Experimental and theoretical studies on induced ferromagnetism of new (1 − x)Na_0.5Bi_0.5TiO₃ + xBaFeO_3−δ solid solution

Abstract

New solid solution of Na_0.5Bi_0.5TiO₃ with BaFeO_3−δ materials were fabricated by sol–gel method. Analysis of X-ray diffraction patterns indicated that BaFeO_3−δ materials existed as a well solid solution and resulted in distortion the structure of host Na_0.5Bi_0.5TiO₃ materials. The randomly incorporated Fe and Ba cations in the host Na_0.5Bi_0.5TiO₃ crystal decreased the optical band gap from 3.11 to 2.48 eV, and induced the room-temperature ferromagnetism. Our density-functional theory calculations further suggested that both Ba for Bi/Na-site and Fe dopant, regardless of the substitutional sites, in Na_0.5Bi_0.5TiO₃ lead to the induced magnetism, which is illustrated in terms of the exchange splitting between spin subbands through the crystal field theory and Jahn–Teller distortion effects. Our work proposes a simple method for fabricating lead-free ferroelectric materials with ferromagnetism property for multifunctional applications in smart electronic devices.

Introduction

The current research trend in materials science is injecting ferromagnetism into ferroelectric materials to create next-generation smart electronic devices^1,2. The development of ferromagnetism materials based on lead-based ferroelectric by doing transition metals, such as PbTiO₃, has been hampered because their materials strong adverse effect on the environment and human health³. Ferroelectric lead-based PbTiO₃ materials are more commonly used than lead-free ferroelectric materials, such as those based on Bi_0.5(Na,K)_0.5TiO₃, (K,Na)NbO₃, or (Ba,Ca)(Zr,Ti)O₃^4,5. Na_0.5Bi_0.5TiO₃ as one of common lead-free ferroelectric compounds has been considered as a promising candidate that can be replacement for lead-based substances because of its stronger polarization³. The high polarization of Na_0.5Bi_0.5TiO₃ materials is due to the lone pair effect of Bi³⁺ in comparison with that of Pb²⁺ in perovskite structures^6,7. Therefore, injecting room-temperature ferromagnetism into lead-free ferroelectric Na_0.5Bi_0.5TiO₃ is one of significant research interests.

Scholars have developed Na_0.5Bi_0.5TiO₃-based materials with room-temperature ferromagnetism property by using transition metals, such as Co, Fe, Mn, or Cr^8,9,10,11. Moreover, the solid solutions of Na_0.5Bi_0.5TiO₃-based materials with BiFeO₃ material exhibits room-temperature ferromagnetism¹². Na_0.5Bi_0.5TiO₃ materials are composed of ferrite compounds, such as CoMn_0.2Fe_1.8O₄¹³. Ju et al. predicted that substituting a transition metal cation to Ti-site results in the magnetic moments because of the spin polarization of the 3d electrons in the transition metal¹⁴. However, the origin of ferromagnetism in transition metal doped lead-free ferroelectric materials were still debated. The pure Na_0.5Bi_0.5TiO₃ materials exhibited the weak-ferromagnetism at room temperature which were possible explained by the surface-effect and/or self-defect^15,16. Zhang et al. predicted that Na and Ti vacancies induced the magnetization rather than Bi or O vacancies¹⁵. Ju et al. reported that Na vacancies located at/near the surface of nanograins of nanocrystalline Na_0.5Bi_0.5TiO₃ materials possibly displayed the ferromagnetism¹⁶. Such predictions were well consisted with recent obtained room temperature ferromagnetism in pure Na_0.5Bi_0.5TiO₃ materials^10,11. However, the magnetization of pure Na_0.5Bi_0.5TiO₃ materials are quite small, normally less than 1 memu/g, which hinted to apply in electronics devices. Injection of transition metal into host lead-free ferroelectric Na_0.5Bi_0.5TiO₃ materials possibly enhanced the magnetization up to ~ 9 memu/g¹⁰. Unlikely the picture of ferromagnetism at room temperature of pure Na_0.5Bi_0.5TiO₃, a various magnetism sources were injected to lead-free ferroelectric materials which resulted in the room temperature ferromagnetism; such as the O-vacancies (in case of Cr-doped Na_0.5Bi_0.5TiO₃), magnetic clusters (in case of Co-doped Na_0.5Bi_0.5TiO₃), or interaction of magnetic cations through oxygen vacancies as intrinsic phenomenon (in case of Fe-, Mn-doped Na_0.5Bi_0.5TiO₃)^8,9,10,11. Therefore, the origin of room temperature ferromagnetism needs to be deep understood to control the magnetization for smart-electronic devices application.

Thank to well solid solution of Na_0.5Bi_0.5TiO₃ material with various type of ABO₃ dopant materials, the physical properties of host Na_0.5Bi_0.5TiO₃ materials were enhanced^{17,18,19,20,21,22,23,24,25,26,27}. Rahman et al. reported that both ferroelectric and piezoelectric properties of Na_0.5Bi_0.5TiO₃ increased via solid solution of BaZrO₃ where the both remanent polarization and piezoelectric constant increased from 22 μC/cm² and 60 pC/N for pure Na_0.5Bi_0.5TiO₃ to 30 μC/cm² and 112 pC/N for 4 mol% BaZrO₃ solid solution in Na_0.5Bi_0.5TiO₃ materials¹⁷. Yang et al. reported that the (Ba_0.7Ca_0.3)TiO₃ solid solution in host Na_0.5Bi_0.5TiO₃ materials resulted in greatly lowered coercive field without degrading remanent polarization¹⁸. Bai et al. reported that the Bi(Me_0.5Ti_0.5)O₃ (Me = Zn, Ni, Mg, Co)-modified Na_0.5Bi_0.5TiO₃ materials displayed the large strain response (> 0.3%) with a high normalized strain S_max/E_max (> 550 pm/V)¹⁹. Zhou et al. reported that BaNb₂O₆ diffused into lattice of Na_0.5Bi_0.5TiO₃ to form a solid solution resulted in enhancement of the dielectric properties of host Na_0.5Bi_0.5TiO₃ materials²⁰. Kaswan et al. reported on ferromagnetism in Bi_0.5Na_0.5TiO₃-Bi_0.8Ba_0.2FeO₃ composite materials²¹. Pattanayak et al. observed the ferromagnetic properties of a BaFe₁₂O₁₉-modified Bi_0.5Na_0.5TiO₃ system²². Recently, Singh et al. reported on the ferromagnetic properties of Bi_0.5Na_0.5TiO₃ materials induced by the addition of LaFeO₃ as solid solution²³. In addition, the magnetic properties of Na_0.5Bi_0.5TiO₃ materials were found to be strong enhancement such magnetization via solid solution with various impurities materials such as ilmenite-type materials (e.g. MnTiO₃, NiTiO₃, FeTiO₃, or CoTiO₃), or perovskite-type materials (e.g. MgFeO_3−δ, SrFeO_3−δ, CaFeO_3−δ, SrMnO_3−δ, CaMnO_3−δ, BaMnO_3−δ, MgMnO_3−δ, SrCoO_3−δ, MgCoO_3−δ, BaCoO_3−δ, or CaCoO_3−δ)^{24,25,26,27,28,29,30,31,32,33,34,35,36,37,38}. The double perovskite-type structural materials containing the transition metals (e.g. Bi(Ti_0.5Fe_0.5)O_3−δ, Bi(Ti_0.5Mn_0.5)O_3−δ, Bi(Ti_0.5Co_0.5)O_3−δ, or Bi(Ti_0.5Ni_0.5)O_3−δ) were also reported to enhance the magnetic properties of Na_0.5Bi_0.5TiO₃ materials when their materials were solid solution into host materials^39,40,41,42. The magnetization of modified- Na_0.5Bi_0.5TiO₃ samples via impurities of ilmenite-type materials, perovskite-type or double perovskite-type structural materials were found to have large magnetization moment which were compared with single transition metal dopants^{8,9,10,11,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42}.

