The integration of room-temperature ferromagnetic behavior in lead-free ferroelectric materials is a new research trend for the development of green functional materials in smart electronic devices1,2. PbTiO3-based compounds are one of the most commonly used ferroelectric materials in electronic devices3. Therefore, ferroelectric PbTiO3-based materials with improved magnetic properties have the potential for the fabrication of next-generation electronic devices.

First, the self-organized ferromagnetism of pure ferroelectric PbTiO3 materials was investigated. The experimental results showed that the weak ferromagnetism in undoped PbTiO3 nanocrystalline at room temperature resulted from intrinsic defects in events such as O and Ti vacancies4. PbTiO3 thin films also exhibited room-temperature ferromagnetism because of defects in the crystal quality of the film during growth5. Shimada et al. predicted that both O and Ti vacancies induce ferromagnetism but through different mechanisms. The ferromagnetism driven by O vacancies originated from the spin-polarized eg state of the nearest Ti atom, whereas that directed by Ti vacancies was attributed to the half-metallic px state of the nearest O atom6. In addition, the ferroelectric property of PbTiO3 materials at room temperature could be attributed to O vacancies formed on the surfaces, such as vacancies induced ferromagnetism due to local non-stoichiometry and orbital symmetry breaking7. Xu et al. conducted first-principle calculations and reported that the O vacancies that formed at the domain wall led to magnetism with a localized spin moment around the vacancies8. Second, the conversion of transition metals to ferroelectric PbTiO3 materials was studied to overcome the limitations associated with the presence of rare multiferroic materials in nature9,10. Fe-doped PbTiO3 nanocrystals were reported to exhibit room-temperature ferromagnetism11. The saturation magnetization of these materials was improved using polyvinyl alcohol as surfactant12. Oanh et al. reported that Mn and Ni substitution at the Ti site in PbTiO3 materials also exhibited room-temperature ferromagnetism13,14. Weston et al. predicted that Co-doped PbTiO3 is a bi-stable magnetic system with strong spin-lattice coupling, where the spin-lattice effect mediates magnetoelectric coupling and the electric field possibly induced spin-crossover15. Third, ferroelectric and ferromagnetic materials with magnetoelectric coupling were fabricated as a multilayer and composite, where the magnetic and electrical-fields possible controlled polarization and magnetization, respectively.

Interestingly, the magnetoelectric effect has been reported in ferromagnetic grains that are distributed randomly in host ferroelectric materials as composites and/or ferromagnetic thin films grown on ferroelectric and multilayered ferroelectric/ferromagnetic thin films16,17,18. Recent developments in the ferromagnetic properties of ferroelectric PbTiO3-based materials have allowed the fabrication of new materials for the next-generation technologies. The application of PbTiO3-based material is limited mainly by the contamination risk of Pb, which accounts for more than 60 wt.% of the material, possibly leading to pollution and harmful effects on human health. Hence, there is a strong need for green ferroelectric materials to replace Pb-based ferroelectric in electronic device application.

Lead-free ferroelectric materials, such as Bi0.5Na0.5TiO3, are candidates for replacing lead-based materials because of their improved properties19. The strong polarization in Bi0.5Na0.5TiO3 materials could be due to the lone pair effect of Bi3+ compared to that of Pb2+ in the perovskite structure20,21. Several materials possessing a perovskite structure exist as a well solid solution in Bi0.5Na0.5TiO3 materials, thereby exhibiting enhanced performance. BiAlO3-modified Bi0.5Na0.5TiO3 materials as a solid solution strongly enhance the electric field-induced strain22. Kang et al. reported that a BaTiO3 solid solution in Bi0.5Na0.5TiO3 materials has the potential for energy harvesting23. Furthermore, Lin et al. reported that a Bi0.5Li0.5TiO3 solid solution in Bi0.5Na0.5TiO3 decreased the sintering temperature and enhanced the piezoelectric coefficient up to 121 pC N−124. BiAlO3 materials are generally fabricated under extreme conditions. Although the properties of Bi0.5Li0.5TiO3 materials are not well known, they exist as a solid solution with enhanced performance properties relative to their host materials25,26. Therefore, modified Bi0.5Na0.5TiO3 materials exhibit excellent properties highlighting their potential in fabricating electronic devices.

The magnetic properties of Bi0.5Na0.5TiO3 materials have been investigated recently. The replacement of Ti cations with Co and Fe cations at the octahedral site of Bi0.5Na0.5TiO3 materials resulted in ferromagnetic ordering at room temperature27,28. Ferromagnetism in Fe-doped Bi0.5Na0.5TiO3 materials is an intrinsic phenomenon, whereas ferromagnetism in Co-doped Bi0.5Na0.5TiO3 materials is due to the presence of magnetic Co clusters27,28. Thanh et al. reported that Mn- and Cr-doped Bi0.5Na0.5TiO3 materials possibly influence room-temperature ferromagnetism29,30. On the other hand, the room-temperature ferromagnetic properties in Mn-doped Bi0.5Na0.5TiO3 materials result from an interaction of the Mn cation through O vacancies, whereas those in Cr-doped Bi0.5Na0.5TiO3 materials were mostly related to self-defects and enhancement via O vacancies29,30. Zhang et al. predicted that a Na or Ti vacancy, rather than a Bi or O vacancy, could induce magnetism31. Ju et al. predicted that substituting a Ti atom with a transition metal produces magnetic moments because of the spin polarization of 3d electrons in a transition metal32. Therefore, room-temperature ferromagnetism in lead-free ferroelectric Bi0.5Na0.5TiO3 materials could be the result of the introduction of a single transition metal into their host lattice. On the other hand, the limitation in the number of transition-metal-doped lead-free Bi0.5Na0.5TiO3 materials has resulted in poor ferromagnetism performance, such as low magnetization at room temperature (approximately several memu/g at room temperature), suggesting a real application in electronic devices. Given the desirable solid solution with ABO3-type materials, the magnetization of Bi0.5Na0.5TiO3 materials is enhanced strongly33,34,35,36. Hue et al. reported that the presence of an ilmenite-type material, such as MnTiO3 or NiTiO3 solid solution, in the host Bi0.5Na0.5TiO3 material could enhance magnetization33,34. This enhancement was also achieved when perovskite-type MgFeO3-δ and SrFeO3-δ solid solutions were added to the host Bi0.5Na0.5TiO3 materials35,36.

