A neutron diffraction investigation of high valent doped barium ferrite with wideband tunable microwave absorption

The barium ferrite BaTixFe12−xO19 (x = 0.2, 0.4, 0.6, 0.8) (BFTO-x) ceramics doped by Ti4+ were synthesized by a modified sol—gel method. The crystal structure and magnetic structure of the samples were determined by neutron diffraction, and confirm that the BFTO-x ceramics were high quality single phase with sheet microstructure. With x increasing from 0.2 to 0.8, the saturation magnetization (Ms) decreases gradually but the change trend of coercivity (Hc) is complex under the synergy of the changed grain size and the magnetic crystal anisotropy field. Relying on the high valence of Ti4+, double resonance peaks are obtained in the curves of the imaginary part of magnetic conductivity (μ″) and the resonance peaks could move toward the low frequency with the increase of x, which facilitate the samples perform an excellent wideband modulation microwave absorption property. In the x = 0.2 sample, the maximum reflection loss (RL) can reach −44.9 dB at the thickness of only 1.8 mm, and the bandwidth could reach 5.28 GHz at 2 mm when RL is less than −10 dB. All the BFTO-x ceramics show excellent frequency modulation ability varying from 18 (x = 0.8) to 4 GHz (x = 0.4), which covers 81% of the investigated frequency in microwave absorption field. This work not only implements the tunable of electromagnetic parameters but also broadens the application of high-performance microwave absorption devices.


Introduction 
The rapid development of electronic information † Jun Li and Yang Hong contributed equally to this work.
In this work, we synthesized BaFe 12−x Ti x O 19 (BFTO-x, x = 0.2, 0.4, 0.6, 0.8) using only tetravalent Ti 4+ ions as high valent dopant ions by a modified sol-gel method. We systematically analyzed the structure, morphology, magnetic properties, and electromagnetic parameters of the sample. By comparing the magnetic structure of the neutron diffraction with the experimental magnetic results, the internal magnetic mechanism of the sample was deeply studied. The modified M-type barium ferrite exhibits better tunability for electromagnetic properties, which has a positive role on the exploration of the novel microwave absorbing materials.

1 Material synthesis
The Ti 4+ doped M-type barium ferrite ceramics (BaFe 12−x Ti x O 19 , x = 0.2, 0.4, 0.6, 0.8) were prepared utilizing the modified sol-gel method that is more effective than conventional solid state method. Barium nitrate (Ba(NO 3 ) 2 ), iron nitrate (Fe(No 3 ) 3 ·9H 2 O), and titanium nitrate (Ti(NO 3 ) 4 ) were weighted in a stoichiometric ratio and dissolved in citric acid solution adequately. The pH value of the solution was adjusted to 8 by adding ammonia water, and then the solution was stirred for 2 h and aged for 12 h at room temperature. The mixed solution was placed in 80 ℃ water bath for 3 h to form a sol, which was then transferred to a dry box at 120 for 1 ℃ -2 days until a dry gel was formed. The aerogel was incubated at 210 for 3 h to remove organic components from the ℃ gel. Calcination was carried out at 1200 to ℃ get the BFTO-x powder. The powder mixed with polyvinyl alcohol (PVA) was pressed into wafers of 13 mm in diameter and sintered at 600 for 4 h to eliminate the ℃ binder, and then the wafers were sintered at 1200 ℃ for 4 h in air atmosphere to obtain the BFTO-x ceramics.

2 Characterizations
The neutron powder diffraction (NPD) experiments were carried out at room temperature using the high resolution neutron powder diffractometer (HRND) (λ = 1.884 Å) at China Mianyang Research Reactor (CMRR), and the corresponding Rietveld refinement was achieved by FullProf and the simulated annealing and representational analysis (SARAh). Morphologies were examined using the field emission scanning electron microscopy (SEM; ZEISS Merlin Compact). www.springer.com/journal/40145 Magnetic properties were investigated using a vibrating sample magnetometer (VSM, Lake Shore 7404). The electromagnetic properties were studied using the air-line method, which were mixed with PVA at a mass ratio of 6:1. The complex permittivity and permeability were measured through the coaxial method from 2 to 18 GHz on a vector network analyzer (Keysight Technologies N5234A), and the sample and paraffin were mixed at a mass ratio of 7:3 and then compressed into a test ring with an outer diameter of 7 mm and an inner diameter of 3 mm.

