Effect of octahedron tilt on the structure and magnetic properties of bismuth ferrite

Multiferroic BiFeO3-based ceramics were synthesized using the rapid liquid-phase sintering method. The rare-earth ion (Sm3+, Gd3+, Y3+) doping causes structural distortion without changing the intrinsic rhombohedral perovskite structure. Raman analysis shows that the effect of doping on E modes is greater than A1 modes, and the microstructure of FeO6 octahedron can be regulated by ion doping. A-site trivalent ion doped ceramics exhibit improved magnetism compared with pure BiFeO3 ceramic, which originated from the suppressed spiral spin structure of Fe ions. The tilt of FeO6 octahedron as a typical structure instability causes the anomalous change of the imaginary part of permittivity at high frequency, and doped ceramics exhibit natural resonance around 16–17 GHz.


Introduction 
Multiferroic materials are one of the most studied materials in recent years due to their unique properties, which exhibit more than two ferroic orders (such as ferroelectricity (T C ), ferromagnetism (T N ), ferroelastic, etc.). More than two orders can be coupled under certain conditions, exhibiting remarkable physical properties and excellent application potential [1][2][3][4]. Multiferroic materials are not only helpful for the applications but also provide a platform for exploring interesting effects like magnetoelectric effect, piezoelectric effect, etc. [5,6].
Among various known multiferroic materials, bismuth ferrite (BiFeO 3 , abbreviated as BFO) is a widely investigated multiferroic material, in which T C ≈ 1100 K and T N ≈ 640 K coexist at room temperature [7,8]. The crystallographic structure of BFO is rhombohedral distorted perovskite structure with the space group R3c. The unit cell has a lattice parameter of a = 3.965 Å and a rhombohedral angle of ~89.3-89.48, and the oxygen octahedron is distorted with the minimum and the maximum O-O distances of 2.710 and 3.015 Å, respectively, and rotated by about 13.8 around the [111] axis [9]. BFO is classified as a G-type antiferromagnet below T N at the magnetic point of view; the combined action of exchange and spin-orbit interactions produce spin canting away from perfect antiferromagnetic ordering. The canted spin structure exhibits a space-modulated spiral structure (SMSS) with a period length of 62 nm, thereby resulting in a helimagnetic structure and a vanishing magnetization in the bulk [10,11].
The SMSS ordering in BFO is stable, and it persists when the temperature varies from 4 K to the Neel temperature [12]. The modification of the spin structure is the key issue for the realization of BiFeO 3based materials, and many attempts to add ferromagnetic properties to the BFO compounds by A-or B-site substitutions were made. Neutron diffraction studies on Bi 1-x La x FeO 3 show that the SMSS modulation period in BFO grows with La, and researchers have found that the leakage current of BFO can be reduced by substituting appropriate element [13]. To improve the electrical and magnetic properties of the BFO, several research groups have attempted to modify with trivalent ions of Nd 3+ , Dy 3+ , or Pr 3+ at the A-site of BFO [14][15][16][17]. Jena et al. [18] found that the spincoated Y-doped BFO film exhibits low field saturation magnetization by suppressing the spiral spin modulated periodicity due to FeO 6 octahedral distortion.
In present study, we studied structure, magnetic properties, and microwave electromagnetic parameters of BiFeO 3 -based ceramics. A-site trivalent ion doping tilted the FeO 6 octahedron in the lattice and changed the space-modulated spiral structure, leading to the improved ferromagnetism of ceramics. Doped samples exhibited enhanced permittivity accompanied natural resonance around 16-17 GHz, and the detailed mechanism has been explained with dielectric loss and defects changed.