Among alkaline-earth iron perovskite AeFeO_3−δ family (Ae = Ba, Ca, Sr, and Mg), BaFeO_3−δ is one of interesting materials because its ferromagnetic domains could be controllable by an applied magnetic field⁴³. BaFeO_3−δ materials exhibited complex of phase such as monoclinic, rhombohedral, pseudo-cubic and cubic which depended on the valence state of Fe and transition between them⁴⁴. Mori et al. reported that BaFeO_3−δ compounds existed in many forms such hexagonal phase in a wide range of oxygen content BaFeO_2.63–2.92 while other phase has exhibited such triclinic I, BaFeO_2.50; triclinic II, BaFeO_2.64–2.67; rhombohedral I and II, BaFeO_2.62–2.64; and tetragonal, BaFeO_2.75–2.81⁴⁵. The cubic perovskite BaFeO₃ with Fe⁴⁺ state has A-type spiral spin structure as ferromagnetism below 111 K⁴⁶. Clemens et al. reported that BaFeO_2.5 materials with Fe³⁺ state exhibited the G-type antiferromagnetic structure with Neel temperature of 720 K⁴⁷. Delattre et al. reported that the BaFeO_2.8 with orthorhombic structural exhibited the strong couple antiferromagnet⁴⁸. Theoretical simulation predicted that the BaFeO₂ materials has tetragonal symmetry and the G-type antiferromagnetic spin configuration⁴⁹. The highest ferromagnetic ordering around 235 K in BaFeO_3−δ were obtained for thin film growing on the SrTiO₃ substrate⁵⁰. Recently, the new system of (1-x)Na_0.5Bi_0.5TiO₃ + xAeFeO_3−δ (Ae = Sr, Ca, and Mg) materials as solid solution were successful fabricated by using the sol–gel technique^28,29,30. The results provided that the impurities cation (such as Sr, Mg) and Fe random incorporated with (Bi,Na)-site and Ti-site, respectively, were exhibited the strong ferromagnetism at room temperature where the magnetization were found to great enhancement than that of single transition metal dopants which were possible resulted from co-modification at A-site via alkaline-earth and Fe cation at B-site of host Na_0.5Bi_0.5TiO₃^28,29,30. In the periodic table of elements, Ba is the largest radius in alkaline earth metals, thus, we expected that the co-modification of Ba cations at A-site and Fe cations at B-site, respectively, of host Na_0.5Bi_0.5TiO₃ materials were resulted exhibition large magnetization during solid solution of BaFeO_3−δ into Na_0.5Bi_0.5TiO₃ materials.

In this work, new system (1-x)Na_0.5Bi_0.5TiO₃ + xBaFeO_3−δ materials as solid solution were fabricated by sol–gel method. The BaFeO_3−δ materials were well solid solution into the host Na_0.5Bi_0.5TiO₃ materials through diffusion and random incorporation of Ba and Fe cations with host lattice of Na_0.5Bi_0.5TiO₃ materials. The structural distortion and reduced optical band gap of host Na_0.5Bi_0.5TiO₃ materials were obtained. The complex magnetic properties of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials was obtained as function of BaFeO_3−δ amounts addition.

Results and discussion

Figure 1a,b shows the EDS spectral of pure Na_0.5Bi_0.5TiO₃ samples and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ sample with 5 mol.% BaFeO_3−δ, respectively. The inset of each figure showed the selected area for EDS elements characterization. All expectational elements such Bi, Na, Ti and O were obtained in EDS spectral of pure Na_0.5Bi_0.5TiO₃ samples, as shown in Fig. 1a. The addition of the Ba and Fe peaks were showed in the EDS spectral of BaFeO_3−δ-modified Bi_0.5Na_0.5TiO₃ samples, as expected, which were presented at the Fig. 1b. The results provided that the BaFeO_3−δ impurities existed in our samples.

Figure 1

The EDS spectral of (a) pure Na_0.5Bi_0.5TiO₃ materials, and (b) BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials with 5 mol% BaFeO_3−δ as solid solution. The inset of each figure shown the selected area for composition characterization.

The chemical maps of Bi_0.5Na_0.5TiO₃ materials modified with 9 mol.% BaFeO_3−δ were analyzed. The distribution of impurity elements in the Na_0.5Bi_0.5TiO₃ materials modified with 9 mol.% BaFeO_3−δ is shown in Fig. 2. The surface morphology of the area selected for chemical mapping is shown in Fig. 2a, whereas Fig. 2b presents the total contribution of all of the chemical elements in the sample. The partial chemical maps of Bi, Na, Ti, O, Ba, and Fe elements are shown in Fig. 2c–h, respectively. The results clearly demonstrated that the constituent chemical elements were homogenously dispersed in the sample.

Figure 2

(a) Selected area for the chemical mapping of 9 mol.% BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials; (b) total chemical element distribution in samples; and (c)–(h) partial chemical element maps of Bi, Na, Ti, O, Ba, and Fe.

