Intrinsic and tunable ferromagnetism in Bi0.5Na0.5TiO3 through CaFeO3-δ modification

New (1-x)Bi0.5Na0.5TiO3 + xCaFeO3-δ solid solution compounds were fabricated using a sol–gel method. The CaFeO3-δ materials were mixed into host Bi0.5Na0.5TiO3 materials to form a solid solution that exhibited similar crystal symmetry to those of Bi0.5Na0.5TiO3 phases. The random distribution of Ca and Fe cations in the Bi0.5Na0.5TiO3 crystals resulted in a distorted structure. The optical band gaps decreased from 3.11 eV for the pure Bi0.5Na0.5TiO3 samples to 2.34 eV for the 9 mol% CaFeO3-δ-modified Bi0.5Na0.5TiO3 samples. Moreover, the Bi0.5Na0.5TiO3 samples exhibited weak photoluminescence because of the intrinsic defects and suppressed photoluminescence with increasing CaFeO3-δ concentration. Experimental and theoretical studies via density functional theory calculations showed that pure Bi0.5Na0.5TiO3 exhibited intrinsic ferromagnetism, which is associated with the possible presence of Bi, Na, and Ti vacancies and Ti3+-defect states. Further studies showed that such an induced magnetism by intrinsic defects can also be enhanced effectively with CaFeO3-δ addition. This study provides a basis for understanding the role of secondary phase as a solid solution in Bi0.5Na0.5TiO3 to facilitate the development of lead-free ferroelectric materials.


Results
Room temperature structure. The X-ray diffraction (XRD) patterns of CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 with a CaFeO 3-δ concentration of up to 9 mol.% showed that CaFeO 3-δ was well dissolved in the host Bi 0.5 Na 0.5 TiO 3 crystal. Figure 1(a) shows the XRD patterns of CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 samples with various CaFeO 3-δ concentrations. All relative peak positions and intensities were indexed to rhombohedral symmetry, indicating that the crystalline structure of CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 samples adopted the crystal structure of the host Bi 0.5 Na 0.5 TiO 3 materials. Furthermore, CaFeO 3-δ existed in form of a solid solution in Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 and the CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 according to CaFeO 3-δ addition amounts is shown in Fig. 1(c). The results show that distorted lattice parameters of Bi 0.5 Na 0.5 TiO 3 compound is not linear as function of CaFeO 3-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 Ca 2+ , Bi 3+ , and Na + cations in coordination number 12 are 1.34, 1.17, and 1.39 Å, respectively, whereas those of Fe 3+/2+ and Ti 4+ cations in a coordination number 6 are 0.645 Å/0.780 Å and 0.605 Å, respectively 42 . Therefore, the average radius of the A-site of (Bi 0.5 Na 0.5 ) 2+ is 1.28 Å, which is smaller than that of Ca 2+ (1.34 Å). On the other hand, the lattice parameters expanded when the Ca 2+ cations substituted Bi 3+ cations in the host lattice, where the lattice parameters were reduced when Ca 2+ cations replaced the Na + cations. Moreover, to maintain a balanced charge, Ca 2+ acted as an acceptor for replacing Bi 3+ cations, resulting in the formation of O vacancies, and Ca 2+ cations acted as a donor for incorporating Na + cations, thereby producing Na-vacancies. Similarly, the radii of Fe 2+/3+ cations are larger than that of Ti 4+ . Therefore, the distorted crystal structure of Bi 0.5 Na 0.5 TiO 3 could be attributed to the replacement of Ti 4+ cations with large Fe 2+/3+ cations. Based on the Hume-Rothery rules, Ca 2+ cations enter at the substituted A-site of Bi 0.5 Na 0.5 TiO 3 materials because of the 4.7% difference between the radius of Ca 2+ and the average radius of (Bi 0.5 Na 0.5 ) 2+43-45 . The differences between the radii of Fe 3+ and Fe 2+ cations and those of Ti 4+ cations substituted at the B-site of Bi 0.5 Na 0.5 TiO 3 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 Fe 3+/2+ and Ti 4+ . 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 constants 46 . The flaccidity of the size of O vacancies on the lattice parameters has a more significant influence than that of dopants in perovskite Bi 0.5 Na 0.5 TiO 3 or BaTiO 3 materials 30,47 . Therefore, CaFeO 3-δ materials exists as a well solid solution in the Bi 0.5 Na 0.5 TiO 3 structure and distort the crystal structure of the latter.
