Polarization origin and iron positions in indium doped barium hexaferrites

Ceramics International 44 (2018) 290–300

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Polarization origin and iron positions in indium doped barium hexaferrites a,b,c,⁎

b,c

d,e,f

T

a,c

S.V. Trukhanov , A.V. Trukhanov , V.A. Turchenko , An.V. Trukhanov , E.L. Trukhanovaa,c, D.I. Tishkevichc, V.M. Ivanovc, T.I. Zubarg, M. Salema, V.G. Kostishyna, L.V. Paninaa, D.A. Vinnikb, S.A. Gudkovab,h a

National University of Science and Technology MISiS, Leninsky Prospekt, 4, 119049 Moscow, Russia Laboratory of Single Crystal Growth, South Ural State University, Lenin Prospect, 76, 454080 Chelyabinsk, Russia c SSPA “Scientific and Practical Materials Research Centre of NAS of Belarus”, P. Brovki str., 19, 220072 Minsk, Belorussia d Joint Institute for Nuclear Research, Joliot-Curie str., 6, 141980 Dubna, Russia e Donetsk Institute of Physics and Technology named after A.A. Galkin of the NAS of Ukraine, 72R. Luxemburg str., 83114 Donetsk, Ukraine f Donetsk Institute of Physics and Technology named after O.O. Galkin of the NAS of Ukraine, Prospect Nauky, 46, Kyiv 03680, Ukraine g A.V. Luikov Heat and Mass Transfer Institute of the NAS of Belarus, P. Brovki str., 15, 220072 Minsk, Belorussia h Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, 141700 Dolgoprudny, Russia b

A R T I C L E I N F O

A B S T R A C T

Keywords: Substituted hexaferrites Neutron powder diffraction Crystal and magnetic structure Spontaneous polarization Magnetic moment

M-type hexaferrite BaFe12−xInxO19 (x = 0.1, 1.2) samples were investigated by high resolution neutron powder diffraction and vibration sample magnetometry in a wide temperature range of 4–730 K. Structural and magnetic parameters were determined including the unit cell parameters, ionic coordinates, thermal isotropic factors, occupation positions, bond lengths and bond angles, microstrain values and magnetic moments. In3+ cations may be located only in the Fe1 - 2a and Fe2 - 2b crystallographic positions with equal probability for the x = 0.1 sample. At x = 1.2 about half of In3+ cations occupy the Fe5 - 12k positions whilst the other half are equiprobably located in the Fe1 – 2a and Fe2 – 2b positions. The spontaneous polarization was observed for these compositions at 300 K. The influence of structural parameters on the temperature behavior of Fe3+(i) - O2- Fe3+(j) (i, j = 1, 2, 3, 4, 5) indirect superexchange interactions was established. With the substitution level increase the superexchange interactions between the magnetic positions inside and outside the sublattices are broken which leads to a decrease in the value of the corresponding magnetic moments.

1. Introduction Ferrites with a hexagonal crystal structure referred to as hexaferrites are traditionally used as permanent magnets and low-loss microwave materials owing to their high saturation magnetization, coercivity and good chemical stability [1–5]. Recently, hexaferrites were reported to possess a spontaneous electrical polarization at room temperature and were classified as magnetically stimulated ferroelectrics having a noncollinear magnetic structure [6]. The coexistence of spontaneous magnetic and electric ordering at room temperature and large magnetoelectric effects were also discovered in M-type hexaferrites with collinear magnetic structure [7–9]. In this case, the magnetoelectricity cannot be explained by the inverse Dzyaloshinskii-Moriya mechanism and there is still some controversy about ferroelectricity in M-type hexaferrites. Ferroelectricity in these materials may be attributed to the symmetric exchange-striction mechanism involving crystal deformations as a result of magnetic ordering. A possible mechanism was

⁎

proposed in [8] associated with lowering the crystal structure symmetry and distorting the FeO6 oxygen octahedron but further investigations are needed. In [10], the temperature dependence of polar phonon modes in BaFe12O19 single crystal was studied in the temperature range of 6–300 K revealing that the Fe(2) cations were dynamically disordered near the (2b) pentahedral positions and the potential relief for Fe(2) ion movement most likely had three minima. At room temperature, Fe(2) cations exhibit rapid diffusion and dynamically occupy (4e) positions. Below 80 K this dynamic disorder gradually becomes static lowering symmetry which becomes of a polar phase with the space group P63mc. M-type hexaferrites (Ba, Sr)Fe12O19 are reported to exhibit quantum paraelectric properties [11–13] along c-axis violating the d°-ness rule (empty d-shell), which is different from perovskite oxides. The competition between the long-range Coulomb interaction and short-range Pauli repulsion in certain oxygen space units may favor an off-center displacement of Fe3+ cation that induces a local electric dipole. In [12]

Corresponding author at: National University of Science and Technology MISiS, Leninsky Prospekt, 4, 119049 Moscow, Russia. E-mail address: [email protected] (S.V. Trukhanov).

http://dx.doi.org/10.1016/j.ceramint.2017.09.172 Received 20 June 2017; Received in revised form 20 September 2017; Accepted 21 September 2017 Available online 23 September 2017 0272-8842/ © 2017 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