Figure 3 (a) shows the X-ray diffraction patterns of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ with various BaFeO_3−δ concentrations. On the basis of diffraction peak position and relative to intensity, all samples were indexed to a perovskite structure with the rhombohedral symmetry of the Na_0.5Bi_0.5TiO₃ compound (JCPDS card no. 00–036-0340, space group R3c). In addition, the impurities phase or phase segregation was not founded in the X-ray diffraction patterns. All X-ray diffraction pattern of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples were indexed to follow the structural of Na_0.5Bi_0.5TiO₃ compound. The results indicated that BaFeO_3−δ materials exhibited a well solid solution in Na_0.5Bi_0.5TiO₃ materials. In other word, the Ba and Fe cations were diffused to randomly incorporate with host lattice of Na_0.5Bi_0.5TiO₃ compound as solid solution. In order to character the influence of Ba and Fe into host crystalline of Na_0.5Bi_0.5TiO₃ compound, the diffraction angle of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Bi_0.5Na_0.5TiO₃ samples was magnified within 31.0° to 34.0° for setline (012)/(110) peaks, as shown in Fig. 3b. The setline peaks were overloaded together which were distinguished via Lorentz fitting, as shown in dot line of Fig. 3b. The results clearly indicated that the diffraction peaks of Na_0.5Bi_0.5TiO₃ materials trended to shift to lower diffraction angle as increasing the BaFeO_3−δ amounts, which provided the evident for expansion of lattice parameter. Furthermore, the lattice parameters a and c of the pure Bi_0.5Na_0.5TiO₃ and the BaFeO_3–δ-modified Bi_0.5Na_0.5TiO₃ as a function of BaFeO_3–δ addition amounts are shown in Fig. 3c. The results show that the distorted lattice parameters of the Bi_0.5Na_0.5TiO₃ compound are not a linear function of the concentrations of the BaFeO_3–δ solid solution, which showed complex lattice parameter distortion. This result could be attributed to the different radii of Ba and Fe cations in the additives and that of Bi, Na, and Ti incorporated randomly in the lattice of the host Na_0.5Bi_0.5TiO₃ materials. Based on the Shamon’ reported, the radius of Ba²⁺ and Fe^2+/3+ cations were 1.61 Å and 0.645 Å/0.780 Å, respectively, while the radius of Bi³⁺, Na⁺ and Ti⁴⁺ cations were 1.17 Å, 1.39 Å and 0.605 Å, respectively⁵¹. Therefore, the Fe cations diffused to substitute for Ti-sites in perovskite structural of Na_0.5Bi_0.5TiO₃ crystal, resulted in expansion of the lattice. The fact that the radius of Ba²⁺ cations are larger than that of both Bi³⁺ and Na⁺ cations were also reflected by expanding the lattice parameter of host Na_0.5Bi_0.5TiO₃ compound. However, we noted that the oxygen vacancies were generated due to unbalance of valence states of Fe^2+/3+ and Ti⁴⁺ at B-site and Ba²⁺ for Bi³⁺ at A-site. In addition, the Na vacancies were created when Ba²⁺ substitute Na⁺. The oxygen vacancies (¤) has radius of 1.31 Å which were smaller than that of oxygen anion (O^2-) of 1.4 Å⁵². Therefore, the existence of oxygen vacancies in the structure led to reduction of the lattice parameter. The structural distortion of Na_0.5Bi_0.5TiO₃ materials was due to co-modification at A- and B-site via alkali earth and transition metal, respectively, which was consistent with recently reported^28,29,30. In other word, the X-ray diffraction characterization of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples provided that the BaFeO_3−δ materials were well solid solution into host Na_0.5Bi_0.5TiO₃ materials.

Figure 3

(a) X-ray diffraction pattern of BaFeO_3−δ solid solution into Na_0.5Bi_0.5TiO₃ with various concentrations within the 2θ range of 20° to 70°; (b) magnified X-ray diffraction within 2θ range of 31°–34° for comparing setline (012)/(110) peaks; and (c) dependence of the lattice parameters of pure Bi_0.5Na_0.5TiO₃ and BaFeO_3−δ-modified Bi_0.5Na_0.5TiO₃ samples on the amounts of BaFeO_3−δ solid solution.

Figure 4a show the Raman scattering of pure Na_0.5Bi_0.5TiO₃ materials and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials with various of BaFeO_3−−δ concentration as solid solutions at room temperature. The results provide that the shape of Raman scattering spectra seem to be unchanged in comparison between that of pure Na_0.5Bi_0.5TiO₃ materials and that of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ s materials. In the wave number ranging from 300 cm⁻¹ to 1000 cm⁻¹, the Raman spectra were possible divided into three main regions and they overlapped each other. The three main band regions were in the range of 300–450 cm⁻¹, 450–700 cm⁻¹ and 700–1000 cm⁻¹, respectively. The combination of experimental investigation and first principles density functional theoretical calculation for Raman vibration modes of Na_0.5Bi_0.5TiO₃ materials exhibited that the lowest frequency modes in range of 246–401 cm⁻¹ are dominated by TiO₆ vibrations, and the higher frequency modes in the range 413–826 cm⁻¹ are primarily associated with the oxygen atoms vibrations⁵³. The random occupation at A-sites of Bi and Na resulted in overlap of Raman scattering peaks in range of 109–134 cm⁻¹ and 155–187 cm⁻¹, which were originated from Bi-O and Na–O vibration modes, respectively⁵³. In addition, Chen et al. reported that the vibration of Ti–O bonds is related to the wave number in range of 200–400 cm⁻¹ while the vibration of TiO₆ octahedra is assigned to the wave number regions from 450 cm⁻¹ to 700 cm⁻¹⁵⁴. The overlapping of Raman scattering modes was hard to characterize the influence of Ba and Fe into vibration modes of host lattice Na_0.5Bi_0.5TiO₃ materials. Therefore, we tried to distinguish the Raman scattering modes via the fitting with Lorentz functions (with correction of fitting over 0.99). The deconvolution Raman scattering modes (blue line) of pure Na_0.5Bi_0.5TiO₃ samples and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples with example for 5 and 9 mol% BaFeO_3−δ, as shown in Fig. 4b. The eight Raman scattering vibrational modes were obtained for both pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples. The results were well consistent with recently observation in vibration of Raman scattering modes of perovskite-type structural AeFeO_3−δ family-modified Na_0.5Bi_0.5TiO₃ materials^28,29,30. The vibration modes at around 595 cm⁻¹ (red dot line marked in the Fig. 4b) trended to shift to high frequency, which were suggested to be related to distorted structure of (Ti,Fe)O₆ framework and/or effective mass effect because of difference between the radius and mass of impurities Fe and host Ti at B-site^28,29,30. In other word, the shifted Raman scattering modes confirmed the substitution of Ba and Fe into the host lattice of Na_0.5Bi_0.5TiO₃ materials.