The solute solution of CaFeO 3-δ into host Bi 0.5 Na 0.5 TiO 3 materials was further confirmed using Raman scattering studies. Figure 2(a) shows the Raman spectra of Bi 0.5 Na 0.5 TiO 3 and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials within range of 200 and 1000 cm −1 . The Raman spectra of the undoped Bi 0.5 Na 0.5 TiO 3 and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials exhibited similar shapes. Therefore, the vibration modes of CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials were similar to those of the undoped Bi 0.5 Na 0.5 TiO 3 materials. This conforms to the XRD patterns, suggesting that the CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials maintained their original crystal structural of host Bi 0.5 Na 0.5 TiO 3 compounds. On the other hand, the Raman scattering spectra of pure and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 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 structure 48 . In addition, experimental and theoretical investigations both predicted that the lowest frequency modes within 246-401 cm −1 are related to the TiO 6 vibration, whereas the highest frequency modes within 413-826 cm −1 are due to the vibration of O atoms 48 . 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 TiO 6 octahedral vibration 49 . 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 Bi 0.5 Na 0.5 TiO 3 and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 materials 48 . The dependent of Raman active peak modes on the CaFeO 3-δ amounts solid solution into host Bi 0.5 Na 0.5 TiO 3 materials was shown in Fig. 2(c). The results clearly show that the Raman peaks shifted to lower frequency as increase of CaFeO 3-δ concentration. However, the shift of Raman peak frequencies was not decreased linearly to the CaFeO 3-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 shift 49 . The XRD peaks for Bi 0.5 Na 0.5 TiO 3 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)O 6 vibration modes. In addition, compared to the average of (Bi, Na), the mass values of Bi and Na cations (m Bi = 208.98 and m Na = 22.99) at the A-site of 164.99 were larger than that of calcium (m Ca = 40.08), whereas the mass of the Ti cation (m Ti = 47.86) was smaller than that of the Fe cation (m Fe = 55.85). The shift of the Raman vibration modes confirmed the random substitution of Ca and Fe cations into the host lattice of Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 materials.
Optical properties. The solute solution of CaFeO 3-δ into the host Bi 0.5 Na 0.5 TiO 3 materials results in a decrease in the optical band gap. Figure 3(a) presents the optical absorbance spectra of undoped Bi 0.5 Na 0.5 TiO 3 and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials at various concentrations at room temperature. The pure www.nature.com/scientificreports www.nature.com/scientificreports/ Bi 0.5 Na 0.5 TiO 3 samples exhibited a single absorbance edge, which is consistent with the recently reported optical properties of Bi 0.5 Na 0.5 TiO 3 materials 29,30,50,51 . The addition of CaFeO 3-δ to Bi 0.5 Na 0.5 TiO 3 caused the absorbance edge to shift to high wavelengths, indicating that the electronic band structures had been modified. Furthermore, the absorbance spectra of the CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 K 0.5 TiO 3 and Bi 0.5 Na 0.5 TiO 3 materials 35,36,52 . In addition, CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials exhibited smooth absorbance edges with slight tails. The appearance of tails in CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials could be related to an intrinsic defects or surface effects 51 . The optical band gap (E g ) was estimated using the Wood and Tauc method 53 . In this approach, the E g values are associated with the absorbance and photon energy, as shown by the following relation: (αhν)~(hν-E g ) 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, E g can be evaluated by extrapolating the linear portion of the curve or tail from the intercept of (αhν) 1/n versus the photon energy hν. A calculation of the electronic band structure showed that Bi 0.5 Na 0.5 TiO 3 has a direct band gap of 2.1 eV, and the optical spectra of Bi 0.5 Na 0.5 TiO 3 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 region 54 . Therefore, n = 1/2 for direct transition was used, as shown in Fig. 3(b). Pure Bi 0.5 Na 0.5 TiO 3 materials exhibited an E g of approximately 3.11 eV, whereas CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials showed lower E g value (2.34 eV for 9 mol.% CaFeO 3-δ solid solution in Bi 0.5 Na 0.5 TiO 3 ). The inset of Fig. 3(b) shows the dependence of E g on the amount of CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials. The decrease in the optical band gap in CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials possibly originated from the random distribution of Ca and Fe cations into the host lattice of the Bi 0.5 Na 0.5 TiO 3 materials. The replacement of a Ti cation with a transition metal, such as Mn and Cr, in the Bi 0.5 Na 0.5 TiO 3 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 structure 29,30 . In addition, the appearance of O vacancies located near the conduction band also affected the optical band gap of the Bi 0.5 Na 0.5 TiO 3 materials 29,30 . Note that O vacancies were generated due to the unbalanced charges between Fe 2+/3+ that substituted for Ti 4+ at the octahedral site and Ca 2+ cations that replaced Bi 3+ . In addition, the O vacancies located in the crystal structure promoted the valence transition of Ti 4+ to Ti 3+55 . The appearance of new state Na + -vacancies or Ti 3+ -defect also contributed to the decrease in the optical band gap. Recently, A-site modified Bi 0.5 Na 0.5 TiO 3 -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 ABO 3 perovskite structures 56,57 . Thus, the random substitution of Ca and Fe ions into the host Bi 0.5 Na 0.5 TiO 3 changed the electronic band structure and decreased the optical band gap.
The CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials as a solid solution suppressed the photoluminescence (PL) of host materials. Figure 4(a) shows the room-temperature PL emission spectra of the Bi 0.5 Na 0.5 TiO 3 samples. The spectra clearly showed a broad blue emission band within 476-505 nm. The PL intensity of Bi 0.5 Na 0.5 TiO 3 materials decreased with increasing amount of CaFeO 3-δ solid solution in the Bi 0.5 Na 0.5 TiO 3 materials. The strong PL peak positions of pure Bi 0.5 Na 0.5 TiO 3 materials and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials were compared via subtraction to the unit, as shown in Fig. 4(b). The peak showed a blue shift as the CaFeO 3-δ concentration was increased. The broad band emission peak of pure Bi 0.5 Na 0.5 TiO 3 materials and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials with 1, 5, 7, and 9 mol.% CaFeO 3-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 reported that a self-trapped excitation possibly originated from the PL of the Bi 0.5 Na 0.5 TiO 3 materials, whereas the distortion of the TiO 6 octahedra due to surface stress resulted in a blue shift in the emission peak 58 . Bac et al. also reported the disordered coupling to a tilt of the TiO 6 -TiO 6 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 Bi 0.5 K 0.5 TiO 3 materials 51 . Interestingly, the addition of CaFeO 3-δ reduced the PL emission intensity of the Bi 0.5 Na 0.5 TiO 3 materials ( Fig. 4[a]), possibly by trapping electrons generated from absorbance photon energy that prevented electron-hole recombination to generate photons through the defects.
Magnetic properties. The complex magnetic properties at room temperature of Bi 0.5 Na 0.5 TiO 3 materials were measured as a function of the CaFeO 3-δ solute solution. Figure 5(a-g) show the magnetic hysteresis loops (M-H) of pure Bi 0.5 Na 0.5 TiO 3 materials and CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials with various amounts of CaFeO 3-δ (0.5, 1, 3, 5, 7, and 9 mol.%) at room temperature. The pure Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 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 reports 30,59 . The slightly addition of CaFeO 3-δ amounts to the host Bi 0.5 Na 0.5 TiO 3 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.% CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 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 CaFeO 3-δ in Bi 0.5 Na 0.5 TiO 3 materials as solid solution, as shown in Fig. 5(d-g). The maximum magnetization was approximately 21.6 memu g −1 for 9 mol.% CaFeO 3-δ solid solution in Bi 0.5 Na 0.5 TiO 3 materials. These results suggest strong enhancement of the magnetization of CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 materials, which is greater than that of pure Bi 0.5 Na 0.5 TiO 3 (~1.5 memu g −1 ) or transition-metal-doped Bi 0.5 Na 0.5 TiO 3 materials (~1.5-2 memu g −1 for Cr-doped Bi 0.5 Na 0.5 TiO 3 , ~3 memu g −1 for Co-doped Bi 0.5 Na 0.5 TiO 3 , ~9 memu g −1 for Mn-doped Bi 0.5 Na 0.5 TiO 3 , and ~11 memu g −1 for Fe-doped Bi 0.5 Na 0.5 TiO 3 ) 27-30,59 . CaFeO 3 , CaFeO 2.5 , www.nature.com/scientificreports www.nature.com/scientificreports/ and CaFeO 2 compounds have antiferromagnetic ordering, with Neel temperatures of 120, 700-725, and 420 K, respectively 36,40,41 . In the formation of a solid solution, however, the CaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 samples exhibited greater room-temperature ferromagnetism than single-transition-metal-doped Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 materials were as follows: (i) interaction of a magnetic cation through O vacancies, such as the F-center mechanism 28,29 , (ii) enhanced magnetism of O vacancies 30 , and (iii) magnetism of clusters embedded in the host materials 27 . Unlike that of single-transition-doped Bi 0.5 Na 0.5 TiO 3 materials, the A-site of Bi 0.5 Na 0.5 TiO 3 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 Ti 4+ to Ti 3+ , thereby inducing ferromagnetism 55,60 . Moreover, the chemical strain due to the difference in the radii of Ca and Fe compared to that of the host lattice Bi 0.5 Na 0.5 TiO 3 materials might have tuned the ferromagnetic ordering, such as the Fe 3+ -□-Fe 3+ interaction or superinteraction of the magnetic polaron between [Fe 3+ -□-Fe 3+ ] versus [Fe 3+ -□-Fe 3+ ] etc. Of note, the tremendous interaction between polarons normally favored antiferromagnetic ordering, whereas the isolated Fe cations displayed paramagnetic ordering. 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(V Bi ), BNT(V Na ), BNT(V Ti ), and BNT(V O ) 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 compounds 61 . 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(V O ), 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 Fig. S3 in the supplemental data. As seen in Fig. 8, the O 2p x,y orbital states play a main role for the induced magnetism of all systems, as the filled p x,y orbital states in the minority-spin channel shift across the Fermi level into the unoccupied band region.