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The magnetic susceptibility χ and specific magnetization M were measured in the temperature range of 4–730 K by Liquid Helium Free High Field Measurement System (VSM) [26]. A low magnetic field of 50 Oe was applied when measuring χ . The specific magnetization was investigated in the presence of a high magnetic field of 10 kOe in heating and cooling modes. The Curie temperature Tc of ferrimagnetparamagnet phase transition was defined as the inflection point in the M vs T plots [27]. The electric polarization hysteresis was measured at room temperature using a modified Sawyer-Tower circuit method [28]. The samples were covered by a silver paste to form capacitors. The samples were short-circuited before the polarization measurement. The driving electric field was produced by sawtooth bipolar voltage pulses applied to the measured capacitor. The voltage waveform parameters were: rise time of 0.01–0.1 s, frequency of 2.5–25 Hz. The voltage amplitude was varied discretely from 200 V to 1000 V with a step of 200 V. The electric response was detected with the help of a high-impedance operational amplifier, the data were digitized by ADC and numerically integrated.

a paraelectric to antiferroelectric phase transition at about 3 K for the BaFe12O19 was theoretically predicted. The lattice instability associated with the distribution of the Fe3+ cations over the (2b) pentahedral crystallographic positions was clearly demonstrated. The diamagnetic substitution of the M-type hexaferrites [14–17] is of interest to engineer the ferroelectric properties at room temperature. In the case of high concentration of d5 cations in iron crystallographic positions the local electric dipoles cannot have long-range ordering down to the lowest temperatures. But the ferroelectric state at room temperature can be achieved by imposing local strains or by chemical substitutions. Thus, in diamagnetically substituted solid solutions the concentration of d5 cations in iron crystallographic positions decreases and dipole-dipole ordering becomes possible at elevated temperatures. For Al-substituted BaFe12−xAlxO19 (x ≤ 1.2) hexaferrites the electric polarization of 0.6 μC/cm2 in the electric field of 110 kV/m and strong coupling between electric and magnetic subsystems at room temperature were found [18]. Furthermore, the diamagnetic substitution can cause a canted magnetic structure, which also promotes the stabilization of the ferroelectric state [19]. In the present work, the investigations into crystal and magnetic structures over a wide temperature range of 4–730 K by powder neutron diffractometry for indium doped hexaferrite BaFe12−xInxO19 (x = 0.1–1.2) solid solutions was performed with the aim to elucidate the mechanisms of ferroelectric ordering and large magnetoelectric effect. Indium doping is isovalent diamagnetic doping. Addition of In3+ cations expands crystal lattice which is due to larger ionic radii of In3+ cation (0.940 Å) unlike smaller ionic radii of Al3+ (0.535 Å) and of Fe3+ (0.690 Å) cations. Doping by In3+ cations is a continuation of our structural researches of barium hexaferrite of partially doped by diamagnetic cations [1,17,18].

3. Results and discussion 3.1. Crystal structure NPD spectra are shown in Fig. 1. A complete interpretation of NPD pattern involves the determination of both crystal and magnetic structures. The crystal structure gives rise to a purely nuclear scattering portion of the diffraction pattern. The magnetic ordering is responsible for additional scattering which is superimposed on the nuclear scattering. This additional scattering depends on the magnetic moments

2. Experimental Polycrystalline BaFe11.9In0.1O19 and BaFe10.8In1.2O19 samples have been obtained from high purity Fe2O3 (99.999%) and In2O3 (99.999%) oxides and BaCO3 carbonate (chem. analysis purity) using a standard solid reaction method. A detailed information about the sample preparation can be found elsewhere [20–22]. The X-ray analysis of the synthesized samples was carried out using DRON-3 diffractometer with the Kα radiation of Cu at room temperature in the range of angles 10° ≤ 2Θ ≤ 100°. A graphite monochromator was used to filter out the Kβradiation. The content of oxygen was controlled by a thermogravimetric analysis. The chemical composition and Fe/In ratio after synthesis have been estimated by Auger data (Scanning Auger Multiprobe PHI660, PerkinElmer) and X-ray activated analysis (Princeton Gamma-Tech, Inc.). Time-of-flight (TOF) neutron powder diffraction technique was used for structural investigations at temperatures 4–730 K with the High Resolution Fourier Diffractometer (HRFD) at the IBR-2M pulsed reactor in the Joint Institute for Nuclear Research, Dubna, Russia [23]. The correlation technique of data acquisition allowed a very high resolution of Δd/d ~ 0.001 to be achieved, which was practically constant in a wide range of dhkl spacing. For the lattice parameters refinements the standard Al2O3 (standard SRM-676 of NIST, USA) was used. Low temperatures (< 300 K) were achieved using a cooling head (model RDK408) and a helium cryocooler (Sumitomo Heavy Industries Ltd). Heating was realized with a vanadium surface furnace and a Eurotherm temperature controller. The Rietveld refinement method [24] was used to define the crystal and magnetic structures with the help of FullProf [25] software program. The peak asymmetry correction was applied and the peak shapes were quantified by a pseudo-Voigt function. For fitting procedure, the background intensities were refined using the Chebyshev polynomial function with six coefficients. Each structural model was refined up to convergence with the best result selected on the basis of standard relevance factors and stability of the refinement. More details about FullProf software use is given in [22].

Fig. 1. Rietveld refined NPD spectrum for the BaFe10.8In1.2O19 at 300 K (a) and 730 K (b). The characteristics are depicted as: experimental points (crosses), calculated function (curve), difference curve (lower curve) normalized to the statistical error and diffraction peak positions (vertical bars) for the atomic (upper row) and magnetic (lower row) structure.