Among members of the alkaline-earth iron-based perovskite AeFeO3-δ family (Ae = Ba, Ca, Sr, and Mg), CaFeO3-δ is interesting because the O deficiency could control the structural and magnetic properties35,36,37,38,39,40,41. Ceretti et al. reported that CaFeO2.5 exhibits a brown millerite structure37. Tassel et al. revealed that CaFeO2 has a layered structure, and Takeda et al. reported that CaFeO3 exhibits a perovskite structure38,39. The latter has antiferromagnetic ordering, with a Neel temperature of 120 K39. In addition, CaFeO2.5 exhibits an antiferromagnetic G-type structure, with a Neel temperature range of 700–725 K36,40. CaFeO2 also shows G-type antiferromagnetic order, with a Neel temperature of 420 K41. Recently, MgFeO3-δ and SrFeO3-δ were reported to forma well solid solution in host Bi0.5Na0.5TiO3 materials, resulting in greater magnetization than those in single-transition-metal-doped Bi0.5Na0.5TiO3 materials35,36. The enhancement of magnetization in alkaline-earth iron-based perovskite-modified Bi0.5Na0.5TiO3 materials possibly originated from the co-modification of both A- and B-sites with alkaline-earth and transition metals. Therefore, CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials may also exhibit high magnetization through the diffusion of Ca and Fe cations in the host lattice and incorporation during the formation of the solid solution. In this study, a new (1-x)Bi0.5Na0.5TiO3-xCaFeO3-δ solid solution compound was prepared using sol–gel technique. Bi0.5Na0.5TiO3 materials with CaFeO3-δ maintained their original rhombohedral structure. Their distorted structure was attributed to the random distribution of Ca and Fe cations. Bi0.5Na0.5TiO3 samples with CaFeO3-δ exhibited stronger room-temperature ferromagnetism than pure Bi0.5Na0.5TiO3 materials or single-transition-metal-doped Bi0.5Na0.5TiO3. These intrinsic and tunable ferromagnetism properties of undoped and doped Bi0.5Na0.5TiO3 were investigated further through density functional theory (DFT) calculations.


Room temperature structure

The X-ray diffraction (XRD) patterns of CaFeO3-δ-modified Bi0.5Na0.5TiO3 with a CaFeO3-δ concentration of up to 9 mol.% showed that CaFeO3-δ was well dissolved in the host Bi0.5Na0.5TiO3 crystal. Figure 1(a) shows the XRD patterns of CaFeO3-δ-modified Bi0.5Na0.5TiO3 samples with various CaFeO3-δ concentrations. All relative peak positions and intensities were indexed to rhombohedral symmetry, indicating that the crystalline structure of CaFeO3-δ-modified Bi0.5Na0.5TiO3 samples adopted the crystal structure of the host Bi0.5Na0.5TiO3 materials. Furthermore, CaFeO3-δ existed in form of a solid solution in Bi0.5Na0.5TiO3 through the diffusion of Ca and Fe cations and incorporation in the host lattice. The impurity phase was not determined by XRD owing to its resolution limit. The Ca and Fe cations modified the lattice parameter of Bi0.5Na0.5TiO3 materials, as shown in Fig. 1(b), where the diffraction angles 2θ increased by 31.0°–34.0°. A broad peak position was obtained because of the overlap of two diffraction peaks, which complicated their comparison. Each XRD peak was distinguished using Lorentz fitting, as shown by the red dotted line in Fig. 1(b). Furthermore, the lattice parameters a and c of the pure Bi0.5Na0.5TiO3 and the CaFeO3–δ-modified Bi0.5Na0.5TiO3 according to CaFeO3–δ addition amounts is shown in Fig. 1(c). The results show that distorted lattice parameters of Bi0.5Na0.5TiO3 compound is not linear as function of CaFeO3–δ amounts, that has complexed distortion in lattice parameters. This could be attributed to cation radius difference between Ca and Fe in additives and Bi, Na and Ti of host material incorporating randomly with host lattice. Based on Shannon’s report, the radii of Ca2+, Bi3+, and Na+ cations in coordination number 12 are 1.34, 1.17, and 1.39 Å, respectively, whereas those of Fe3+/2+ and Ti4+ cations in a coordination number 6 are 0.645 Å/0.780 Å and 0.605 Å, respectively42. Therefore, the average radius of the A-site of (Bi0.5Na0.5)2+ is 1.28 Å, which is smaller than that of Ca2+ (1.34 Å). On the other hand, the lattice parameters expanded when the Ca2+ cations substituted Bi3+ cations in the host lattice, where the lattice parameters were reduced when Ca2+ cations replaced the Na+ cations. Moreover, to maintain a balanced charge, Ca2+ acted as an acceptor for replacing Bi3+ cations, resulting in the formation of O vacancies, and Ca2+ cations acted as a donor for incorporating Na+ cations, thereby producing Na-vacancies. Similarly, the radii of Fe2+/3+ cations are larger than that of Ti4+. Therefore, the distorted crystal structure of Bi0.5Na0.5TiO3 could be attributed to the replacement of Ti4+ cations with large Fe2+/3+ cations. Based on the Hume–Rothery rules, Ca2+ cations enter at the substituted A-site of Bi0.5Na0.5TiO3 materials because of the 4.7% difference between the radius of Ca2+ and the average radius of (Bi0.5Na0.5)2+43,44,45. The differences between the radii of Fe3+ and Fe2+ cations and those of Ti4+ cations substituted at the B-site of Bi0.5Na0.5TiO3 materials are 6.6% and 28.9%, respectively, which, according to the Hume–Rothery rules, is too large to allow replacement because of the increased lattice energy. The lattice energy can be reduced if the difference in the sizes between the O vacancies and O anion is consistent. O vacancies were formed because of the unbalanced charges between Fe3+/2+ and Ti4+. Chatzichristodoulou et al. reported that the effective radius of O vacancies (1.31Å) is smaller than that of the O anion ion (1.4Å), resulting in a decrease lattice constants46. The flaccidity of the size of O vacancies on the lattice parameters has a more significant influence than that of dopants in perovskite Bi0.5Na0.5TiO3 or BaTiO3 materials30,47. Therefore, CaFeO3-δ materials exists as a well solid solution in the Bi0.5Na0.5TiO3 structure and distort the crystal structure of the latter.