Electronic band structure. The intrinsic defects and random incorporation of Ca and
To imitate the presences of Ti 3+ and Ti 2+ valence states, we inject 1 and 2 ein 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 µ B per f.u. for 1 and 2 edoped 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.
We now explore the enhanced ferromagnetism of the Bi 0.5 Na 0   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.
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 µ B per unit cell, which corresponds to 0.64 (0.16) µ B for the 6 (24) f.u. cell structure. In Table 2      www.nature.com/scientificreports www.nature.com/scientificreports/ Based on the PDOS analyses, the schematic diagrams of the octahedral environment of Fe 2+ 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 Fe 2+ ion split by high-spin state according to crystal field theory were filled by the five majority-spin electrons in the low-lying t 2g orbital levels and by the electrons in the minority-spin t 2g state. Therefore, according to Hund's rule, the calculated magnetic moment of 4 µ B 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 t 2g and e g 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 Fe 2+ and Fe 3+ might be possible in a practical situation if an O vacancy exists near the doping sites.

Discussion
Lead-free ferroelectric Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 materials highlighted the potential to extend the function materials to smart electronic devices application. On the other hand, the magnetic performance of Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 materials are required. In the present study, new solid solution of CaFeO 3-δ -Bi 0.5 Na 0.5 TiO 3 materials with greatly enhanced magnetic properties compared Bi 0.5 Na 0.5 TiO 3 materials were fabricated. On the other hand, the substitution of Ca and Fe cations at the A-site and B-site, respectively, in perovskite Bi 0.5 Na 0.5 TiO 3 materials, resulted in complex magnetic properties of the host materials. The origin of ferromagnetism in CaFeO 3-δ -Bi 0.5 Na 0.5 TiO 3 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 Fe 3+ -□-Fe 3+ . The risk of Fe cations substitution in the host Bi 0.5 Na 0.5 TiO 3 materials resulted in super-exchange between [Fe 3+ -□-Fe 3+ ] versus [Fe 3+ -□-Fe 3+ ] which normally favoured antiferromagnetic ordering. In addition, the isolated Fe cations distributed randomly into the host Bi 0.5 Na 0.5 TiO 3 crystal exhibited paramagnetic behaviour. Thus, the complex magnetic properties of Bi 0.5 Na 0.5 TiO 3 materials possibly tuned by varying the concentration of CaFeO 3-δ as a solid solution. However, unlike single Fe dopants, the presence of Ca cations into the host lattice exhibited complex results where both Ca 2+ substitution for Bi 3+ and Ca 2+ 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 Bi 0.5 Na 0.5 TiO 3 materials. It was also predicted that the presences of www.nature.com/scientificreports www.nature.com/scientificreports/ Ti 3+ and Ti 2+ 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 Bi 0.5 Na 0.5 TiO 3 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 Bi 0.5 Na 0.5 TiO 3 -based materials, but may also be extended to lead-free ferroelectric BaTiO 3 -based, (Ba,Ca)(Ti,Zr)O 3 -based, or (K,Na)NbO 3 -based materials etc. states, respectively. In (b), the black, orange, red, and blue lines represent the s, p y , p z , and p x orbital states, respectively. The Fermi level is set to zero energy. (c) Schematic representations of the octahedral environment of the Fe 2+ 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 t 2g and high-lying e g states, respectively.  Table 2. Magnetization per formula unit cell (μ B /f.u.) of Bi 0.5 Na 0.5 TiO 3 with Bi and Na site Ca, and Ti site Fe substitutions for the 6 and 24 f.u. cells adopted in the DFT calculations.