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Table 1 The crystal structure parameters, atomic coordinates and R-factors for the BaFe10.8In1.2O19 obtained from NPD data (SG = P63/mmc (No. 194)) at different temperatures. The atom positions are: Ba (2d) (2/3, 1/3, 1/4), (Fe/In)1 (2a) (0, 0, 0); (Fe/In)2 (2b) (0, 0, 1/4); (Fe/In)3 (4fIV*) (1/3, 2/3, z); (Fe/In)4 (4fVI*) (1/3, 2/3, z); (Fe/In)5 (12k) (x, 2x, z); O1 (4e) (0, 0, z); O2 (4f) (1/3, 2/3, z); O3 (6 h) (x, 2x, 1/4); O4 (12k) (x, 2x, z); O5 (12k) (x, 2x, z). fIV - tetrahedral oxygen coordination; fVI - octahedral oxygen coordination. Atomic parameters

a, (Å) c, (Å) V, (Å3) Fe3/In3 (4fIV) z Fe4/In4 (4fVI) z Fe5/In5 (12k) x z Biso O1 (4e) z O2 (4f) z O3 (6h) x O4 (12k) x z O5 (12k) x z Biso Rwp, % Rexp, % R B, % RMag, % χ2

Temperature 10 K

100 K

150 K

300 K

730 K

5.9335(6) 23.4474(2) 714.93(11)

5.9333(4) 23.4453(3) 714.83(2)

5.9331(3) 23.4452(3) 714.84(4)

5.9324(2) 23.4455(9) 714.62(5)

5.9641(2) 23.5984(9) 726.94(5)

0.0301(8)

0.0255(3)

0.0251(3)

0.0242(3)

0.0255(3)

0.1892(7)

0.1892(5)

0.1895(5)

0.1824(3)

0.1876(3)

0.1595(18) − 0.1075(3) 0.103(5)

0.1596(2) − 0.1074(3) 0.205(3)

0.1633(2) − 0.1073(3) 0.478(3)

0.1661(9) − 0.1075(1) 0.345(4)

0.1675(7) −0.1076(1) 0.912(5)

0.1387(9)

0.1384(2)

0.1433(4)

0.1455(4)

0.1477(4)

− 0.0453(9)

− 0.0465(7)

− 0.0485(9)

− 0.0514(4)

− 0.0555(4)

0.1623(4)

0.1644(2)

0.1674(4)

0.1785(19)

0.1797(18)

0.1494(2) 0.0541(5)

0.1505(3) 0.0544(5)

0.1524(2) 0.0542(5)

0.1577(14) 0.0531(2)

0.1543(12) 0.0513(2)

0.5082(2) 0.1507(4) 0.302(3) 9.16 6.56 11.3 12.2 1.93

0.5083(3) 0.1506(5) 0.352(3) 5.31 4.64 9.32 5.42 1.85

0.5085(4) 0.1505(3) 0.453(3) 3.41 5.31 7.62 6.33 2.01

0.5082(2) 0.1504(2) 0.454(3) 3.81 2.72 6.41 5.92 1.96

0.5025(2) 0.1475(2) 0.875(3) 4.91 3.85 7.02 – 1.62

octahedral Fe5 – 12k positions. The remaining In3+ cations are distributed almost evenly among the octahedral Fe1 – 2a and bipyramidal Fe2 – 2b positions. A larger multiplicity of 12k position gives a small content ratio of ~ 4% for In3+ cations in Fe5 – 12k position. No occupancy is found in Fe3 – 4fIV and Fe4 – 4fVI positions, and In3+ cations prefer the positions of Fe1 – 2a, Fe2 – 2b and Fe5 – 12k. All possible and most likely combinations of the occupation of nonequivalent crystallographic positions by In3+ cations were consistently tried. The optimum values of the R-factors were determined. After such combinatorial analysis the most likely distribution of In3+ cations for different temperatures was found. The errors of position occupancy refinements were sufficiently small (< 10−6). The preference positions are also in agreement with the changes in bond distances when considering the patterns of BaFe12O19 and BaFe11.9In0.1O19 samples. For BaFe11.9In0.1O19 samples, the In3+ cations have equal probability for the location only in Fe1 - 2a and Fe2 - 2b positions [22]. In this case, the discrepancy between the experimental data and the calculated crystal and magnetic structures is minimal. It is interesting that the In-occupation behavior at larger substitution level (x = 1.2) is similar to the Al-occupation behavior at small substitution level (x = 0.1) in a wide temperature range [31]. The unit cell parameters for BaFe10.8In1.2O19 samples are shown in Fig. 3. At 300 K they are: a = 5.9326(2) Å, c = 23.4458(9) Å, V = 714.64(5) Å3 (see Fig. 3 and Table 1). It is well known that for the parent un-substituted BaFe12O19 hexaferrite at 300 K the unit cell parameters are: a = 5.893 Å, c = 23.194 Å, V = 697.5 Å3 [32]. These values are obtained by the powder X-ray diffraction method and their accuracy may not be very high [33]. The addition of In3+ cations to the parent BaFe12O19 compound retains a single phase for both concentrations x = 0.1 and 1.2. This is evidenced by the absence of new nuclear diffraction reflections in the NPD spectra. The solid solutions on the base of barium hexaferrite form with a = 5.8955(2) Å, c =