Figure 4

(a) Raman scattering spectra of BaFeO_3−δ solid solution into Na_0.5Bi_0.5TiO₃ with various concentrations from 200 cm⁻¹ to 1000 cm⁻¹; and (b) deconvolution Raman peaks of pure Na_0.5Bi_0.5TiO₃ and 5 and 9 mol% BaFeO_3−δ solid solution into Na_0.5Bi_0.5TiO₃.

Figure 5a shows the optical absorption spectra of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ with various BaFeO_3−δ concentrations. Pure Na_0.5Bi_0.5TiO₃ samples exhibited a single absorbance edge, consistent with the reported optical properties of Na_0.5Bi_0.5TiO₃ materials^9,10,11,55. However, pure Na_0.5Bi_0.5TiO₃ materials exhibited the unsharp transition which were tailored with slightly tail. The small tail at long wavelength in absorbance spectroscopy of pure Na_0.5Bi_0.5TiO₃ materials were suggested to be related with self-defect and/or surface effect cause of unsaturation bonding pair of atoms at the surface^55,56. The addition BaFeO_3−δ to Na_0.5Bi_0.5TiO₃ material as solid solution led to a red shift of the absorbance edge. The appearance of peaks around 485 nm in the absorbance spectra of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials indicated the new local states of Fe cations in the middle electronic band structure of Na_0.5Bi_0.5TiO₃ materials^28,29,30,57. Optical band gap (E_g) values of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials were calculated using the plot of (αhν)² versus photon energy hν, as shown in Fig. 5b, where α, h and ν are the absorbance coefficient, the Planck constant and the frequency, respectively. The band gap energy of pure Na_0.5Bi_0.5TiO₃ materials were estimated to be approximately 3.09 eV, whereas that of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials exhibited value of 2.48 eV for 9 mol. % BaFeO_3−δ solid solution in host Na_0.5Bi_0.5TiO₃ materials. The detail dependence of E_g values of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ compound as function of BaFeO_3−δ concentration is shown in the inset of Fig. 5b. The optical band gap of Na_0.5Bi_0.5TiO₃ material in which the Ti-sites substituted with the transition metal, as B-site modified, decreased in lead-free ferroelectric Bi-based materials; this phenomenon could be due to the presence of new local states in the electronic structure of both the highest occupied molecular orbital and the lowest unoccupied molecular orbital in the total band structure^{9,10,11,14,57}. In addition, the reduced optical band gap in A-site modified Na_0.5Bi_0.5TiO₃-based material was possibly a result of changes in the bonding type between hybridizations A-O⁵⁸. Oxygen vacancies created because of unbalanced charges between impurities and hosts (e.g. Fe^2+/3+ substitute for Ti⁴⁺, and Ba²⁺ replacement for Bi³⁺) also led to the reduction in the optical band gap because the oxygen vacancy states normally located below and near the conduction band^{9,10,11,59,60}. Thus, we suggest that the random substitution of Ba and Fe ions into the host Na_0.5Bi_0.5TiO₃ could alter the electronic band structure, resulting in reduction of the optical band gap.

Figure 5

(a) UV–Vis absorption spectra of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples as a function of BaFeO_3−δ concentration; and (b) the (αhν)² proposal with photon energy (hν) of Na_0.5Bi_0.5TiO₃ samples as a function of the amount of BaFeO_3−δ added. The inset of (b) shows the optical band gap E_g value of Na_0.5Bi_0.5TiO₃ samples as a function of the amount of BaFeO_3−δ added.

Figure 6a shows the room-temperature PL emission spectra of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples with various BaFeO_3−δ amount. The PL spectral of all samples exhibited a broad band emission while strong emission showed in range from 479 to 505 nm. The addition of BaFeO_3−δ into host Na_0.5Bi_0.5TiO₃ materials as solid solution suppressed the emission peak, as shown in inset of Fig. 6a. However, we noted that a slight addition of BaFeO_3−δ concentration enhanced the emission intensity. In addition, the PL spectral of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples was overlapped together, suggesting to multi-emission peaks with closed together. Thus, we tried to distinguish the multi-emission peaks via Lorentz fitting. The deconvoluted emission peaks of pure Na_0.5Bi_0.5TiO₃ samples were shown in Fig. 6b. The broad band visible luminescence was also recently reported for ferroelectric titanates-based materials at room temperature such as BaTiO₃, SrTiO₃, PbTiO₃ etc.⁶¹. The observations in broad band emission were also archived in Bi_0.5K_0.5TiO₃ materials, which were related to the surface effect and/or self-defect effect⁵⁶. Normally, the coordination status of the atoms at the surface of materials is unsaturated, resulting in unpaired states, that make them different from that in the bulk⁶². The unsaturated atoms that existed at the surface region of Na_0.5Bi_0.5TiO₃ materials formed local levels in the forbidden gaps, this displayed the effect of the self-trapped excitons⁶³. Therefore, the incident photon was absorbed by the Na_0.5Bi_0.5TiO₃ powder as it is illuminated with the excited source. The absorption photons could create some localized levels and form small polarons. The interaction between the holes in the valence band and polarons formed by the intermediate self-trapped excitons caused blue shift of the luminescence⁶³. In addition, the structural distortion because of coupling of TiO₆-TiO₆ adjacent octahedra generate the localized electronic levels above the valence band. The recombination from these levels may result in the photoluminescence of Bi_0.5K_0.5TiO₃ materials⁶². The photoluminescence of ferroelectric materials is not generally governed by band-to-band transition, owning to the difficulty in recombination of electron–hole pairs and the separation of the natural polarization domain in the materials. In this kind of materials, the surface states were in charge of the luminescence, in which many unsaturated atoms that presented on the surface of the ferroelectric materials creates the localized levels in the forbidden gaps. Interestingly, the intensity of PL emission of Na_0.5Bi_0.5TiO₃ materials was suppressed by the addition of BaFeO_3−δ, as shown in the inset of Fig. 6b. The PL emission spectra of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials did not change, indicating the lack of Ba and Fe substitution at the A- and B-sites, respectively, in the new electron–hole transitions. Thus, the substitution of Fe cation with Ti at the octahedral sites created oxygen vacancies; such vacancies acted as the chapping electron generated from absorbance photon energy, thereby prevented the recombination of the electron–hole pairs to generate photons.

Figure 6

(a) PL spectral of pure Bi_0.5Na_0.5TiO₃ materials and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples as a function of BaFeO_3−δ concentration, and (b) deconvolution of PL spectral of pure Bi_0.5Na_0.5TiO₃ materials. The inset of (a) shown the magnification of PL spectral of pure and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples as a function of BaFeO_3−δ concentration.