Figure 1
figure 1

(a) XRD spectra (b) its deconvolution ranged from 31.0° to 34.0° and (c) lattice constants of pure and CaFeO3–δ-modified Bi0.5Na0.5TiO3 materials as solid solution at 0.5, 1, 3, 5, 7 and 9 mol.%.

The solute solution of CaFeO3-δ into host Bi0.5Na0.5TiO3 materials was further confirmed using Raman scattering studies. Figure 2(a) shows the Raman spectra of Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials within range of 200 and 1000 cm−1. The Raman spectra of the undoped Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials exhibited similar shapes. Therefore, the vibration modes of CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials were similar to those of the undoped Bi0.5Na0.5TiO3 materials. This conforms to the XRD patterns, suggesting that the CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials maintained their original crystal structural of host Bi0.5Na0.5TiO3 compounds. On the other hand, the Raman scattering spectra of pure and CaFeO3-δ-modified Bi0.5Na0.5TiO3 were separated approximately into three overlapping active bands: 300–450, 450–700, and 700–1000 cm−1. The overlap in the Raman scattering modes may originate from the random distribution of Na and Bi cations at the A-site in the perovskite structure48. In addition, experimental and theoretical investigations both predicted that the lowest frequency modes within 246–401 cm−1 are related to the TiO6 vibration, whereas the highest frequency modes within 413–826 cm−1 are due to the vibration of O atoms48. Chen et al. assigned the Raman scattering in the range of 200–400 cm−1 to Ti-O vibration, whereas the Raman scattering in the range of 450–700 cm−1 is related to the TiO6 octahedral vibration49. Hence, distinguishing each mode and comparing the roles of Ca and Fe cations in the lattice vibration are difficult. Despite this, an attempt was made to distinguish the Raman modes for pure Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials using a Lorentz fit within the range of 250–950 cm−1. The Raman active modes within the said wave-number range were obtained with a correction of fitting over 0.99. Figure 2(b) shows the Raman modes for pure Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 with 1, 5, and 9 mol.%. Each active mode was well indexed based on the calculation and experimental results for the active Raman modes in Bi0.5Na0.5TiO3 materials48. The dependent of Raman active peak modes on the CaFeO3-δ amounts solid solution into host Bi0.5Na0.5TiO3 materials was shown in Fig. 2(c). The results clearly show that the Raman peaks shifted to lower frequency as increase of CaFeO3-δ concentration. However, the shift of Raman peak frequencies was not decreased linearly to the CaFeO3-δ concentration, but has complex function. Normally, the increase in the ionic radii results in a distortion of the structure, leading to a high frequency shift, whereas the increase in the mass results in a low-frequency shift49. The XRD peaks for Bi0.5Na0.5TiO3 materials shifted to low diffraction angles. Therefore, the Raman scattering modes were expected to shift to a high frequency. On the other hand, the mass values of the Ca and Fe cations were larger than those of the average A-site (Bi, Na) and Ti cations, possibly leading to a low-frequency shift. Thus, the low-frequency shifts in Raman scattering modes were related to the (Ti,Fe)O6 vibration modes. In addition, compared to the average of (Bi, Na), the mass values of Bi and Na cations (mBi = 208.98 and mNa = 22.99) at the A-site of 164.99 were larger than that of calcium (mCa = 40.08), whereas the mass of the Ti cation (mTi = 47.86) was smaller than that of the Fe cation (mFe = 55.85). The shift of the Raman vibration modes confirmed the random substitution of Ca and Fe cations into the host lattice of Bi0.5Na0.5TiO3 materials; this substitution occurred because of the difference in the mass values of Ca and Fe cations compared to those of (Bi, Na) and Ti, respectively, and the distorted structure of the samples. In other words, the shifted Raman scattering modes confirmed the incorporation of Ca and Fe into the host lattice of the Bi0.5Na0.5TiO3 materials.

Figure 2
figure 2

(a) Raman spectra of pure Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 samples as solid solutions with various concentrations, (b) deconvolutions of the Raman spectra of pure Bi0.5Na0.5TiO3 and CaFeO3-δ solid solutions in Bi0.5Na0.5TiO3 with 1, 5, and 9 mol% CaFeO3-δ, and (c) Raman actives modes of Bi0.5Na0.5TiO3 dependence on the CaFeO3-δ amount as solid solution.