associated with non-equivalent crystallographic positions, their orientation relative to each other and also on the magnetic form factors. To separate the magnetic and nuclear contributions to the diffraction peaks the samples were heated up above Tc. Fig. 1 demonstrates an excellent agreement between the observed and calculated profiles. In the refining process the actual magnetic structure has been defined [29]. The P63/mmc (No. 194) space group was used for analyzing the NPD data at T = 730 K. The unit cell has two formula units (Z = 2). The unit cell parameters, atomic coordinates, cation distribution and Rietveld relevance factors (R-factors) obtained during processing the NPD spectra are summarized in Table 1. The thermal vibrations of atoms were used in the isotropic approximation. The magnetic structure was used in the collinear approximation [30]. Low values of fitting parameters suggest that the refinement of neutron data is effective. The Fe3+ cation in Fe1 – 2a position is 6-fold coordinated by 6 O2anions in O4 positions (Fig. 2). The Fe3+ cation in Fe2 – 2b position is 5-fold coordinated by 2 O2- anions in O1 polar positions and by 3 O2anions in O3 equatorial positions. The Fe3+ cation in Fe3 – 4fIV position is 4-fold coordinated by 1 O2- anion in O2 polar position and by e 3 O2anions in O4 equatorial positions. The Fe3+ cation in Fe4 – 4fVI position is 6-fold coordinated by 3 O2- anions in O3 positions and by 3 O2- anions in O5 positions. The Fe3+ cation in Fe5 – 12k position is 6-fold coordinated by 1 O2- anion in O3 position, by 1 O2- anion in O2 position, by 2 O2- anions in O4 positions and by 2 O2- anions in O5 positions [29]. The coherent scattering lengths for the Fe3+ and In3+ cations differ significantly: fFe = 9.450 barn and fIn = 4.065 barn. This is a good condition for fitting the occupation value of different crystallographic positions. The determination of occupancy positions involves some difficulties when analyzing NPD patterns since the number of variable parameters increases. The structural refinement for BaFe10.8In1.2O19 samples shows that about half of In3+ cations (47%) occupy the 292

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Fig. 2. Schematic representation of the oxygen surrounding for each iron crystallographic position.

23.2173(7) Å, V = 698.84(3) Å3 [22] and a = 5.9326 Å, c = 23.4458 Å, V = 714.64 Å3 [21] unit cell parameters at 300 K for the x = 0.1 and 1.2, respectively. The unit cell parameters for x = 0.1 are larger than those for the parent compound and smaller than the values for x = 1.2. This is explained by a larger ionic radius of In3+ cation (0.940 Å) comparing to Fe3+ (0.690 Å) cation [34]. With the temperature increase up to 730 K the unit cell parameters also increase but the temperature dependence is not linear (Fig. 3). At 300 K the differences between the unit cell parameters for x = 0.1 and x = 1.2 is the smallest. In the case of a-parameter, its value for x = 1.2 is larger than that for x = 0.1 by 0.63% at 300 K comparing to 0.76% and 0.83%, respectively at 10 K and 730 K. The value of c- parameter for x = 1.2 at 300 K is larger than that for x = 0.1 by 0.98%. At 10 K

and 730 K, the difference is 1.29% and 1.04%, respectively. For the unit cell volume V the difference between the two compositions is 2.85%, 2.26% and 2.73%, respectively at 10, 300 and 730 K. In low (< 300 K) and high (> 300 K) temperature regions, the temperature rate of parameters changing is different for x = 0.1 and 1.2 (Fig. 3). Thus, for x = 1.2 the largest temperature gradient of aparameter dahT/dT = 7.34·10−5 Å/K is seen in the high temperature region and its value is dalT/dT = − 0.38 10−5 Å/K in the low temperature region (indexes h and l correspond to high and low temperature regions, respectively). In fact, the value of a decreases with temperature in the low temperature region (the gradient is negative). For x = 0.1 the temperature gradients for a-parameter are dahT/dT = 4.58·10−5 Å/K and dalT/dT = 2.34·10−5 Å/K, respectively for high and 293

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are calculated following the procedure described in [22]. High anisotropy of the crystal structure leads to a difference in the coefficients of linear thermal expansion for a (αa ~ 7.51·10−6 K−1 (x = 0.1) and αa ~ 7.42·10−6 K−1 (x = 1.2)) and с (αc ~ 13.11·10−6 K−1 (x = 0.1) and αc ~ 12.89·10−6 K−1 (x = 1.2)) axes. The coefficients of volume thermal expansion are αV ~ 27.82·10−6 K−1 (x = 0.1) and αV ~ 27.65·10−6 K−1 (x = 1.2). At low (< 150 K) temperatures the Invar effect, i.e. a quasi-zero thermal expansion coefficient, is observed for the both samples. In this range the decrease in temperature may lead to a small increase in some unit cell parameters. Thus, decreasing the temperature from 100 K down to 10 K leads to increase in the values of a by Δa = 0.0014 Å for x = 0.1 and by Δa = 0.0007 Å for x = 1.2. On the other hand, the values of c and V decrease by Δc = 0.029 Å and ΔV ~ 0.55 Å3 for x = 0.1 and increase by Δc = 0.0017 Å and ΔV ~ 0.19 Å3 for x = 1.2, when the temperature is decreased from 100 K. Therefore, it is demonstrated that with increasing the substitution concentration the number of the unit cell parameters which rise with the temperature decrease from 100 K down to 10 K increases. A similar dependence of the unit cell parameters at low temperatures was previously observed in metallic oxides [36]. The most likely explanation of the Invar effect is anharmonicity of low energy phonon modes. The temperature dependences of main Fe-O bond lengths and Fe-OFe bond angles in BaFe12−xInxO19 for x = 0.1 and 1.2 extracted from NPD are shown in Figs. 4 and 5. In the temperature range from 4 K up to 730 K abrupt changes of the structural parameters were not found. For x = 0.1 the majority of bond lengths decrease as temperature is decreasing. The Fe1-O4, Fe2-O3 and Fe3-O2 bond lengths increase with temperature decreasing. The largest changes in the bond lengths are detected for Fe2 cation relative to O3 anion, Fe4 cation relative to O5 anion and for Fe4 cation relative to O3 anion (Fig. 4). With the concentration level increase up to x = 1.2 almost all the bond lengths change the behavior with respect to temperature. Only the Fe5-O1 bond length continues to decrease when the temperature decreases (Fig. 4). In this case the largest changes in the bond lengths are detected for Fe5 cation relative to O2 anion, for Fe5 cation relative to O1 anion and for Fe2 cation relative to O3 anion [37]. For x = 1.2 some bond lengths become longer (Fe2-O3 and Fe4-O5) or shorter (Fe3-O4 and Fe4-O3) than the corresponding bond lengths for x = 0.1 with the temperature increase. For x = 0.1 the Fe2-O3-Fe4, Fe5-O1-Fe5 and Fe5-O4-Fe5 bond angles decrease with decreasing the temperature while the Fe3-O4-Fe5, Fe5-O2-Fe5 and Fe4-O3-Fe4 bond angles increase (Fig. 5). The largest changes in the bond angles as the temperature decreases are detected for Fe4-O3-Fe4, Fe5-O2-Fe5 (they increase) and for Fe5-O4-Fe5 (it decreases). With the indium concentration increase from x = 0.1 to x = 1.2 the Fe2-O3-Fe4, Fe5-O2-Fe5 and Fe4-O3-Fe4 bond angles change the correlation. It can be concluded that Fe3+ (In3+) cations in the octahedral 2a and 12k and pentahedral 2b positions are undergone the largest displacements with the change in temperature and (or) substitution level. With increasing x the temperature behavior of the bond characteristics becomes reversed.