Furthermore, the role of BaFeO_3−δ solid solution in Na_0.5Bi_0.5TiO₃ materials in imparting magnetism was dependent on the applied magnetic field at room temperature, as shown in Fig. 7a–g for pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials with BaFeO_3−δ concentration of 0.5, 1, 3, 5, 7 and 9 mol%, respectively. The pure Na_0.5Bi_0.5TiO₃ exhibited the anti-S-shape in M-H curves, indicating the combination of diamagnetism and weak ferromagnetism, as shown in Fig. 7a. The diamagnetism in pure Na_0.5Bi_0.5TiO₃ samples originated from the electronic configuration of Ti⁴⁺ as 3d°, whereas the weak ferromagnetism originated from self-defects^{9,10,11,14,16,30,64,65}. The typical hysteresis loop of ferromagnetism was obtained for pure Na_0.5Bi_0.5TiO₃ materials after subtract the diamagnetic components, as shown in inset of Fig. 7a. The saturation magnetization was estimated around 1.5 memu/g which were well consisted with recently reported by Ju et al.¹⁶. In addition, the remanent magnetization (M_r) and coercive field (H_C) of pure Na_0.5Bi_0.5TiO₃ materials were approximately 0.11 memu/g and 73 Oe, respectively, which were solid evidence for presentation of ferromagnetic state at room temperature. The estimation for their values were also performed with recently reported by Thanh et al. and Ju et al. which those were possibly originated from self-defect such as Na-, Ti- or O-vacancies^10,16. The M-H curves trend to switch from anti-S-shape to S-shape in the BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples as the BaFeO_3−δ concentration in the solid solution increase, providing evidence regarding the strength enhancement of ferromagnetic ordering in the samples. As shown in Fig. 7c, the typical ferromagnetic hysteresis loops were obtained where the magnetization trended to saturate as the external applied magnetic field increase, and the strength of ferromagnetic increase. However, further increasing amounts of BaFeO_3−δ into host Na_0.5Bi_0.5TiO₃, the M-H curves exhibited the unsaturation with low applied external magnetic field, as shown in Fig. 7d–g. The dependence of shape in magnetic hysteresis loop of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials represented that the magnetic properties of BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials were very complex, on the one hand the magnetic properties of Na_0.5Bi_0.5TiO₃ materials were strong dependent of the concentration of BaFeO_3−δ as solid solution. The M_r and H_C values of BaFeO_3−δ-modified Bi_0.5Na_0.5TiO₃ materials were approximately 51–106 Oe and 0.12–0.48 memu/g, respectively. These results were consistent with the recently observed M_r and H_C of transition-metal-doped lead-free and lead-based ferroelectric materials^{8,9,10,11,60,64,65,66,67,68}. The nonzero M_r and H_C values of BaFeO_3−δ-modified Bi_0.5Na_0.5TiO₃ materials provided solid evidence for the presence of the ferromagnetic state at room temperature. In additon, the maximum magnetization was estimated around 23 memu/g for 9 mol% BaFeO_3−δ solid solution in host Na_0.5Bi_0.5TiO₃ materials. That value was larger than that of self-defect induced magnetism of pure Na_0.5Bi_0.5TiO₃ materials or single transition metals doped Na_0.5Bi_0.5TiO₃ materials, in which around ~ 1.5 memu/g for Cr-doped Na_0.5Bi_0.5TiO₃, ~ 3 memu/g for Co-doped Na_0.5Bi_0.5TiO₃, ~ 9 memu/g for Mn-doped Na_0.5Bi_0.5TiO₃, ~ 15 memu/g for Fe-doped Na_0.5Bi_0.5TiO₃ materials, and ~ 4 memu/g for Ni-doped Na_0.5Bi_0.5TiO₃ materials^{8,9,10,11,60,68}. Herein, we need to remark that the origin of ferromagnetism ordering of transition metal impurities containing Na_0.5Bi_0.5TiO₃ materials at room temperature were still debated. The weak-ferromagnetism in pure Na_0.5Bi_0.5TiO₃ materials were possibly originated from self-defect and/or surface defect (such as Ti and Na-vacancies) while the magnetization of Na_0.5Bi_0.5TiO₃ materials were slightly enhanced via oxygen vacancies^11,14,16,30. The Mn-, Ni- and Fe-doped Na_0.5Bi_0.5TiO₃ materials exhibited the room temperature ferromagnetism which were related to intrinsic phenomenon where the transition cations such of Mn, Ni and Fe interacted with the oxygen vacancies, like F-center interaction mechanism, e.g. Mn^2+/3+–¤–Mn^2+/3+ or Fe^2+/3+–¤–Fe^2+/3+ pairs etc., which were favored for ferromagnetic ordering^{8,9,10,11,60,64}. Unlikely Mn-, Ni- and Fe- cations impurities in Na_0.5Bi_0.5TiO₃ materials, the Co impurities trended to form Co-clusters embedding in host Na_0.5Bi_0.5TiO₃ materials which displayed the room temperature ferromagnetism⁸. Recently, our experimental observation along with first principle calculation predicted that the interaction of Co cations into host Na_0.5Bi_0.5TiO₃ materials possibly displayed the weak ferromagnetism at room temperature⁶⁴. In addition, Hung et al. reported that MgFeO_3−δ solid solution in Na_0.5Bi_0.5TiO₃ materials exhibited strong magnetization, which were estimated to be around 39.6 memu/g, where the Mg cations played an importance role for mediating ferromagnetism²⁸. The SrFeO_3−δ- and CaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials also showed strong enhancement of the magnetization at room temperature^29,30. Note that the Mg cations possibly substituted for both A-site (Bi³⁺, Na⁺) and B-site in Na_0.5Bi_0.5TiO₃ crystal structure while Sr and Ca cations only replaced with A-site in host Na_0.5Bi_0.5TiO₃ crystal structure^28,29,30. Thus, we suggested that the possible room temperature ferromagnetism in BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials were strongly related to the interaction of Fe cations through oxygen vacancies, like F-central interaction, which were recently suggested for Mn-, Ni-, Co- and Fe-doped Na_0.5Bi_0.5TiO₃ materials^{9,10,60,64,69}. A recent X-ray photoelectron spectroscopy (XPS) analysis of CaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ materials showed that Fe cations are stable in the Fe²⁺ and Fe³⁺ valence state together with O vacancies³⁰. Therefore, we suggest that the interaction pair Fe^2+/3+–¤–Fe^2+/3+ favors ferromagnetic ordering⁶⁹. The unsaturation in the M–H curves of magnetic hysteresis loops of Na_0.5Bi_0.5TiO₃ materials (under 6 kOe of applied magnetic field) as the amount of the BaFeO_3−δ solid solution increase suggested magnetic polaron interaction, wherein the interaction between Fe^2+/3+–¤–Fe^2+/3+ versus Fe^2+/3+–¤–Fe^2+/3+ resulted in antiferromagnetic-like ordering^{9,69,70,71,72,73}. In addition, isolated Fe cations displayed paramagnetic properties^{9,69,70,71,72,73}. Thus, the combination of the complex signal of ferromagnetic interaction and antiferromagnetic-like and paramagnetic properties was observed when the BaFeO_3−δ solid solution was present at high concentrations in host Na_0.5Bi_0.5TiO₃ materials. However, unlike single Fe-doped Na_0.5Bi_0.5TiO₃ materials, the modification at A-site (Bi³⁺, Na⁺) via Ba²⁺ cations in host Na_0.5Bi_0.5TiO₃ materials also possibly contributed a source to the ferromagnetism ordering, in which the substitution of Ba²⁺ cations for Bi³⁺ cations in crystal structure created the O-vacancies while Ba²⁺ cations incorporated for Na⁺ cations generated the Na-vacancies. Both O- and Na- vacancies are origin of the ferromagnetism, but they work in different ways^16,30. Nevertheless, both the experimental observation and theoretical prediction have agreed that Na-vacancies induce the nonzero magnetic moment^16,30. Therefore, the strength of magnetic moments can be increased by increasing the number of Na-vacancies. However, unlikely Na-vacancies, the O-vacancies were predicted to be agent of the nonmagnetic moment³⁰. The O-vacancies were important in promoting the reduction in valence state from Ti⁴⁺ to Ti³⁺ (even Ti²⁺) because of oxygen vacancies bounding surround^{30,31,74,75,76}. The theorey predicted that Ti⁴⁺ has no magnetic moment whereas the Ti³⁺ or Ti²⁺ have nonzero magnetic moment³⁰. Thus, the enhancement in O-vacancies were indirectly induced by the magnetic moment along with the contribution of magnetization of Ti^3+/2+ defects, resulting in increased magnetic moment that were over the self-defects compared with pure Na_0.5Bi_0.5TiO₃ samples. Recently, XPS results have shown that the Ti⁴⁺ cations in Na_0.5Bi_0.5TiO₃ materials were possible reduced to Ti³⁺ via modification of CaFeO_3−δ- and SrMnO_3−δ-modified as solid solution^30,31. Therefore, we suggested that the increasing the O-vacancies was promoted by the magnetization of self-defect of Ti³⁺ cations. Recently, the interaction between Co^3+/2+ cations and reduction of valence state of Ti^4+-δ pair through O-vacancies were suggested to favor the ferromagnetic ordering³⁵. Therefore, we suggested that the appearance of interaction Fe^2+/3+–¤–Ti^4+-δ pair may arouse increasing of the strength of ferromagnetic ordering. We recently reported that the magnetic properties of various magnetic compound, such as Mn₂O₃, Mn₅Ge₃ etc., could be tunable by a strain^77,78. Therefore, due to the difference radius with ions of host lattice, the Ba cations possibly caused a chemical pressure, possibly resulting in the change of interaction between them through oxygen vacancies; finally, resulted in modification of magnetic ordering strength. Recent experimental and theoretical studies have suggested that transition metals may fill A- and B-sites in the perovskite structure of lead-free ferroelectrics, thus resulting in complex magnetic properties^{27,79,80,81,82,83}. Liu et al. reported that K_0.45Na_0.49Li_0.06NbO₃ materials modified with Cu at the A-site show paramagnetic properties⁸⁰. However, Yang et al. reported that Cu modification at the B-site of EuMnO₃ materials changes magnetic properties from paramagnetic to antiferromagnetic ordering⁸¹. Deng et al. found that the paramagnetic properties of EuMnO_3−δ materials were changed to antiferromagnetic via modification at the Eu site by Mn cations⁸². Magnetic phase transition from paramagnetic to antiferromagnetic properties has also been reported for DyMnO₃ materials modified with the Mn cation at the Dy-site⁸³. Theoretical and experimental studies have suggested that CoTiO₃-modified Na_0.5Bi_0.5TiO₃ materials have complex magnetic properties that are strongly dependent on the location of Co impurities at the A-site or B-site in the host structure^27,79. Notably, the radii of Fe^2+/3+ cations with VIII coordination are 0.92 Å and 0.78 Å, respectively, which are comparable with the radii of Bi³⁺ (1.17 Å) and Na⁺ (1.39 Å) cations⁸⁴. Therefore, we suggested that Fe cations were random incorporated at both the A-site and B-site likely contributing to the complex magnetic properties of the host Bi_0.5Na_0.5TiO₃ materials. The role of Fe cation substitution at the A- and B-sites in the magnetic properties of Na_0.5Bi_0.5TiO₃ materials was further investigated by using density-functional theory (DFT) calculation.