Optical properties

The solute solution of CaFeO3-δ into the host Bi0.5Na0.5TiO3 materials results in a decrease in the optical band gap. Figure 3(a) presents the optical absorbance spectra of undoped Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials at various concentrations at room temperature. The pure Bi0.5Na0.5TiO3 samples exhibited a single absorbance edge, which is consistent with the recently reported optical properties of Bi0.5Na0.5TiO3 materials29,30,50,51. The addition of CaFeO3-δ to Bi0.5Na0.5TiO3 caused the absorbance edge to shift to high wavelengths, indicating that the electronic band structures had been modified. Furthermore, the absorbance spectra of the CaFeO3-δ-modified Bi0.5Na0.5TiO3 samples showed absorbance peaks at approximately 485 nm, indicating the local states of the Fe cations. This result is consistent with the recent observation of the absorbance spectra of Fe cation impurities in Bi-based ferroelectric materials, such as Bi0.5K0.5TiO3 and Bi0.5Na0.5TiO3 materials35,36,52. In addition, CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials exhibited smooth absorbance edges with slight tails. The appearance of tails in CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials could be related to an intrinsic defects or surface effects51. The optical band gap (Eg) was estimated using the Wood and Tauc method53. In this approach, the Eg values are associated with the absorbance and photon energy, as shown by the following relation: (αhν)~(hν-Eg)n, where α, h, and ν are the absorbance coefficient, Planck constant, and frequency, respectively; n is a constant related to different types of electronic transition (n = 1/2, 2, 3/2, or 3 for directly allowed, indirectly allowed, directly forbidden, or indirectly forbidden transition, respectively)53. Thus, Eg can be evaluated by extrapolating the linear portion of the curve or tail from the intercept of (αhν)1/n versus the photon energy . A calculation of the electronic band structure showed that Bi0.5Na0.5TiO3 has a direct band gap of 2.1 eV, and the optical spectra of Bi0.5Na0.5TiO3 were determined mainly by the contributions from the O 2p valence bands to the Ti 3d and Bi 6p conduction bands in the low-energy region54. Therefore, n = 1/2 for direct transition was used, as shown in Fig. 3(b). Pure Bi0.5Na0.5TiO3 materials exhibited an Eg of approximately 3.11 eV, whereas CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials showed lower Eg value (2.34 eV for 9 mol.% CaFeO3-δ solid solution in Bi0.5Na0.5TiO3). The inset of Fig. 3(b) shows the dependence of Eg on the amount of CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials. The decrease in the optical band gap in CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials possibly originated from the random distribution of Ca and Fe cations into the host lattice of the Bi0.5Na0.5TiO3 materials. The replacement of a Ti cation with a transition metal, such as Mn and Cr, in the Bi0.5Na0.5TiO3 materials resulted in a decrease in the optical band gap because the impurities of these transition metal cations formed new local states in the middle of the electronic band structure29,30. In addition, the appearance of O vacancies located near the conduction band also affected the optical band gap of the Bi0.5Na0.5TiO3 materials29,30. Note that O vacancies were generated due to the unbalanced charges between Fe2+/3+ that substituted for Ti4+ at the octahedral site and Ca2+ cations that replaced Bi3+. In addition, the O vacancies located in the crystal structure promoted the valence transition of Ti4+ to Ti3+55. The appearance of new state Na + -vacancies or Ti3+-defect also contributed to the decrease in the optical band gap. Recently, A-site modified Bi0.5Na0.5TiO3-based material showed the decline of the optical band gap because of the changes in the bond type between the hybridization of A-O in the ABO3 perovskite structures56,57. Thus, the random substitution of Ca and Fe ions into the host Bi0.5Na0.5TiO3 changed the electronic band structure and decreased the optical band gap.

Figure 3
figure 3

(a) UV-Vis absorption spectra of pure Bi0.5Na0.5TiO3 and (1-x)Bi0.5Na0.5TiO3 + x CaFeO3-δ samples as the function of CaFeO3-δ solid solution, and (b) the (αhν)2 proposal with photon energy (hν) of pure Bi0.5Na0.5TiO3 as the function of the CaFeO3-δconcentration solid solution. Inset of Fig. 3(b) shows the optical band gap of the Bi0.5Na0.5TiO3 samples as a function of the CaFeO3-δ concentrations.

The CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials as a solid solution suppressed the photoluminescence (PL) of host materials. Figure 4(a) shows the room-temperature PL emission spectra of the Bi0.5Na0.5TiO3 samples. The spectra clearly showed a broad blue emission band within 476–505 nm. The PL intensity of Bi0.5Na0.5TiO3 materials decreased with increasing amount of CaFeO3-δ solid solution in the Bi0.5Na0.5TiO3 materials. The strong PL peak positions of pure Bi0.5Na0.5TiO3 materials and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials were compared via subtraction to the unit, as shown in Fig. 4(b). The peak showed a blue shift as the CaFeO3-δ concentration was increased. The broad band emission peak of pure Bi0.5Na0.5TiO3 materials and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials with 1, 5, 7, and 9 mol.% CaFeO3-δ were deconvoluted by a Lorentzian fit with the roughest square of more than 0.99, as shown in Fig. 4(c). The PL of ferroelectric materials is not generally dominated by a band-to-band transition, considering the difficulty in combining electron–hole pairs due to the separation of the nature polarization domain in the materials. On the other hand, the surface states are the dominant cause of luminescence in perovskites. Numerous unsaturated atoms exist on the surface of the perovskites, forming localized levels within the forbidden gaps of the materials. Lin et al. reported that a self-trapped excitation possibly originated from the PL of the Bi0.5Na0.5TiO3 materials, whereas the distortion of the TiO6 octahedra due to surface stress resulted in a blue shift in the emission peak58. Bac et al. also reported the disordered coupling to a tilt of the TiO6-TiO6 adjacent octahedral that resulted in structural distortion and generation of localized electronic levels above the valence band; these phenomena are mainly responsible for the PL emission of Bi0.5K0.5TiO3 materials51. Interestingly, the addition of CaFeO3-δ reduced the PL emission intensity of the Bi0.5Na0.5TiO3 materials (Fig. 4[a]), possibly by trapping electrons generated from absorbance photon energy that prevented electron–hole recombination to generate photons through the defects.

