamping effect, which has an undesirable effect on ME coupling; nevertheless, they provide a clean single-crystalline structure.⁶ A simple way to obtain ME material is to develop a solid solution in the form of bulk or nanostructured composites and multiphase materials. Composites composed of FE and FM constituents, preferably having a similar structure, offer improved phase connectivity between the constituent phases. Furthermore, size reduction can offer a large surface area for interactions, and the core–shell structure can enhance the ME effect through better mechanical coupling between the constituent phases.⁷ In such composites (bulk/nano), preferably with FE and FM ground states, ME coupling can arise from the interplay of piezoelectricity and magnetostriction, or from charge-carrier modulation in the ferromagnetic phase via the so-called as field effect.⁸ Because the preparation of bulk solid-solution composites of two distinct ferroic materials is easy and economical, it is practical to consider a prototype FE material, like barium titanate (BTO), and an FM material, such as colossal magnetoresistance (CMR) manganites or ferro-/ferrimagnetic oxides, as parent composition for composites.

BaTiO₃ is an outstanding ferroelectric and piezoelectric material that is widely employed in piezoelectric transducers, high-permittivity capacitors and infrared detectors.⁹ BTO is also employed in water splitting and wastewater treatment for degrading the water pollutants, such as dyes, due to its tunable bandgap (E_g) in the ultraviolet (UV) region.^10–13 It exhibits a vivid temperature-dependent crystal structure and correspondingly varying dielectric properties. BTO has a paraelectric cubic structure (<393 K) belonging to the Pm3̄m space group (SG). A phase transition occurs below 393 K to a tetragonal lattice (SG: P4mm), which is a polar phase responsible for the emergence of FE in BTO. This phase sustains up to 278 K, below which further phase transitions occur to orthorhombic and, at <183 K, rhombohedrally distorted structure, both of which are also FE. The abrupt distortion of the crystal lattice at 393 K is responsible for spontaneous polarization, P_s = 18 µC sm⁻², which then increases to 26 µC sm⁻² at RT.^14–17 In fact, the physical quantities such as the large electric polarization, high piezoelectric coefficient and tunable wide band gap make BaTiO₃ a truly multifunctional material. However, pure BTO is diamagnetic, and thus it is unattractive for magnetoelectric functionality.¹⁸ There were several attempts to improve the ME effects in BTO, such as the substitution of Ti⁴⁺ and Ba²⁺ with magnetic ions or the fabrication of FE/FM heterostructures. However, forming composites of BTO with another FM perovskite appears to be a simple and viable option.

Mixed-valent rare-earth manganites (MVMs) are one such oxides that display a robust ferromagnetic metallic (FMM) ground state. Hole or electron doping in these materials induces mixed valency, which is responsible for the FMM behavior. Depending on the percentage of substitution, MVMs display distinct magnetic and electrical ground states,^19–22 and hence they have been exploited in various applications such as magnetic field sensors, temperature sensors, gas sensors, electric field sensors, spin transistors, spin valves, p–n junctions, field-effect devices, capacitors, and energy storage devices.²³ The most intriguingly and vastly studied property of MVMs is magnetoresistance (MR).²⁴ Manganites have also been explored in their composite forms with other oxides, metals, and polymers for applications in magnetoresistance, magnetocaloric effects and their optical activity. In this context, due to the stable RT FMM state of MVMs, they appear as an appropriate candidate for forming composites with BTO to realise a stable ME material. Both barium titanate and manganites possess perovskite structure, so that maximum compatibility between the constituent phases can be achieved; meanwhile, the starting material and synthesis procedure are easy and economical.^25,26 To narrow down a manganite precursor from a vast array of compositions, one must choose a material with a magnetic transition temperature (T_C) at or above RT and a formation temperature comparable to that of BTO. In a given set, MVMs with a 67 : 33 Mn³⁺ to Mn⁴⁺ ratio exhibit the maximum possible T_C. Thus, amongst the possible choices, La_0.835Na_0.165MnO₃ (LNMO), with a T_C of 343 K,²⁷ can be a starting material for composite formation.

Due to the similar structure of BTO and LNMO, and the close ionic radii and valence states of the elements involved in the composites, the formation of stable composite specimens with improved magnetic properties is quite expected.²⁸ Apart from achieving multiferroicity, nowadays, researchers also focus on how to obtain large MR and magnetocaloric effects (MCEs) at low magnetic fields and at RT for practical applications.²⁹ MR can arise from intrinsic effects as well as extrinsic effects. Intrinsic effects, being universal and material-independent, offer less freedom for tailoring. However, extrinsic MR is commonly attributable to grain-boundary (GB) effects related to the natural and artificial GB. This extrinsic MR is ascribed to the spin-polarised inter-grain tunnelling of conduction electrons. If a composite is formed in such a way that one of the constituents is an insulator, it might adjust the tunnelling barrier and act as a pinning centre for domain-wall displacement. Thus, a small applied magnetic field is sufficient to align neighbouring ferromagnetic grains to enhance the magnetoresistance.^28,30–33 Another major issue in MCE materials is their narrow range of working temperature (T_FWHM) around the T_C. Materials with large entropy changes show sharp phase transition, limiting the T_FWHM to few kelvins around the T_C (< 10 K). Composites essentially extend the magnetic transition range through interfacial exchange coupling, strain effects, diffusion and grain-scale inhomogeneity, thus improving T_CFWHM. Furthermore, the visible and near-infrared band gap of manganites may tailor the ultraviolet band gap of BTO to enable visible range optical activity, which is an attractive feature for photovoltaic applications (e.g., photoelectrochemical water splitting) and photocatalysis (dye degradation). Thus, with these motivations, the composites of BTO and LNMO with compositions (1 − x)BTO:xLNMO in the bulk form were prepared to investigate their structural, optical, magnetic and ferroelectric properties, with the aim of tuning the E_g towards the visible side of the EM spectrum and realizing a ferromagnetic ground state in the composites.

2. Materials and methods

The synthesis of composite materials, consisting of varying percentages of BaTiO₃ and La_0.835Na_0.165MnO₃, with compositions denoted as (1 − x)BTO:xLNMO (where x ranges from 0 to 100%; samples are code as BL0, BL10, BL20, BL30, BL50, and BL100), were achieved through a two-step solid-state reaction process. Precursors such as highly pure (Sigma Aldrich, powders, >99.5% trace metals basis) La₂O₃, Na₂CO₃ and MnO were weighed in a stoichiometric ratio of 0.835 : 0.165 : 1 and ground. Isopropyl alcohol (IPA) was used as the wet medium for grinding. The resulting mixture was dried and then calcined at 800 °C for 12 hours in three cycles. The resulting mixture was pressed into pellets and sintered at 950 °C for 12 hours. Similarly, BaTiO₃ was prepared by weighing BaCO₃ and TiO₂ in a 1 : 1 ratio and mixing them using the same procedure as for the manganite. The mixture was calcined at 1200 °C for 4 hours in three cycles. The resulting powder was pressed into pellets and sintered at 1300 °C for 4 hours.

The second step involved processing the pellets obtained from the first step into a fine powder. The crushed powders were weighed in stoichiometric proportion, ground using an agate mortar and pestle in a wet medium containing IPA, dried, and then ground a second time with polyvinyl alcohol (PVA) as a binder. The resulting solid solution was pressed into rectangular pellets and sintered at 950 °C for 4 hours.

To investigate the structure of the prepared specimens, XRD patterns were recorded using a Bruker D2 phaser powder X-ray diffractometer (angular accuracy of ±0.02° and minimum step size of 0.005°). Morphology and elemental compositions were traced using a ZEISS Ultra-55 field-emission scanning electron microscope (lateral resolution of 1.0–4.0 nm at 15–0.1 kV, with typical accuracy <1 nm). Elemental composition and chemical states were analyzed using a Trmo scientific K-alpha X-ray photoelectron spectrometer (Al K-alpha source, energy resolution of ∼0.5 eV and accuracy of ±0.1–0.2 eV). Optical characters were studied using a PerkinElmer Lambda 950 UV-visible-NIR spectrometer (adjustable resolution of 0.05–5.00 nm and wavelength accuracy ≤±0.08 nm) over the spectral range from 175 nm to 2000 nm. Ferroelectric measurements were carried out using a P–E loop tracer (Radiant Technologies, accuracy of ±0.1–0.25% of full scale). Magnetic measurements were carried out using a superconducting quantum interference device (SQUID)-based vibrating sample magnetometer (magnetic field of ±7 T (0.1–0.5% of the set value), a temperature range of 2 K to 400 K (± 0.2–0.5 K) and accuracy over moment of 10⁻⁸–10⁻⁷ emu) with a magnetic field sweep of ±50 kOe over a temperature range of 5–400 K.

3. Results and discussion

3.1 Structure, morphology and electronic structure

After the synthesis of BaTiO₃ and La_0.835Na_0.165MnO₃, X-ray diffraction patterns were recorded at RT in the 2θ range of 10° to 90° to examine the structural dynamics of the parent compounds and their composites. The XRD patterns are shown in Fig. 1. Theoretical validations of structure formability and stability are discussed in the SI.

Fig. 1 (A) RT XRD patterns of BL0 and BL100. The @ and # indicate the major reflections of BL0 and BL100, respectively. (B) Stacked RT XRD patterns of the composite samples. (C) Stacked major reflections of the prepared samples, presented to visualize the evolution of each phase in the composites.

Clearly, BL0 and BL100 exhibit distinct XRD patterns, and the composites show the presence of contributions from both BL0 and BL100 depending on the percentage of substitution. The approximate percentage of constituent phases present in the composites after final sintering was calculated from the intensities of these powder X-ray diffraction (PXRD) patterns. The major reflections corresponding to BL0 and BL100 were considered, and the relation was used to estimate the percentage of each phase present in the composites.³⁴ The calculated percentages are shown in Table 2, and they are approximately equal to the mole percentages used during synthesis. BaTiO₃ often crystallizes in a tetragonal structure with space group (SG) P4mm (SG no. 99).^35,36 On the other hand, La_0.835Na_0.165MnO₃ crystalizes in a rhombohedral structure with SG R3̄c (SG no. 167).³⁷ With this knowledge, to confirm tetragonal and rhombohedral distortions in BL0 and BL100, and to prove the immiscibility of the parent structure in the composites, it is essential to extract the best estimate for Bragg peak intensities (Miller indices and hkl) and then to perform structure matching across the whole diffractogram. Therefore, whole powder pattern decomposition (WPPD) was performed using the Le Bail (LB) method to extract the peak intensities.^38,39 The LB method successfully decomposed the whole powder pattern of BL0 under the P4mm SG, even though there were some unindexed peaks prominently visible at 24°, 28° and 30.6°. On the other hand, there was a complete failure of profile matching in BL100 under the R3̄c space group alone. Ideally, the PXRD pattern of a rhombohedral crystal exhibits twin peaks at the major reflections.^40–43 However, in BL100, there exists a shoulder at the immediate lower 2θ of the major peak (indicated as $ in Fig. 1), which persists even in the composites. This indicates the existence of an overlapping contribution to the diffracted X-ray intensity essentially from another phase. With rigorous investigations, this phase was identified as a monoclinic self-doped La_0.90MnO₃-like structure with space group I12/a1 (SG no. 15).⁴⁴ The reason behind segregation is the volatility of alkali metal carbonates (one of the precursors) at high temperature (above 850 °C) and their solubility.^45,46 If the reaction temperature is raised to an extent where rare-earth manganites usually form (1300 °C to 1500 °C), the resultant composition will become self-doped or deficient manganite due to the evaporation of Na₂O or other Na-containing vapours.^47–49 Suppose a lower sintering temperature is adopted, the diffusion of constituents during the solid-state reaction is inhibited, leading to inhomogeneity and the formation of mixed phase manganites.⁵⁰ There were also unindexed peaks at 31.6° and 36.1°, which were identified as bixbyite La₂O₃ with a cubic structure belonging to the Ia3̄ SG SG and parasitic Mn₃O₄ formed due to the evaporation of sodium or incomplete reaction of MnO, which crystalizes in a tetragonal structure (I4₁/amd SG), respectively. Once the profile matching is completed, Rietveld refinement was performed for structure matching, considering outputs from the LB method (lattice parameters, zero-point, background and profile parameters). The Rietveld-refined powder XRD patterns are shown Fig. 2. The summary of the refinement is tabulated in Table 1.

Fig. 2 Rietveld-refined powder XRD patterns of BL0 and BL100. Symbols (bubbles and asterisks) represent the observed data (y_obs), the overlaid solid curve corresponds to the calculated profile (y_cal), the vertical bars indicate the Bragg peak positions (Bragg pos) and the nearly horizontal line at the bottom represents the difference curve (y_obs–y_cal). The respective SG are marked on the left of the Bragg positions.