Fig. 3. Temperature dependence of the lattice parameters: a in (a), c in (b) and V in (c) for BaFe11.9In0.1O19 (full symbols) and BaFe10.8In1.2O19 (open symbols).

low temperature regions (see Fig. 3a) [35]. Similar temperature behaviors are observed for c-parameter and volume V of the unit cell. The corresponding temperature rates in the high temperature range are: for x = 1.2 dchT/dT = 35.40·10−5 Å/K, dVhT/dT = 28.70·10−3 Å3/K and for x = 0.1 dchT/dT = 31.88·10−5 Å/ K, dVhT/dT = 20.56·10−3 Å3/K. In the low temperature range they are: for x = 1.2 dclT/dT = − 0.66·10−5 Å/K, dVlT/dT = − 1.38·10−3 Å3/K and for x = 0.1 dclT/dT = 23.59·10−5 Å/K dVlT/dT = 12.62·10−3 Å3/ K (see Fig. 3b,c). The observed temperature gradients evidence that in the high temperature region the unit cell parameters increase with temperature faster with increasing the concentration. In the low temperature region the increase of the concentration leads to negative changing rates of the unit cell parameters. A comparison of the effect of Al3+ and In3+ cations on the structural parameters of barium hexaferrite may be made. For BaFe11.9Al0.1O19 hexaferrite at 300 K the unit cell parameters are a = 5.8898(2) Å, c = 23.1971(6) Å, V = 696.91(3) Å3 [31]. These values are smaller than those for the parent BaFe12O19 and BaFe11.9In0.1O19 hexaferrites owing to a larger ionic radius of In3+ cation (0.940 Å) and a smaller ionic radius of Al3+ cation (0.535 Å) in comparison with the ionic radius of Fe3+ (0.690 Å) cation [34]. At a fixed temperature of 300 K the unit cell volume V for the Al-substituted samples changes with a rate of dV/dx = − 10.04 Å3 [20], while for the In-substituted samples the rate is dV/dx = 14.82 Å3 [21]. A negative changing rate of the volume indicates the decrease in the lattice parameters with Alsubstitution. With increasing the temperature the unit cell parameters increase for all the samples with Al and In-substitution but the rates of parameter change are larger in the latter case, especially for higher substitution level. A general trend of the lattice parameters decrease with decreasing temperature is due to decrease in the thermal energy of the random motion of ions. The coefficients of linear and volume thermal expansion

3.2. Polarization and magnetic properties In BaFe12O19 compound all the iron cations have 3+ valency based on the law of macrobody electroneutrality. The indium doping is isovalent, i.e. they have 3+ valency. Thus all the iron cations are Fe3+ ones in BaFe12O19 compound and BaFe12−xInxO19 solid solutions with x = 0.1 and 1.2. Fig. 6 shows the hysteresis loops of the dielectric polarization at room temperature for BaFe12−xInxO19 samples with x = 0.1 and 1.2. The maximum value of the electric field, which could be achieved at measurements without the occurrence of electric breakdown, was 97 kV/m. In this electric field, the remanence polarization was 3.7 mC/ m2 and 4 mC/m2 for samples with x = 0.1 and 1.2, respectively. 294

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Fig. 4. Temperature dependence of the main Fe-O bond lengths for BaFe11.9In0.1O19 (left column) and BaFe10.8In1.2O19 (right column): (a) – Fe3-O2, Fe2-O1 and Fe4-O3; (b) – Fe5-O2, Fe1-O4 and Fe4-O5; (c) – Fe5-O1, Fe3-O4 and Fe2-O3. Dash line is a linear fitting.

Fig. 5. Temperature dependence of the main Fe-O-Fe bond angles for BaFe11.9In0.1O19 (left column) and BaFe10.8In1.2O19 (right column): (a) – Fe3-O4-Fe5 and Fe2-O3-Fe4; (b) – Fe5-O2Fe5 and Fe5-O1-Fe5; (c) – Fe4-O3-Fe4 and Fe5-O4-Fe5. Dash line is a linear fitting.

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Fig. 7. Temperature dependence of the specific magnetization (a) at a magnetic field of 1 T and the inverse magnetic susceptibility (b) for BaFe11.9In0.1O19 and BaFe10.8In1.2O19 in heating (full circle) and cooling (open circle) modes. Insert demonstrates the temperature derivative of the specific magnetization with Tc indicated.