Figure 4
figure 4

(a) Real, (b) normalized PL spectra, and (c) its deconvolutions in pure Bi0.5Na0.5TiO3 samples, and Bi0.5Na0.5TiO3 solid solution with various CaFeO3-δ concentrations.

Magnetic properties

The complex magnetic properties at room temperature of Bi0.5Na0.5TiO3 materials were measured as a function of the CaFeO3-δ solute solution. Figure 5(a–g) show the magnetic hysteresis loops (M–H) of pure Bi0.5Na0.5TiO3 materials and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials with various amounts of CaFeO3-δ (0.5, 1, 3, 5, 7, and 9 mol.%) at room temperature. The pure Bi0.5Na0.5TiO3 materials exhibited an anti-S-shape M–H curve, which was attributed to the compensation of the diamagnetism of the empty 3d orbital of Ti and weak ferromagnetism of intrinsic defects or surface defects. The critical S-shape in the M–H curve of the ferromagnetic thin films were obtained in pure Bi0.5Na0.5TiO3 materials after subtracting diamagnetism components, as shown in the inset of Fig. 5(a). The saturation of magnetization was approximately 1.5 memu g−1, which is similar to the results of recent reports30,59. The slightly addition of CaFeO3-δ amounts to the host Bi0.5Na0.5TiO3 materials give rise to reduction of diamagnetic components, as shown in Fig. 5(b). The M–H curve was saturated under the applied external magnetic field for 1 mol.% CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials as a solid solution, as shown in Fig. 5(c), further confirming the ferromagnetic state ordering at room temperature. On the other hand, the unsaturation magnetization under the applied magnetic field was obtained with the further addition of CaFeO3-δ in Bi0.5Na0.5TiO3 materials as solid solution, as shown in Fig. 5(d–g). The maximum magnetization was approximately 21.6 memu g−1 for 9 mol.% CaFeO3-δ solid solution in Bi0.5Na0.5TiO3 materials. These results suggest strong enhancement of the magnetization of CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials, which is greater than that of pure Bi0.5Na0.5TiO3 (~1.5 memu g−1) or transition-metal-doped Bi0.5Na0.5TiO3 materials (~1.5–2 memu g−1 for Cr-doped Bi0.5Na0.5TiO3, ~3 memu g−1 for Co-doped Bi0.5Na0.5TiO3, ~9 memu g−1 for Mn-doped Bi0.5Na0.5TiO3, and ~11 memu g−1 for Fe-doped Bi0.5Na0.5TiO3)27,28,29,30,59. CaFeO3, CaFeO2.5, and CaFeO2 compounds have antiferromagnetic ordering, with Neel temperatures of 120, 700–725, and 420 K, respectively36,40,41. In the formation of a solid solution, however, the CaFeO3-δ-modified Bi0.5Na0.5TiO3 samples exhibited greater room-temperature ferromagnetism than single-transition-metal-doped Bi0.5Na0.5TiO3 materials. Therefore, modification of the A-site in perovskite, together with the presence of a transition metal at the B-site in lead-free ferroelectric materials, is important for the current integration and development of magnetism for ferroelectric materials. The possible mechanisms of room-temperature ferromagnetic ordering in transition-metal-doped Bi0.5Na0.5TiO3 materials were as follows: (i) interaction of a magnetic cation through O vacancies, such as the F-center mechanism28,29, (ii) enhanced magnetism of O vacancies30, and (iii) magnetism of clusters embedded in the host materials27. Unlike that of single-transition-doped Bi0.5Na0.5TiO3 materials, the A-site of Bi0.5Na0.5TiO3 materials was modified by Ca, causing complications, such as Na and O vacancies (□). Both defects possibly induced ferromagnetism. In addition, the risk of O vacancies promoted the valence transition from Ti4+ to Ti3+, thereby inducing ferromagnetism55,60. Moreover, the chemical strain due to the difference in the radii of Ca and Fe compared to that of the host lattice Bi0.5Na0.5TiO3 materials might have tuned the ferromagnetic ordering, such as the Fe3+-□-Fe3+ interaction or superinteraction of the magnetic polaron between [Fe3+-□-Fe3+] versus [Fe3+-□-Fe3+] etc. Of note, the tremendous interaction between polarons normally favored antiferromagnetic ordering, whereas the isolated Fe cations displayed paramagnetic ordering.

Figure 5
figure 5

M–H curves of (1-x)Bi0.5Na0.5TiO3 + xCaFeO3-δ concentration solid solution with various amounts.