Table 1 Summary of Rietveld refinement results for BL0 and BL100

P.Q	Sample code
	BL0	BL100
Space group	P4mm	R3̄c	I12/a1	Ia3̄	I41/amd
a = b (Å)	3.99 ± 0.003	5.48 ± 0.009	7.77 ± 0.001	9.789	5.75 ± 0.007
b (Å)	3.99 ± 0.003	5.48 ± 0.009	5.50 ± 0.005		5.75 ± 0.007
c (Å)	4.03 ± 0.004	13.32 ± 0.001	5.46 ± 0.009		9.49 ± 0.004
V (Å^3)	64.30	347.62 ± 0.003	233.93 ± 0.006	937.96 ± 0.009	314.60 ± 0.003
Phase fraction (%)	100	63.52	35.63	0.44	0.41
ρest (g cm^−3)	6.02 ± 0.002	6.33	6.59 ± 0.003	9.22 ± 0.009	3.81 ± 0.008
Rwp	16.3	12.5	12.5	12.5	12.5
Rexp	11.68	11.62	11.62	11.62	11.62
χ^2	1.95	1.16	1.16	1.16	1.16
RB	4.60	2.65	3.88	54.7	68.6

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The linear nature of the difference curve, the small difference between R_wp and R_exp, the value of χ² close to unity and the small values of R_B are indicators of good agreement between the experimental and calculated data governed by the proposed structural model (the meaning and implications of R factors are given in the SI). Thus, it is confirmed that the specimen BL0 belongs to a polar tetragonal structure, and BL100 has nonpolar rhombohedral structure. The synthesis of single-phase BaTiO₃ is a challenging due to the complex phase diagram of BaO/BaCO₃ and TiO₂ precursors, depending on the Ba/Ti ratio (g*), temperature (T) and oxygen partial pressure (PO₂). For a fixed T and PO₂, it was found that if g* is close to 1, then single-phase BaTiO₃ with systematically tunable ferroelectric properties can be realised. However, if g* is far away from unity, the solubility of either of the precursors terminates, and defects (partial Schottky defects and oxygen vacancy defects in the BaTiO₃ solid solution) are established in the Ba, Ti and O sublattices. The defects promote the perturbation of equilibrium, and Ti-rich or Ba-rich phases are formed alongside BaTiO₃. On the Ba-rich side (g* > 1), Ba₂TiO₄ and Ba_1.054Ti_0.946O_2.946 are the most favourable secondary phases, depending on g*, T and whether they are quenched or slow cooled to ambient temperature. Similarly, on the Ti-rich side (g* > 1), the secondary phases are BaTi₂O₅ and Ba₆Ti₁₇O₄₀. Furthermore, the thermodynamic stability of Ba_1.054Ti_0.946O_2.946 and BaTi₂O₅ is limited to relatively lower temperatures (1150 °C and 1120 °C–1250 °C, respectively). Once these temperatures are crossed, these compositions undergo peritectoid reactions to form BaTiO₃ and Ba₂TiO₄/Ba₆Ti₁₇O₄₀. A serious consideration on secondary phases in ferroelectric and ferroelastic materials is required, as the surface nucleation of these secondary phases on the primary BaTiO₃ phase can create stresses and affect ferroelectric properties due to different thermal coefficients of expansion between the two phases.^51,52 Therefore, if the temperature is fixed at 1300 °C–1320 °C (as in the present case, sintering was carried out at 1300 °C) and the PO₂ is normal, the possible secondary phases that can be identified in the present investigation are Ba₂TiO₄, BaTi₄O₉⁵³ and BaCO₃⁵² (the phase fraction of each secondary phase is <1.7%). The short soaking time and slow cooling of BL0 to ambient temperature contributed to the precipitation of secondary phases.⁵² Though these secondary phases may have obvious effects on physical and optical properties, the major phase fraction (98%) is essentially polar BaTiO₃ with a tetragonal lattice.

The phase equilibrium in the binary La₂O₃–Mn-based oxide system is well established, and it has been found that the major ternary phase that can form in the perovskite phase is LaMnO₃ solid solution.⁵⁴ Any other impurity phases are formable only at very high temperature (1650 K), under a reducing atmosphere, or at pressures greater than 30 kbar. However, phase segregation in BL100 arises from three main factors: (i) thermal stability and solubility of one of the precursors at 950 °C (Na₂CO₃), (ii) limited solid-state diffusion at relatively low sintering temperatures, and (iii) incomplete oxidation of the MnO precursor. The successful substitution of Na⁺ for La³⁺ depends on the solubility of Na⁺ in the host matrix and compensation for Na⁺ volatilization at high T. Monovalent cations have a narrow solid solubility range in rare-earth manganites, typically up to about x < 0.15–0.2.^55–57 Beyond this value of x, there occurs the precipitation of secondary phases such as Mn₃O₄ or corresponding metallic phases, as observed in the case of Na⁺ and Ag⁺ substitution.^58,59 Furthermore, even if the concentration of monovalents is restricted below the critical concentration (x < 0.15), elevated soaking temperatures and prolonged dwell times may cause evaporation of monovalents. To avoid such evaporation, either flux-assisted synthesis, addition of excess metal carbonates and microwave-assisted synthesis or chemical synthesis routes are employed.^60–63 In the present synthesis, 5% excess Na₂CO₃ was added to compensate for evaporation. The other precursor that needs attention at this point is MnO. Usually, the preferred precursor for the solid-state synthesis of manganites is MnO₂, as it can be easily reduced to form Mn³⁺ cat the B-site of the perovskite or a mixed valence state of Mn³⁺/Mn⁴⁺ at low temperatures. In contrast, MnO, having Mn²⁺, must be oxidized to achieve such charge states in the perovskite structure. Finally, the calcination temperature adopted in the present study was 800 °C. Considering all these parameters, the existence of secondary phases, majorly the La_0.9MnO₃-like phase and small traces of La₂O₃ and Mn₃O₄, is attributable to the lack of diffusion and can be understood based on bulk diffusion-controlled kinetics at the immediate phase boundaries of La₂O₃/Na₂CO₃ and MnO. It is established that the actual formation of lanthanum manganite takes place at the La₂O₃/LaMnO₃ phase boundary. O and Mn ions diffuse from the MnO/LaMnO₃ phase boundary and annihilate with the corresponding vacancies at the La₂O₃/LaMnO₃ interface. O₂(gas) also takes part in the reaction, as in MnO, Mn is present in the 2+ oxidation state. O₂ transport takes place preferably via pores along the La₂O₃/product interface. At low sintering temperatures, it is seen that in the solid-state diffusion of ions, La³⁺ is quite slower (at least one orders smaller) species compared Mn³⁺/Mn⁴⁺, and diffusion of Na⁺ is quite restricted due to charge-compensation mechanisms with O. Apart from the ionic transport of Mn³⁺ and/or Mn⁴⁺, there is ambipolar diffusion of Mn–O pairs due to comparable activation energies for Mn³⁺ and O²⁻, which are again sluggish species in solid-state diffusion. Considering all these characteristics of diffusion kinetics and their dependence on annealing temperature and PO₂, Marian Palcut et al.⁶⁴ have inferred that the compositional limit on the La-deficient side of LaMnO₃ formation is La_0.89±0.01MnO_3±Δ. Once formed, it is significantly stable with a change of temperature and oxygen partial pressure. A similar finding has been reported for NdMnO₃, where a stable Nd-deficient composition, Nd_0.88MnO_2.92, was found. The Nd₂O₃ and Mn₃O₄ phases have precipitated beyond the solubility limit.⁶⁵ The final stoichiometry of lanthanum manganite depends on its thermal history, and it is of paramount importance in defect chemistry of these materials. This, in fact, is true as a sample prepared elsewhere with similar initial conditions as ours, but with MnO₂ as the precursor, exhibited (though not identified by the author) similar structural distortions in XRD patterns (a shoulder on the main peak), consistent with La_0.89±0.01MnO_3±Δ, even after post-annealing treatment at 1150 °C for 72 h.⁶⁶ In the present investigation, it is asserted that the low calcination temperature contributed to the generation of secondary phase, perhaps similar in structure to La_0.9MnO₃, due to diffusion inhibition during the solid-state reaction. The activation energy at the given annealing temperature (800 °C) was sufficiently high to prevent diffusion of the constituent ions and ambipolar Mn–O pairs, which led to phase segregation. Furthermore, as the samples were air-annealed, the supply of oxygen was insufficient to completely oxidize MnO. As a result, the La₂O₃/Na₂CO₃–MnO system could not attain equilibrium, and based on the local availability of the mixture, a phase-segregated La_0.835Na_0.165MnO₃:La_0.9MnO₃ perovskite composite was formed. Furthermore, based on the thermal history of the solid-solution, once the La_0.9MnO₃ phase is formed, it continues to exist even after repeated high-temperature annealing, thus asserting the cause for the existence of the monoclinic La_0.9MnO₃-like phase in BL100 and the composites.

Fig. 3 shows Rietveld-refined PXRD patterns of all the composites, and Table 2 shows the consolidation of the output of the refinement. The proximity of R factors R_wp and R_exp indicates the goodness of fit. Furthermore, the R_B is expected to be a small number, and χ² is close to unity. The negligible difference between y_abs and y_cal is a visual marker of goodness of fit. The refinement thus confirms the expected immiscible two-phase characteristic of the composite. The phase fractions obtained from the refinement are close to the nominal values (Table 2). The disagreement between phase fractions obtained from the intensity ratio I_(B/L)/T_T and those from Rietveld refinement is because of the non-included intensity of impurity phases like La_0.9MnO₃, La₂O₃ and Mn₃O₄ during the calculation. Furthermore, even within the Rietveld-refined phase fractions, there are deviations in phase fractions at higher concentrations, such as in BL30 and BL50. This led to the identification of a new phase in the composites alongside Ba₂TiO₄ and Mn₃O₄ (marked as & and # in Fig. 3). Careful examination of the PXRD patterns for composites (BL30 and BL50) reveals a new peak at 2θ = 26.3°, which belongs to the [103] reflection of a hexagonal structure with a P6₃/mmc SG. This very minor phase (phase fraction < 3%) belongs to moderately substituted BaTi_1−xMn_xO₃^67,68 or an oxygen-deficient BaTiO₃ structure.^69,70 Mn cations can readily replace Ti in BaTiO₃ due to close proximity in their ionic radius (Ti⁴⁺: 0.605 Å. Mn³⁺: 0.645 Å and Mn⁴⁺: 0.53 Å). At the higher reaction temperature of 950 °C, the diffusion of cations, Mn and Ti, can replace each other, particularly at a surface-terminated regions of the structure.

Fig. 3 Rietveld-refined powder XRD patterns of BL10, BL20, BL30 and BL50. The respective SG are indicated to the left of the Bragg positions.

Table 2 Summary of Rietveld refinement results for BL10, BL20, BL30 and BL100

PQ	SC
	BL10			BL20			BL30			BL50
Note: SC stands for sample code, PQ stands for physical quantity, RR stands for Rietveld refinement, I(B/L)/IT is the intensity ratio of titanate or manganite to the total intensity.
Space group	P4mm	R3̄c	I12/a1	P4mm	R3̄c	I12/a1	P4mm	R3̄c	I12/a1	P4mm	R3̄c	I12/a1
a = b (Å)	3.99 ± 0.005	5.51 ± 0.004	7.85 ± 0.002	3.99 ± 0.004	5.51 ± 0.001	7.83 ± 0.005	3.99 ± 0.005	5.51 ± 0.005	7.84 ± 0.008	3.99 ± 0.004	5.52 ± 0.001	7.85
b (Å)	3.99 ± 0.005	5.51 ± 0.004	5.53 ± 0.002	3.99 ± 0.004	5.51 ± 0.001	5.52 ± 0.005	3.99 ± 0.005	5.51 ± 0.005	5.53 ± 0.005	3.99 ± 0.004	5.52 ± 0.001	5.53 ± 0.008
c (Å)	4.03 ± 0.001	13.34 ± 0.001	5.48 ± 0.004	4.03 ± 0.001	13.33 ± 0.004	5.47 ± 0.008	4.03 ± 0.001	13.33 ± 0.009	5.48 ± 0.009	4.03 ± 0.001	13.33 ± 0.002	5.50
V (Å^3)	64.34 ± 0.002	351.26 ± 0.003	238.20 ± 0.007	64.31 ± 0.002	350.66 ± 0.008	237.11 ± 0.004	64.33 ± 0.004	351.40 ± 0.007	238.43 ± 0.009	64.28 ± 0.007	351.91 ± 0.003	239.06 ± 0.009
Phase fraction (%) RR	91.10	6.26	2.64	78.80	13.52	7.68	66.80	22.30	10.90	41.63	31.91	26.46
Phase fraction (%) I(B/L)/IT	94	6.5		86	14		77	23		57	43
ρest (g cm^−3)	6.01 ± 0.009	6.31 ± 0.002	7.18 ± 0.005	6.02 ± 0.002	6.32 ± 0.003	7.21 ± 0.008	6.01 ± 0.009	6.30 ± 0.009	7.17 ± 0.008	6.02 ± 0.004	6.30	7.15 ± 0.009
Rwp	15.2	15.2	15.2	15.6	15.6	15.6	15.2	15.2	15.2	16.6	16.6	16.6
Rexp	11.54	11.54	11.54	11.46	11.46	11.46	11.72	11.72	11.72	11.65	11.65	11.65
χ^2	1.73	1.73	1.73	1.86	1.86	1.86	1.68	1.68	1.68	2.02	2.02	2.02
RB	10.9	15.0	19.9	5.38	6.74	11.2	3.33	6.51	9.61	6.14	8.52	9.64

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To discuss the major phases of the composite, the tetragonal BaTiO₃ continues to persist with the attributes of the parent BL0. In tetragonally distorted BaTiO₃ the c/a ratio defines the extent of tetragonality. The first reported single crystal of BaTiO₃^35,71 had a c/a ratio of 1.0101 ± 0.002. In the present investigation, across the entire series, the c/a ratio is found to be 1.01 ± 0.009. This indicates that lattice expansion or deviation in tetragonality is negligible. However, the c/a ratio is found to increase from BL10 to BL100 in the rhombohedral phase. The crystal volume is found to sharply increase towards BL10 from BL100 in both rhombohedral and monoclinic phases. This finding is slightly unusual, considering no further substitution of foreign atoms during composite formation. It is observed, and has been already established, that at reduced PO₂ and low sintering temperatures, the product phase is La-deficient, and vacancies on both La and O sublattices are dominant. If so, the vacant sites that are available for Mn³⁺ diffusion are most likely the La vacancies and become one of the possible migration paths. Furthermore, the average valence of Mn decreases with decreasing PO₂.⁶⁴ Bond valence sum calculation for the monoclinic phase indicate that the average valency of the Mn site is less than 3. This indicates that there is a significant population of Mn²⁺ along with Mn³⁺ and Mn⁴⁺, diffusing through the vacancies. During such diffusion, there is a high likelihood of Mn antisite defects to occur on the La sublattice. If one considers ionic size, the presence of Mn on the La site is favoured for a lower valence of manganese (Mn²⁺), as ionic size increases with decreasing valence (Mn²⁺: 1.13 Å). Furthermore, in a study by Hundley et al.⁷² a charge disproportionation model was proposed for deficient manganites, according to which it is stated that in octahedrally coordinated systems, the Mn²⁺–Mn⁴⁺ pair is found to be a more stable pair than Mn³⁺–Mn³⁺. Consequently, a portion of the manganese ions form Mn₃O₄ as a secondary phase, and the other portion occupies the A-site as Mn²⁺ along with La³⁺ and alkali/alkaline-earth metal ions. In this context of deficiency, an unusual behaviour of heavily self-doped La_1−xMnO₃ was identified by Orgiani et al. The heavily deficient composition, namely La_0.66MnO_3−Δ, grown as a film on a SrTiO₃ substrate, showed full generation of Mn⁴⁺. Surprisingly, this composition showed the high metallicity in place of an antiferromagnetic insulating ground state. The study clearly established that this unusual behaviour was a consequence of a multiple double-exchange mechanism mediated by Mn²⁺ present at the A-site of the crystal lattice.⁷³ It has already discussed that the occurrence of Mn²⁺ at the A-site is promoted by cationic and anionic vacancies at the A-site. Though an increase in unit cell volume cannot be explained on the basis of the existence of Mn²⁺ at the A-site, the mere origin of it (A-site cationic and anionic vacancies) explains the observation. The increase in cell parameters and unit cell volume from BL100 to BL10 is related to the decreasing concentration of oxygen due to the formation of anionic vacancies and the increase in radius of La and Na sites due to vacancies. The only way to compensate for the oxygen vacancies is through a reduction in the average valence of manganese ions. This is why some of Mn⁴⁺ are reduced to Mn³⁺, and Mn³⁺ to Mn²⁺. This progressive increase in ionic radius increases the average ionic radius and, in turn, the unit cell volume. Moreover, anion vacancies at oxygen sites reduce the electrostatic bonding forces, which also leads to an increase in unit cell volume. Furthermore, it is observed that cationic vacancies have a higher ionic radius than their corresponding cations. Systems with alkali/alkaline-earth metal deficiencies always show an increase in volume compared to their parent compositions.^47,74,75 Thus, it is believed that the presence of Mn antisite defects (Mn²⁺) on the La³⁺ sublattice, along with A-site cationic vacancies and anionic vacancies, is responsible for the observed increase in the crystal volume of the major manganite phase. To validate these assertions, detailed studies on the surface morphology, elemental composition and electronic structure were carried out by analysing FESEM micrographs, energy-dispersive elemental spectra and X-ray photoelectron spectra.