1 Effects of titanium substitution on crystal structure and microstructure
The neutron diffraction patterns of BFTO-x (x = 0.2, 0.4, 0.6, 0.8) ceramics are shown in Fig. 1(a), which contains the complete neutron diffraction pattern before and after refinement using Rietveld method.
Since the neutron diffraction patterns include both structural and magnetic information, the process of BFTO-x refinement using FullProf can be divided into two parts: structural and magnetic phases [30]. The detailed results of refinement contained structural and magnetic parameters also appear in Fig. 1(a), and the corresponding refinement factors of each components are also shown in Fig. 1(a). Compared with the neutron diffraction Bragg positions of pure barium ferrite, no other impurity peaks were found, indicating that the four components were single phase with space group P63/mmc. Moreover, the corresponding magnetic space group of BFTO-x is R-3m:H, which was determined by utilizing the SARAh Analysis to calculate the possible magnetic space groups [31].  Therefore, certain amounts of barium ions are contained in the close-packed structure of oxygen ions. Meanwhile, Fe 3+ ions exist in the interstices of oxygen ions, forming a stable hexahedral structure. Fe 3+ ions are distributed over five different positions in BaFe 12 O 19 , named 12k, 2a, 2b, 4f 1 , and 4f 2 [32]. Magnetic moment orientations of Fe 3+ in three positions (12k, 2a, 2b) spin up while those of 4f 1 and 4f 2 positions spin down. In order to obtain the information of exact occupation of Ti, the method of neutron diffraction intensity fitting was utilized to explore the occupation probability of Ti as listed in Table 1. The result of fitting shows that Ti tends to occupy the position 2a, 2b, and 12k, in where Fe is spin-up.
The surface morphologies of BFTO-x ceramics are shown in Fig. 2. It can be observed that all components Table 1 Occupation probability of BFTO-x ceramics perform typical hexagonal plates, and the grain boundary is distinct. The particle size of BFTO-x ceramics varies with the increase of x, where the grain size of BFTO-0.4 about 1 µm is larger than those of the other three components. Compared with the solid state sintering method, the grain size of BFTO ceramics prepared by the sol-gel process is smaller, which has an important effect on coercive force [33].

2 Effects of titanium substitution on magnetic properties
The magnetic properties of BFTO-x (x = 0.2, 0.4, 0.6, 0.8) ceramics are derived from magnetic hysteresis loops at room temperature in Fig. 3   between Fe 3+ -O 2 -Fe 3+ [36]. It is known that H c is mainly affected by anisotropic field (H a ) and grain size [37,38]. That is, the larger the grain size of ceramics, the smaller the H c . On the other hand, H c is proportional to H a . According to the formula H a = 2K 1 /M s , H a is proportional to the magnetic crystal anisotropy constant (K 1 ), and inversely proportional to M s [39,40]. According to the contribution of different lattice positions to K 1 , the 2b position has the greatest effect on K 1 . Therefore, the more components are doped, the greater the effect on H c . For the components x = 0.2, 0.6, and 0.8, H c has a is declining trend with the increase of the doping. Because the changes of the grain size and M s are weak, the declining trend of the H c is contributed to the influence of K 1 . The reason for the sharp decline of H c of BFTO-0.4 ceramic sample is relatively complex and can be attributed to two aspects [41,42]. Firstly, the SEM image of BFTO-x ceramics shows that the grain size of BFTO-0.4 ceramic sample is larger than that of other components, so the H c of BFTO-0.4 ceramic will be smaller. Secondly, the increase of Ti 4+ doping and the occupied position would have a greater influence on K 1 , which also causes the obvious change of H c . However, compared to BFTO-0.2 ceramic sample, the M s change of BFTO-0.4 ceramic sample is smaller than that of BFTO-0.2. Therefore, the effect of M s on H c can be neglected, and the change of H c mainly depends on the grain size and K 1 .
Moreover, refined magnetic structure shows that non-collinear magnetic structure exists in BFTO-x ceramics [30,43]. The magnetic moment of primitive cell varies with the doping content of Ti, which is the same with experimental data, and the corresponding results are listed in Table 2. The experimental magnetic where M(BFTO-x) is the molar mass of BFTO-x and N A is the Avogadro constant. From the result of magnetic refinement, the theoretical M pc fluctuates with the increase of Ti doping, which is consistent with the trend of experimental result.