Electronic band structure

The intrinsic defects and random incorporation of Ca and Fe cations into the host lattice of Bi0.5Na0.5TiO3 materials give rise to the induced magnetism. To get insights on the weak ferromagnetism of Bi0.5Na0.5TiO3 with vacancy defects, we model all possible single atomic vacancies in the 6 and 24 formula unit (f.u.) cells of Bi0.5Na0.5TiO3. The corresponding vacancy concentrations are about 3.3 at.% (1 vacancy per 30-atom cell) and 0.83 at.% (1 vacancy per 120-atom cell), respectively. Figure 6(a–e) show the model geometries that are composed of 6 f.u. cells (for simplicity, 24 f.u. cell structures are omitted) of the rhombohedral structure for the pristine and defected Bi0.5Na0.5TiO3 with single Bi- [denoted as BNT(VBi)], Na- [BNT(VNa)], Ti- [BNT(VTi)], and O-site vacancy [BNT(VO)], respectively.

Figure 6
figure 6

Optimized atomic structures of (a) BTN, (b) BNT(VBi), (c) BNT(VNa), (d) BNT(VTi), and (e) BNT(VO). The larger pink, yellow, and blue spheres denote the Bi, Na, and Ti atoms, respectively. The small red sphere indicates the O atom. The open-circle symbols represent the presence of various vacancies.

The important role of intrinsic defects on the electronic band structure has been obtained using by DFT calculations. Figure 7 shows the spin-decomposed total density of states (TDOS) of the BNT, BNT(VBi), BNT(VNa), BNT(VTi), and BNT(VO) compounds. In the pure BNT, the majority- and minority-spin states were entirely degenerated, indicating the feature of a nonmagnetic ground state. The calculated band gap (~2.25 eV) of BNT is found to be somewhat smaller than the measured value of 3.08 eV, which is typical in DFT calculations for correlated oxide compounds61. The presence of an O vacancy shifts the band states downward and develops midgap states immediately below the Fermi level. This phenomenon is a reflection of the excess electrons (2 electrons per O vacancy) in the unit cell. Unlike the BNT(VO), the degeneracy of the spin sub-bands, particularly around the Fermi level, of the BNT does not persist anymore in the presence of the Bi, Na, and Ti vacancies. As shown in Table 1, the induced magnetism was approximately 0.13 (0.10) µB for the 6 (24) f.u. BNT(VBi), 0.09 (0.0) µB for the 6 (24) f.u. BNT(VNa), and 0.30 (0.0) µB for the 6 (24) f.u. BNT(VTi). Note that for the BNT(VNa) and BNT(VTi) the induced magnetism showed the concentration dependence of the vacancy in the sample. On the other hand, the bandgap of the pure BNT remained relatively unchanged for the BNT(VNa), while it was reduced significantly for the BNT(VBi) and BNT(VTi). Our calculations indicate that a weak ferromagnetism of Bi0.5Na0.5TiO3 found in experiments can be the result of the formation of Bi or Na or Ti vacancies or, possibly, two or all of them during the sample growth.

Figure 7
figure 7

Top to bottom: Spin-decomposed total density of states (TDOS) of the BTN, BNT(VBi), BNT(VNa), BNT(VTi), and BNT(VO). The blue and yellow areas represent the majority-spin and minority-spin states, respectively. The Fermi level is set to zero energy.

Table 1 Magnetization per formula unit cell (μB/f.u.) of Bi0.5Na0.5TiO3 with various vacancies for the 6 and 24 f.u. cells adopted in the DFT calculations.

The further analyses with the atom and orbital projected DOS (PDOS) indicate that the vacancy induced magnetism mainly comes from the O atoms nearby the vacancy sites. We thus plot only the s- and p-orbital PDOS of the O atom for the BNT(VBi), BNT(VNa), and BNT(VTi) in Fig. 8. For comparison, the same for the pure BNT is also presented. For the BNT, the valence and conduction bands are characterized mainly by the O-2p and Ti-3d orbital states, respectively. Both Ti and O contributed to the filled midgap state in the BNT(VO), as shown in Fig. S3 in the supplemental data. As seen in Fig. 8, the O 2px,y orbital states play a main role for the induced magnetism of all systems, as the filled px,y orbital states in the minority-spin channel shift across the Fermi level into the unoccupied band region.

Figure 8
figure 8

Left to right: The s- and p-orbital decomposed PDOS of the O atom for the BTN, BNT(VBi), BNT(VNa), and BNT(VTi). The black, orange, red, and blue lines represent the s, py, pz, and px orbital states, respectively. The Fermi level is set to zero energy.

To imitate the presences of Ti3+ and Ti2+ valence states, we inject 1 and 2 e- in the 6 f.u. cell of the pristine BNT and plot the d-orbital PDOS of the Ti atom in Fig. 9. This serves as a n-type doping, where the spin channel states split. The calculated magnetic moments are 0.083 and 0.32 µB per f.u. for 1 and 2 e- doped BNT, respectively, which mainly resides at the Ti site. As expected, PDOS states move downward toward the Fermi level; the majority-spin states are partly occupied while the minority-spin states remain unoccupied.

Figure 9
figure 9

Left to right: The d-orbital decomposed PDOS of the Ti atom of the pristine BTN for zero, +1 e-, and +2 e- injected charges. The black, orange, red, green, and blue lines represent the dxy, dyz, dz2, dxz, and dx2y2 orbital states, respectively. The Fermi level is set to zero energy.