Fig. 4 shows FESEM micrographs of all the specimens at the same magnification. Apparently, there is a clear visual distinction between the grain size of BL0 and BL100, as well as their porosity. BL0 shows minimal closed porosity, whereas BL100 shows vivid open porosity. Grain sizes were estimated using ImageJ software, and the corresponding distributions are shown in Fig. 4. The grain sizes follow a lognormal distribution, with mean grain sizes of 4.34 µm² and 0.47 µm² for BL0 and BL100, respectively. Porosity exhibits the opposite trend, which is 1.53% of the given area for BL0 and 10.28% of the given area for BL100. Interestingly, a wide spread of grain size distribution is observed for BL100, whereas BL0 has very similar grain sizes. The lognormality has its origin (SI) in dwell time, and based on this time, various parameters such as the rate of change of product volume and the drift and diffusion of constituents will be decided. Suppose the dwell time is fixed, ion mobility, grain boundary energy, and overall grain growth are mainly decided by the soaking temperature. In other words, the rate constant for solid-state diffusion kinetics is temperature-dependent and follows an Arrhenius-type relationship, given by , where k₀ is a constant, Q is the activation energy for grain boundary migration, R is the universal gas constant and T is the temperature. Furthermore, in the context of diffusion, the ion diffusion coefficient, which is a function of temperature, shows Arrhenius-type behaviour, and it can be expressed as , where η₀, R and β are constants and T is the sintering temperature.⁷⁶ Thus, knowing the dynamics of grain growth, it can be concluded that the high sintering temperature and low activation energy in BL0 enable steady grain growth and lead to homogeneous distribution of large grains. In contrast, for BL100, the low sintering temperature and high activation energy hinder steady grain growth and favor the nucleation of smaller grains. Here, the mobility and activation energy of the constituents are not sufficient to achieve sufficient grain boundary migration and volume expansion. As a result, BL100 shows evident open porosity with a wide distribution of small grains. The composites show broken BL0 particles surrounded by BL100 particles. The major cause of this is the size of the initial constituents. The very dissimilar size of BL0 and BL100 and low sintering temperature seem to be insufficient to achieve uniform connectivity between the two dissimilar particles.

Fig. 4 FESEM micrographs of (1 − x)BTO:x(LNMO), x = 0, 10, 20, 30, 50 and 100, recorded at 4.00k× magnification. The histograms show the grain size distribution of BL0 and BL100 under lognormal distribution. The columns represent counts per scale; the overlaid curve is the kernel-smoothed representation of the respective distribution.

Fig. 5 shows the area analysis and point analysis performed using EDS for the identification of elemental composition. Panels A and B correspond to BL0 and BL100, respectively, and stand as testimony of the expected elemental compositions: Ba, Ti, and O (a) for BL0, and La, Na, Mn and O (b) for BL100. Apparently, in the 50 : 50 composite, point analyses at two different locations show Ba, Ti, and O (c) and La, Na, Mn, and O (d). This precisely verifies the immiscibility of the two phases and their independent existence within the composites. Stoichiometric calculations demand atomic percentage of 20 : 20 : 60 for BaTiO₃ to be an ABO₃ perovskite, whereas in La_0.835Na_0.165MnO₃, it is 16.7 : 3.3 : 20 : 60. The atomic percentages obtained from the EDS spectra of BL0 are 19.9 : 18.0 : 62.1 (excluding carbon concentration). Though the Ba concentration is close to the nominal one, the Ti concentration shows a deficiency. This is typical for Ba-excess solid solutions in BaTiO₃. As the solubility limit of Ba-excess is lower than that of Ti-excess in BaTiO₃ phase formation, the evolution of secondary phases such as Ba₂TiO₄ alongside unreacted or atmosphere-adsorbed BaCO₃, is inevitable. The elemental composition of BL100 is deviates from the nominal one (7.5 : 1.0 : 6.6 : 85), which states that there is a large surface termination of the perovskite structure with oxygen-rich impurities.

Fig. 5 EDS spectra obtained from area analysis and point analysis. (A) and (B) are area analysis of BL0 and BL100, respectively. (C) and (D) are point analysis on BL50, (C) showing BL0 grain in BL50 specimen and (D) showing clusters of BL100 grains. (a)–(d) are corresponding EDS spectra, showing the binding energy map of elements present in the analysis.

Fig. 6 shows the XPS survey spectra of BL0 and BL100, chosen for surface analysis based on structural implications (mixed valence in BaTiO₃ and La_0.835Na_0.165MnO₃, as well as cationic and anionic vacancies). It should be noted that the chemical state and valence states of elements in the bulk of the composites are expected to be similar to those of their parent compounds and largely remain unaltered due to the low sintering temperature employed during their synthesis. Considering the C 1s core line as a reference, the spectrum of BL0 was corrected for its binding energy (B.E) to account for the shift due to charging (2 eV); meanwhile, there was no charging observed in BL100. All the features observed in the survey spectra are testimony of desired elements. Strong signals at 779.8 eV, 459.5 eV, 833.4 eV, 1071 eV, 641.6 eV, 528.6 eV and 528.9 eV correspond to Ba 3d, Ti 2p, La 3d, Na 1s, Mn 2p and O 1s core-level binding energies, respectively.⁷⁷ Additionally, reference signals are observed at 286.6 eV and 284.4 eV for BL0 and BL100 eV, respectively, corresponding to adventitious carbon. This is a ubiquitous hydrocarbon contamination that accumulates on the surface of the specimen during handling and storage. However, favourably, it plays a role of reference for charging correction to all other elements during the scan. Having known the B.E positions and separations using first- and second-derivative methods, deconvolution was carried out using CasaXPS peak fitting software to assign each of these features and to investigate different types of chemical bonding and valence states involved in the structure formation. The resulting B.E positions, assignments, and spin–orbit splitting (SOS) values are tabulated in Table 3.

Fig. 6 X-ray photoelectron survey spectra of BL0 and BL100, recorded using an Al K-α source.

Table 3 Binding energy positions, binding energy separations, FWHM of core lines, area ratios and assignments for each component of the core-level spectra obtained from deconvolution

Sample code	Element code	Core level	Peak name	Species	Peak position	BE separation	FWHM	Area	% Area	Area ratio
BL0	BaI	3d	3d5/2	Ba^2+	779.64	15.32	1.43	501 807.8	27.04	1.43
			3d3/2		794.96		1.44	349 284.8	18.82
	BaII	3d	3d5/2	Ba^2+	781.13	15.32	1.75	533 530.5	28.75	1.51
			3d3/2		796.45		1.69	352 405.0	18.99
	Ti^3+	2p	3d3/2	Ti^3+	458.00		1.75	10 947.9	4.55
	Ti^4+	2p	3d3/2	Ti^4+	459.47	5.77	1.12	152 711.4	63.33	1.99
			3d1/2		465.24		2.03	76 718/93	30.64
	OI	1s	1s	O^2−	528.59	1.99, 4.46	1.34	233 133.2	57.23
	OII			Ov	530.58		2.14	165 024.7	40.51
	OIII			OH	533.05		2.13	9238.2	2.27
	CI	1s	1s	C–C	284.61	1.63, 3.51	1.61	81 659.3	72.58
	CII			C–O	286.24		1.01	6227.4	5.54
	CIII			O–C=O	288.12		2.19	24 620.7	21.88
BL100	LaI	3d	3d5/2	cf^0	833.30	4.5	1.52	105 933.9	17.80
	LaII			cf^1L AB	834.60	3.2	3.45	266 887.6	44.84
	LaIII			cf^1L B	837.80		2.40	222 393.5	37.36
	NaI	1s	1s		1070.63		1.27	19 790.7	40.45
	NaII				1071.58		1.53	21 022.1	50.64
	NaIII				1072.89		1.60	3696.6	8.91
	MnII	2p	2p3/2	Mn^2+	640.81		2.00	25 150.2	14.11
	MnIII			Mn^3+	641.06		3.07	89 259.7	50.08
	MnIV			Mn^4+	642.43		2.40	43 423.7	24.36
	Mn^3+mp			Mn^3+	644.17		1.97	14 495.9	8.13
	Mn^2+mp			Mn^2+	645.73		2.07	5902.90	3.31
	OI	1s	1s	O^2−	528.85	0.98, 2.04, 3.96	1.14	163 556.5	43.09
	OII			O^2−	529.83		1.10	25 725.5	6.78
	OIII			Ov	530.89		2.00	120 386.7	31.72
	OIV			OH	532.81		2.80	69 910.1	18.42
	CI	1s	1s	C–C	284.45	1.28, 3.55	1.31	46 132.1	55.65
	CII			C–O	285.73		2.09	17 433.2	21.03
	CIII			O–C=O	288.00		2.51	19 327.0	23.32

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The deconvolution of the core-level spectra for BaTiO₃ and La_0.835Na_0.165MnO₃, along with the respective C 1s core spectra, is shown in Fig. 7. The Ba 3d core spectrum shows the characteristic doublet structure, with each peak further resolved into two distinct components (Ba_I and Ba_II). The B.E separation of Ba_I and Ba_II with respect to their higher-energy doublet is 15.32 eV, and the area ratios are 1.43 and 1.51, respectively. This confirms that the doublet arises from spin–orbit splitting of Ba 3d electrons. The coupling splits the 3d subshell into two levels with different total angular momentum . The lower-energy 3d_5/2 components are located at 779.64 eV and 781.13 eV, and the higher-energy 3d_3/2 components are located at 794.96 eV and 796.45 eV. These B.E positions (particularly for Ba_I) are negatively shifted relative to metallic Ba, which is typical of Ba²⁺ in a perovskite/oxide lattice.³⁹ Broad humps 10–11 eV above the 3d_5/2 and 3d_3/2 core lines correspond to inelastic loss features. The point of interest in the Ba 3d core spectrum is the existence of two different components with similar FWHMs within a single core line (3d_5/2 and 3d_3/2), which indicates that Ba exists in two different chemical environments but with the same oxidation state. No doubt that Ba_I is in a perovskite environment, but there are several attributions to the Ba_II component, such as BaCO₃ and Ba(OH)₂. This speculation is based on the B.E positions at 781.13 eV and 796.45 eV for the Ba_II component. However, the C 1s (panel 8) and O 1s (panel 3) core-level spectra, which sensitively reflect the surface contamination, do not show any such signature to confirm the existence of BaCO₃ and Ba(OH)₂. The C 1s photoelectron spectrum of BL0 exhibits a prominent peak at 284.6 eV, belonging to adventitious carbon of the type C–C/C_xH_y. Additional components at 286.24 eV and 288.12 eV, whose intensity is significantly lower than that of adventitious carbon, are attributable to other carbonaceous species, perhaps C–O and O–C=O. It should be noted that the B.E position in the C 1s core line spectra for carbonates (e.g., BaCO₃) exists in the range 289–290.4 eV; however, no such component is observed in the in the C 1s core spectrum of BL0. Further observation of carbonate in XPS spectra is difficult because it forms discrete particles rather than a continuous surface layer. The O 1s core spectrum is composed of three components: O_I, O_II and O_III situated at 528.59 eV, 530.58 eV and 533.05 eV, respectively. The first component, O_I, belongs to lattice oxygen in the BaTiO₃ perovskite framework. The second component, O_II, belongs to oxygen vacancies, and the third component, O_III, belongs to adsorbed oxygen species such as H₂O. However, the presence of Ba(OH)₂ cannot be confirmed, as it is highly reactive with CO₂ and forms BaCO₃ immediately. There are also studies that attribute Ba_II to a near-surface phase related to relaxation of residual strain. However, more evidential and physically significant attributions are as follows: (1) Ba_II is not a result of surface contamination but of perovskite origin, attributable to Ba²⁺ in the BaTiO₃ lattice having domains with their c-axis aligned along the surface normal, whereas Ba_I corresponds to Ba²⁺ in the BaTiO₃ lattice having domains with their a-axis aligned along the surface normal.⁷⁸ (2) Ba²⁺ in Ba₂O, which is a result of the reduction of BaO to Ba₂O at high temperatures due to the displacement of O atoms that are trapped in the vicinity of BaO.⁷⁹ In both spectra, common attributes are the O_II band, corresponding to oxygen vacancies, and the appearance of a minor Ti³⁺ band in the Ti 2p core spectra as a consequence of partial reduction of Ti⁴⁺ to Ti³⁺ to compensate for charge imbalance caused by oxygen vacancies. The deconvoluted Ti 2p core spectrum is shown in panel 2. A mere visual of the spectrum indicates that there exists a doublet of symmetric nature, but careful inspection revels that there is significant tailing on the lower B.E side of the major component of the doublet. Deconvolution identifies the major component of the doublet at 459.47 eV and its moiety at 463.24 eV, having a B.E separation of 5.77 eV and an intensity ratio of 1.99. The intensity of higher-energy component is significantly lower than that of the main peak, and its FWHM is unusually larger (two times) than that of the major peak. These features of the observed spectra are ascribed to the typical spin–orbit coupling character of Ti⁴⁺ ions in a perovskite environment, such as SrTiO₃, BaTiO₃ and oxide lattices such as TiO₂.⁸⁰ Spin–orbit coupling splits the Ti 2p core line into two components, the lower-energy 2p_3/2 band and a higher-energy 2p_1/2 band, with a separation of approximately 5.6–5.8 eV and an intensity ratio of 2 : 1. Partial reduction of Ti⁴⁺ at high temperatures creates Ti³⁺ in quantities less than the detection limit of the instrument, but deconvolution without the Ti³⁺ component did not result in a good fit with a low residual standard deviation. Therefore, the lower-energy feature at 458.00 eV is attributable to Ti³⁺ ions, and it is not visible in the Ti 2p_1/2 band because its intensity is substantially lower compared to the main peak.