Fig. 6. Field dependence of the dielectric polarization at room temperature (300 K) for BaFe12−xInxO19 hexaferrites with x = 0.1 (a) and 1.2 (b).

Therefore, the remanence polarization increased by about 10% with the increase in the substitution level from 0.1 to 1.2. The obtained values of the polarization are approximately 2 orders of magnitude lower than that reported in [8,9] and 3 orders of magnitude larger than that in [19]. The reason for such differences is related with the effect of leakage currents occurring because of a relatively low resistivity of the samples. In [9], the maximum values of driving electric field were approximately three times larger. The resistivity increase may be achieved by various technological methods, for example, by introducing isolation interfaces between the ferrite grains [9]. In most of hexaferrites, the electrical resistivity is not high enough to support a strong electric field. In some cases the resistivity increases at low temperatures or for particular substitution. The resistivity can also depend on a frequency and an amplitude of the applied voltage, which gives an additional contribution to the measured polarization. To obtain a correct picture of true polarization processes, the conducting processes must be separated from the polarization associated with the displacement of ions. At 300 K, the resistivity of the samples under study was of the order of 109 Ω*cm and was independent of temperature and applied voltage (in the range of parameters used). With increasing a frequency, a complex-valued resistance (or impedance) increases which should lead to a decrease in the polarization. In our case, with increase in the frequency from 2.5Hz to 25 Hz, the decrease in the maximum polarization by 10% was observed. This behavior of the polarization indicates that the main contribution to its formation is given by the processes associated with the displacement of ions. With the substitution level increase the remanence polarization and the maximal polarization slightly increase by 10%. This can be

explained by increase in the concentration of empty d-shells and the formation of strong asymmetric covalent bonds in the Fe5 - 12k crystallographic position. In addition, since In3+ cation a larger ionic radius comparing to Fe3+ cation, the substitution concentration increase causes the local distortions and microstrains in the crystal lattice. For better understanding the mechanisms involved in enhancing the polarization, the permittivity and loss tangent should be investigated. But as it follows from [38] for aluminum cation substitution, with the substitution level increase from x = 0.5 to x = 3.5 at room temperature, the dielectric constant and loss tangent decrease for a fixed frequency of the alternating current. The temperature dependences of the specific magnetization and inverse magnetic susceptibility for BaFe12−xInxO19 at x = 0.1 and 1.2 are given in Fig. 7. The value of TC is 692 K and 550 K for x = 0.1 and 1.2, respectively. For the parent compound BaFe12O19, TC is 740 K [39]. The basic magnetic parameters such as TC and the magnetization saturation MS are determined by the intensity of the Fe3+(i) - O2- - Fe3+(j) (i, j = 1, 2, 3, 4, 5) indirect superexchange interactions which depend on the periodicity of the exchange-linked chains and on the structural parameters (bond length and bond angle). These indirect superexchange interactions have a different sign, i.e. they are competing. Tc can also be expressed in terms of the number of Fe3+(i) - O2- - Fe3+(j) indirect superexchange interactions. This is in agreement with a similar explanation provided in [40]. The presence of diamagnetic In3+ cations in the solid solutions leads to a reduced number of neighbors of magnetic Fe3+ cations and the magnetic order is distorted at lower temperatures [41]. At 4 K and for applied magnetic field of 1 T the specific magnetization is 67 emu/g for BaFe11.9In0.1O19 and 58 emu/g for BaFe10.8In1.2O19. These values 296

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Fig. 8. Comparative temperature dependences of the magnetic moment per iron ion for BaFe11.9In0.1O19 (full circle) and BaFe10.8In1.2O19 (open circle) samples in different positions: (a) − 2a, (b) − 2b, (c) – 4 fIV, (d) − 4 fVI, (e) − 12k, (f) - total magnetic moment per iron ion obtained by NPD. Dash line represents a polynomial fitting.

are lower than for the un-doped compound. The reduction in the magnetization was caused by incomplete coordination of the Fe3+ cations at the particle surface leading to a noncollinear spin configuration, which causes the formation of a surface spin canting. The specific magnetization continuously decreases from 4 K up to 730 K. The shape of M(T) curves in hexaferrites obeys the temperature dependence of the magnetic moments of iron cations in the Fe5 - 12k positions. The temperature variation of the hyperfine fields of the Fe5 12k positions and the subsequent decrease in curvature of M(T) with x increase have already been demonstrated for the substituted Sr1−xLaxFe12−xCoxO19 ferrites [42]. A broad transition to the paramagnetic state resembles a second-order phase transition. The absence of the temperature hysteresis of the specific magnetization is also characteristic of the second-order phase transition. A continuous decrease in the specific magnetization may be understood in terms of distortions of the intersublattice Fe3+(i) - O2- F e3+(j) (i ≠ j) exchange interactions and the intrasublattice Fe3+(i) - O2- - Fe3+(j) (i = j) indirect superexchange interactions. The inverse magnetic susceptibility is given in Fig. 7b. For the both samples only positive values of the paramagnetic Curie temperature Θp are observed. These values are slightly lower than the corresponding values of TC. This fact indicates the dominant character of the ferromagnetic intrasublattice Fe3+(i) - O2- - Fe3+(j) (i = j) indirect superexchange interactions. The high temperature susceptibility for both samples obeys the Curie-Weiss law. The Curie constant C ~ ctgα is proportional to the slope of the tangent of inverse susceptibility and depends on the In3+ cation concentration. The value of C is slightly smaller for x = 0.1 than for x = 1.2. The effective permeability µeff ~ C1/2 in the paramagnetic region (> 740 K) behaves similar to C [43]. This fact indicates the decrease in the average magnetic moment per one Fe3+ cation with substitution as a trend. With increasing x the positive Fe3+(i) - O2- - Fe3+(j) (i = j) interactions in a particular magnetic sublattice are broken by introduction of diamagnetic In3+