3 Effects of titanium substitution on electromagnetic and microwave absorption properties
The complex permittivity (ε = ε′ − jε″) and complex permeability (μ = μ′ − jμ″) of BFTO-x ceramics are shown in Fig. 4, which are measured by the air-line method within 2-18 GHz. As observed, the real part of permittivity ε′ of x = 0.4 component can reach 25, while the ε′ of the other components is smaller to some extent. For the imaginary part of permittivity ε″, there are remarkable dielectric relaxation phenomena in all samples, which can contribute to increasing RL of the absorbing sample. In Fig. 4(d), the apparent resonance phenomenon can be observed. It is necessary to note that the natural resonance frequency of the component x = 0.2 is larger than 18 GHz, while the natural resonance frequency of the other three components at a frequency range of 6-14 GHz illustrated in the inset of Fig. 4(d) is within the measured frequency range.
According to the formula f r = 1.4gH a , the natural resonant frequency (f r ) is correlated with the magnetic H a of the ceramic sample and the Hollande factor (g) [44]. Due to the low H a of BFTO-0.4 ceramic, the natural resonant frequency of the x = 0.4 sample is the lowest and appears near 8 GHz, while double resonance peaks were obtained in x = 0.6 and x = 0.8 components. The high-valence ionic Ti 4+ doping, which destroys the valence equilibrium of barium ferrite, will produce a new g factor, and the appearance of double resonance peaks shows that there are two g factors in these samples. With the increase of Ti 4+ doping, the H a decreases, and the natural resonance frequency moves to the lower frequency range. Therefore, the appearance of double resonance peak is advantageous to obtain the larger bandwidth. More evidence can be found in Fig. S2 in the ESM, which shows the dielectric and magnetic loss of PVA mixed BFTO-x ceramics. The large dielectric and magnetic loss was obtained in the x = 0.2 sample, which indicates a large RL. The loss curves of x = 0.6 and 0.8 have evident fluctuation, and could get large bandwidth.
The RL of PVA mixed BFTO-x ceramics can be calculated from the measured electromagnetic parameters [45], as shown in Fig. 5. Relying on the dielectric and magnetic loss, the four components of PVA mixed BFTO-x ceramics have obtained a large RL. The maximum RL of −44.9 dB means that the absorption of electromagnetic waves can reach 99.99% which was obtained in the x = 0.2 sample, and the thickness is relatively thin, only 1.8 mm. The absorption of electromagnetic waves can also reach 90% in the other three components. The apparent double absorption peaks appear in Figs. 5(c) and 5(d), which maybe origin from the presence of more than one of the Hollande factors in the wave-absorbing material that can benefit for widening the bandwidth of the material. RL and bandwidth are two important indexes to evaluate the performance of absorbing materials, and high-loss and large-bandwidth materials can be used in a wider range of applications [46]. Figure 6 shows the 3D RL contour plots of BFTO-x ceramics, and all samples perform wide bandwidth in the specific frequency and thickness. Although the absorption of electromagnetic waves by this material is not the best, we can find that with the doping of Ti 4+ ions, the absorbing properties of M-type barium ferrite have changed significantly. This change is mainly due to the transition of trivalent Fe ions to divalent Fe ions, which affects the permeability of the material and the impedance matching, and broadens the absorbing effect at high frequencies [47][48][49]. Figure 7(a) shows the relationship between bandwidth and RL of BFTO-x samples, and the maximum RL and bandwidth are listed in Table 3. For x = 0.2, the greatest loss can be obtained at the thickness of 1.8 mm, and the bandwidth can reach to 5.28 GHz at 2 mm when RL is less than −10 dB, while the bandwidth of the other three components is about 3 GHz.    In the ion-doped barium ferrite ceramic, the strong absorbing ability originates from the high attenuation constant [50]. The attenuation constant is expressed by Eq. (2): (2) where f is the microwave frequency and c is the velocity of light. According to Eq. (2), the attenuation constants of the four components of BFTO-x ceramics can be calculated, as shown in Fig. 7(b). Within the measuring frequency range of 2-18 GHz, four components have a large attenuation constant, wherein the attenuation constant of x = 0.4 component is the largest, 350. The variation trend of attenuation constants is similar to that of the imaginary part of magnetic permeability, and there is a double resonance peak in x = 0.6 and 0.8 components. Therefore, the dielectric constant and permeability are the two parameters that determine the microwave absorbing performance, and magnetic and dielectric loss is critical to improve the attenuation of materials to electromagnetic waves.
Besides, frequency modulation is also a standard for measuring the overall performance of absorbing materials. As can be seen from Figs. 4-7, the excellent frequency modulation can be obtained in the four components of BFTO-x ceramics. RL peaks of the x = 0.2 component are reduced from ~17 to 6 GHz with varying thicknesses, and the frequency modulation range covers 69% of the measuring frequency range, enabling the control of a wide range of absorption frequencies. The frequency regulation ranges of x = 0.4, 0.6, and 0.8 components are 4-12, 5-18, and 6-18 GHz, respectively. Compared with Refs. [5,17,22], both the effective absorption bandwidth and the maximum loss of BFTO ceramics have been enhanced to a certain extent in this work. The maximum RL peaks of the four components also moved with the Ti 4+ doping content, varying from 18 GHz (x = 0.8) to 4 GHz (x = 0.4), which covers 81% of the investigated frequency.
In conclusion, all of the four components of BFTO-x ceramics show excellent frequency modulation ability.

Conclusions
The hexagonal sheet like BaTi x Fe 12−x O 19 (x = 0.2, 0.4, 0.6, 0.8) ceramics were synthesized by a modified sol-gel method. Through the refined analysis of neutron diffraction, Ti 4+ tends to occupy the position 2a, 2b, and 12k of the structure. M s decreases gradually with the increase of Ti 4+ doping, but the change of the coercive force is complex under the synergy of the changed grain size and the magnetic crystal anisotropy field. The excellent microwave absorption performance −44.9 dB with board bandwidth in the x = 0.2 component can be attributed to the double resonance peak induced by high valent doping of Ti 4+ . Meanwhile, the RL peak position of the x = 0.6 component can be www.springer.com/journal/40145 adjusted from 18 to 5 GHz and the remaining components cover up to 50% of the frequency adjusted range, which have a significant potential application value in microwave absorption field.