Figure 7

M–H curves at room temperature of (a) undoped Na_0.5Bi_0.5TiO₃, and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples with (b) 0.5 mol%, (c) 1 mol%, (d) 3 mol%, (e) 5 mol%, (f) 7 mol% and (g) 9 mol% BaFeO_3−δ as solid solution. Inset of (a) shown the M-H curve of pure Bi_0.5Na_0.5TiO₃ material after substrate diamagnetic components.

To elucidate the origin of the observed ferromagnetism in BaFeO_3−δ-doped Na_0.5Bi_0.5TiO₃, the density-functional theory (DFT) calculations were performed using the Vienna ab initio Simulation Package (VASP)^85,86. The generalized gradient approximation (GGA) formulated by Perdew, Burke, and Ernzerhof (PBE) was used for the electron exchange correlation potential⁸⁷. Figure 8a shows the side and top views of the rhombohedral crystal structure of the 24 formula unit (f.u.) cell (120-atom) adopted for Bi_0.5Na_0.5TiO₃ (BNT). As model systems shown in Fig. 8b,c, we have considered the substitution of one Ba atom for the Bi-site, denoted as B(Ba)NT, and Na-site [BN(Ba)T], in the 24 f.u. cell structure of the BNT. This corresponds to about 0.83 at.% doping for the A-site (Bi and Na) substitution, which is within the range of the present experimental doping concentrations (0.5–9 mol.%). To represent the presence of the Fe substitution in a sample, we replaced one Ti [BNT(Fe)], Ba [B(Fe)NT], and Na [BN(Fe)T] atom with the Fe atom in the same unit cell, as shown in Fig. 9a–c. For all systems, we used an energy cutoff of 500 eV for the plane-wave basis and a k-point mesh of 5 × 5 × 5 for the Brillouin zone integration. To obtain optimized atomic structures, the atomic positions as well as lattice parameters were fully relaxed until the largest force becomes less than 10⁻² eV/Å and the change in the total energy between two ionic relaxation steps is smaller than 10⁻⁵ eV. Note that the severe distortions of octahedral TiO₃ lattice were observed for all geometries after optimization.