We now explore the enhanced ferromagnetism of the Bi0.5Na0.5TiO3 with the Bi- [denoted B(Ca)NT] and Na-site Ca [BN(Ca)T], and Ti-site Fe substitutional dopant [BNT(Fe)]. Figure 10(a–c) show the 6 f.u. model structures of the B(Ca)NT, BN(Ca)T, and BNT(Fe) compounds, where only one atomic site was replaced by the substitutional dopant atom. We have also considered the 24 f.u. cell structures with a single-site doping but their atomic structures are not presented in the present paper. If one assumes full occupations of the Ca and Fe atom dopants in the host Bi0.5Na0.5TiO3, the highest experimental impurity concentration of 9 mol.% (as an example case) can be converted into (Bi0.96Ca0.04)0.5Na0.5TiO3 for Ca→Bi, Bi0.5(Na0.6Ca0.4)0.5TiO3 for Ca→Na, and Bi0.5Ca0.5Ti0.9Fe0.1O3 for Fe→Ti. In the computation, the doping concentration of 3.3 at.% (1 dopant per 30-atom cell) corresponds to [(Bi/Na)0.67Ca0.33]0.5(Na/Bi)0.5TiO3 for Ca→Bi/Na and Bi0.5Na0.5Ti0.84Fe0.16O3 for Fe→Ti, while it is [(Bi/Na)0.92Ca0.08]0.5(Na/Bi)0.5TiO3 for Ca→Bi/Na and Bi0.5Na0.5Ti0.96Fe0.04O3 for Fe→Ti for 0.83 at.% doping (1 dopant per 120-atom cell). Thus, we believe that the amount of the impurity defects in the experimental sample is somehow reflected in the present calculations. The TDOS of the B(Ca)NT, BN(Ca)T, and BNT(Fe) systems are shown in Fig. 11. The B(Ca)NT and BN(Ca)T exhibits nonmagnetic features, whereas there is a significant midgap state around the Fermi level for the BNT(Fe). In particular, such a midgap state is nondegenerate in the spin subbands, indicating the strong ferromagnetic nature.

Figure 10
figure 10

Optimized atomic structures of (a) B(Ca)TN, (b) BN(Ca)T, and (c) BNT(Fe). The larger pink, yellow, blue, green, and brown spheres denote the Bi, Na, Ti, Ca, and Fe atoms, respectively. The small red sphere indicates the O atom.

Figure 11
figure 11

Top to bottom: Spin-decomposed total density of states (TDOS) of the B(Ca)TN, BN(Ca)T, and BNT(Fe). The blue and yellow areas represent the majority-spin and minority-spin states, respectively. The Fermi level is set to zero energy.

To obtain more understanding, we show the d-orbital PDOS of the Fe atom of BNT(Fe) in Fig. 12(a). The corresponding s- and p-PDOS of the neighboring O atom is also shown in Fig. 12(b). Both the Fe and O provide the contribution to the midgap state. This indicates a strong orbital hybridization between the Fe 3d and O 2p states. In particular, the majority-spin bands of Fe were fully occupied, whereas the minority-spin states were partially unoccupied. Consequently, the Fe atom exhibited a substantially large exchange splitting between the spin sub-bands of the majority- and minority-spin states, resulting in a magnetic moment of approximately 4 µB per unit cell, which corresponds to 0.64 (0.16) µB for the 6 (24) f.u. cell structure. In Table 2, we present the calculated magnetization per f.u. cell (μB/f.u.) of the B(Ca)NT, BN(Ca)T, and BNT(Fe) systems for the 6 and 24 f.u. structures. The induced moment at the neighboring O-site to the Fe was relatively minimal in the order of approximately 0.1 µB.

Figure 12
figure 12

The PDOSs of the (a) d-orbital states of the Fe and (b) s- and p-orbital states of the O atom for the BNT(Fe). In (a), the black, orange, red, green, and blue lines represent the dxy, dyz, dz2, dxz, and dx2y2 orbital states, respectively. In (b), the black, orange, red, and blue lines represent the s, py, pz, and px orbital states, respectively. The Fermi level is set to zero energy. (c) Schematic representations of the octahedral environment of the Fe2+ ion (left) and its energy levels of d-orbital states with the high-spin-state crystal field (right). The larger orange and smaller red spheres represent the Fe and O atoms, respectively. The red upward and blue downward arrows denote the spin-up and spin-down electrons at the low-lying t2g and high-lying eg states, respectively.

Table 2 Magnetization per formula unit cell (μB/f.u.) of Bi0.5Na0.5TiO3 with Bi and Na site Ca, and Ti site Fe substitutions for the 6 and 24 f.u. cells adopted in the DFT calculations.

Based on the PDOS analyses, the schematic diagrams of the octahedral environment of Fe2+ ion (left) and its energy levels of the d-orbital states with the high-spin state crystal field (right) were produced, as shown in Fig. 12(c). The 6 d-orbitals of Fe2+ ion split by high-spin state according to crystal field theory were filled by the five majority-spin electrons in the low-lying t2g orbital levels and by the electrons in the minority-spin t2g state. Therefore, according to Hund’s rule, the calculated magnetic moment of 4 µB of the Fe replacement for the Ti-site can be explained by the electronic configuration of the high-spin state in crystal field theory through unpaired electron spin count. Furthermore, both t2g and eg states in PDOS were split slightly, due mainly to the Jahn–Teller effect because severe octahedron distortion occurred in the presence of the Ti-site Fe atoms. Mixed oxidation states of Fe2+ and Fe3+ might be possible in a practical situation if an O vacancy exists near the doping sites.