Experimental
Polycrystalline BFO and Bi 0.95 M 0.05 FeO 3 (M = Sm, Gd, and Y, abbreviated as BSFO, BGFO, and BYFO, respectively) samples were prepared by the rapid liquid-phase sintering method. Stoichiometric ratios of Bi 2 O 3 , Fe 2 O 3 , Sm 2 O 3 , Gd 2 O 3 , and Y 2 O 3 were mixed with agate balls for 24 h using alcohol as the solvent. Each component has an increase of 2.5% Bi 2 O 3 on the base of the stoichiometric ratio, considering the volatilization characteristic of Bi 2 O 3 . The powders were pressed into pellets of 8 mm in diameter under 500 MPa rapidly sintered in air at 800 ℃ for 20 min, and then took a rapid air quenching process.
The phase composition and crystalline structure of the samples were analyzed using X-ray diffraction (XRD, Panalytical X'PERT PRO MPD, with Cu Kα radiation). Morphologies were examined using field emission scanning electron microscopy (SEM, ZEISS Merlin Compact). Raman measurement was performed using a laser confocal Raman spectrometer (inVia-Reflex, Renishaw). The magnetic properties were investigated by a vibrating sample magnetometer (VSM). The electromagnetic parameters were measured from 2 to 18 GHz with a vector network analyzer (Keysight Technologies N5234A).