cations. It is well known that for complex 3d-metall oxide compounds the intensity I of intrasublattice indirect superexchange interactions depends on both the Mv+ – O2- - Mv+ bond angles and Mv+ – O2- bond lengths through the overlapping integrals between the 3d-orbitals of Mmetal cation and the 2p-orbitals of O2- anion [44]. The intensity I ~ cos (Mv+ – O2- - Mv+) is directly proportional to cosine of the bond angle and I ~ 1/(Mv+ – O2-) is inversely proportional to the bond length. Based on this modelling approach and Figs. 4 and 5, it can be concluded that the main contribution to weakening the magnetic ordering at low temperatures results from the destruction of intersublattice Fe3+(i) - O2F e3+(j) (i ≠ j; i, j = 3, 4, 5) exchange interactions between Fe3, Fe4, Fe5 sublattices. Fe3+ and In3+ cations in the Fe4 – 4fIV and Fe5 – 12k positions may be responsible for the electric polarization origin. The maximum value of specific magnetization decreases with temperature increasing. The atomic magnetic moment for both samples is not saturated in the external magnetic field up to 2 T for all temperatures below Tc [45]. The consolidated ordered magnetic moment at 10 K in the field of 2 T is 16 µB per formula unit or 1.3 µB per nominal Fe3+ cation for BaFe11.9In0.1O19 and 13 µB per formula unit or 1.1 µB per nominal Fe3+ cation for BaFe10.8In1.2O19. Taking into account the magnetic structure of M-type hexaferrite according to Gorter's model [30] with iron up-spins on Fe1 - 2a, Fe2 - 2b and Fe5 - 12k positions and down-spins on Fe3 - 4fIV and Fe4 − 4fVI positions, the moment per formula unit of 20 µB is expected for BaFe12O19 for a perfect structure in the ground state. Assuming In3+ cations to be located at the up-spin Fe1 - 2a, Fe2 - 2b and Fe5 – 12 K positions, the consolidated ordered magnetic moment of 19.5 µB per formula unit is expected for BaFe11.9In0.1O19 and 14 µB per formula unit for BaFe10.8In1.2O19. The measured maximum magnetic moment is smaller compared to the calculated one. Some reduction of the consolidated moment might be caused by the incomplete coordination of Fe3+ cations at the particle surface leading to a noncollinear spin configuration, which causes the 297

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Fig. 9. Illustration of the polarization origin mechanism in BaFe12−xInxO19 samples as a consequence of the distortion of the oxygen octahedron in the crystallographic Fe5 - 12k position. (a) - normal oxygen octahedron with a small Fe3+ cation at the central position, (b) – noncentrosymmetric polar distortion of the Fe-O bond lengths as a result of the displacement of the Fe3+ cation towards O2- anions.

We can analyze the temperature behavior of magnetic moment in each crystallographic position taking into account the In3+ cation distribution. Any magnetic moment for x = 0.1 is always larger comparing to that for x = 1.2. In the Fe1 - 2a and Fe2 - 2b positions the magnetic moments are similar and large practically for all temperatures. In the Fe3 – 4fIV and Fe4 – 4fVI positions the magnetic moments are also similar but small. There is considerable difference between the total magnetic moment and the magnetic moment in Fe5 – 12k position for both concentrations. This is explained by the In3+ cation distribution with the substitution concentration increase. For the magnetic moment in some positions a nonmonotonic temperature behavior is observed. For x = 0.1 the curve of the magnetic moment in the Fe3 – 4 fIV and Fe4 – 4 fVI positions has the inflection point in the 100–150 K temperature range. With concentration increase to x = 1.2 the inflection point appears for the Fe1 - 2a and Fe2 - 2b crystallographic positions. The presence of the inflection point can be explained by the temperature behavior of the bond lengths and bond angles with the substitution concentration increase. Below 300 K the magnetic moments in the Fe1 2a and Fe2 − 2b positions are equal for x = 0.1 and x = 1.2. At 10 K the largest (~ 32%) difference between the magnetic moments for x = 0.1 and x = 1.2 is observed for the Fe5 – 12k position. The smallest (~ 8%) difference is observed for the Fe3 – 4fIV and Fe4 – 4 fVI positions [53]. If the magnetic moment of Fe3+ cation at 0 K is equal 5 μB then the total magnetic moment of parent BaFe12O19 will be equal to 20 μB per formula unit in case of a perfect collinear magnetic structure. Low values of 18.2 μB for x = 0.1 and 13.4 μB for x = 1.2 of the total magnetic moment obtained here are explained by the influence of diamagnetic In3+ cations and thermal fluctuations [54]. Fig. 9 presents an illustration of the mechanism of spontaneous polarization in the BaFe12−xInxO19 samples involving the distortion of the oxygen octahedron in the crystallographic Fe5 - 12k position [55]. It is well known that the crystal structure of M-type hexaferrites could be described as an alternative stacking of the RSR*S* blocks along the c axis. S and S* are spinel blocks, R and R* are hexagonal barium-containing blocks. The S(R) and S*(R*) blocks are mirror-symmetrical with respect to the a-b plane along the c axis. For the Fe5 - 12k position the noncentrosymmetric displacement of Fe3+(In3+) cation towards O1 or O2 apical anions is only possible [56]. As it can be seen from Fig. 5,