Fig. 7 Deconvoluted XPS core-level spectra of each element in BL0 and BL100.

The deconvolution of the La 3d core spectra is shown in panel 4. If monochromatic Al Kα radiation is used for photoionization, the strongest signal of La, which is La 3d core line, appears with an intense hostile La Auger signal (LaM_4,5N_4,5N_4,5: La MNN) whose interference is usually observed in the energy range of approximately 840 eV to 870 eV. This region is above the La 3d_5/2 SOS component; thus, only the La 3d_5/2 core line was considered for deconvolution. The deconvolution was carried out considering three peaks: cf⁰, cf¹L AB and cf¹L B. In perovskites, La is expected to exist in the +3 ground state (3d¹⁰4f⁰). Upon interaction with X-rays, photoelectrons are ejected, resulting in final states described as cf⁰(3d¹⁰4f⁰ + hν → 3d⁹4f⁰ + e) and cf¹L(3d¹⁰4f⁰ + hν → 3d⁹4f¹L + e), which are also called as unscreened and screened core-level photoemissions, respectively. Here, c represents the La core hole, 0 and 1 represent the absence or presence of an f electron, e is the photoelectron and L is a hole in the ligand valence band.³⁹ The screened core-level peak is further divided into bonding (B) and antibonding (AB) contributions, where in most of the compounds, the cf¹L antibonding and cf⁰ overlap. It should be noted that the intensity and separation between the main peaks and satellites are subtle and depends solely on the ligand atom involved in bonding. Having said this, rare-earth compounds are hygroscopic under ambient conditions, and they spontaneously react with moisture to form La(OH)₃, not only on the surface but also within the bulk of the sample. La, having formal 3+ oxidation state in La-based perovskites, La₂O₃ and La(OH)₃, makes it difficult to identify its local environment; however, the work of M.F. Sunding et al.⁸¹ provides a clear pathway to deconvolute and differentiate La-based compounds and to rule out possible hydroxylation. Accordingly, the B.E separation of 4.9 eV between La 3d cf⁰ and cf¹L B component, 3.7 eV between cf¹L B and cf¹L AB component and the intensity ratio of 90 : 10 for are generic to La₂O₃ and La-based perovskites. In contrast, for La(OH)₃, they are 3.9 eV, 2.0 eV and 57 : 43, respectively. In the present investigation, the observed values are 4.5 eV, 3.2 eV and 82.2 : 17.8. This indicates that the local environment of La is essentially La₂O₃ or perovskite-type, with the possibility of partial hydroxylation. The Na 1s core-level deconvolution is shown in panel 5, where the 1s core line appears to be asymmetric towards higher binding energy with sufficient tailing. Consequently, the Na 1s photoelectron spectrum was deconvoluted into three components: Na_I, Na_II and Na_III, which are situated at 1070.63 eV, 1071.58 eV and 1072.89 eV, respectively. The first two components of highest intensity may be related to sodium in different crystallographic positions,⁸² and the third component belongs to Na₂O and/or ionic Na species bound to the surrounding support through –O–Na bonds (in general NaO_x).⁸³ The formation of sodium carbonate or hydroxides would give rise to a Na 1s peak at sufficiently lower B.E, around Na_I and Na_II, and it appears as a shoulder to the main peak. However, this possibility is ruled out, as there is no carbonate peak observed in the C 1s core spectrum (289–290.4 eV) of BL100. The deconvoluted Mn 2p spectrum is shown in panel 6. Transition metals usually possess different valence states, with core lines separated by marginal B.E. differences and severe overlap. This makes deconvolution a challenging. Alongside the multiple valence states of the transition metals in mixed-valent oxides, each transition metal ion, due to its high-spin state, exhibits a broad distribution of multiplets (5 for Mn) with B.E separations on the order of 1 eV.^84,85 Due to these challenges, deconvolution of Mn core spectra in mixed-valent oxides is usually not preferred; however, knowledge of B.E separation between the SOS and the separation from the main peak to oxygen core line are appropriate criteria to infer the chemical state and environment of Mn in each compound. Detailed descriptions of this can be found in some of the notable works.^84–87 In the present case, the large FWHM of Mn 2p_3/2 and Mn 2p_1/2 validates the coexistence of different valence state of Mn, essentially Mn³⁺ and Mn⁴⁺, in the sample under investigation (BL100). Furthermore, the shoulder at lower B.E indicates the possibility of the Mn²⁺ oxidation state to be present. Thus, the major peak corresponding to Mn 2p_3/2 was deconvoluted into three major contributions, belonging to Mn²⁺, Mn³⁺ and Mn⁴⁺, from lower to higher B.E. values. The III and IV contributions are assigned to Mn³⁺ and Mn²⁺ multiplets, respectively.⁸⁴ The estimated area ratios are 17.42 : 58.21 : 24.36 for Mn²⁺, Mn³⁺ and Mn⁴⁺. The O 1s core spectrum of BL100 is composed of four components: O_I, , O_II and O_III situated at 528.85 eV, 529.83 eV, 530.89 eV and 532.81 eV, respectively. The first two components, O_I and , belong to lattice oxygen in the La_0.835Na_0.165MnO₃ perovskite framework. The second component, O_II, belongs to oxygen vacancies, and the third component, O_III, belongs to oxide ions with low electron density in very low coordination states. Such oxygen can be associated with cation vacancies in the oxide structure. The C 1s spectrum of BL100 is very similar to that of BL0, containing three components. A prominent peak at 284.45 eV corresponds to adventitious carbon of the type C–C/C_xH_y. Additional components at 285.73 eV and 288.00 eV, whose intensities are significantly lower than that of the adventitious carbon, are attributable to other carbonaceous species, perhaps C–O and O–C=O. These findings clearly establish mixed valency in BL0 (Ti⁴⁺ and Ti³⁺) and BL100 (Mn²⁺, Mn³⁺ and Mn⁴⁺), and cationic and anionic vacancies in them. These chemical and physical attributes are expected to have vivid reflections in the optical, magnetic and ferroelectric properties of these materials.

3.2 Optical studies

To investigate the optical absorption of BaTiO₃ and its composites with La_0.835Na_0.165MnO₃ (LNMO) and to estimate their optical bandgap, DRS was employed, and the corresponding room-temperature DRS spectra for each composition are shown in Fig. 8. The basic principle of DRS is provided in the SI.

Fig. 8 Room-temperature relative reflectance (R%) as a function of wavelength for (1 − x)BaTiO₃:(x)La_0.835Na_0.165MnO₃ (x = 0, 10, 20, 30, 50, and 100).

The spectrum of BL0 can be divided into three distinct regions. Region I corresponds to approximately λ < 200 nm, at which a large, diffused reflectance is shown by the specimen. Post 200 nm, an abrupt inflection appears, which corresponds to absorption of electromagnetic radiation. This region is regarded as region II, which is typically a strong absorption region extending to 400 nm. Beyond 400 nm, nearly 80% of the incident intensity is diffusively reflected. This marks region III of the observed optical behavior. The observed characteristics of DRS highlight that BL0 is an excellent UV absorber, hinting at its use as an absorber or filter in various applications such as photovoltaics, photocatalysis and cosmetics.^88,89 Upon compositing with 10% LNMO (BL10), the characteristic region III nearly disappears, having just 20% reflected intensity. This signature continues till BL30, with a continued enhancement in absorption. Beyond BL30, the entire spectrum of EM radiation above 200 nm, extending up to infrared, is strongly absorbed. In other words, the act of compositing two perovskites, BaTiO₃ and La_0.835Na_0.165MnO₃, successfully transforms the composites into UV-visible absorbers. This development is crucial in the field of optoelectronics, photovoltaics and photocatalysis.⁹⁰

At this point, it is essential to comment on material-specific characteristics of the specimen. The absorption coefficient, α(λ), describes how strongly a substance absorbs light at a given wavelength per unit distance.⁹¹ This physical property is of primary importance while discussing the spectroscopic attributes of the material. As the Kubelka–Munk function (KMF), F(R), is directly proportional to absorption coefficient, the variation of F(R) as a function of energy (E) is plotted and shown in Fig. 9.

Fig. 9 Variation in F(R) plotted as a function of E in the energy range of 1.5 eV to 7 eV for (1 − x)BaTiO₃:(x)La_0.835Na_0.165MnO₃ (x = 0, 10, 20, 30, 50, and 100).

Evidently, the variation of F(R) a function E shows significant slope changes at definite energies due to the absorption of corresponding photons in the UV and visible region of the EM spectra. In BL0, the absorption maximum is found at 3.66 eV or 343.5 nm, and for BL100, it is found at 1.94 eV or 652.6 nm. Furthermore, a characteristic higher-energy absorption is observed in the UVC region at 5.70 eV and 5.01 eV for BL0 and BL100, respectively. Theoretical calculations emphasize that, in BaTiO₃, the VB exist from −4 eV to 0 eV comprising majorly O 2p (p_x, p_y, and p_z) orbitals, and the CB is located approximately from 3 eV to 12 eV, majorly consisting Ti 3d (d_xy, d_yz, d_xz, d_x² and d_x²−y²) orbitals at lower energies. The superposition of O 2p and Ti 3d orbitals in the VB and CB leads to strong hybridization, and such hybridization is observed around −4 eV to 0 eV and nearly 3 eV to 10 eV. This results in Ti–O covalent bonds in the TiO₆ environment, whereas Ba–O bonding is ionic in nature.^92–94 Knowing the band structure and the energy separation between absorption doublets (e.g., 3.61–4.51 = 0.85 eV), all absorptions observed in the spectra of BL0 shall correspond to transitions between O 2p levels and the various levels in the conduction band.^95,96 The absorption maxima at 3.61 eV and 3.86 eV shall correspond to the strongest absorptions above the indirect absorption edge (located at around 3.2 eV).^97,98 The absorption edge (cannot be distinctly observed in the spectra) traces its origin to excitation of electrons from O 2p orbitals in the VB to the partially filled Ti 3d t_2g orbitals in the CB (R → Γ). However, some early reports consider these absorptions to correspond to indirect Γ → X or direct Γ₁₅ → Γ_25′ and Γ₁₅ → Γ₁₅ transitions, representing 2p to Ti 3d t_2g and 2p to Ti 3d e_g electron excitations, respectively.^99–102 Keeping the 3.61 eV–3.86 eV range (direct Γ transitions) as the central absorption energy, a small hump observed in the lower energy range from 2.66 eV to 3.00 eV corresponds to electronic transitions related to off-stochiometric phase of BaTiO₃ having oxygen and/or cationic vacancies, which validates the structural and XPS findings.¹⁰³ The vacancies or defects establish new levels between the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO). The absorptions observed at higher energies essentially at the UV regime, 4.51 eV (X transitions: X_5′ → X₅), 5.70 eV (direct M transitions) and 6.42 eV (Γ transitions and/or X transitions: X_5′ → X₁), correspond to higher-order ligand-to-metal charge-transfer (LMCT) transitions, essentially from O 2p to Ti 3d e_g orbitals in the CB.^95,104–107 Note that the Γ, X, M, and R are the usual high symmetry points in the Brillouin zone of the crystal lattice. In fact, the transition at 4.5 eV is a generic transition of BaTiO₃, SrTiO₃ and PbTiO₃ perovskites. This further confirms that the majority phase in BL0 is perovskite BaTiO₃. LMCT transitions to Ba 5p orbitals from O 2p is ruled out, as the energy range (3.2 eV–7.5 eV) corresponds majorly to transition between Ti 3d and O 2p-derived states.^98,108,109 Thus, the optical studies support the structural findings that BL0 majorly contains BaTiO₃, but it is essentially off-stoichiometric in nature.