Lead-free ferroelectric Bi0.5Na0.5TiO3 materials are promising candidates for replacing for PZT-based materials in electronic devices because of requirement for environmental and human health protection. Recently, the discovery of room temperature ferromagnetism in intrinsic defects Bi0.5Na0.5TiO3 materials highlighted the potential to extend the function materials to smart electronic devices application. On the other hand, the magnetic performance of Bi0.5Na0.5TiO3 materials was lower such as magnetization which was usually less than 1 memu/g and of the diamagnetic component has a strong influence. Therefore, advancements in the magnetic performance properties of Bi0.5Na0.5TiO3 materials are required. In the present study, new solid solution of CaFeO3-δ-Bi0.5Na0.5TiO3 materials with greatly enhanced magnetic properties compared Bi0.5Na0.5TiO3 materials were fabricated. On the other hand, the substitution of Ca and Fe cations at the A-site and B-site, respectively, in perovskite Bi0.5Na0.5TiO3 materials, resulted in complex magnetic properties of the host materials. The origin of ferromagnetism in CaFeO3-δ-Bi0.5Na0.5TiO3 system was examined. The random incorporation of Fe cations at the Ti-site possibly induced ferromagnetism via super-exchange interaction of Fe cations through oxygen vacancies, such as Fe3+-□-Fe3+. The risk of Fe cations substitution in the host Bi0.5Na0.5TiO3 materials resulted in super-exchange between [Fe3+-□-Fe3+] versus [Fe3+-□-Fe3+] which normally favoured antiferromagnetic ordering. In addition, the isolated Fe cations distributed randomly into the host Bi0.5Na0.5TiO3 crystal exhibited paramagnetic behaviour. Thus, the complex magnetic properties of Bi0.5Na0.5TiO3 materials possibly tuned by varying the concentration of CaFeO3-δ as a solid solution. However, unlike single Fe dopants, the presence of Ca cations into the host lattice exhibited complex results where both Ca2+ substitution for Bi3+ and Ca2+ substitution for Na+ cations produced the oxygen vacancies. The influence of intrinsic defects, including Bi, Na, Ti, and O vacancies on the electronic band structure was examined using DFT calculation to determine the contribution of intrinsic defects to the magnetic properties of the host Bi0.5Na0.5TiO3 materials. It was also predicted that the presences of Ti3+ and Ti2+ valence states could produce an intrinsic magnetism in the sample. In addition, a replacement of Ca for the Bi and Na sites and Fe for the Ti site was also clarified by the DFT calculations. We attribute the origin of weak ferromagnetism in pure Bi0.5Na0.5TiO3 mainly to the presence of the intrinsic defects. The theoretical prediction also indicates that the Bi and Na vacancies may induce a significant magnetic moment than that of oxygen vacancies. Indeed, these intrinsic defects in turn result in net magnetic moment for their neighbour oxygen sites. We suggest that the controlled valence state of transition metal defects was important for achieving optical magnetic moments in current integration ferromagnetic in lead-free ferroelectric materials. In other words, the co-modification of the A-site via alkali materials and B-site via transition metals were important parameters for estimating the increasing magnetic performance of lead-free ferroelectric materials. This study opens a new way to estimate the enhancement of the magnetic performance of lead-free ferroelectric materials via using the solid solution method in the current development of green multi-ferroics functional materials. In addition, this work not only applied to lead-free ferroelectric Bi0.5Na0.5TiO3-based materials, but may also be extended to lead-free ferroelectric BaTiO3-based, (Ba,Ca)(Ti,Zr)O3-based, or (K,Na)NbO3-based materials etc.


Sample preparation

The CaFeO3-δ solid solution was prepared in Bi0.5Na0.5TiO3 materials via sol–gel method to obtain (1-x)BNT-xCaFeO3-δ (x = 0, 0.5, 1, 3, 5, 7, and 9 mol.%). Raw materials such as Bi(NO3)3.5H2O, Ca(NO3)2, NaNO3, and Fe(NO3)3.9H2O were weighed and dissolved in deionized water and acetic acid. Subsequently, acetylacetone (CH3COCH2COCH3) was added to avoid hydrolysis. Tetraisopropoxytitanium (IV) (C12H28O4Ti) was also added and stirred continuously until it became transparent. The gels were prepared by drying the solution at 100 °C. The powdered samples were fabricated by sintering at 900 °C for 3 h in air.

Sample characterization

The chemical composition of the samples was analyzed by energy-dispersive spectroscopy (EDS). Fig. S1(a,b) are EDS spectra of selected area for pure Bi0.5Na0.5TiO3 and CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials with 5 mol.% CaFeO3-δ as solid solution, respectively. The amount of sodium added was approximately 30 mol.% to compensate for the Na loss during the gelling and sintering processes after evaluation by electron probe microanalysis (EPMA)35,36. The valence state of Fe 2p cations in CaFeO3-δ-modified Bi0.5Na0.5TiO3 materials were measured by X-ray photoelectron spectroscopy (XPS), as shown for an example in Fig. S2. The crystal structure quality and vibrational modes of the powdered samples were determined by XRD and Raman spectroscopy, respectively. The absorbance of the samples was measured by ultraviolet–visible spectroscopy (UV-Vis). The PL spectra were recorded using a laser at excitation wavelength of 475 nm, and the magnetization at room temperature was measured using a vibrating sample magnetometer

Electronic band structural calculations

To understand the observed magnetic and electronic properties, DFT calculations were performed within the projected augmented wave method62, as implemented in the Vienna ab initio simulation package (VASP)63,64. The generalized gradient approximation (GGA) formulated by Perdew, Burke, and Ernzerhof (PBE) was used to describe the electron exchange correlation potential65. An energy cutoff value of 500 eV was used for the plane-wave basis and a k-point mesh of 8 × 8 × 8 (5 × 5 × 5) for the 6 (24) f.u. cell of Bi0.5Na0.5TiO3 for the Brillouin zone (BZ) integration. To obtain optimized atomic structures, the atomic positions and lattice parameters were allowed to be fully relaxed until the largest force became less than 10−2 eV/Å and the change in the total energy between the two ionic relaxation steps was smaller than 10−5 eV.