Figure 8

(a) Side and top views of the optimized atomic structure of Na_0.5Bi_0.5TiO₃ (BNT). The same with (b) Bi-site Ba [B(Ba)NT] and (c) Na-site Ba [BN(Ba)T] substitution.

Figure 9

(a) Side views of the optimized atomic structure of the (a) Ti-site [BNT(Fe)], (b) Bi-site [B(Fe)NT], and (c) Na-site Fe [BN(Fe)T] substitution. The atomic symbols follow the same convention used in Fig. 8. Brown spheres are the Fe substitutional atoms.

We first investigate the energetics of the Ba- and Fe-doped BNT. Here, the formation energy (H_f) is defined as ${H}_{f}=H-\sum_{i}{\mu }_{i}{n}_{i}$, where H is the total energy of the system, and ${\mu }_{i}$ and ${n}_{i}$ are the chemical potential and the number of species i in the unit cell. The calculated H_f values of BNT, B(Ba)NT, BN(Ba)T, B(Fe)NT, BN(Fe)T, and BNT(Fe) are shown in Table 1. We find that the H_f of BNT is -2.385 eV/atom, which indicates the pure BNT is quite stable. Our calculations further indicate that the Ba substitute prefers either the Bi or Na sites (A-site), as their enthalpies of formation are competitive (− 2.402 and − 2.392 eV/atom). The Fe dopant atoms may also occupy both the A- and B-site (Ti), although the absolute values of H_f for the A-site (− 2.376 eV/atom for the Bi and − 2.355 eV/atom for the Na) are higher than that (− 2.335 eV/atom) of the B (Ti)-site in magnitude. Nevertheless, in a real sample, the latter substitution (B-site) might appear more than the A-site (Bi and Na) substitution, as the A-site is mainly occupied by the Ba atoms.

Table 1 The DFT results of the formation energy H_f (eV/atom), magnetic energy ΔE (eV/atom), and magnetization M (μ_B/f.u.) of BNT, B(Ba)NT, BN(Ba)T, B(Fe)NT, BN(Fe)T, and BNT(Fe) compounds. We also list the magnetic moment m (μ_B/atom) of the Fe dopant atom for the 1 Fe atom doped 24 f.u. cell of B(Fe)NT, BN(Fe), and BNT(Fe).

Table 1 shows the calculated magnetic energy (ΔE = E_sp – E_non-sp, where E_sp and E_non-sp are the total energies of the spin-polarized and non-spin-polarized states, respectively), total magnetization per f.u. (M), and atom resolved magnetic moment (m) of the dopant atoms. Our calculations show that all the Fe-doped structures are magnetic, while the Ba-doped ones are nonmagnetic. The calculated magnetization ranges from 0.14 to 0.21 µ_B/f.u. (or approximately 3.6 to 5.5 emu/g with [emu/g] = 1.078⋅10²⁰ (M_f.u./N_A) [µ_B/f.u.], where the N_A and M_f.u. are the Avogadro constant and the molar mass per f.u., respectively) at 0.83 at. % doping. These theoretical magnetization values are much higher than the maximum experimental value of 23 memu/g for 9 mol.% BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃. The induced magnetization mainly comes from the local atomic moment of the Fe dopant atoms, as shown in Table 1.

Figure 10 presents the spin-resolved density of states (DOS) of BNT, B(Ba)NT, BN(Ba)T, B(Fe)NT, BN(Fe)T, and BNT(Fe) compounds. We have also analyzed the orbital projected DOS (PDOS) of the Fe 3d orbital states in Fig. 11 for the selected B(Fe)NT, BN(Fe)T, and BNT(Fe) as they exhibit magnetic nature. For BNT, the valence and conduction bands are characterized by the O-2p and Ti-3d orbital states with a band gap of ~ 2.25 eV, respectively. The majority- and minority-spin states are entirely degenerate, which indicates a feature of nonmagnetic ground state. The calculated band gap of BNT is smaller than the measured value (3.08 eV), which is quite typical in DFT calculations for oxide perovskites⁸⁸. The Bi-site Ba gives rise to the upward shift of the valence band states toward the Fermi level. The opposite appears for BN(Ba)T, where the Fermi level shifts upward and touches the minimum of the conduction bands. Thus, the former and latter systems are referred to as p- and n-doped semiconductors, while kept the absolute value of the band gap. On the other hand, as shown in the bottom panels in Fig. 10, for B(Fe)NT, BN(Fe)T, and BNT(Fe), there are some midgap states around the Fermi level. In particular, for BNT(Fe), a finite DOS peak state appears right at the Fermi level in the majority-spin state while the other spin channel exhibits an insulating behavior. This is a feature of the half-metallic electronic nature. Furthermore, for all the Fe-doped compounds, substantially large exchange splitting between the spin subbands (i.e., majority-spin and minority-spin) is prominent (Fig. 10). These peak states are due to the strong orbital hybridization between the Fe 3d and O 2p states. As shown in Fig. 11, the majority-spin bands of the Fe are fully occupied, and the minority-spin states are almost unoccupied for the BNT(Fe) and B(Fe)NT but partially occupied for the BN(Fe)T. Overall, one can expect the large magnetic moment at the Fe site, as addressed in Table 1. Induced moments at the neighboring sites to the Fe are rather small.

Figure 10

Top to bottom: The DFT results of the spin-resolved DOS for the BNT, B(Ba)NT, BN(Ba)T, BNT(Fe), B(Fe)NT, and BN(Fe)T. The Fermi level is set to zero energy.

Figure 11

The DFT results of the d-orbital decomposed PDOS of the Fe substitutional atom for the (a) BNT(Fe), (b) B(Fe)NT, and (c) BN(Fe)T. The black, orange, red, green, and blue lines represent the d_xy, d_yz, d_z², d_xz, and d_x²_–y² orbital states, respectively. The Fermi level is set to zero energy.