formation of surface spin canting [46]. As a result of partial substitution of Fe3+ cations by diamagnetic In3+ cations which are distributed statistically equivalent for the Fe1 2a, Fe2 - 2b and Fe5 – 12k positions, the change in the values of the magnetic moments in the corresponding positions can be expected. Fig. 8 shows the temperature dependences of the magnetic moments of Fe3+ cations in different crystallographic positions: Fe1 - 2a, Fe2 - 2b, Fe3 - 4fIV, Fe4 - 4fVI and Fe5 - 12k for x = 0.1 and 1.2. The absence of the additional magnetic peaks determines the wave vector of the ferromagnetic structure as k = [0, 0, 0]. The magnetic structure for all temperatures is fully consistent with the model proposed by Gorter [30]. All the magnetic moments of Fe3+ cations are oriented along the easy direction coinciding with the hexagonal c axis. The introduction of the canting angle in each crystallographic position or in all positions together at the refinement procedure did not lead to a decrease in the R-factors. Previously, the exchange integrals J for the parent BaFe12O19 compound were calculated using the generalized gradient approximation and considering the Hubbard parameter method [47]. Taking into account different values of exchange integrals based on different experimental crystal structure parameters the dominant antiferromagnetic nature of the Fe3+(i) - O2- - Fe3+(j) (i, j = 1, 2, 3, 4, 5) indirect superexchange interactions was revealed [48]. The exchange integrals within the block layers were estimated to be of the order of 10−3 eV for the superexchange interactions such as Fe1 - Fe3 and Fe2 Fe4 [49]. Large exchange integrals have large bond angles of 125.119° for the Fe1 - O4 - Fe3 and 138.421° for Fe2 - O3 - Fe4 [50]. The strength of the superexchange interaction follows the Goodenough–Kanamori rules increasing as the Fe3+ - O2- - Fe3+ bond angle deviates from 180° [51]. It can be assumed that for a low concentration of In3+ cations in the solid solution they should be distributed statistically throughout nonequivalent crystallographic positions in the hexaferrite lattice. However in our case, in order to reduce the discrepancy between the experimental data and performed calculations of magnetic and crystal structures it should be assumed that the substitution of Fe3+ cations by In3+ cations preferably occurs into the Fe1 - 2a and Fe2 - 2b crystallographic positions for x = 0.1, and into the Fe1 - 2a, Fe2 - 2b and Fe5 12k crystallographic positions for x = 1.2 [52]. 298

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Fe3+(In3+) cation is shifted to the O2 anion with temperature increase. The Fe5 – O1 bond length increases and the Fe5 – O2 bond length decreases when temperature increases from 4 K up to 730 K. This behavior is most pronounced for the composition with x = 1.2. For x = 0.1 the tendency of the Fe5 – O2 bond length decrease is less noticeable [57]. This correlates with the distribution of the indium cations between the crystallographic positions when the substitution level increases. The displacement of the Fe3+(In3+) cation to O2 anion in the S and S* blocks leads to the appearance of a nonzero dipole moment [58]. As a consequence of this displacement of the Fe3+(In3+) cation in Fe5 – 12k position towards O2 anion and the appearance of the nonzero dipole moment, the z-component of the spontaneous polarization is formed [59]. The 10% -increase in the spontaneous polarization with the substitution level increase is explained by the increase in the concentration of empty d-shells and the formation of strong asymmetric covalent bonds in the Fe5 - 12k crystallographic position [60]. In addition, since In3+ cation has a larger ionic radius comparing to Fe3+ cation, the increase in the substitution concentration causes also the local distortions and microstrains of the crystal lattice [61–64].

[2]

[3]

[4] [5]

[6] [7] [8] [9]

[10]

4. Conclusions

[11]

The diamagnetically substituted BaFe12−xInxO19 solid solutions with x = 0.1 and x = 1.2 are synthesized by standard ceramic technology. These samples are investigated by high resolution neutron powder diffraction and by vibration sample magnetometry in a wide temperature range of 4–730 K. The analysis of NPD data was performed by the Rietveld method using the FullProf software program. The temperature dependence of the crystal and magnetic structure parameters and exchange interactions are discussed. A complete picture of structural and magnetic parameters was established which includes: the unit cell parameters, ionic coordinates, thermal isotropic factors, position occupations, bond lengths and bond angles, magnetic parameters and magnetic moments. The influence of structural parameters on the temperature behavior of Fe3+(i) - O2- - Fe3+(j) (i, j = 1, 2, 3, 4, 5) indirect superexchange interactions was investigated which was based on the comparative analysis of the structural features and exchange interactions. The electric polarization was investigated for these compositions at 300 K. As a consequence of the displacement of Fe3+(In3+) cation in Fe5 – 12k position towards O2 anion and the appearance of nonzero dipole moment the z-component of the spontaneous polarization is formed.

[12]

[13] [14]

[15]

[16]

[17]

[18]

[19]

Acknowledgement [20]

This work was carried out with financial support in part from the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST "MISiS" among the leading world scientific and educational centers (Nos. К42017-041 and К3-2017-059), and by the Belarusian Republican Foundation for Basic Research (No. F17D-003) and Joint Institute for Nuclear Research (No. 04-4-1121-2015/2017). In SUSU this work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. Additionally the work was partially supported by the Ministry of Education and Science of the Russian Federation (10.9639.2017/8.9). Additionally this work was performed using equipment of MIPT Shared Facilities Center and with financial support from the Ministry of Education and Science of the Russian Federation (Grant No. RFMEFI59417X0014). L. Panina acknowledges support under the Russian Federation State contract for organizing a scientific work. The authors express special gratitude to Professor A.M. Balagurov for his help and support.

[21]

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