Similar to BaTiO₃, LaMnO₃ has a perovskite structure, meaning the Mn ion is in octahedral coordination with oxygen. The electronic configuration of Mn in octahedral coordination of parent manganites (e.g., LaMnO₃ and CaMnO₃) is such that it has 4 or 3 electrons in the d orbital. The electrostatic crystal field (cf) is established due to O²⁻ in the surrounding, which splits the d levels into two sub-bands (cf splitting energy, Δ_cf = 10 Dq = 1.5 eV): the low-energy t_2g orbitals (d_xy, d_yz, and d_xz,) and the high-energy e_g orbitals (d_x² and d_x²−y²). It is important to note that the Jahn–Teller effect further splits these bands in the case of perovskites having Mn³⁺ at the B-site, as it has only one electron in the e_g band containing degenerate orbitals. In the case of LaMnO₃ or in general in rare-earth manganites, the Fermi level (E_F) lies between these split bands. Thus, the band structure is such that partially filled Mn 3d t_2g orbitals, O 2p orbitals, and low-lying partially filled or empty Mn 3d e_g orbitals majorly form the VB, and the Mn 3d e_g orbitals form the HOMO (there are, however, speculations on the position of t_2g orbitals whether they are above or below the O 2p orbitals). The empty Mn 3d e_g band appears as the LUMO.¹¹⁰ Thus, if the external energy (photon energy) exceeds 1 eV, the optical spectra can be satisfactorily interpreted in terms of electronic transitions between energy levels of the MnO₆ complex or between levels of two neighbouring Mn ions and between the O 2p orbitals and Mn 3d e_g levels.¹¹¹ It should be noted that the O 2p orbitals strongly hybridize with the lower-energy Mn 3d e_g band (partially filled or empty), raising the speculation on the HOMO levels, whether they are of Mn or O. Apparently, this band structure results in parent manganites having a very narrow band gap of 0.4 eV to 1.5 eV, which is susceptible to temperature variations. Hole doping and/or oxygen off-stoichiometry shall reduce the band gap or may even close it due to the formation of hole states above the E_F and the tailing of the CB towards the E_F, respectively.^55,112–114

It has been proven that in hole-doped manganites, the band gap, if exists at all, increases as temperature increases, accounting for the FM-to-PM transition, and there is a finite, nonzero gap in the PM region even in metallic manganites.¹¹¹ It is established in various studies that a broad absorption band around 2 eV above the absorption edge (centered at 1.94 eV in the present case) corresponds to multiple overlapping electronic transitions of different origins. It contains forbidden or weakly dipole-allowed 2p–3d CT transitions and dipole-forbidden, spin-allowed intra-Mn or also called intersite low-energy high-spin d–d CT transitions. They are denoted as t_2g(π) → e_g (1.3 eV–1.9 eV), t_2u(π) → e_g (2.3 eV–2.7 eV) and d(e_g)–d(e_g) (2 eV–2.2 eV).^115–118 The spectral features around 3 eV–3.8 eV originate from weakly dipole-allowed 2p–3d CT t_1u(π) → e_g transitions of π–σ nature, and the feature from 5 eV to 5.3 eV belongs to strongly dipole-allowed 2p–3d CT t_1u(π) → e_g transitions of σ–σ nature. Perhaps, there even exist weak signatures of weak low-spin d–d CT transitions in this region, ranging from 4.7 eV to 5.3 eV. As the specimen under discussion is mixed-valent, some researchers assign the d–d CT transition to ⁵E_g → ⁵T_2g (d(e_g)–d(t_2g)) for Mn³⁺ and ⁴A_2g → ⁴T_2g (d(t_2g)–d(t_2g)) for Mn⁴⁺.¹¹⁹ The shoulder observed at 3.2 eV (3.25 eV in the present case) may correspond to the dipole-allowed 2p–3d CT transition t_1u(π) → e_g of Mn³⁺ (ref. 114) and/or 2p–3d CT transition t_1g(π) → t_2g of Mn⁴⁺ (also denoted as ⁴A_2g → ⁴T_1g).^120–123 Due to the complexity of band structure of manganites, one may assign the observed absorbance to different origins based on the respective scenario. Nevertheless, at lower energies, the absorption is without any doubt majorly d–d transitions involving e_g states, and at higher energies, it is majorly due to p–d transitions involving O 2p and Mn 3d e_g states. A very interesting part of the absorption spectrum of BL100 is the first high-energy shoulder of the maximum, i.e. at 2.41 eV. This feature is typical to ferromagnetic hole-doped semiconducting manganites (metallic to be precise). It is not seen in magnetic insulators such as Pr_0.8Sr_0.2MnO₃. This means that the spectral feature is an identifier of the type of electrical ground state of the specimen and appears only when the band structure is changed such that the contribution of free charge carriers becomes predominant, or to state it differently, this feature arises from optimal mixed valency (Mn³⁺/Mn⁴⁺), giving rise to metallicity in the sample. Undoubtably, this feature is associated with d(t_2g)–d(e_g)) transitions or Mn⁴⁺ t_2g → O 2p → Mn⁴⁺ e_g interband transitions.^120,124 Meanwhile, the broad absorption maximum observed at 5 eV is attributable to U_pd interactions, which correspond to the energy cost of transferring an O 2p electron to a neighbouring d ion to create a p⁵dⁿ⁺¹ charge excitation from the p⁶dⁿ state.⁵⁵ The slope change at energies higher than 5 eV perhaps corresponds to O 2p → e_g↓ and t_2g↓ transitions, as they appear at relatively higher energies in the conduction band (5 to 6 eV).¹¹² For instance, the low-intensity shoulder at 6.48 eV perhaps corresponds to charge-transfer transition from O 2p to Mn⁴⁺, essentially 1t_1g → 7a_1g, 6t_1u → 7a_1g and 1t_1g → 2t_2g.¹²⁵ There are no signatures of O 2p → La 5d transitions, as La 5d orbitals appear at significantly higher energies (nearly 9 eV),^112,113 and there is no possibility of any optical transitions corresponding to Na, as the states related to Na⁺ (s and p orbitals) are located well below the Fermi level. However, the presence of Na⁺ certainly improves the covalency between Mn 3d and O 2p or in other words, the hybridization between the Mn 3d and O 2p orbitals.¹²⁶ Based on the occurrence of strong absorption features at low energy (<2 eV) and high energy (4.5 eV to 5.5 eV), BL100 can be regarded as a metal with no band gap or a semiconductor with an extremely narrow band gap. To sum up, unlike BaTiO₃, where the observed spectral features correspond only to p–d CT transition across the entire spectral range, there is a vivid bifurcation in manganites where the features below 3 eV majorly originate from d–d CT transitions, and transitions above 3 eV correspond majorly to p–d CT transitions.¹²³ Thus, the variation of F(R) as a function of E clearly establishes the fact that BL0 is a charge-transfer insulator, and BL100 is a metal at RT.

The composites show optical signatures of the end members of the series, with competing absorption maxima depending on the concentration of either of the end members. Interestingly, the slope changes observed at lower energies show broadening and a red shift with respect to the BL100 end member of the series. The characteristic 2p–3d strongest absorption typical of BaTiO₃ exists in the energy range between the maxima of BL100 and BL0, undoubtably showing softening and a red shift with respect to BL0. The broad secondary maxima observed at 5 eV in BL100 disappears in the composites, whereas the rest of the high-energy slope changes resemble those of BL0. This indicates that at low energies, the composites inherit the manganite nature, and at high energies, they behave like BaTiO₃. They are both Mott–Hubbard insulators and CT insulators. This confirms the true composite nature of the specimens, where the electronic structures of the parent specimens distinctly exists in the corresponding composites without a significant tradeoff at the cost of others. However, the red shift and softening of absorption signatures at low energies indicate changes in the band structure or reduction in corresponding gap perhaps due to the addition of intermediary levels. These intermediary levels come from defect states introduced into the sample. It is worth noting that the persistence of absorption features that resemble mixed-valent manganites in the range of 2.2–2.5 eV (in this case at 2.3 eV) in the composites indicates appreciable amount of free charge carriers in the composites. This feature is enhanced with an increase in the amount of La_0.835Na_0.165MnO₃. This feature exists even in BL10, ascertaining that it shall have conducting ferromagnetic nature, unlike BaTiO₃, which is an insulating diamagnet.

Using an analogy with Tauc's law , the KMF enables one to estimate the optical band gap. By replacing α by F(R) in Tauc's law, it becomes . The physical quantity (F(R)hν)^m is plotted against the photon energy hν. Here, B is an independent parameter of photon energy that characterizes the degree of disorder in the polycrystalline material under investigation. Here, m = 2 corresponds to a direct allowed optical transition, and m = 1/2 corresponds to an indirect allowed optical transition. The x-intercept of the plot, extrapolated from the linear region of (F(R)hν)^m versus hν, gives the optical band gap E_g of the specimen.¹²⁷

Fig. 10 depicts the variation of (F(R)hν)² versus hν and of versus hν, enabling the estimation of direct allowed and indirect allowed band gap of BL0 and BL100. The estimated E_g of BL0 for direct and indirect allowed transitions are 3.23 eV¹²⁸ and 3.01 eV, respectively (Table 4). It should be noted that the absorption edge in case of BL100 is not observed. However, based on prior knowledge of the band gap of La-based manganites, and assuming that there exists an absorption edge, E_g for BL100 is estimated to be 1.26 eV and 0.20 eV for direct and indirect allowed transitions, respectively. A rough estimate of E_g can also be obtained from the first-order derivative of F(R) with respect to E.¹²⁷ The obtained values of band gaps for BL0 and BL100 are consistent with earlier reports;^{96,98,100,118,129–133} however, there are discrepancies in the literature on the nature of the allowed optical transition for BaTiO₃, whether it is direct or indirect. It has been reported that both tetragonal and cubic phases of BaTiO₃ exhibit an indirect band gap (R → Γ) very close in energy to the direct band gap (Γ → Γ), making it difficult to discriminate between the two by experimental techniques.^102,134,135 The natural logarithm applied to Tauc's law indicates that ln(F(R)hν) plotted against ln(hν − E_g) should yield a linear relationship with slope 1/m, which is the constant of optical transition. The proximity of 1/m to the ideal values 1/2 and 2 validates the possible optical transition. The value of 1/m estimated for BL0 are 0.50 and 2.06. This states that BL0 has a likelihood to be both direct and indirect band gap material and validates the anomaly of nature of allowed optical transitions reported. The value of 1/m estimated for BL100 are 0.50 and 1.96. This indicates that BL100 has a direct band gap, which is in accordance with many optical studies on manganites with similar value of E_g.^{118,126,136–138} Nevertheless, this study emphasize that may it be direct or indirect gap, BL100 has a large population of free charge carriers. The band structure is such that, due to hole doping (33%) and oxygen off-stoichiometry, the LUMO levels are significantly shifted towards the E_F. The band gap becomes extremely narrow, or it has disappeared, giving metallic nature to BL100 at RT (below T_C). Furthermore, other than the prominent low-energy linear region enabling the estimation of optical band gap, the Tauc plot consists of another linear region at the higher energy side, which corresponds to perhaps multiple higher-order charge-transfer transitions, essentially from the O 2p valence band to the Ti 3d conduction band (e_g orbital).¹⁰¹ This feature is also seen in BL100, which shall correspond to multiple p–d CT and d–d transition between t_2g and e_g (Mn 3d) orbitals. Generally, BaTiO₃ is unlikely to show the said characteristic unless otherwise there exist mixed valency in the system. In the present case, mixed valency can arise from oxygen off-stoichiometry or cationic vacancies in the system. The existence of mixed valency in BL0 has already been established through magnetic and XPS analysis. To addon, the profound linearity found in the low-energy region (Fig. 10) indicates that the prepared sample not only contains the BaTiO₃ phase with a wide band gap but also a nonstoichiometric phase with a narrow band gap (2.24 eV), which extends absorption to the visible region of the EM spectra.¹⁰³ This stand as further evidence to mixed valency in BL0. The estimated CT gap (E^Dir_CT) is found to be 4.36 eV, which is similar to the reported value elsewhere.¹³⁹ The CT gap of BL100 is 3.58 eV.

Table 4 Comparison of the direct allowed band gap (E^Dir_g), indirect allowed band gap (E^Indir_g), charge transfer gap (E^Dir_CT) and Urbach energy (E_U) for relative analysis

Concentration (%)	E^Dirg eV	E^Indirg eV	E^DirCT eV	E0 eV	EU meV	S
0	3.23	3.01	4.36	3.18	93.83	0.276
10	3.13	2.64	4.26	3.26	217.28	0.119
20	2.99	2.26	3.55	3.27	597.78	0.0433
30	2.95	1.95	3.40	3.28	136.28	0.190
50	2.38/1.06	−0.31/−0.45	0.85	—	—	—
100	1.26	0.2	3.58	—	—	—

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Fig. 10 Tauc plot of (F(R)hν)^m versus hν for m = 2 and m = 1/2 to estimate the direct allowed and indirect allowed band gap of BL0 to BL100.

Fig. 11A and B show the Tauc's plots of BL10, BL20 and BL30; the Tauc plot of BL50 is not shown here. BL50 is found to have two vivid linear regions at lower energies (1.5 eV–2 eV and 3.2 eV–3.33 eV), corresponding separately to the band gap energies of BL100 and BL0, respectively. The variation of E_g relative to BL0 is shown in Fig. 11C. The variation shows a relatively linear fall up to BL30, being abrupt thereafter. The E^Dir_CT also shows a similar variation, which is not shown here. It should be noted that each of these Tauc's plots contains two distinct linear regions in the first absorption regime: one at the lower-energy part and the other at the higher-energy range of the inclination (3.00 eV–3.3 eV and 3.3 eV–3.50 eV). This means that the overall absorption is not abrupt, but rather gradual upon compositing. As per standard analysis for band gap estimation, the immediate linear region next to the exponential growth is considered in the present investigation for estimation of E_g. Before one attempt to explain the reduction in E_g, it is essential to consider the overall softening of inclination of α(λ) in the strong absorption regime and the significant tailing of absorption below the absorption edge. Both findings, especially the tailing (Urbach tail), are a direct indication of high defect densities or disorders in the system.^{92,107,140,141} Absorption coefficient has exponential growth with respect to energy in the tail region. The relationship is given by , where α₀ and E₀ are constants called Urbach focus (E₀, α₀) or convergence point. The α₀ (scaling parameter) and E_U (rate parameter) decide the exponential growth. E₀ is frequently referred to as the absorption edge energy, and it is roughly equal to the energy of the lowest free exciton at zero lattice temperature, or, in other words, the energy of the band edge in an ideal or unperturbed structural environment. The expression is widely known as the Urbach rule or Martienssen–Urbach (MU) rule.^94,139,142 The MU rule enables the estimation of E_U by taking the natural logarithm of F(R), where it shows exponential growth (only the tail part) near the absorption edge. The resulting variation as a function of energy E or (E − E₀) is then fitted to a straight line, and the inverse of slope represents E_U. However, in the present investigation, the differential analysis and deconvolution proposed by Canul et al.¹⁴³ is used to estimate E₀ and E_U. The advantage of this method over the conventional method is that it enables the estimation of E₀ and E_U even in materials with nonlinear band edges and complex fine structure. To illustrate the estimation E₀ and E_U, the plots depicting the calculation for BL0 are shown in Fig. 12.