Based on the PDOS analyses for the BNT(Fe) and B(Fe)NT compounds, we infer that the six (five) d-orbitals of Fe²⁺ (Fe³⁺) ion split by high-spin state through the crystal field theory are filled by the 5 majority-spin electrons in the low-lying t_2g orbital levels and 1 electrons (no electron) in the minority-spin t_2g state. Thus, according to Hund's rule, the calculated magnetic moments of 4 and 5 μ_B of the Fe replacement for the Ti and Bi sites can be explained by the electronic configuration of the high-spin state in the crystal field theory through the unpaired electron spin count. For the BN(Fe)T, the magnetic moment of the Fe atom is reduced compared with those for the other two systems, as some minority-spin states are partially occupied (Fig. 11c). Furthermore, for all compounds, both the t_2g and e_g states in PDOS are slightly split, which is mainly due to the Jahn–Teller effect as the severe octahedron distortion occurs in the presence of the Fe substitution.

We now investigate the doping concentration dependent magnetization of the Fe and Ba doped BNT. Figure 12 shows the calculated M of BNT(Fe), B(Fe)NT, and BN(Fe)T as function of the concentration of the dopant atoms. For the 2 (or 1.67 at.%) and 4 (or 3.33 at.%) Fe atoms in the 24 f.u. cell, we have also considered the spin antiparallel coupling between the Fe dopant atoms. For both cases, the spin parallel coupling (ferromagnetic) is more preferable than the spin antiparallel coupling.

Figure 12

The DFT results of the magnetization (µ_B/f.u.) of BNT(Fe), B(Ba)NT, and BN(Ba)T as function of the concentration of the dopant atoms.

Clearly, the magnetization increases linearly from 0.16 µ_B/f.u. (4.2 emu/g) to 0.66 µ_B/f.u. (17.3 emu/g) as the Fe concentration increases from 0.83 at.% to 3.33 at.%, as shown in Fig. 12. Our calculated magnetization is much larger than the measured values (23 memu/g at 9 mol.%), which is presumably due to the different concentrations and stoichiometries between the theory (here only the Fe doping) and experiment (Ba and Fe co-doping). Interestingly, the Ba doping for the A-site (Bi and Na) induces magnetism (M = 0.05 µ_B/f.u.) at about 2.5 at.% (Fig. 12). It is further found that the calculated magnetization increases as the doping concentration increases. Our atom resolved magnetization analyses indicate that the induced magnetization mainly comes from the Ti and O atoms neighboring to the Ba dopant site. The underlying mechanism can be explained by the spin-polarized charge transfer between the dopant and neighboring atoms in the unit cell, as revealed from the Ti- and O-PDOS analyses shown in Fig. 13.

Figure 13

The DFT results of PDOS of the Ti and O atoms for (a) and (c) (Ba)NT and (b) and (d) BN(Ba)T at 3.33 at./% Ba doping. The Fermi level is set to zero energy.

We finally explored the magnetic and electronic properties of the O-vacancy defected BNT(Fe). We have considered the presence of a single vacancy and double vacancies in the Fe-included octahedral cell to imitate different valence states of the Fe dopant atom. Our calculations show that the total magnetization (4 μ_B) of the BNT(Fe) compound decreases by 1 and 2 μ_B for the single-vacancy and double-vacancy systems, respectively. From the electronic structure analyses shown in Fig. 14a–c, the PDOS of the Fe dopant atom in BNT(Fe) shift toward the low energy region and some minority-spin states are partially occupied in the presences of the single and double oxygen vacancies. This is because of the extra electrons accumulated at the Fe site, originated from the O deficiency in the unit cell. Furthermore, the obtained magnetic moments are simply the reflections of the Fe²⁺ and Fe³⁺ ionic states in the high spin states and mixture of them in a real sample, as addressed in the previous  experiment³⁰.

Figure 14

The DFT results of the d-orbital decomposed PDOS of the Fe substitutional atom for the BNT(Fe) with the (a) vacancy-free, (b) single-vacancy, and (c) double-vacancy. The black, orange, red, green, and blue lines represent the d_xy, d_yz, d_z², d_xz, and d_x²_–y² orbital states, respectively. The Fermi level is set to zero energy.

Conclusion

The solid solution of BaFeO_3−δ and Na_0.5Bi_0.5TiO₃ ceramics have been successfully synthesized by a chemical route sol–gel method. The Ba and Fe ions were distributed randomly into the Na_0.5Bi_0.5TiO₃ lattices which caused in the distortion of lattice structure and decreased the optical band gap. The complex magnetic properties were observed in this solid solution. This work shows a simple way for enhancement of room-temperature ferromagnetism in lead-free ferroelectric materials by solid solution.

Experiment

(1 − x)Na_0.5Bi_0.5TiO₃ + xBaFeO_3−δ (BNT-xBFO; x = 0.5%, 1%, 3%, 5%, 7% and 9%) samples were fabricated by sol–gel method. The raw materials were consisted of Bi(NO₃)₃^.5H₂O, NaNO₃, Fe(NO₃)₃^.9H₂O, tetraisopropoxytitanium (IV) (C₁₂H₂₈O₄Ti) and BaCO₃. The solution was chosen which are acetic acid (CH₃COOH) and deionized water with volume ratio of $V_{H_{2}O}$:$V_{CH_{3}COOH}$ = 5:2 while an acetylacetone (CH₃COCH₂COCH₃) were selected as ligand. Fist, the BaCO₃ were weighted and distinguee under mix acid acetic and deionized water. Thus, the raw materials such Bi(NO₃)₃.5H₂O, NaNO₃, Fe(NO₃)₃.9H₂O were weighted to add the solution. To following, the solution was added with tetraisopropoxytitanium after adding to avoid hydrolysis. The solution was magnetic stirred under several hours to make homogeneous solution of sol. The sol was dried under 100 °C to prepare gels in oval. The dried gel was rout grounded and annealed under 800 °C for three hours in air then nature cooling down to room temperature. The as-prepared samples were rout ground for further samples characterization.

The chemical composition and chemical mapping of samples was carried out via energy dispersive spectroscopy (EDS, S-4800 Hitachi). The sodium is lighter element which were easy evaporated during the gelling and annealing processing that make samples nonstoichiometric composition. Therefore, the sodium nitrate was weighed to extra around 40–50 mol% to prevent the sodium evaporation^{9,10,11,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,60}. The crystalline structural of pure Na_0.5Bi_0.5TiO₃ and BaFeO_3−δ-modified Na_0.5Bi_0.5TiO₃ samples were characterized through X-ray diffraction (XRD, Brucker D8 Advance). The vibration modes of samples were measured by using Raman spectroscopy (with a 475 nm LASOS laser and a DU420A-Oe detector). The optical properties were studied by Ultraviolet–Visible (UV–Vis, Jasco V-670) and photoluminescence (PL, excited with 475 nm LASOS laser and a DU420A-Oe CCD detector) spectroscopy. Magnetic properties were characterized by a vibrating sample magnetometer (VSM, Lakeshore 7404). All experimental were performed at room temperature.