Results and discussion
In order to evaluate the phase formation and crystallinity of the samples, an XRD study was performed, and the effect of the substitution of doped ions for Bi 3+ ion on the structure of BiFeO 3 was investigated by Rietveld refinement, which was performed by using the GSAS program. Figure 1(a) shows the XRD patterns and the refinement curves of the as-prepared samples, and Fig.  1(b) provides the partial enlarged diffraction peaks around 32. Yobs and Ycal represent the intensity of the experimental diffraction peak and the fitted diffraction peak, and Ydif is the difference between Yobs and Ycal. All the exhibited peaks of four samples can be well indexed by BiFeO 3 (ICDD-PDF No. 71-2494) with a rhombohedral perovskite structure. The corresponding lattice parameters and fitting factors are listed in Table 1, ion introduction plays a significant effect on the crystal structure. Since the radius of the doped ions is smaller than that of the bismuth ion (eight-coordination ionic radius: r(Bi 3+ ) = 0.117 nm, r(Sm 3+ ) = 0.1079 nm, r(Gd 3+ ) = 0.1053 nm, r(Y 3+ ) = 0.1019 nm), the unit cell volume shrinks after doping. Figure 1(b) also exhibits the change of the crystal structure according to the law of Bragg diffraction, the diffraction peaks shift to the high angle as the radius of doped ions decreases. In addition, affected by the change of ion radius in the sublattice, the state of the local electronic cloud changed, so the bond length (Fe-O) and the bond angle (Fe-O-Fe) have changed in the FeO 6 octahedron, and the FeO 6 octahedron distorted. The smaller average  ionic radius of A-site results in a larger distortion of the lattice.
The angle of rotation of oxygen octahedron is a typical structural parameter of BFO, which changes monotonously with the tolerance factor. Therefore, the distortion of oxygen octahedron can be qualitatively analyzed through the change of tolerance factor. For cubic perovskite with standard matching ions, this rotation angle is zero. However, in BFO rhombohedral perovskite system, the rotation angle is nonzero for the influence of overlap between the electronic clouds of ions.
In the doped system of perovskite structure compounds, the tolerance factor, defined as τ = (r A + r O )/( 2 (r B + r O )), is usually used to depict the stable extent of the structure. r A , r B , and r O stand for the ionic radius of A-site, B-site, and O-site in the ABO 3 , respectively [19,20]. The τ is 0.8887 for the pure BFO, and it is 0.8871, 0.8866, and 0.8860 for BSFO, BGFO, and BYFO, respectively. It can be seen that the structure of the four components is relatively stable. The smaller the tolerance factor, the more severe the bending between the oxygen octahedrons. The smaller A-site ions can not fill the space fully leading to the distorted octahedron, shrinking the unit cell space. The octahedral tilt is ~11-14 along the [111] triple-axis and the related Fe-O-Fe band angle is 154-156 [20].
SEM technology was used in pure and doped BFO samples, as shown in Fig. 2. All the samples exhibit distinct morphologies and boundaries, and a certain amount of pores exist in the ceramics. In order to avoid heterogeneous phases during sintering, rapid liquidphase sintering and air quenching were adopted, which have caused a change in the porosity of the ceramics. The grain size of pure BFO was found to be 1-3 μm; with the introduction of doped ions, the average grain sizes of doped ceramics are smaller than that of BFO, which are around 0.5-1 μm. The difference in the ionic radius of the A-site will cause the shrinkage of unit cells which will hinder the nucleation of crystallites, and the grain sizes are smaller in the submicron scale. The crystal structure of BFO is a distorted rhombohedral perovskite at room temperature, which belongs to space group R3c. According to the group theory, the multiferroic BFO exhibits 13 optical phonon modes, expressed by the equation as where the A 1 mode polarized along and the doubly degenerate E modes polarized in the x-y plane are both Raman and IR active. The peaks, which represent the Raman modes, were obtained by the Raman spectra and decomposed into individual components, as shown in Fig. 3. In our polycrystalline ceramics, all the 13 Raman active modes were observed, which matched well with the above structure. Bi atoms participate in low-frequency modes below A 1 (TO1), whereas O atoms dominate in modes above E(TO4). Fe atoms are involved mainly in modes between E(TO2) and E(TO4), but also contribute to the development of some higher-wavenumber modes. We observed all Raman modes of the rhombohedral structure of BiFeO 3 predicted by theory from the spectrum, and labeled them in Fig. 3. Table 2 exhibits the comparison of the Raman mode positions after being deconvoluted of different component samples. By comparing Raman shifts of different modes, it is found that the doping has a certain effect on the E modes, but has little effect on the A 1 modes. Figure 4 exhibits the M-H hysteresis loops for pure and doped BFO ceramics under the maximum applied field of 15 kOe at room temperature. BFO possesses a space-modulated spiral structure superimposed on the G-type antiferromagnetic ordering with a period of 62 nm [21]. The behavior of the magnetization goes up with the increasing of the magnetic field in a linear relation, indicating that the BFO has an antiferromagnetic nature due to the spin cycloid and the sloping angle of Fe-O-Fe [22]. Table 3 shows the remanent magnetization (M r ) and coercivity (H c ) of pure and doped BFO ceramics. The M r of the Sm, Gd, and Y doped samples has an obvious upgrade comparing with the undoped BFO. Trivalent ion doping can change the lattice structure and restrain the intrinsic space-modulated spiral structure of BFO; as a result, the magnetic performance is improved. In the FeO 6 octahedron, doping will lead to the variation of the bond distance (Fe-O) and bond angle (Fe-O-Fe), which indicates that the octahedron has been distorted, and the potential magnetization can be released [23]. The results indicate that the rare earth ion doping can effectively improve the magnetic properties of BFO at room    temperature. BiFeO 3 is a typical weak magnetic material with the unique periodic spiral spin structure. The main reason for the unsaturated hysteresis loop is that the periodic spiral spin structure suppresses the spin magnetic moment of each Fe ion, especially in ceramic-based materials with larger grains. The periodic spiral spin structure will superimpose a net magnetic moment, which cannot opportunely respond with the change of the external magnetic field since the spin magnetic moment of each Fe ion is restricted. In order to explore the microwave electromagnetic properties of samples, the air-line method was employed to measure the complex permittivity and complex permeability within the 2-18 GHz, as shown in Figs. 5(a) and 5(b). According to Fig. 5, the real part of permittivity is improved for doped components, and accompanied by a certain resonance at 16-17 GHz.
Among the samples, BGFO shows better dielectric loss. Due to the use of a rapid liquid-phase sintering method, the complex permittivity for each component is at a low level. The leakage current caused by oxygen vacancy is widely considered to be a major influential factor in the dielectric loss for BFO in the microwave band [24,25], and we suppose that other defects generated during the preparation process will also have a negligible effect on the dielectric properties of ceramics. The real part of complex permeability μ′ is around 1, and the imaginary part (μ″) is close to zero. The feature of the complex permeability for ceramics exhibits the inherent weak ferromagnetism of samples, which is consistent with previous magnetic analysis.

Conclusions
A series of doped BFO ceramics were successfully synthesized by the rapid liquid-phase sintering method. The participation of rare-earth ions modulated the spatial structure of BFO to a certain extent, and tilted the FeO 6 octahedron. The space-modulated spiral structure of BFO was further suppressed due to the minor change in a periodic structure, which is originated from the tilting of oxygen octahedron by the doping of trivalent ions, improved ferromagnetism of doped ceramics. Moreover, doped ceramics exhibit enhanced permittivity accompanied natural resonance around 16-17 GHz, and the obtained results provide a feasible route to further regulate the microwave electromagnetic performance of bismuth ferrite-based ceramics.

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