Fig. 11 Tauc's plots of BL10, BL20 and BL30, estimating the direct allowed and indirect allowed band gaps (A) and (B) and the variation in E_g across the series.

Fig. 12 Plots of F(R), ln F(R), the first-order derivative of ln F(R) with respect to energy, and the inverse of this derivative for the estimation of the Urbach focus and Urbach energy, E₀ and E_U.

The E_U of BL0 is close to the reported value for tetragonal polycrystalline bulk BaTiO₃, which is 84–86 meV. As E_U a measure of total disorder, it is expected to increase with structural disorders and defects at the micro- to nano-scale. For instance, nanocrystalline BaTiO₃ films have an E_U of 260 meV. The slightly higher value of E_U for BL0, i.e., 97 meV, asserts the existence of defects in BaTiO₃. Prior to the estimation of E_U, the gradual increase of α(E,T) in the tail region itself is a visual proof for resident disorders in the system, which gives rise to weak absorptions due to electronic transitions between extended bands and localized states (Urbach-band-tail states) in the forbidden gap. The disorder in this case is likely produced by impurities or defects, such as O and Ti vacancies.¹⁴⁴ Another parameter that indicates the inclination and width of straight-line near the absorption edge is the steepness parameter, S, given by . This parameter is a measure of the strength of electron–phonon interactions. A reduction in S indicates enhanced electron–phonon interaction in the composites.

Finally, the task of compositing BTO with LNMO results in composites with a high density of defect states, effectively extending the absorption into the visible region of the EM spectra, or to state it differently, the act of compositing BTO and LNMO results in a systematic reduction in E_g. This development can effectively translate into applications in photodetection, photovoltaics and high-temperature optoelectronics. Furthermore, the visible band gap, high Urbach energy and induced magnetism are perfect combinations of characteristics needed for water splitting and photocatalysis for degradation of pollutants such as dyes.

3.3 Magnetic characteristics

The temperature dependence of magnetic susceptibility, χ(T), in zero field–cooled (ZFC) and field-cooled (FC) modes, along with the first order derivative, dχ/dT, and the inverse susceptibility, χ⁻¹(T), for BL0 and BL100 are shown in Fig. 13 (panels A, D, B, E, C and F, respectively). The BaTiO₃ in its stochiometric form is a ferroelectric insulator. A perfect BaTiO₃ lattice is diamagnetic due to null value of free electron spin (S = 0) in each ionic species that are involved in the formation of BaTiO₃.¹⁴⁵ However instead of showing diamagnetism, BL0 shows χ(T) variations that change between small positive values, showing inflections at two points as T reduces from 400 K. The first abrupt shift in FC susceptibility to a higher positive value occurs at 127 K, followed by a second at 16.5 K. The increase is almost semi-saturated (constant slope) till 16.5 K and then there is sudden escalation to continuously growing susceptibility. The nature of ZFC susceptibility is contrasting in the case of both χ(T) and χ⁻¹(T). Interestingly, the ZFC χ shows an intermediate transition at 118 K, and the magnitude of ZFC susceptibility shows a maximum (cusp) at 125 K, before it decreases to a magnitude less than its high-temperature value (below 118 K). The χ⁻¹(T)_ZFC shows a dip at 125 K, then escalates to a significantly larger value and falls off again below 16.5 K. The FC and ZFC curves show a significant bifurcation below 127 K; however, the bifurcation starts far above (230 K) the transition temperature. The difference between FC and ZFC susceptibilities, Δχ, is nonzero from ∼230 K, and it is equal to 2.85 × 10⁻⁶ emu g⁻¹ Oe⁻¹ at the lowest measured temperature. This implies a very high magnetic anisotropy in the system. Here, all transitions are identified using dχ/dT. The minimum (#) observed in dχ/dT (127 K) indicates a weakly ferro/ferrimagnetic (FM/FEM) transition, and the maximum (@) at 118 K indicates spin frustration. The overall behavior below 230 K, particularly below 127 K, suggests a cluster glass (CG) or a spin glass (SpG)–like state.¹⁴⁶ It is assumed that a random distribution of clusters of nonmagnetic, stochiometric BaTiO₃ containing Ti⁴⁺ and ferromagnetic nonstoichiometric BaTiO₃ and its nonequilibrium phases (containing mixed valency as a consequence of B-site deficiencies and oxygen vacancies) of different sizes is responsible for magnetic frustrations at low temperatures. Density functional calculations by Raeliarijaona et al.¹⁴⁷ revealed the underlying mechanism that establishes FM in ferroelectric BaTiO₃ by considering the native vacancies. The possible vacancy states that can induce FM in BaTiO₃ are V⁰_O1, V⁰_O2, V_Ti³⁻, V_Ti²⁻, V_Ti¹⁻, V⁰_Ti and V⁰_Ba, depending on processing conditions. Here, V^X_q denotes a vacancy of species X carrying a charge of q. Under O-rich conditions, cationic vacancies are most favourable and vice versa. Generally, the most considered vacancies are V_Ti³⁻ and V⁰_O1 due to their extended stability under two extreme PO₂ conditions. Amongst all, FM induced by V_Ti³⁻ is very stable and has a large magnetic moment compared to other vacancy species, whereas the moments associated with V⁰_O1 and V⁰_O2 are minimal. Furthermore, based on these calculations, the AFM state is not possible in BaTiO₃, as there is no species of vacancy that contains a null magnetic moment and possesses the negative energy difference essential for AFM ordering. The origin of FM induced by cationic vacancies lies in spin polarization of itinerant holes at O 2p orbitals, whereas the magnetism from oxygen vacancies originates from the spin polarization of itinerant electrons at Ti t_2g orbitals.¹⁴⁸ Finally, this induced magnetism due to cationic and anionic vacancies shows a significant temperature dependence. It is interesting to note that the net magnetic moment of V⁰_O1 becomes virtually null beyond 120 K, but the FM from V_Ti³⁻ can survive even at very high temperatures (∼1300 K). It has also been identified that V⁰_O1 vacancies are more susceptible to forming due to their low formation energy.¹⁴⁸ Therefore, an oxygen vacancy at the surface can effectively create mixed valency for Ti (Ti³⁺/Ti²⁺), which directly contributes to the FM in BaTiO₃.¹⁴⁹ These findings from the literature enable the assertion that perhaps both V⁰_O1 and V_Ti³⁻ are possible vacancies that exist in BL0 under a given normal PO₂ and short sintering durations. The magnetic transition observed at 127 K is in agreement with the FM transition induced by oxygen vacancies. It is believed here that there exists a random distribution of FM clusters of different sizes in BL0. Upon ZFC, these clusters freeze into random orientations dictated by a local anisotropy field. When field-cooled, the clusters align, and they lead to the onset of a large FM-type magnetization, unlike in cases of competing FM and AFM interactions, where the FC curve saturates. The failure to fit the Curie–Weiss law at temperatures above the transition temperature or freezing temperature T_f is because of the significant diamagnetic background in the paramagnetic susceptibility. The observed RT FM in BL0 with a robust SpG state at low temperature is attention-worthy for a wide range of multiferroicity in the so-called prototype ferroelectric BaTiO₃.

Fig. 13 Temperature dependence of the magnetic susceptibility of BL0 (A) and BL100 (D) measured in zero-field cooled and field-cooled mode at a magnetization intensity of 100 Oe. The dχ/dT (BL0:B and BL100:E) indicates the different inflection points in the susceptibility curve. The inverse susceptibility (BL0:C and BL100:F) is used to depict the typical magnetic nature of the specimens.

Reported studies on La_0.835Na_0.165MnO₃ reveal that it is a second-order soft ferromagnetic semiconductor with a Curie temperature T_C in the range of 321–343 K.^37,150 In the present case, BL100 shows a sharp PM to FM transition with a decrease in temperature. The transition temperature, T_C, is 331.6 K (marked as %). This value does not match any previously reported value, perhaps due to the nonstoichiometry observed in BL100 compared to nominal La_0.835Na_0.165MnO₃. The large magnetic sensitivity, nearly −1.6 emu g⁻¹ K⁻¹, indicates the abruptness of the magnetic transition and reflects a significant response of magnetic moments to a small change in the applied magnetic field (100 Oe). Furthermore, a small hump in the FC curve is observed around 296 K (marked as &), which is interesting as the monoclinic manganite secondary phase is concerned. Such a hump is a consequence of a PM to FM transition in a La_0.9MnO₃-like phase.^151–153 Generally, La_1−xMnO₃ has a limiting value of the self-doping range. Any composition x > 0.125 exhibits saturation with respect to physical properties such as the extent of rhombohedrality (constant rhombohedral angle α) saturate, leading to the precipitation of parasitic Mn₃O₄ impurity phase and a constant T_C (250–260 K).^{44,151,153–155} However, the unusually high transition temperature of 296 K can be due to multiple double-exchange interactions facilitated by the incorporation of Mn²⁺ at the A-site of the crystal lattice.⁷³ The occurrence of two different T_C values, essentially for rhombohedral and monoclinic manganites, can be understood by considering the static coherent Jahn–Teller (JT) distortion. Ferromagnetism in manganites occurs due to the simultaneous hopping of e_g electrons between B-site cations (Mn³⁺ and Mn⁴⁺) via a bonding ligand. The strength of this hopping depends on the extent of mixed valency, the average bond length (〈Mn–O〉) and the average bond angle (〈Mn–O–Mn〉). Structural distortions and mismatches in the orbital overlap between ligands and cations play a crucial role in deciding the transfer integral for double-exchange hopping. This dictates the correlation between ferromagnetism and JT distortion mediated by spin-charge-lattice coupling. The coherent distortion parameter, σ_JT, is defined as . Here, (Mn–O)_i are the three independent Mn–O bond lengths, and 〈Mn–O〉 is the average Mn–O bond length.¹⁵⁶ In the rhombohedral R3̄c SG, all three Mn–O distances are equal. Thus, the coherent JT distortion parameter is zero. The static coherent JT distortion of the MnO₆ octahedra provides an additional carrier localization in distorted perovskites. Therefore, the absence of static coherent JT distortion is favourable for the hopping of e_g electrons and leads to an enhanced DE interaction, which gives rise to a high Curie temperature T_C for rhombohedral manganites. In contrast, σ_JT calculated for the monoclinic phase is nonzero but has a value of 0.050. This accounts for the lower T_C observed for the monoclinic phase and thus two transitions observed in the χ(T) variation of BL100. In this context, the bandwidth of conduction electrons indicates whether an electron is itinerant or localized, thus deciding the exchange interactions between magnetic ions, Mn³⁺ and Mn⁴⁺. The bandwidth W is defined as , where , and d_Mn–O is 〈Mn–O〉. The estimated bandwidths for the rhombohedral and monoclinic phases are 0.095 and 0.093, respectively. Clearly, the smaller bandwidth of the monoclinic phase reduces orbital overlap between ligands and cations involved in the hopping mechanism. The bandwidth estimated for BL0 is found to be 0.086, which justifies the insulating nature of BL0 amidst weak ferromagnetism that it displays and the low T_C of 127 K. The ZFC of BL100 shows a small cusp at 42 K, indicative of a ferrimagnetic transition of Mn₃O₄.

The temperature dependence of χ(T) in ZFC and FC modes, the χ⁻¹(T) and temperature dependence of dχ/dT for BL10, BL20, BL30 and BL50 are shown in Fig. 14. Each composite displays a vivid PM to FM transition similar to that of BL100, except for the fact that an unusual thermal hysteresis is observed between the ZFC and FC curves in the temperature range from 290 K to 330 K, where they finally merge to show PM nature. Here, the ZFC curve appears above the FC curve, which is a mere consequence of loosely held titanate and manganite particles/gains at the microscopic level (the poor compactness and large porosity are discussed in the microstructural analysis of composites). A similar feature has been reported in Fe³⁺-doped CdS nanoparticles, where the said feature observed in powders disappears after proper pelleting.¹⁵⁷ The susceptibility increases as the BL100 concentration increases, indicating the inclusion of magnetic material into the nonmagnetic matrix. Interestingly, the small jumps observed at 296 K and 42 K in the FC curves, as well as the cusp at 42 K observed in the ZFC curve of BL100, become very prominent in the temperature-dependent variation of χ(T) and dχ/dT (marked as & and $ in Fig. 11, respectively,). The consistency of the T_C (∼331 K) across the composite composition indicates minimal or no structural intercalation between the manganite and titanate phase.

Fig. 14 Temperature-dependent variation of dc susceptibility (left y-axis of left panel), temperature-dependent variation of inverse susceptibility (right y-axis of left panel) and the first-order derivative of susceptibility (right panel) for all the composite compositions.

At this point, to confirm the FM nature of the samples and to estimate the effective paramagnetic moment, the high-temperature susceptibility was fitted to the Curie–Wiess law. The Curie–Weiss (CW) law for composite system containing diamagnetic components is given by . Here, is the Curie constant (N_A is the Avogadro's number, k_B is the Boltzmann constant, and μ_eff is the effective magnetic moment), θ_p is the Weiss constant, and χ₀ is the temperature-independent term of the susceptibility. The term χ₀ is a sum of the negative (diamagnetic) Larmor core susceptibility, the positive Pauli paramagnetic spin susceptibility of conduction electrons, the negative Landau susceptibility due to the orbital circulation of conduction electrons in the magnetic field, and the positive Van Vleck paramagnetic susceptibility, where all four contributions are of the same order of magnitude. The experimental determination of χ₀ was performed by plotting χ versus , and χ₀ is estimated by extrapolating to the high-temperature limit , where the contribution of becomes negligible.^158,159 Alternatively, a nonlinear fit of the high-temperature susceptibility data to the CW law can yield the parameters χ₀, C and θ_p. Furthermore, versus T is plotted to determine C and θ_p, resulting in a linear fit. Conventional CW analysis is adopted for BL100, as it is soft ferromagnet and temperature-independent contributions to the χ are negligible. BL0 was not fitted due to a strong diamagnetic signal above T_f. The Curie constant obtained from the linear fit of χ − χ₀⁻¹ or from nonlinear curve fitting, where χ in the units of emu mol⁻¹ would give μ^exp_eff through . The theoretical value of μ_eff (μ^th_eff) is obtained using the expression , where μ_eff(Mn³⁺) = 4.9µ_B and μ_eff(Mn³⁺) = 3.87µ_B. In this investigation, for a charge ratio of 67 : 33, μ^th_eff = 4.59µ_B. The values of χ₀, C, θ_p and μ_eff obtained from the fit alongside the T_C and μ^th_eff are tabulated in Table 5.

Table 5 Temperature-independent susceptibility χ₀, Curie constant C, Wiess constant θ_p, effective paramagnetic moment μ_eff, estimated both experimentally and theoretically, and the Curie temperature T_C

Sample code	Nonlinear curve fitting,				Linear fit to χ − χ0^−1			TC (K)	μ^theff (µB)
	χ0 × 10^−6 emu g^−1 Oe^−1	C (emu mol^−1 K)	θp (K)	μ^expeff (µB)	C (emu mol^−1 K)	θp (K)	μ^expeff (µB)
BL10	1.57	0.187	317.0	1.22	0.187	316.9	1.22	330.8	4.59
BL20	2.12	0.439	318.7	1.87	0.439	381.8	1.87	331.6	4.59
BL30	3.78	0.607	317.2	2.20	0.606	317.3	2.20	331.8	4.59
BL50	7.66	0.964	313.3	2.78	0.965	313.3	2.78	331.6	4.59
BL100	—	—	—	—	3.85	330.2	5.55	331.6	4.59

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In the present case, the positive value of χ₀ perhaps indicates Van Vleck paramagnetic susceptibility, possibly due to the low-lying excited states of Mn³⁺. It is found to increase with an increase in BL100 component, indicating its dependence on the population of Mn3+.¹⁶⁰ The positive value of θ_P indicates the existence of FM interactions in the samples, which confirms a PM to FM second-order phase transition. The higher value of μ^exp_eff compared to μ^th_eff in BL100 indicates that the sample does not have the expected 67 : 33 charge ratio; rather, there is a larger population of higher-moment species of Mn. This higher magnetic moment can come from an unexpectedly larger population of Mn³⁺ and Mn²⁺. In the high spin state, the spin-only magnetic moment of Mn ions increases with decreasing oxidation state, i.e. μ_Mn²⁺ > μ_Mn³⁺ > μ_Mn⁴⁺, which are 5.92µ_B, 4.9µ_B, and 3.87µ_B, respectively. Studies on La_1−xSr_xMnO₃ through electron spin resonance and magnetic measurements have shown that perovskite manganites are inhomogeneous ferromagnet, which means FM clusters are found even above T_C.^161,162 As a result, it leads to a larger value of μ^exp_eff compared to μ^th_eff. However, in BL100, θ_p = T_C, which means it perfectly follows the classical CW law and hence is a homogenous ferromagnet. Spinal Mn₃O₄ also contains Mn²⁺ at tetrahedral sites (and two Mn³⁺ at octahedral sites); however, the percentage of detectable Mn₃O₄ is too low to consider it to be a source of excess Mn²⁺ and Mn³⁺. This means that the only possibility of having higher μ^exp_eff compared to μ^th_eff is the presence higher concentration of Mn³⁺ and Mn²⁺ in the perovskite lattice. Structural investigations have already been suggested the presence of Mn²⁺ in BL100, in both rhombohedral and monoclinic phases. Here, the CW analysis confirms the presence of Mn²⁺ in BL100 and supports the existence of multiple double-exchange mechanisms due to the presence of Mn antisite defects, where Mn²⁺ occupies La and Na sites in the perovskite lattice. Suppose that one considers the magnetic contribution in the composites comes only from the manganite phase, the magnetic phase fraction can be estimated from the computed magnetic moment. The phase fraction was found to be 22%, 34%, 40% and 50% for BL10, BL20, BL30 and BL50, respectively. One can notice that in BL50, the magnetic phase fraction is exactly nominal, but the structural phase fraction is found to be 10% less than the nominal phase fraction. It is quite interesting to note that the structural phase fraction is almost nominal in BL10, BL20 and BL30, but the magnetic phase fraction exceeds 10%. This confirms the magnetic nature of BL0, and in the composite, the contribution to the magnetic moment not only comes from the manganite phase but also from the titanate phase. To support the claim, magnetic isotherms were recorded for all the samples at 5 K and at 300 K.

Fig. 15 depicts the magnetic isotherms of BL0 recorded at 5 K and 300 K. Both hysteresis loops show a negative linear slope in the evolution of M for the positive field increment and vice versa. This occurs at very high fields (40 kOe) for the 5 K isotherm and just at 1 kOe in the case of 300 K isotherm. However, at low fields, the M variation is abrupt, showing a sudden positive increase with a change in H. This behaviour is evidence of FM spin clusters embedded in a diamagnetic background. To extract the FM magnetization from the diamagnetic response, a linear fit (M = χH, χ < 0) was applied to the high-field M–H data at 5 K (shaded region, A). The diamagnetic susceptibility was found to be −1.24 × 10⁻⁷ emu g⁻¹ Oe⁻¹ for the 5 K isotherm. Using this value, the corrected M was obtained by subtracting e χ_diaH form M_obs. The calculated values of M_s, M_r and H_c are 0.017 emu g⁻¹, 3.30 × 10⁻⁴ emu g⁻¹ and 100.97 Oe, respectively. Quite differently, the experimental data of 300 K was fitted using the equation .^163,164 Here, M_s stands for the saturation magnetization, H_c is the intrinsic coercivity, and M_r is the remanent magnetization. The first term in the equation represents the usual function for ferromagnetic hysteresis curve, and χH stands for the linear diamagnetic or paramagnetic contribution to the M–H loops. The obtained values of M_s, M_r, H_c and χ_dia are 0.002 emu g⁻¹, 2.33 × 10⁻⁵ emu g⁻¹, 11.61 Oe, −3.73 × 10⁻⁷ emu g⁻¹ Oe⁻¹, respectively. Considering the χ_dia, the M was corrected and is shown in Fig. 15D. One can notice here that the hysteresis loop at 5 K is S-shaped with finite remanence and coercivity, whereas the hysteresis loop at 300 K shows soft ferromagnetic nature with complete saturation and squeezing toward the H = 0, indicating a bi-magnetic nature. The M_s at 5 K is an order of magnitude higher than at 300 K. Such an S-shaped loop, which is only observed at low temperatures (below T_f), is characteristic of both metallic and non-metallic spin glasses and indicates the presence of short-range magnetic correlation in the system at low temperatures.^165–167 This observation supports the claim of a CG/SpG nature in BL0 at temperatures below 127 K. It is interesting to see that BL0 displays room-temperature ferromagnetism. As discussed in the previous section, FM at RT is generally induced by Ti vacancies; however, a Cu-doped TiO₂ shows FM at room temperature due to oxygen vacancies near the impurity, such as Cu.¹⁶³ Therefore, it is believed that FM in insulating oxide perovskite can be realized by cationic vacancies and anionic vacancies, which results from spin polarization of itinerant holes at ligand orbitals and spin polarization of itinerant electrons at B-site cationic orbitals, as discussed earlier.

Fig. 15 Hysteresis loops of magnetization versus applied field intensity of BL0 record at 5 K (A) and 300 K (C) for a field cycle of 0 ± 50 kOe. Each isotherm is corrected for high-field diamagnetic contributions ((B) and (D), respectively) using linear and nonlinear fitting.

Fig. 16 shows the M–H hysteresis loops of BL100 recorded at 5 K (A) and 300 K (B). Before one would analyse the magnetic field dependence of magnetization, it is essential to account for the demagnetization effect in randomly shaped magnetic specimens subjected to an external magnetic field (H_ext). Due to the random dimensionality, the internal field experience by the specimen (H_int) is quite different from that of H_ext. The demagnetization correction is expected to reveal the intrinsic field experienced by the ferromagnetic material due to the dimensional variations. Once the demagnetization corrections are applied, the magnetic field axis can be defined as H_int = H_ext − N_dM, where N_d is the demagnetizing factor, and M is the corresponding magnetization.¹⁶⁸ For a multidomain grain system, N_d can be obtained from the initial knowledge of H_c and M_r, the initial susceptibility χ or the initial inverse slope of the M–H curve. The approximate value of N_d is given by .¹⁶⁹ Furthermore, the values of H_c, M_r and M_s shed light on the nature of FM in the sample. A rough estimate of the saturation magnetization, M_s, can be obtained from Arrott plots, where extrapolation of the linear portion of the M² versus curve to the M² axis at higher values yields M_s.¹⁷⁰ The obtained values of M_s, H_c and M_r are summarized in Table 6. The sudden increase in M at low H, the small magnitude H_c and M_r, the saturation of M at high H and the positive slope of Arrott plots (not shown here) signify a second-order phase transition (SOPT) and the soft ferromagnetic nature of all the samples below the Curie point (except for BL0).¹⁷¹ It is interesting to note that M_r, H_c and M_s in the composite are found to slightly increase with increasing ferromagnetic BL100 content (however, H_c in BL0 is the highest among all samples, 101 Oe).

Fig. 16 Hysteresis loops of magnetization versus internal field intensity of BL100 record at 5 K (A) and 300 K (B) for a field cycle of 0 ± 50 kOe. (C) and (D) Magnetic isotherms of the composites under similar conditions as BL100. Each isotherm has been corrected for demagnetization effects.

Table 6 Retentivity (M_r), coercivity (H_c), demagnetization factor (N_d), saturation magnetization (M_S), magnetocrystalline anisotropy constant (K₁), and anisotropy field (H_a) obtained from hysteresis loop analysis, Arrott plots and LAS

Specimen	Mr emu g^−1	Hc Oe	Nd			Ms emu g^−1		K1 × 10^3 erg g^−1	Ha Oe
							LAS
BL0	0.00033	101.0	—	—	—	0.02	—	—		—
BL10	0.2	35.8	215.7	250.0	238.6	6.8	7.1	3.5	977.3	0.03
BL20	0.4	31.0	76.2	100.0	89.0	15.9	16.5	12.0	1451.1	0.03
BL30	0.7	31.6	44.8	62.5	53.3	22.4	23.3	18.4	1573.7	0.03
BL50	2.0	47.7	23.6	35.7	30.2	36.4	38.3	18.7	976.7	0.05
BL100	1.3	14.2	10.8	11.9	11.5	93.7	96.4	89.3	1851.6	0.01

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The M_s value observed in BL50 is the highest of all composites (36.4 emu g⁻¹), which is 39% of BL100. Conversely, the coercivity of the composites and BL0 is higher than that of BL100, and the retentivity of BL50 is higher than that of BL100. This clearly indicates that a robust FM network is established in the composite with obvious broken FM network leading to dilution. The higher H_c in the composites indicates the anisotropy in the sample. To understand the effect of magnetic anisotropy, all 5 K M–H curves in the first quadrant of the hysteresis loop were fitted using the law of approach to ferromagnetic saturation (LAS) to extract the magnetocrystalline anisotropy (MCA, K₁), anisotropy field (H_a) and M_s.

There are several forms of the LAS,¹⁷² depending on the type of FM material, composition and particle size. Its efficacy is proven mainly in single-domain, noninteracting particle systems. In the case of magnetic materials with a multi-domain structure, the process of magnetization varies across different regions of the magnetization curve. The lower-field region, below saturation, consists of a mixture of domain wall motion and domain rotation. As M approaches saturation, the magnetization process is mainly dominated by domain rotation. If the high-field region is carefully selected, LAS can still be applied to multidomain structures to extract M_s, (K₁) and (H_a). The fit is shown in Fig. 17. The region where domain rotation is dominant is approximately above 4πM_s of H; therefore, the fit is applied to this region of the M–H curve or sufficiently above the Rayleigh region. Some authors report that the LAS works only if the following conditions are met: H ≫ H_c and .¹⁷³ In the present case, the LAS is defined as .^174,175 Here, the parameter a is attributable to various structural defects and intrinsic fluctuations; hence, represents the contribution from random anisotropy. The parameter is related to the uniaxial magnetocrystalline anisotropy constant, K₁, and anisotropy field, H_a. χ_hf, corresponds to the high-field susceptibility. The fit is applied only to the 5 K M–H curve in the first quadrant, as the 300 K M–H curves lack approach to saturation. The obtained values of M_s, K₁ and H_a are tabulated in Table 6. The close agreement between the M_s values obtained from the two different approaches indicate the validity of the fitting model. The K₁ values are significantly lower in the composites compared to BL100. Interestingly, H_a shows a local minimum at BL50, hinting a correlation between the structural and magnetic phase fractions discussed earlier. In other words, the magnetism in the composites strictly follows the magnetic phase fraction, i.e. the percentage of La_0.835Na_0.165MnO₃. M_s increases with BL100 content and so is the M_r. The squareness ratio, defineas , is less than 0.5, which indicates that the samples possess a multidomain structure and that BL100 particles are randomly distributed in the composites, free from grain interaction effects.¹⁷⁶ Furthermore, M_s is correlated to the Bohr magneton (µB per f.u.), and it can be determined using the following equation: .¹⁷⁷ The value changes from 0.3µB per f.u. for BL0 to 3.7µB per f.u. for BL100. The continuous increase in M_s is obviously due to the incorporation of soft ferromagnetic La_0.835Na_0.165MnO₃. However, the sudden increase and saturation behaviour of K₁ and H_a require attention. K₁ is a measure of energy per unit volume required to move the magnetization vector from the easy axis to the hard axis. As a result, the small fraction of BL100 in BL10 weakens magnetic interactions. This means the energy required to move the M vector per unit volume is low. The saturation behaviour of K₁ in BL30 and BL50 reflects a similar magnetic concentration in the composites due to non-stochiometric substitution. In manganites, Mn³⁺ is a source of MCA, which means a smaller fraction of Mn³⁺ in the composites is responsible for the lower values of K₁. To put it in other words, the dilution of La_0.835Na_0.165MnO₃ in a nonmagnetic matrix results in the averaging of magnetic anisotropies. Finally, magnetic materials with strong MCA offer superior properties for applications in magnetoresistive random-access memories (MRAMs) and multifunctional spintronic devices.¹⁷⁸

Fig. 17 5 K magnetization data in the first quadrant of the hysteresis loop under the governance of law of approach to ferromagnetic saturation.

3.4 Ferroelectric characters

Reported temperature-dependent dielectric measurements on BaTiO₃ showed that below 120 °C, cubic BaTiO₃ spontaneously changes to tetragonal crystals and becomes polarized along the tetrad axis or cube face direction [001] (P_s ≈ 14–16 µC cm⁻²). Interestingly, it further shows orthorhombic and rhombohedral phase transitions at −5 °C and −90 °C, respectively, having slightly lower polarization values (∼12 µC cm⁻² to 8 µC cm⁻²) along the cube-edge direction [110] and the cube-diagonal direction [111]. Ferroelectricity in BaTiO₃ is a consequence of masking of short-range Coulombic repulsion between Ti⁴⁺ and O²⁻. Ferroelectricity occurs when the long-range force due to dipole–dipole interactions overcomes the short-range Coulombic repulsion. This allows nearly permanent movement of Ti⁴⁺ from the centrosymmetric position and O²⁻ from the face centre position such that some of the Ti–O bonds can be shorter than the others, and the effective charges on Ti and O can significantly deviate from 4+ and 2−. The covalent hybridization between Ti and the O ions helps weakens the short-range Coulombic repulsion.¹⁷⁹ Knowing the origin of FE in BaTiO₃ to understand the possible FE in the composites, BL10 is selected for recording the P–E hysteresis loop.

Fig. 18(1) depicts the RT polarization (P) versus electric field (E) hysteresis loops (P–E loops) of BL10 under E₀ magnitude of 250 V (1.63 kV cm⁻¹), 500 V (3.27 kV cm⁻¹) and 1000 V (6.54 kV cm⁻¹). Note that it was possible to obtain P–E loops only up to 1000 V, post which there was a dielectric breakdown. The measurements were carried out under unpoled conditions. At first glance, one can see that loops lack saturation polarization. Many reports call such behaviour necessarily as lossy or leaky ferroelectricity, but not sufficiently, because in a real scenario, such behaviour results from the combined effect of a linear capacitor and a parallel resistor. Here, the hysteresis features shall appear with increasing conductivity, but neither saturated polarization nor switching current can be observed.¹⁸⁰ Thus, BL10 is lossy or leaky but not ferroelectric. To confirm the said assertion, the influence of the electric field on the P–E loop area (A) and leakage current density (J) was considered for evidential analysis. When comparing P–E loops at different AC field amplitudes (E₀), the area under the loop is a key parameter. The hysteresis area is strongly associated with the nucleation and growth of the domain, domain wall motion and domain switching.¹⁸¹ The areas under the loops were obtained by integration, and to investigate the dependence of A on E₀, the graph of the ln A versus ln E₀ was plotted (Fig. 18(2)). The variation follows a linear trend and can be modelled as ln A = β ln E₀ + b. Here, β is the slope of the straight line. The β for BL10 is 2.19 ± 0.01. If BL10 was to be a ferroelectric, it would show three distinct regions in the ln A versus ln E₀ plot. The first linear region signifies the domain wall motion. The slope in the first region would be high, indicating that domains easily follow the external electric field. The second region would be a nonlinear region, which is associated with abrupt changes in the polarization value at a given E₀. Here, the domain switching mechanism leads to a sudden enhancement in the values of current and polarization. The third region would again a linear region, which denotes the complete saturation, and almost all the dipoles here are orientated along the direction of the applied electric field. This region typically exhibits a smaller slope compared to the first region. The case of BL10 reflects only the first linear region due to its stability only at low amplitudes of the AC field. The earlier reports state that even in leaky ferroelectrics, the β of the first linear region is not less than 3. The low β value in BL10 indicates that domain wall motion is restricted. This restriction does not allow nucleation and growth necessary for eventual saturation. This finding demands attention towards the microstructure of BL10 compared to the parent BL0. An ideal ferroelectric material is, by default, insulating in nature. The lossy nature in any ferroelectric is then directly related to the increase in its conductivity. Studying the variation of J in a leaky ferroelectric becomes apparent because it enables one to understand the interfacial and internal variation of currents (displacement, leakage and capacitive). Fig. 18(3) shows leakage current density versus electric field curves (J–E curves) of BL10 under various E₀ magnitudes. The curves are symmetric with respect to positive and negative field sweeps. The J is found to be 1.72 A m⁻² at E₀ of 1.63 kV cm⁻¹ and grows to 8.42 A m⁻² at 6.54 kV cm⁻¹. These values of current density are typically large compared to BaTiO₃ films, in which the corresponding values are found to be 0.005 A m⁻² even at a field intensity of 100 kV cm⁻¹.^182–184 The variation of J is such that there exists a gradual change when going from low AC field to a higher, with a tendency to saturate at high fields. The change in J with an increase in the electric field prompts the presence of a specific conduction mechanism in the specimen. There is an array of mechanisms that decide the variation of J with respect to E in oxides. The notable ones are Ohmic conduction, space-charge-limited conduction (SCLC), Poole–Frenkle emission (PFE) and field-assisted hopping (FAH) conduction.^185–188 Ohmic conduction is an interface-limited conduction mechanism, whereas SCLC, PFE and FAH are bulk-limited conduction mechanisms. The existence of interface-limited conduction mechanisms arises from the difference in Fermi levels between the metal (electrode) and the insulator or semiconductor (BL10). This energy difference creates a potential barrier between the metal and the insulator, which charges must overcome. Essentially, this barrier is Schottky in nature, thus, the current density at low fields takes the form . Here, is the field-dependent term, A* is the effective Richardson constant, T is the temperature, ϕ_B is the Schottky barrier height, k_B is the Boltzmann constant, q is the electron charge, E is the applied electric field, ε₀ is the permittivity of free space, and ε_r is the relative dielectric constant of the ferroelectric material. Suppose the energy different between the electrode and the FE medium is low, the interface may behave ohmically, and the current density may take the form J = eμn_eE, where e is the electronic charge, μ is the carrier mobility, n_e is the carrier concentration, and E is the applied electric field. Bulk-limited SCLC arises from a current-blocking space charge. The existence of SC in an insulator under an electric field is a salient feature of FEs. It happens when charges are injected into the insulator from the electrode at a rate faster than they can travel through it. The current density in such case is given by . Here, t is the thickness of the specimen. PFE essentially dominates the high-field regime of the J–E characteristics, where conduction involves consecutive hopping of charges between defect trap centres. The release of trapped charges can happen thermally as well as through the influence of a high field. The expression for current density is given by , where , and C and ϕ_t are a constant and the barrier height, respectively. On the other hand, according to FAH conduction mechanism, if the thermal energy is insufficient, charge carriers trapped in defect states become incapable of overcoming the barrier height between trap sites. As a result, if the field is essentially large, charge migration between trap centres primarily occurs by the process of tunnelling. It should be noted at this point that the ohmic conduction and SCLC mechanisms follow a power-law behaviour such that J ∝ Eⁿ, where n is the power-law exponent obtained from the slope of a log–log plot of J versus E. If n ∼ 1, the underlying conduction is ohmic and if n ∼ 2, the conduction mechanism is SCLC. On the other hand, Schottky, PFE and FAH conduction mechanisms follow semi-log nature log_e(J) versus E^1/2, log_e(J/E) versus E^1/2 and log_e(J) versus E, respectively. Fig. 18(4)–(6) shows the log–log plots of J–E curves for positive field sweeps up to E₀. Essentially, the slope is near unity in the range 0.55 to 0.72, indicating that ohmic conduction dominates in BL10. An interesting observation in the log–log plots is the trend of the slope. First and foremost, there is no single linear region in the entire logarithmic J–E variation, but multiple linear regions exist. Second, the slope increases with increasing AC field at a 250 V amplitude, whereas the trend is reversed in 1000 V amplitude. Necessarily, it prompts further investigation into the possible Schottky nature of conduction in the material. Consequently, log_e(J) versus E^1/2 was plotted and found that the plot for 250 V field amplitude indeed shows linear behaviour, indicating the Schottky nature of the electrode–sample interface. This means that the specimen at low polarizing fields is insulating in nature; however, at high polarizing fields, conductive channels are activated, which turns the sample to ohmic conductor rather than an insulating ferroelectric. The overall conduction mechanism in BL10 can be considered as grain boundary-limited conduction (GBLC). GBLC is identified by ohmic conduction, and s slope less than 1 indicates band bending with increasing field. Thus, the deviation from typical ferroelectric behaviour, including the decline of P_r and P_s, lossy loops and high leakage current density, collectively indicate a degradation in ferroelectric properties in the composites. These changes are a consequence of the presence of a non-ferroelectric phase, which restricts ferroelectric domain wall motion. The closer examination of the microstructural properties of BL10 clarifies this behavior. FESEM micrographs of BL10 show a scattered distribution of BaTiO₃ grains surrounded by fine manganite grains. LNMO manganite is a metallic ferromagnet at RT. In a broader sense, even though there is no continuous grain–grain boundary assembly, LNMO can be considered as a conducting medium around the BaTiO₃ grains at the boundaries. Thus, if the amplitude of the AC field is low, the electrode–BaTiO₃ and LNMO–BaTiO₃ interfaces can be considered as Schottky or depletion junctions, which is why band bending happens. However, as the amplitude of the electric field increases, the breakdown of leakage current occurs before it could enter SCLC, turning the mechanism into ohmic conduction. Thereby, even though FE polarization is not achieved, the leaky FE behaviour at low E₀ is essentially an attractive character in theses marginally substituted composites. It can be exploited in spintronics, non-volatile memory, neuromorphic computing and artificial synapses, low-energy nanoelectronics and logic devices, and magnetoelectric sensors.

Fig. 18 (1) Plot of electric polarization versus electric field under the bias voltages of 250 V (1.63 kV cm⁻¹), 500 V (3.27 kV cm⁻¹) and 1000 V (6.54 kV cm⁻¹). (2) Log–log plot of the area under the loop versus E₀. (3). Variation in current density with applied potential. (4)–(6) Log–log plots of current density versus E to understand the various conduction mechanisms that drive current in the BL10 specimen.

4. Conclusion

In conclusion, the synthesis of multiferroic (1 − x)BaTiO₃:(x)La_0.835Na_0.165MnO₃ composite system (x = 0, 0.1, 0.2, 0.3, 0.5 and 1) was attempted using the conventional solid-state reaction method at a low sintering temperature (950 °C) and short soaking duration (4 h). The result is nonstoichiometric Ti-deficient BaTiO_3−Δ and A-site cation-deficient La_0.835Na_0.165MnO_3−Δ. Such nonequilibrium states are the result of the termination of solubility of precursors under the given A-site/B-site cationic ratio, oxygen partial pressure and annealing temperature. The nonequilibrium BaTiO₃ phases are Ba₂TiO₄, BaTi₄O₉ and BaCO₃, whereas for La_0.835Na_0.165MnO₃, they are La_0.9MnO₃-like phase, La₂O₃ and Mn₃O₄. These impurities, once formed, are stable throughout the composite composition, giving them vivid optical, magnetic and electric characteristics. The microstructures of the prepared BaTiO₃ and La_0.835Na_0.165MnO₃ are dramatically different due to their initial processing conditions. BaTiO₃ has large grains due to elevated sintering temperature (1300 °C), whereas La_0.835Na_0.165MnO₃ grains are significantly small with loosely bound grain distribution. The combination of the distinct optical characteristics of two different perovskite materials, one being the UV absorber (BaTiO₃) and the other being the UV-visible absorber, has created excellent visible photoactive materials (x = 10, 20, and 30) with a band gap tunable from 3.23 eV to 2.95 eV at x = 30. The samples possess high Urbach energy due to a large population of defect states established in the forbidden gap of the parent BaTiO₃. The composites can thus be exploited for water splitting and the degradation of water pollutants, employing a large light-harvesting window. An interesting outcome of the exercise is the induction of ferromagnetism in insulating, nonmagnetic BaTiO₃ at room temperature. Ti deficiency renders ferromagnetism in BaTiO₃ through spin polarization of itinerant holes at O 2p orbitals and spin polarization of itinerant electrons in Ti t_2g orbitals. The random distribution of clusters of nonmagnetic stochiometric BaTiO₃ containing Ti⁴⁺ and weakly ferromagnetic, nonstoichiometric BaTiO₃ and its nonequilibrium phases containing Ti³⁺ of different sizes brings out magnetic frustration, perhaps displaying a cluster glass ground state. However, a deeper analysis is needed to understand the dynamics at low temperatures. The A-site cationic-deficient La_0.835Na_0.165MnO₃, along with the La_0.9MnO₃, displays excellent magnetic sensitivity. The composites possess a prominent ferromagnetic ground state with significant magnetocrystalline anisotropy. The intention of inducing ferromagnetism in ferroelectric BaTiO₃ through composites is fulfilled; however, failure in establishing multiferroicity is faced due to the generation of large free carriers in the insulating ferroelectric BaTiO₃ matrix. The composites are no longer ferroelectric insulators, but they have translated into an ohmic conductor.

Author contributions

LDM: conceptualization, data curation, formal analysis, investigation, methodology, visualization, writing – original draft. EKH: investigation, validation, writing – review & editing. MDD: funding acquisition, project administration, supervision.

Conflicts of interest

The authors declare that there are no competing interests to declare.

Data availability

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d5ma01177a.

Due to the large amount of raw data and related calculation in this paper, it is not possible to upload all the data to the public network, so we will disclose the raw data and relevant calculation involved in the research process on request.

Acknowledgements

The Manipal Academy of Higher Education and UGC DAE Consortium for scientific research (UDCSR/MUM/CD/CRS-M-240/2017/1008) are acknowledged for their support in carrying out the present research. The authors are thankful to Dr Mukul Gupta (UGC DAE CSR, Indore) for XRD measurements, Dr Sujay Chakravarty (UGC DAE CSR, Kalpakkam Node) for magnetization measurements. Mendonca L. D. is thankful to Patricia Mendonca, Leslie David Mendonca and Stella Ronny Lewis for their invaluable cooperation throughout the work and during the preparation of the manuscript. Pramod R. Nadig, Vignesh K. R. Kavya D. M. and Srujana B. S. are acknowledged for fruitful discussions on structuring the entire manuscript over the course of time.

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